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Publications of Anita T. Layton    :chronological  alphabetical  combined listing:

%% Books   
@book{fds223268,
   Author = {Anita T. Layton and Sarah D. Olson},
   Title = {Biological Fluid Dynamics: Modeling, Computation, and
             Applications},
   Journal = {AMS Contemporary Mathematics},
   Year = {2014},
   Key = {fds223268}
}

@book{fds216729,
   Author = {Anita T. Layton and Aurelie Edwards},
   Title = {Mathematical Modeling of Renal Physiology},
   Series = {Lecture Notes on Mathematical Modelling in the Life
             Sciences},
   Publisher = {Springer},
   Editor = {Angela Stevens and Michael C. Mackey},
   Year = {2013},
   Key = {fds216729}
}

@book{fds198051,
   Author = {Anita T. Layton and John Stockie and Zhilin Li and Huaxiong Huang},
   Title = {Fluid Motion Driven by Immersed Structures},
   Journal = {A special issue of Commun Comput Phys},
   Volume = {2},
   Year = {2012},
   Key = {fds198051}
}

@book{fds202895,
   Author = {Thoma Witelski and David Ambrose and Andrea Bertozzi and Anita
             Layton and Zhilin Li},
   Title = {Fluid Dynamics, Analysis and Numerics},
   Journal = {Special issue of Discrete and Continuous Dynamical Systems -
             Series B},
   Year = {2012},
   Key = {fds202895}
}

@book{fds243650,
   Author = {Layton, AT and Wei, G},
   Title = {Interface methods for biological and biomedical
             problems},
   Journal = {International Journal for Numerical Methods in Biomedical
             Engineering},
   Volume = {28},
   Number = {3},
   Pages = {289-290},
   Year = {2012},
   ISSN = {2040-7939},
   url = {http://dx.doi.org/10.1002/cnm.2477},
   Doi = {10.1002/cnm.2477},
   Key = {fds243650}
}


%% Papers Published   
@article{fds329189,
   Author = {Edwards, A and Layton, AT},
   Title = {Cell Volume Regulation in the Proximal Tubule of Rat Kidney
             : Proximal Tubule Cell Volume Regulation.},
   Journal = {Bulletin of Mathematical Biology},
   Year = {2017},
   Month = {September},
   url = {http://dx.doi.org/10.1007/s11538-017-0338-6},
   Abstract = {We developed a dynamic model of a rat proximal convoluted
             tubule cell in order to investigate cell volume regulation
             mechanisms in this nephron segment. We examined whether
             regulatory volume decrease (RVD), which follows exposure to
             a hyposmotic peritubular solution, can be achieved solely
             via stimulation of basolateral K[Formula: see text] and
             [Formula: see text] channels and [Formula: see
             text]-[Formula: see text] cotransporters. We also determined
             whether regulatory volume increase (RVI), which follows
             exposure to a hyperosmotic peritubular solution under
             certain conditions, may be accomplished by activating
             basolateral [Formula: see text]/H[Formula: see text]
             exchangers. Model predictions were in good agreement with
             experimental observations in mouse proximal tubule cells
             assuming that a 10% increase in cell volume induces a
             fourfold increase in the expression of basolateral
             K[Formula: see text] and [Formula: see text] channels and
             [Formula: see text]-[Formula: see text] cotransporters. Our
             results also suggest that in response to a hyposmotic
             challenge and subsequent cell swelling, [Formula: see
             text]-[Formula: see text] cotransporters are more efficient
             than basolateral K[Formula: see text] and [Formula: see
             text] channels at lowering intracellular osmolality and
             reducing cell volume. Moreover, both RVD and RVI are
             predicted to stabilize net transcellular [Formula: see text]
             reabsorption, that is, to limit the net [Formula: see text]
             flux decrease during a hyposmotic challenge or the net
             [Formula: see text] flux increase during a hyperosmotic
             challenge.},
   Doi = {10.1007/s11538-017-0338-6},
   Key = {fds329189}
}

@article{fds328946,
   Author = {Burt, T and Noveck, RJ and MacLeod, DB and Layton, AT and Rowland, M and Lappin, G},
   Title = {Intra-Target Microdosing (ITM): A Novel Drug Development
             Approach Aimed at Enabling Safer and Earlier Translation of
             Biological Insights Into Human Testing.},
   Journal = {Clinical and Translational Science},
   Volume = {10},
   Number = {5},
   Pages = {337-350},
   Year = {2017},
   Month = {September},
   url = {http://dx.doi.org/10.1111/cts.12464},
   Doi = {10.1111/cts.12464},
   Key = {fds328946}
}

@article{fds328036,
   Author = {Chen, Y and Sullivan, JC and Edwards, A and Layton,
             AT},
   Title = {Sex-specific computational models of the spontaneously
             hypertensive rat kidneys: factors affecting nitric oxide
             bioavailability.},
   Journal = {American Journal of Physiology: Renal Physiology},
   Volume = {313},
   Number = {2},
   Pages = {F174-F183},
   Year = {2017},
   Month = {August},
   url = {http://dx.doi.org/10.1152/ajprenal.00482.2016},
   Abstract = {The goals of this study were to 1) develop a computational
             model of solute transport and oxygenation in the kidney of
             the female spontaneously hypertensive rat (SHR), and 2)
             apply that model to investigate sex differences in nitric
             oxide (NO) levels in SHR and their effects on medullary
             oxygenation and oxidative stress. To accomplish these goals,
             we first measured NO synthase (NOS) 1 and NOS3 protein
             expression levels in total renal microvessels of male and
             female SHR. We found that the expression of both NOS1 and
             NOS3 is higher in the renal vasculature of females compared
             with males. To predict the implications of that finding on
             medullary oxygenation and oxidative stress levels, we
             developed a detailed computational model of the female SHR
             kidney. The model was based on a published male kidney model
             and represents solute transport and the biochemical
             reactions among O2, NO, and superoxide ([Formula: see text])
             in the renal medulla. Model simulations conducted using both
             male and female SHR kidney models predicted significant
             radial gradients in interstitial fluid oxygen tension (Po2)
             and NO and [Formula: see text] concentration in the outer
             medulla and upper inner medulla. The models also predicted
             that increases in endothelial NO-generating capacity, even
             when limited to specific vascular segments, may
             substantially raise medullary NO and Po2 levels. Other
             potential sex differences in SHR, including [Formula: see
             text] production rate, are predicted to significantly impact
             oxidative stress levels, but effects on NO concentration and
             Po2 are limited.},
   Doi = {10.1152/ajprenal.00482.2016},
   Key = {fds328036}
}

@article{fds328608,
   Author = {Layton, AT and Edwards, A and Vallon, V},
   Title = {Adaptive changes in GFR, tubular morphology, and transport
             in subtotal nephrectomized kidneys: modeling and
             analysis.},
   Journal = {American Journal of Physiology: Renal Physiology},
   Volume = {313},
   Number = {2},
   Pages = {F199-F209},
   Year = {2017},
   Month = {August},
   url = {http://dx.doi.org/10.1152/ajprenal.00018.2017},
   Abstract = {Removal of renal mass stimulates anatomical and functional
             adaptations in the surviving nephrons, including elevations
             in single-nephron glomerular filtration rate (SNGFR) and
             tubular hypertrophy. A goal of this study is to assess the
             extent to which the concomitant increases in filtered load
             and tubular transport capacity preserve homeostasis of water
             and salt. To accomplish that goal, we developed
             computational models to simulate solute transport and
             metabolism along nephron populations in a uninephrectomized
             (UNX) rat and a 5/6-nephrectomized (5/6-NX) rat. Model
             simulations indicate that nephrectomy-induced SNGFR increase
             and tubular hypertrophy go a long way to normalize
             excretion, but alone are insufficient to fully maintain salt
             balance. We then identified increases in the protein density
             of Na+-K+-ATPase, Na+-K+-2Cl- cotransporter, Na+-Cl-
             cotransporter, and epithelial Na+ channel, such that the UNX
             and 5/6-NX models predict urine flow and urinary Na+ and K+
             excretions that are similar to sham levels. The models
             predict that, in the UNX and 5/6-NX kidneys, fractional
             water and salt reabsorption is similar to sham along the
             initial nephron segments (i.e., from the proximal tubule to
             the distal convoluted tubule), with a need to further reduce
             Na+ reabsorption and increase K+ secretion primarily along
             the connecting tubules and collecting ducts to achieve
             balance. Additionally, the models predict that, given the
             substantially elevated filtered and thus transport load
             among each of the surviving nephrons, oxygen consumption per
             nephron segment in a UNX or 5/6-NX kidney increases
             substantially. But due to the reduced nephron population,
             whole animal renal oxygen consumption is lower. The
             efficiency of tubular Na+ transport in the UNX and 5/6-NX
             kidneys is predicted to be similar to sham.},
   Doi = {10.1152/ajprenal.00018.2017},
   Key = {fds328608}
}

@article{fds326523,
   Author = {Chen, Y and Fry, BC and Layton, AT},
   Title = {Modeling glucose metabolism and lactate production in the
             kidney.},
   Journal = {Mathematical Biosciences},
   Volume = {289},
   Pages = {116-129},
   Year = {2017},
   Month = {July},
   url = {http://dx.doi.org/10.1016/j.mbs.2017.04.008},
   Abstract = {The metabolism of glucose provides most of the ATP required
             for energy-dependent transport processes. In the inner
             medulla of the mammalian kidney, limited blood flow and O2
             supply yield low oxygen tension; therefore, a substantial
             fraction of the glucose metabolism in that region is
             anaerobic. Lactate is considered to be a waste product of
             anaerobic glycolysis, which yields two lactate molecules for
             each glucose molecule consumed, thereby likely leading to
             the production and accumulation of a significant amount of
             lactate in the inner medulla. To gain insights into the
             transport and metabolic processes in the kidney, we have
             developed a detailed mathematical model of the renal medulla
             of the rat kidney. The model represents the radial
             organization of the renal tubules and vessels, which centers
             around the vascular bundles in the outer medulla and around
             clusters of collecting ducts in the inner medulla. Model
             simulations yield significant radial gradients in
             interstitial fluid oxygen tension and glucose and lactate
             concentrations in the outer medulla and upper inner medulla.
             In the deep inner medulla, interstitial fluid concentrations
             become much more homogeneous, as the radial organization of
             tubules and vessels is not distinguishable. Using this
             model, we have identified parameters concerning glucose
             transport and basal metabolism, as well as lactate
             production via anaerobic glycolysis, that yield predicted
             blood glucose and lactate concentrations consistent with
             experimental measurements in the papillary tip. In addition,
             simulations indicate that the radial organization of the rat
             kidney may affect lactate buildup in the inner
             medulla.},
   Doi = {10.1016/j.mbs.2017.04.008},
   Key = {fds326523}
}

@article{fds325778,
   Author = {Layton, AT},
   Title = {A new microscope for the kidney: mathematics.},
   Journal = {American Journal of Physiology: Renal Physiology},
   Volume = {312},
   Number = {4},
   Pages = {F671-F672},
   Year = {2017},
   Month = {April},
   url = {http://dx.doi.org/10.1152/ajprenal.00648.2016},
   Doi = {10.1152/ajprenal.00648.2016},
   Key = {fds325778}
}

@article{fds323660,
   Author = {Jiang, T and Li, Y and Layton, AT and Wang, W and Sun, Y and Li, M and Zhou,
             H and Yang, B},
   Title = {Generation and phenotypic analysis of mice lacking all urea
             transporters.},
   Journal = {Kidney international},
   Volume = {91},
   Number = {2},
   Pages = {338-351},
   Year = {2017},
   Month = {February},
   url = {http://dx.doi.org/10.1016/j.kint.2016.09.017},
   Abstract = {Urea transporters (UT) are a family of transmembrane
             urea-selective channel proteins expressed in multiple
             tissues and play an important role in the urine
             concentrating mechanism of the mammalian kidney. UT
             inhibitors have diuretic activity and could be developed as
             novel diuretics. To determine if functional deficiency of
             all UTs in all tissues causes physiological abnormality, we
             established a novel mouse model in which all UTs were
             knocked out by deleting an 87 kb of DNA fragment containing
             most parts of Slc14a1 and Slc14a2 genes. Western blot
             analysis and immunofluorescence confirmed that there is no
             expression of urea transporter in these all-UT-knockout
             mice. Daily urine output was nearly 3.5-fold higher, with
             significantly lower urine osmolality in all-UT-knockout mice
             than that in wild-type mice. All-UT-knockout mice were not
             able to increase urinary urea concentration and osmolality
             after water deprivation, acute urea loading, or high protein
             intake. A computational model that simulated UT-knockout
             mouse models identified the individual contribution of each
             UT in urine concentrating mechanism. Knocking out all UTs
             also decreased the blood pressure and promoted the
             maturation of the male reproductive system. Thus, functional
             deficiency of all UTs caused a urea-selective
             urine-concentrating defect with little physiological
             abnormality in extrarenal organs.},
   Doi = {10.1016/j.kint.2016.09.017},
   Key = {fds323660}
}

@article{fds320875,
   Author = {Layton, AT and Laghmani, K and Vallon, V and Edwards,
             A},
   Title = {Solute transport and oxygen consumption along the nephrons:
             effects of Na+ transport inhibitors.},
   Journal = {American Journal of Physiology: Renal Physiology},
   Volume = {311},
   Number = {6},
   Pages = {F1217-F1229},
   Year = {2016},
   Month = {December},
   url = {http://dx.doi.org/10.1152/ajprenal.00294.2016},
   Abstract = {Sodium and its associated anions are the major determinant
             of extracellular fluid volume, and the reabsorption of Na+
             by the kidney plays a crucial role in long-term blood
             pressure control. The goal of this study was to investigate
             the extent to which inhibitors of transepithelial Na+
             transport (TNa) along the nephron alter urinary solute
             excretion and TNa efficiency and how those effects may vary
             along different nephron segments. To accomplish that goal,
             we used the multinephron model developed in the companion
             study (28). That model represents detailed transcellular and
             paracellular transport processes along the nephrons of a rat
             kidney. We simulated the inhibition of the Na+/H+ exchanger
             (NHE3), the bumetanide-sensitive Na+-K+-2Cl- transporter
             (NKCC2), the Na+-Cl- cotransporter (NCC), and the
             amiloride-sensitive Na+ channel (ENaC). Under baseline
             conditions, NHE3, NKCC2, NCC, and ENaC reabsorb 36, 22, 4,
             and 7%, respectively, of filtered Na+ The model predicted
             that inhibition of NHE3 substantially reduced proximal
             tubule TNa and oxygen consumption (QO2 ). Whole-kidney TNa
             efficiency, as reflected by the number of moles of Na+
             reabsorbed per moles of O2 consumed (denoted by the ratio
             TNa/QO2 ), decreased by ∼20% with 80% inhibition of NHE3.
             NKCC2 inhibition simulations predicted a substantial
             reduction in thick ascending limb TNa and QO2 ; however, the
             effect on whole-kidney TNa/QO2 was minor. Tubular K+
             transport was also substantially impaired, resulting in
             elevated urinary K+ excretion. The most notable effect of
             NCC inhibition was to increase the excretion of Na+, K+, and
             Cl-; its impact on whole-kidney TNa and its efficiency was
             minor. Inhibition of ENaC was predicted to have opposite
             effects on the excretion of Na+ (increased) and K+
             (decreased) and to have only a minor impact on whole-kidney
             TNa and TNa/QO2 Overall, model predictions agree well with
             measured changes in Na+ and K+ excretion in response to
             diuretics and Na+ transporter mutations.},
   Doi = {10.1152/ajprenal.00294.2016},
   Key = {fds320875}
}

@article{fds320876,
   Author = {Layton, AT and Vallon, V and Edwards, A},
   Title = {A computational model for simulating solute transport and
             oxygen consumption along the nephrons.},
   Journal = {American Journal of Physiology: Renal Physiology},
   Volume = {311},
   Number = {6},
   Pages = {F1378-F1390},
   Year = {2016},
   Month = {December},
   url = {http://dx.doi.org/10.1152/ajprenal.00293.2016},
   Abstract = {The goal of this study was to investigate water and solute
             transport, with a focus on sodium transport (TNa) and
             metabolism along individual nephron segments under differing
             physiological and pathophysiological conditions. To
             accomplish this goal, we developed a computational model of
             solute transport and oxygen consumption (QO2 ) along
             different nephron populations of a rat kidney. The model
             represents detailed epithelial and paracellular transport
             processes along both the superficial and juxtamedullary
             nephrons, with the loop of Henle of each model nephron
             extending to differing depths of the inner medulla. We used
             the model to assess how changes in TNa may alter QO2 in
             different nephron segments and how shifting the TNa sites
             alters overall kidney QO2 Under baseline conditions, the
             model predicted a whole kidney TNa/QO2 , which denotes the
             number of moles of Na+ reabsorbed per moles of O2 consumed,
             of ∼15, with TNa efficiency predicted to be significantly
             greater in cortical nephron segments than in medullary
             segments. The TNa/QO2 ratio was generally similar among the
             superficial and juxtamedullary nephron segments, except for
             the proximal tubule, where TNa/QO2 was ∼20% higher in
             superficial nephrons, due to the larger luminal flow along
             the juxtamedullary proximal tubules and the resulting
             higher, flow-induced transcellular transport. Moreover, the
             model predicted that an increase in single-nephron
             glomerular filtration rate does not significantly affect
             TNa/QO2 in the proximal tubules but generally increases
             TNa/QO2 along downstream segments. The latter result can be
             attributed to the generally higher luminal [Na+], which
             raises paracellular TNa Consequently, vulnerable medullary
             segments, such as the S3 segment and medullary thick
             ascending limb, may be relatively protected from
             flow-induced increases in QO2 under pathophysiological
             conditions.},
   Doi = {10.1152/ajprenal.00293.2016},
   Key = {fds320876}
}

@article{fds320877,
   Author = {Sgouralis, I and Kett, MM and Ow, CPC and Abdelkader, A and Layton, AT and Gardiner, BS and Smith, DW and Lankadeva, YR and Evans,
             RG},
   Title = {Bladder urine oxygen tension for assessing renal medullary
             oxygenation in rabbits: experimental and modeling
             studies.},
   Journal = {American journal of physiology. Regulatory, integrative and
             comparative physiology},
   Volume = {311},
   Number = {3},
   Pages = {R532-R544},
   Year = {2016},
   Month = {September},
   url = {http://dx.doi.org/10.1152/ajpregu.00195.2016},
   Abstract = {Oxygen tension (Po2) of urine in the bladder could be used
             to monitor risk of acute kidney injury if it varies with
             medullary Po2 Therefore, we examined this relationship and
             characterized oxygen diffusion across walls of the ureter
             and bladder in anesthetized rabbits. A computational model
             was then developed to predict medullary Po2 from bladder
             urine Po2 Both intravenous infusion of [Phe(2),Ile(3),Orn(8)]-vasopressin
             and infusion of N(G)-nitro-l-arginine reduced urinary Po2
             and medullary Po2 (8-17%), yet had opposite effects on renal
             blood flow and urine flow. Changes in bladder urine Po2
             during these stimuli correlated strongly with changes in
             medullary Po2 (within-rabbit r(2) = 0.87-0.90). Differences
             in the Po2 of saline infused into the ureter close to the
             kidney could be detected in the bladder, although this was
             diminished at lesser ureteric flow. Diffusion of oxygen
             across the wall of the bladder was very slow, so it was not
             considered in the computational model. The model predicts
             Po2 in the pelvic ureter (presumed to reflect medullary Po2)
             from known values of bladder urine Po2, urine flow, and
             arterial Po2 Simulations suggest that, across a
             physiological range of urine flow in anesthetized rabbits
             (0.1-0.5 ml/min for a single kidney), a change in bladder
             urine Po2 explains 10-50% of the change in pelvic
             urine/medullary Po2 Thus, it is possible to infer changes in
             medullary Po2 from changes in urinary Po2, so urinary Po2
             may have utility as a real-time biomarker of risk of acute
             kidney injury.},
   Doi = {10.1152/ajpregu.00195.2016},
   Key = {fds320877}
}

@article{fds320878,
   Author = {Layton, AT},
   Title = {Recent advances in renal hypoxia: insights from bench
             experiments and computer simulations.},
   Journal = {American Journal of Physiology: Renal Physiology},
   Volume = {311},
   Number = {1},
   Pages = {F162-F165},
   Year = {2016},
   Month = {July},
   url = {http://dx.doi.org/10.1152/ajprenal.00228.2016},
   Abstract = {The availability of oxygen in renal tissue is determined by
             the complex interactions among a host of processes,
             including renal blood flow, glomerular filtration,
             arterial-to-venous oxygen shunting, medullary architecture,
             Na(+) transport, and oxygen consumption. When this delicate
             balance is disrupted, the kidney may become susceptible to
             hypoxic injury. Indeed, renal hypoxia has been implicated as
             one of the major causes of acute kidney injury and chronic
             kidney diseases. This review highlights recent advances in
             our understanding of renal hypoxia; some of these studies
             were published in response to a recent Call for Papers of
             this journal: Renal Hypoxia.},
   Doi = {10.1152/ajprenal.00228.2016},
   Key = {fds320878}
}

@article{fds320180,
   Author = {Herschlag, G and Liu, J-G and Layton, AT},
   Title = {Fluid extraction across pumping and permeable walls in the
             viscous limit},
   Journal = {Physics of Fluids},
   Volume = {28},
   Number = {4},
   Pages = {041902-041902},
   Year = {2016},
   Month = {April},
   url = {http://dx.doi.org/10.1063/1.4946005},
   Doi = {10.1063/1.4946005},
   Key = {fds320180}
}

@article{fds320885,
   Author = {Sgouralis, I and Layton, AT},
   Title = {Conduction of feedback-mediated signal in a computational
             model of coupled nephrons.},
   Journal = {Mathematical Medicine and Biology: A Journal of the
             IMA},
   Volume = {33},
   Number = {1},
   Pages = {87-106},
   Year = {2016},
   Month = {March},
   url = {http://dx.doi.org/10.1093/imammb/dqv005},
   Abstract = {The nephron in the kidney regulates its fluid flow by
             several autoregulatory mechanisms. Two primary mechanisms
             are the myogenic response and the tubuloglomerular feedback
             (TGF). The myogenic response is a property of the
             pre-glomerular vasculature in which a rise in intravascular
             pressure elicits vasoconstriction that generates a
             compensatory increase in vascular resistance. TGF is a
             negative feedback response that balances glomerular
             filtration with tubular reabsorptive capacity. While each
             nephron has its own autoregulatory response, the responses
             of the kidney's many nephrons do not act autonomously but
             are instead coupled through the pre-glomerular vasculature.
             To better understand the conduction of these signals along
             the pre-glomerular arterioles and the impacts of
             internephron coupling on nephron flow dynamics, we developed
             a mathematical model of renal haemodynamics of two
             neighbouring nephrons that are coupled in that their
             afferent arterioles arise from a common cortical radial
             artery. Simulations were conducted to estimate internephron
             coupling strength, determine its dependence on vascular
             properties and to investigate the effect of coupling on
             TGF-mediated flow oscillations. Simulation results suggest
             that reduced gap-junctional conductances may yield stronger
             internephron TGF coupling and highly irregular TGF-mediated
             oscillations in nephron dynamics, both of which
             experimentally have been associated with hypertensive
             rats.},
   Doi = {10.1093/imammb/dqv005},
   Key = {fds320885}
}

@article{fds320886,
   Author = {Fry, BC and Edwards, A and Layton, AT},
   Title = {Impact of nitric-oxide-mediated vasodilation and oxidative
             stress on renal medullary oxygenation: a modeling
             study.},
   Journal = {American Journal of Physiology: Renal Physiology},
   Volume = {310},
   Number = {3},
   Pages = {F237-F247},
   Year = {2016},
   Month = {February},
   url = {http://dx.doi.org/10.1152/ajprenal.00334.2015},
   Abstract = {The goal of this study was to investigate the effects of
             nitric oxide (NO)-mediated vasodilation in preventing
             medullary hypoxia, as well as the likely pathways by which
             superoxide (O2(-)) conversely enhances medullary hypoxia. To
             do so, we expanded a previously developed mathematical model
             of solute transport in the renal medulla that accounts for
             the reciprocal interactions among oxygen (O2), NO, and O2(-)
             to include the vasoactive effects of NO on medullary
             descending vasa recta. The model represents the radial
             organization of the vessels and tubules, centered around
             vascular bundles in the outer medulla and collecting ducts
             in the inner medulla. Model simulations suggest that NO
             helps to prevent medullary hypoxia both by inducing
             vasodilation of the descending vasa recta (thus increasing
             O2 supply) and by reducing the active sodium transport rate
             (thus reducing O2 consumption). That is, the vasodilative
             properties of NO significantly contribute to maintaining
             sufficient medullary oxygenation. The model further predicts
             that a reduction in tubular transport efficiency (i.e., the
             ratio of active sodium transport per O2 consumption) is the
             main factor by which increased O2(-) levels lead to hypoxia,
             whereas hyperfiltration is not a likely pathway to medullary
             hypoxia due to oxidative stress. Finally, our results
             suggest that further increasing the radial separation
             between vessels and tubules would reduce the diffusion of NO
             towards descending vasa recta in the inner medulla, thereby
             diminishing its vasoactive effects therein and reducing O2
             delivery to the papillary tip.},
   Doi = {10.1152/ajprenal.00334.2015},
   Key = {fds320886}
}

@article{fds320181,
   Author = {Xie, L and Layton, AT and Wang, N and Larson, PEZ and Zhang, JL and Lee,
             VS and Liu, C and Johnson, GA},
   Title = {Dynamic contrast-enhanced quantitative susceptibility
             mapping with ultrashort echo time MRI for evaluating renal
             function.},
   Journal = {American Journal of Physiology: Renal Physiology},
   Volume = {310},
   Number = {2},
   Pages = {F174-F182},
   Year = {2016},
   Month = {January},
   url = {http://dx.doi.org/10.1152/ajprenal.00351.2015},
   Abstract = {Dynamic contrast-enhanced (DCE) MRI can provide key insight
             into renal function. DCE MRI is typically achieved through
             an injection of a gadolinium (Gd)-based contrast agent,
             which has desirable T1 quenching and tracer kinetics.
             However, significant T2* blooming effects and signal voids
             can arise when Gd becomes very concentrated, especially in
             the renal medulla and pelvis. One MRI sequence designed to
             alleviate T2* effects is the ultrashort echo time (UTE)
             sequence. In the present study, we observed T2* blooming in
             the inner medulla of the mouse kidney, despite using UTE at
             an echo time of 20 microseconds and a low dose of 0.03
             mmol/kg Gd. We applied quantitative susceptibility mapping
             (QSM) and resolved the signal void into a positive
             susceptibility signal. The susceptibility values [in parts
             per million (ppm)] were converted into molar concentrations
             of Gd using a calibration curve. We determined the
             concentrating mechanism (referred to as the concentrating
             index) as a ratio of maximum Gd concentration in the inner
             medulla to the renal artery. The concentrating index was
             assessed longitudinally over a 17-wk course (3, 5, 7, 9, 13,
             17 wk of age). We conclude that the UTE-based DCE method is
             limited in resolving extreme T2* content caused by the
             kidney's strong concentrating mechanism. QSM was able to
             resolve and confirm the source of the blooming effect to be
             the large positive susceptibility of concentrated Gd. UTE
             with QSM can complement traditional magnitude UTE and offer
             a powerful tool to study renal pathophysiology.},
   Doi = {10.1152/ajprenal.00351.2015},
   Key = {fds320181}
}

@article{fds320182,
   Author = {Burt, T and Rouse, DC and Lee, K and Wu, H and Layton, AT and Hawk, TC and Weitzel, DH and Chin, BB and Cohen-Wolkowiez, M and Chow, S-C and Noveck, RJ},
   Title = {Intraarterial Microdosing: A Novel Drug Development
             Approach, Proof-of-Concept PET Study in Rats.},
   Journal = {Journal of nuclear medicine : official publication, Society
             of Nuclear Medicine},
   Volume = {56},
   Number = {11},
   Pages = {1793-1799},
   Year = {2015},
   Month = {November},
   url = {http://dx.doi.org/10.2967/jnumed.115.160986},
   Abstract = {Intraarterial microdosing (IAM) is a novel drug development
             approach combining intraarterial drug delivery and
             microdosing. We aimed to demonstrate that IAM leads to
             target exposure similar to that of systemic full-dose
             administration but with minimal systemic exposure. IAM could
             enable the safe, inexpensive, and early study of novel drugs
             at the first-in-human stage and the study of established
             drugs in vulnerable populations.Insulin was administered
             intraarterially (ipsilateral femoral artery) or systemically
             to 8 CD IGS rats just before blood sampling or 60-min
             (18)F-FDG uptake PET imaging of ipsilateral and
             contralateral leg muscles (lateral gastrocnemius) and
             systemic muscles (spinotrapezius). The (18)F-FDG uptake
             slope analysis was used to compare the interventions. Plasma
             levels of insulin and glucose were compared using area under
             the curve calculated by the linear trapezoidal method. A
             physiologically based computational pharmacokinetics/pharmacodynamics
             model was constructed to simulate the relationship between
             the administered dose and response over time.(18)F-FDG slope
             analysis found no difference between IAM and systemic
             full-dose slopes (0.0066 and 0.0061, respectively; 95%
             confidence interval [CI], -0.024 to 0.029; P = 0.7895), but
             IAM slope was statistically significantly greater than
             systemic microdose (0.0018; 95% CI, -0.045 to -0.007; P =
             0.0147) and sham intervention (-0.0015; 95% CI, 0.023-0.058;
             P = 0.0052). The pharmacokinetics/pharmacodynamics data were
             used to identify model parameters that describe membrane
             insulin binding and glucose-insulin dynamics.Target exposure
             after IAM was similar to systemic full dose administration
             but with minimal systemic effects. The computational
             pharmacokinetics/pharmacodynamics model can be generalized
             to predict whole-body response. Findings should be validated
             in larger, controlled studies in animals and humans using a
             range of targets and classes of drugs.},
   Doi = {10.2967/jnumed.115.160986},
   Key = {fds320182}
}

@article{fds320183,
   Author = {Burt, T and Rouse, DC and Lee, K and Wu, H and Layton, AT and Hawk, TC and Weitzel, DH and Chin, BB and Cohen-Wolkowiez, M and Chow, S-C and Noveck, RJ},
   Title = {Intraarterial Microdosing: A Novel Drug Development
             Approach, Proof-of-Concept PET Study in Rats},
   Journal = {Journal of nuclear medicine : official publication, Society
             of Nuclear Medicine},
   Volume = {56},
   Number = {11},
   Pages = {1793-1799},
   Year = {2015},
   Month = {November},
   url = {http://dx.doi.org/10.2967/jnumed.115.160986},
   Doi = {10.2967/jnumed.115.160986},
   Key = {fds320183}
}

@article{fds300274,
   Author = {Layton, AT and Edwards, A},
   Title = {Predicted effects of nitric oxide and superoxide on the
             vasoactivity of the afferent arteriole.},
   Journal = {American Journal of Physiology: Renal Physiology},
   Volume = {309},
   Number = {8},
   Pages = {F708-F719},
   Year = {2015},
   Month = {October},
   ISSN = {1931-857X},
   url = {http://dx.doi.org/10.1152/ajprenal.00187.2015},
   Abstract = {We expanded a published mathematical model of an afferent
             arteriole smooth muscle cell in rat kidney (Edwards A,
             Layton, AT. Am J Physiol Renal Physiol 306: F34-F48, 2014)
             to understand how nitric oxide (NO) and superoxide (O(2)(-))
             modulate the arteriolar diameter and its myogenic response.
             The present model includes the kinetics of NO and O(2)(-)
             formation, diffusion, and reaction. Also included are the
             effects of NO and its second messenger cGMP on cellular
             Ca²⁺ uptake and efflux, Ca²⁺-activated K⁺ currents,
             and myosin light chain phosphatase activity. The model
             considers as well pressure-induced increases in O(2)(-)
             production, O(2)(-)-mediated regulation of L-type Ca²⁺
             channel conductance, and increased O(2)(-) production in
             spontaneous hypertensive rats (SHR). Our results indicate
             that elevated O(2)(-) production in SHR is sufficient to
             account for observed differences between normotensive and
             hypertensive rats in the response of the afferent arteriole
             to NO synthase inhibition, Tempol, and angiotensin II at
             baseline perfusion pressures. In vitro, whether the myogenic
             response is stronger in SHR remains uncertain. Our model
             predicts that if mechanosensitive cation channels are not
             modulated by O(2)(-), then fractional changes in diameter
             induced by pressure elevations should be smaller in SHR than
             in normotensive rats. Our results also suggest that most NO
             diffuses out of the smooth muscle cell without being
             consumed, whereas most O(2)(-) is scavenged, by NO and
             superoxide dismutase. Moreover, the predicted effects of
             superoxide on arteriolar constriction are not predominantly
             due to its scavenging of NO.},
   Doi = {10.1152/ajprenal.00187.2015},
   Key = {fds300274}
}

@article{fds300275,
   Author = {Nganguia, H and Young, Y-N and Layton, AT and Hu, W-F and Lai,
             M-C},
   Title = {An Immersed Interface Method for Axisymmetric
             Electrohydrodynamic Simulations in Stokes
             flow},
   Journal = {Communications in computational physics},
   Volume = {18},
   Number = {02},
   Pages = {429-449},
   Year = {2015},
   Month = {August},
   ISSN = {1815-2406},
   url = {http://dx.doi.org/10.4208/cicp.171014.270315a},
   Doi = {10.4208/cicp.171014.270315a},
   Key = {fds300275}
}

@article{fds320184,
   Author = {Burt, T and Wu, H and Layton, AT and Rouse, DC and Chin, BB and Hawk, TC and Weitzel, DH and Cohen-Wolkowiez, M and Chow, S and Noveck,
             RJ},
   Title = {INTRA-ARTERIAL MICRODOSING (IAM), A NOVEL DRUG DEVELOPMENT
             APPROACH, PROOF OF CONCEPT IN RATS},
   Journal = {Clinical Therapeutics},
   Volume = {37},
   Number = {8},
   Pages = {E40-E41},
   Year = {2015},
   Month = {August},
   Key = {fds320184}
}

@article{fds300276,
   Author = {Sgouralis, I and Layton, AT},
   Title = {Mathematical modeling of renal hemodynamics in physiology
             and pathophysiology.},
   Journal = {Mathematical Biosciences},
   Volume = {264},
   Pages = {8-20},
   Year = {2015},
   Month = {June},
   ISSN = {0025-5564},
   url = {http://dx.doi.org/10.1016/j.mbs.2015.02.016},
   Abstract = {In addition to the excretion of metabolic waste and toxin,
             the kidney plays an indispensable role in regulating the
             balance of water, electrolyte, acid-base, and blood
             pressure. For the kidney to maintain proper functions,
             hemodynamic control is crucial. In this review, we describe
             representative mathematical models that have been developed
             to better understand the kidney's autoregulatory processes.
             We consider mathematical models that simulate glomerular
             filtration, and renal blood flow regulation by means of the
             myogenic response and tubuloglomerular feedback. We discuss
             the extent to which these modeling efforts have expanded the
             understanding of renal functions in health and
             disease.},
   Doi = {10.1016/j.mbs.2015.02.016},
   Key = {fds300276}
}

@article{fds311145,
   Author = {Layton, AT and Vallon, V and Edwards, A},
   Title = {Modeling oxygen consumption in the proximal tubule: effects
             of NHE and SGLT2 inhibition.},
   Journal = {American Journal of Physiology: Renal Physiology},
   Volume = {308},
   Number = {12},
   Pages = {F1343-F1357},
   Year = {2015},
   Month = {June},
   ISSN = {1931-857X},
   url = {http://dx.doi.org/10.1152/ajprenal.00007.2015},
   Abstract = {The objective of this study was to investigate how
             physiological, pharmacological, and pathological conditions
             that alter sodium reabsorption (TNa) in the proximal tubule
             affect oxygen consumption (QO2 ) and Na(+) transport
             efficiency (TNa/QO2 ). To do so, we expanded a mathematical
             model of solute transport in the proximal tubule of the rat
             kidney. The model represents compliant S1, S2, and S3
             segments and accounts for their specific apical and
             basolateral transporters. Sodium is reabsorbed
             transcellularly, via apical Na(+)/H(+) exchangers (NHE) and
             Na(+)-glucose (SGLT) cotransporters, and paracellularly. Our
             results suggest that TNa/QO2 is 80% higher in S3 than in
             S1-S2 segments, due to the greater contribution of the
             passive paracellular pathway to TNa in the former segment.
             Inhibition of NHE or Na-K-ATPase reduced TNa and QO2 , as
             well as Na(+) transport efficiency. SGLT2 inhibition also
             reduced proximal tubular TNa but increased QO2 ; these
             effects were relatively more pronounced in the S3 vs. the
             S1-S2 segments. Diabetes increased TNa and QO2 and reduced
             TNa/QO2 , owing mostly to hyperfiltration. Since SGLT2
             inhibition lowers diabetic hyperfiltration, the net effect
             on TNa, QO2 , and Na(+) transport efficiency in the proximal
             tubule will largely depend on the individual extent to which
             glomerular filtration rate is lowered.},
   Doi = {10.1152/ajprenal.00007.2015},
   Key = {fds311145}
}

@article{fds243614,
   Author = {Layton, AT},
   Title = {Recent advances in renal hemodynamics: insights from bench
             experiments and computer simulations.},
   Journal = {American Journal of Physiology: Renal Physiology},
   Volume = {308},
   Number = {9},
   Pages = {F951-F955},
   Year = {2015},
   Month = {May},
   ISSN = {1931-857X},
   url = {http://dx.doi.org/10.1152/ajprenal.00008.2015},
   Abstract = {It has been long known that the kidney plays an essential
             role in the control of body fluids and blood pressure and
             that impairment of renal function may lead to the
             development of diseases such as hypertension (Guyton AC,
             Coleman TG, Granger Annu Rev Physiol 34: 13-46, 1972). In
             this review, we highlight recent advances in our
             understanding of renal hemodynamics, obtained from
             experimental and theoretical studies. Some of these studies
             were published in response to a recent Call for Papers of
             this journal: Renal Hemodynamics: Integrating with the
             Nephron and Beyond.},
   Doi = {10.1152/ajprenal.00008.2015},
   Key = {fds243614}
}

@article{fds243615,
   Author = {Fry, BC and Edwards, A and Layton, AT},
   Title = {Impacts of nitric oxide and superoxide on renal medullary
             oxygen transport and urine concentration.},
   Journal = {American Journal of Physiology: Renal Physiology},
   Volume = {308},
   Number = {9},
   Pages = {F967-F980},
   Year = {2015},
   Month = {May},
   ISSN = {1931-857X},
   url = {http://dx.doi.org/10.1152/ajprenal.00600.2014},
   Abstract = {The goal of this study was to investigate the reciprocal
             interactions among oxygen (O2), nitric oxide (NO), and
             superoxide (O2 (-)) and their effects on medullary
             oxygenation and urinary output. To accomplish that goal, we
             developed a detailed mathematical model of solute transport
             in the renal medulla of the rat kidney. The model represents
             the radial organization of the renal tubules and vessels,
             which centers around the vascular bundles in the outer
             medulla and around clusters of collecting ducts in the inner
             medulla. Model simulations yield significant radial
             gradients in interstitial fluid oxygen tension (Po2) and NO
             and O2 (-) concentration in the OM and upper IM. In the deep
             inner medulla, interstitial fluid concentrations become much
             more homogeneous, as the radial organization of tubules and
             vessels is not distinguishable. The model further predicts
             that due to the nonlinear interactions among O2, NO, and O2
             (-), the effects of NO and O2 (-) on sodium transport,
             osmolality, and medullary oxygenation cannot be gleaned by
             considering each solute's effect in isolation. An additional
             simulation suggests that a sufficiently large reduction in
             tubular transport efficiency may be the key contributing
             factor, more so than oxidative stress alone, to
             hypertension-induced medullary hypoxia. Moreover, model
             predictions suggest that urine Po2 could serve as a
             biomarker for medullary hypoxia and a predictor of the risk
             for hospital-acquired acute kidney injury.},
   Doi = {10.1152/ajprenal.00600.2014},
   Key = {fds243615}
}

@article{fds320887,
   Author = {Ford Versypt and AN and Makrides, E and Arciero, JC and Ellwein, L and Layton, AT},
   Title = {Bifurcation study of blood flow control in the
             kidney.},
   Journal = {Mathematical Biosciences},
   Volume = {263},
   Pages = {169-179},
   Year = {2015},
   Month = {May},
   url = {http://dx.doi.org/10.1016/j.mbs.2015.02.015},
   Abstract = {Renal blood flow is maintained within a narrow window by a
             set of intrinsic autoregulatory mechanisms. Here, a
             mathematical model of renal hemodynamics control in the rat
             kidney is used to understand the interactions between two
             major renal autoregulatory mechanisms: the myogenic response
             and tubuloglomerular feedback. A bifurcation analysis of the
             model equations is performed to assess the effects of the
             delay and sensitivity of the feedback system and the time
             constants governing the response of vessel diameter and
             smooth muscle tone. The results of the bifurcation analysis
             are verified using numerical simulations of the full
             nonlinear model. Both the analytical and numerical results
             predict the generation of limit cycle oscillations under
             certain physiologically relevant conditions, as observed in
             vivo.},
   Doi = {10.1016/j.mbs.2015.02.015},
   Key = {fds320887}
}

@article{fds320888,
   Author = {Sgouralis, I and Evans, RG and Gardiner, BS and Smith, JA and Fry, BC and Layton, AT},
   Title = {Renal hemodynamics, function, and oxygenation during cardiac
             surgery performed on cardiopulmonary bypass: a modeling
             study.},
   Journal = {Physiological Reports},
   Volume = {3},
   Number = {1},
   Year = {2015},
   Month = {January},
   url = {http://dx.doi.org/10.14814/phy2.12260},
   Abstract = {Acute kidney injury, a prevalent complication of cardiac
             surgery performed on cardiopulmonary bypass (CPB), is
             thought to be driven partly by hypoxic damage in the renal
             medulla. To determine the causes of medullary hypoxia during
             CPB, we modeled its impact on renal hemodynamics and
             function, and thus oxygen delivery and consumption in the
             renal medulla. The model incorporates autoregulation of
             renal blood flow and glomerular filtration rate and the
             utilization of oxygen for tubular transport. The model
             predicts that renal medullary oxygen delivery and
             consumption are reduced by a similar magnitude during the
             hypothermic (down to 28°C) phase of CPB. Thus, the
             fractional extraction of oxygen in the medulla, an index of
             hypoxia, is increased only by 58% from baseline. However,
             during the rewarming phase (up to 37°C), oxygen consumption
             by the medullary thick ascending limb increases 2.3-fold but
             medullary oxygen delivery increases only by 33%.
             Consequently, the fractional extraction of oxygen in the
             medulla is increased 2.7-fold from baseline. Thus, the renal
             medulla is particularly susceptible to hypoxia during the
             rewarming phase of CPB. Furthermore, autoregulation of both
             renal blood flow and glomerular filtration rate is blunted
             during CPB by the combined effects of hemodilution and
             nonpulsatile blood flow. Thus, renal hypoxia can be markedly
             exacerbated if arterial pressure falls below its target
             level of 50 mmHg. Our findings suggest that tight control of
             arterial pressure, and thus renal oxygen delivery, may be
             critical in the prevention of acute kidney injury associated
             with cardiac surgery performed on CPB.},
   Doi = {10.14814/phy2.12260},
   Key = {fds320888}
}

@article{fds299957,
   Author = {Fields, B and Page, K},
   Title = {Preface},
   Volume = {2015-June},
   Year = {2015},
   Month = {January},
   ISBN = {9781450335638},
   Key = {fds299957}
}

@article{fds320185,
   Author = {Herschlag, G and Liu, J-G and Layton, AT},
   Title = {An Exact Solution for Stokes Flow in a Channel with
             Arbitrarily Large Wall Permeability},
   Journal = {SIAM Journal on Applied Mathematics},
   Volume = {75},
   Number = {5},
   Pages = {2246-2267},
   Year = {2015},
   Month = {January},
   url = {http://dx.doi.org/10.1137/140995854},
   Doi = {10.1137/140995854},
   Key = {fds320185}
}

@article{fds226446,
   Author = {Anita T. Layton},
   Title = {Mathematical physiology},
   Booktitle = {Princeton Companion to Applied Mathematics},
   Editor = {Nicholas J. Higham},
   Year = {2015},
   ISBN = {978-0691150390},
   Key = {fds226446}
}

@article{fds226967,
   Author = {Julia Arcerio and Laura Ellwein and Ashlee N. Ford Versypt and Elizabeth Makride and Anita T. Layton},
   Title = {Modeling blood flow in the kidney},
   Volume = {158},
   Pages = {55-73},
   Booktitle = {The IMA Volumes in Mathematics and its Applications:
             Applications of Dynamical Systems in Biology and
             Medicine},
   Year = {2015},
   Key = {fds226967}
}

@article{fds243618,
   Author = {Fry, BC and Layton, AT},
   Title = {Oxygen transport in a cross section of the rat inner
             medulla: impact of heterogeneous distribution of nephrons
             and vessels.},
   Journal = {Mathematical Biosciences},
   Volume = {258},
   Pages = {68-76},
   Year = {2014},
   Month = {December},
   ISSN = {0025-5564},
   url = {http://dx.doi.org/10.1016/j.mbs.2014.09.009},
   Abstract = {We have developed a highly detailed mathematical model of
             oxygen transport in a cross section of the upper inner
             medulla of the rat kidney. The model is used to study the
             impact of the structured organization of nephrons and
             vessels revealed in anatomic studies, in which descending
             vasa recta are found to lie distant from clusters of
             collecting ducts. Specifically, we formulated a
             two-dimensional oxygen transport model, in which the
             positions and physical dimensions of renal tubules and
             vessels are based on an image obtained by immunochemical
             techniques (T. Pannabecker and W. Dantzler,
             Three-dimensional architecture of inner medullary vasa
             recta, Am. J. Physiol. Renal Physiol. 290 (2006)
             F1355-F1366). The model represents oxygen diffusion through
             interstitium and other renal structures, oxygen consumption
             by the Na(+)/K(+)-ATPase activities of the collecting ducts,
             and basal metabolic consumption. Model simulations yield
             marked variations in interstitial PO2, which can be
             attributed, in large part, to the heterogeneities in the
             position and physical dimensions of the collecting ducts.
             Further, results of a sensitivity study suggest that
             medullary oxygenation is highly sensitive to medullary blood
             flow, and that, at high active consumption rates, localized
             patches of tissue may be vulnerable to hypoxic
             injury.},
   Doi = {10.1016/j.mbs.2014.09.009},
   Key = {fds243618}
}

@article{fds243619,
   Author = {Pannabecker, TL and Layton, AT},
   Title = {Targeted delivery of solutes and oxygen in the renal
             medulla: role of microvessel architecture.},
   Journal = {American Journal of Physiology: Renal Physiology},
   Volume = {307},
   Number = {6},
   Pages = {F649-F655},
   Year = {2014},
   Month = {September},
   ISSN = {1931-857X},
   url = {http://dx.doi.org/10.1152/ajprenal.00276.2014},
   Abstract = {Renal medullary function is characterized by
             corticopapillary concentration gradients of various
             molecules. One example is the generally decreasing axial
             gradient in oxygen tension (Po2). Another example, found in
             animals in the antidiuretic state, is a generally increasing
             axial solute gradient, consisting mostly of NaCl and urea.
             This osmolality gradient, which plays a principal role in
             the urine concentrating mechanism, is generally considered
             to involve countercurrent multiplication and countercurrent
             exchange, although the underlying mechanism is not fully
             understood. Radial oxygen and solute gradients in the
             transverse dimension of the medullary parenchyma have been
             hypothesized to occur, although strong experimental evidence
             in support of these gradients remains lacking. This review
             considers anatomic features of the renal medulla that may
             impact the formation and maintenance of oxygen and solute
             gradients. A better understanding of medullary architecture
             is essential for more clearly defining the
             compartment-to-compartment flows taken by fluid and
             molecules that are important in producing axial and radial
             gradients. Preferential interactions between nephron and
             vascular segments provide clues as to how tubular and
             interstitial oxygen flows contribute to safeguarding active
             transport pathways in renal function in health and
             disease.},
   Doi = {10.1152/ajprenal.00276.2014},
   Key = {fds243619}
}

@article{fds243621,
   Author = {Fry, BC and Edwards, A and Sgouralis, I and Layton,
             AT},
   Title = {Impact of renal medullary three-dimensional architecture on
             oxygen transport.},
   Journal = {American Journal of Physiology: Renal Physiology},
   Volume = {307},
   Number = {3},
   Pages = {F263-F272},
   Year = {2014},
   Month = {August},
   ISSN = {1931-857X},
   url = {http://dx.doi.org/10.1152/ajprenal.00149.2014},
   Abstract = {We have developed a highly detailed mathematical model of
             solute transport in the renal medulla of the rat kidney to
             study the impact of the structured organization of nephrons
             and vessels revealed in anatomic studies. The model
             represents the arrangement of tubules around a vascular
             bundle in the outer medulla and around a collecting duct
             cluster in the upper inner medulla. Model simulations yield
             marked gradients in intrabundle and interbundle interstitial
             fluid oxygen tension (PO2), NaCl concentration, and
             osmolality in the outer medulla, owing to the vigorous
             active reabsorption of NaCl by the thick ascending limbs. In
             the inner medulla, where the thin ascending limbs do not
             mediate significant active NaCl transport, interstitial
             fluid composition becomes much more homogeneous with respect
             to NaCl, urea, and osmolality. Nonetheless, a substantial
             PO2 gradient remains, owing to the relatively high oxygen
             demand of the inner medullary collecting ducts. Perhaps more
             importantly, the model predicts that in the absence of the
             three-dimensional medullary architecture, oxygen delivery to
             the inner medulla would drastically decrease, with the
             terminal inner medulla nearly completely deprived of oxygen.
             Thus model results suggest that the functional role of the
             three-dimensional medullary architecture may be to preserve
             oxygen delivery to the papilla. Additionally, a simulation
             that represents low medullary blood flow suggests that the
             separation of thick limbs from the vascular bundles
             substantially increases the risk of the segments to hypoxic
             injury. When nephrons and vessels are more homogeneously
             distributed, luminal PO2 in the thick ascending limb of
             superficial nephrons increases by 66% in the inner stripe.
             Furthermore, simulations predict that owing to the Bohr
             effect, the presumed greater acidity of blood in the
             interbundle regions, where thick ascending limbs are
             located, relative to that in the vascular bundles,
             facilitates the delivery of O2 to support the high metabolic
             requirements of the thick limbs and raises NaCl
             reabsorption.},
   Doi = {10.1152/ajprenal.00149.2014},
   Key = {fds243621}
}

@article{fds243622,
   Author = {Edwards, A and Castrop, H and Laghmani, K and Vallon, V and Layton,
             AT},
   Title = {Effects of NKCC2 isoform regulation on NaCl transport in
             thick ascending limb and macula densa: a modeling
             study.},
   Journal = {American Journal of Physiology: Renal Physiology},
   Volume = {307},
   Number = {2},
   Pages = {F137-F146},
   Year = {2014},
   Month = {July},
   ISSN = {1931-857X},
   url = {http://dx.doi.org/10.1152/ajprenal.00158.2014},
   Abstract = {This study aims to understand the extent to which modulation
             of the Na(+)-K(+)-2Cl(-) cotransporter NKCC2 differential
             splicing affects NaCl delivery to the macula densa. NaCl
             absorption by the thick ascending limb and macula densa
             cells is mediated by apical NKCC2. A recent study has
             indicated that differential splicing of NKCC2 is modulated
             by dietary salt (Schieβl IM, Rosenauer A, Kattler V, Minuth
             WW, Oppermann M, Castrop H. Am J Physiol Renal Physiol 305:
             F1139-F1148, 2013). Given the markedly different ion
             affinities of its splice variants, modulation of NKCC2
             differential splicing is believed to impact NaCl
             reabsorption. To assess the validity of that hypothesis, we
             have developed a mathematical model of macula densa cell
             transport and incorporated that cell model into a previously
             applied model of the thick ascending limb (Weinstein AM,
             Krahn TA. Am J Physiol Renal Physiol 298: F525-F542, 2010).
             The macula densa model predicts a 27.4- and 13.1-mV
             depolarization of the basolateral membrane [as a surrogate
             for activation of tubuloglomerular feedback (TGF)] when
             luminal NaCl concentration is increased from 25 to 145 mM or
             luminal K(+) concentration is increased from 1.5 to 3.5 mM,
             respectively, consistent with experimental measurements.
             Simulations indicate that with luminal solute concentrations
             consistent with in vivo conditions near the macula densa,
             NKCC2 operates near its equilibrium state. Results also
             suggest that modulation of NKCC2 differential splicing by
             low salt, which induces a shift from NKCC2-A to NKCC2-B
             primarily in the cortical thick ascending limb and macula
             densa cells, significantly enhances salt reabsorption in the
             thick limb and reduces Na(+) and Cl(-) delivery to the
             macula densa by 3.7 and 12.5%, respectively. Simulation
             results also predict that the NKCC2 isoform shift
             hyperpolarizes the macula densa basolateral cell membrane,
             which, taken in isolation, may inhibit the release of the
             TGF signal. However, excessive early distal salt delivery
             and renal salt loss during a low-salt diet may be prevented
             by an asymmetric TGF response, which may be more sensitive
             to flow increases.},
   Doi = {10.1152/ajprenal.00158.2014},
   Key = {fds243622}
}

@article{fds243620,
   Author = {Sgouralis, I and Layton, AT},
   Title = {Theoretical assessment of renal autoregulatory
             mechanisms.},
   Journal = {American Journal of Physiology: Renal Physiology},
   Volume = {306},
   Number = {11},
   Pages = {F1357-F1371},
   Year = {2014},
   Month = {June},
   ISSN = {1931-857X},
   url = {http://dx.doi.org/10.1152/ajprenal.00649.2013},
   Abstract = {A mathematical model of renal hemodynamics was used to
             assess the individual contributions of the tubuloglomerular
             feedback (TGF) mechanism and the myogenic response to
             glomerular filtration rate regulation in the rat kidney. The
             model represents an afferent arteriole segment, glomerular
             filtration, and a short loop of Henle. The afferent
             arteriole model exhibits myogenic response, which is
             activated by hydrostatic pressure variations to induce
             changes in membrane potential and vascular muscle tone. The
             tubule model predicts tubular fluid and Cl(-) transport.
             Macula densa Cl(-) concentration is sensed as the signal for
             TGF, which acts to constrict or dilate the afferent
             arteriole. With this configuration, the model afferent
             arteriole maintains stable glomerular filtration rate within
             a physiologic range of perfusion pressure (80-180 mmHg). The
             contribution of TGF to overall autoregulation is significant
             only within a narrow band of perfusion pressure values
             (80-110 mmHg). Model simulations of ramp-like perfusion
             pressure perturbations agree well with findings by Flemming
             et al. (Flemming B, Arenz N, Seeliger E, Wronski T, Steer K,
             Persson PB. J Am Soc Nephrol 12: 2253-2262, 2001), which
             indicate that changes in vascular conductance are markedly
             sensitive to pressure velocity. That asymmetric response is
             attributed to the rate-dependent kinetics of the myogenic
             mechanism. Moreover, simulations of renal autoregulation in
             diabetes mellitus predict that, due to the impairment of the
             voltage-gated Ca(2+) channels of the afferent arteriole
             smooth muscle cells, the perfusion pressure range in which
             single-nephron glomerular filtration rate remains stable is
             reduced by ~70% and that TGF gain is reduced by nearly 40%,
             consistent with experimental findings.},
   Doi = {10.1152/ajprenal.00649.2013},
   Key = {fds243620}
}

@article{fds243623,
   Author = {Moss, R and Layton, AT},
   Title = {Dominant factors that govern pressure natriuresis in
             diuresis and antidiuresis: a mathematical
             model.},
   Journal = {American Journal of Physiology: Renal Physiology},
   Volume = {306},
   Number = {9},
   Pages = {F952-F969},
   Year = {2014},
   Month = {May},
   ISSN = {1931-857X},
   url = {http://dx.doi.org/10.1152/ajprenal.00500.2013},
   Abstract = {We have developed a whole kidney model of the urine
             concentrating mechanism and renal autoregulation. The model
             represents the tubuloglomerular feedback (TGF) and myogenic
             mechanisms, which together affect the resistance of the
             afferent arteriole and thus glomerular filtration rate. TGF
             is activated by fluctuations in macula densa [Cl(-)] and the
             myogefnic mechanism by changes in hydrostatic pressure. The
             model was used to investigate the relative contributions of
             medullary blood flow autoregulation and inhibition of
             transport in the proximal convoluted tubule to pressure
             natriuresis in both diuresis and antidiuresis. The model
             predicts that medullary blood flow autoregulation, which
             only affects the interstitial solute composition in the
             model, has negligible influence on the rate of NaCl
             excretion. However, it exerts a significant effect on urine
             flow, particularly in the antidiuretic kidney. This suggests
             that interstitial washout has significant implications for
             the maintenance of hydration status but little direct
             bearing on salt excretion, and that medullary blood flow may
             only play a signaling role for stimulating a
             pressure-natriuresis response. Inhibited reabsorption in the
             model proximal convoluted tubule is capable of driving
             pressure natriuresis when the known actions of vasopressin
             on the collecting duct epithelium are taken into
             account.},
   Doi = {10.1152/ajprenal.00500.2013},
   Key = {fds243623}
}

@article{fds243616,
   Author = {Li, Y and Sgouralis, I and Layton, AT},
   Title = {Computing viscous flow in an elastic tube},
   Journal = {Numerical Mathematics: Theory, Methods and Applications
             (NM-TMA)},
   Volume = {7},
   Number = {4},
   Pages = {555-574},
   Year = {2014},
   Month = {January},
   ISSN = {1004-8979},
   url = {http://dx.doi.org/10.4208/nmtma.2014.1303si},
   Abstract = {©2014 Global-Science Press. We have developed a numerical
             method for simulating viscous flow through a compliant
             closed tube, driven by a pair of fluid source and sink. As
             is natural for tubular flow simulations, the problem is
             formulated in axisymmetric cylindrical coordinates, with
             fluid flow described by the Navier-Stokes equations. Because
             the tubular walls are assumed to be elastic, when stretched
             or compressed they exert forces on the fluid. Since these
             forces are singularly supported along the boundaries, the
             fluid velocity and pressure fields become unsmooth. To
             accurately compute the solution, we use the velocity
             decomposition approach, according to which pressure and
             velocity are decomposed into a singular part and a remainder
             part. The singular part satisfies the Stokes equations with
             singular boundary forces. Because the Stokes solution is
             unsmooth, it is computed to second-order accuracy using the
             immersed interface method, which incorporates known jump
             discontinuities in the solution and derivatives into the
             finite difference stencils. The remainder part, which
             satisfies the Navier-Stokes equations with a continuous body
             force, is regular. The equations describing the remainder
             part are discretized in time using the semi-Lagrangian
             approach, and then solved using a pressure-free projection
             method. Numerical results indicate that the computed overall
             solution is secondorder accurate in space, and the velocity
             is second-order accurate in time.},
   Doi = {10.4208/nmtma.2014.1303si},
   Key = {fds243616}
}

@article{fds243617,
   Author = {Layton, AT},
   Title = {Mathematical modeling of urea transport in the
             kidney.},
   Journal = {Sub-Cellular Biochemistry},
   Volume = {73},
   Pages = {31-43},
   Booktitle = {Urea Transporters},
   Publisher = {Springer},
   Editor = {Baoxue Yang},
   Year = {2014},
   Month = {January},
   ISSN = {0306-0225},
   url = {http://dx.doi.org/10.1007/978-94-017-9343-8_3},
   Abstract = {Mathematical modeling techniques have been useful in
             providing insights into biological systems, including the
             kidney. This article considers some of the mathematical
             models that concern urea transport in the kidney. Modeling
             simulations have been conducted to investigate, in the
             context of urea cycling and urine concentration, the effects
             of hypothetical active urea secretion into pars recta.
             Simulation results suggest that active urea secretion
             induces a "urea-selective" improvement in urine
             concentrating ability. Mathematical models have also been
             built to study the implications of the highly structured
             organization of tubules and vessels in the renal medulla on
             urea sequestration and cycling. The goal of this article is
             to show how physiological problems can be formulated and
             studied mathematically, and how such models may provide
             insights into renal functions.},
   Doi = {10.1007/978-94-017-9343-8_3},
   Key = {fds243617}
}

@article{fds243627,
   Author = {Edwards, A and Layton, AT},
   Title = {Calcium dynamics underlying the myogenic response of the
             renal afferent arteriole.},
   Journal = {American journal of physiology. Renal physiology},
   Volume = {306},
   Number = {1},
   Pages = {F34-F48},
   Year = {2014},
   Month = {January},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/24173354},
   Abstract = {The renal afferent arteriole reacts to an elevation in blood
             pressure with an increase in muscle tone and a decrease in
             luminal diameter. This effect, known as the myogenic
             response, is believed to stabilize glomerular filtration and
             to protect the glomerulus from systolic blood pressure
             increases, especially in hypertension. To study the
             mechanisms underlying the myogenic response, we developed a
             mathematical model of intracellular Ca(2+) signaling in an
             afferent arteriole smooth muscle cell. The model represents
             detailed transmembrane ionic transport, intracellular Ca(2+)
             dynamics, the kinetics of myosin light chain
             phosphorylation, and the mechanical behavior of the cell. It
             assumes that the myogenic response is initiated by
             pressure-induced changes in the activity of nonselective
             cation channels. Our model predicts spontaneous vasomotion
             at physiological luminal pressures and KCl- and
             diltiazem-induced diameter changes comparable to
             experimental findings. The time-periodic oscillations stem
             from the dynamic exchange of Ca(2+) between the cytosol and
             the sarcoplasmic reticulum, coupled to the stimulation of
             Ca(2+)-activated potassium (KCa) and chloride (ClCa)
             channels, and the modulation of voltage-activated L-type
             channels; blocking sarco/endoplasmic reticulum Ca(2+) pumps,
             ryanodine receptors (RyR), KCa, ClCa, or L-type channels
             abolishes these oscillations. Our results indicate that the
             profile of the myogenic response is also strongly dependent
             on the conductance of ClCa and L-type channels, as well as
             the activity of plasmalemmal Ca(2+) pumps. Furthermore,
             inhibition of KCa is not necessary to induce myogenic
             contraction. Lastly, our model suggests that the kinetic
             behavior of L-type channels results in myogenic kinetics
             that are substantially faster during constriction than
             during dilation, consistent with in vitro observations
             (Loutzenhiser R, Bidani A, Chilton L. Circ. Res. 90:
             1316-1324, 2002).},
   Doi = {10.1152/ajprenal.00317.2013},
   Key = {fds243627}
}

@article{fds243633,
   Author = {Ryu, H and Layton, AT},
   Title = {Tubular fluid flow and distal NaCl delivery mediated by
             tubuloglomerular feedback in the rat kidney},
   Journal = {Journal of Mathematical Biology},
   Volume = {68},
   Number = {4},
   Pages = {1023-1049},
   Year = {2014},
   Month = {January},
   ISSN = {0303-6812},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/23529284},
   Abstract = {The glomerular filtration rate in the kidney is controlled,
             in part, by the tubuloglomerular feedback (TGF) system,
             which is a negative feedback loop that mediates oscillations
             in tubular fluid flow and in fluid NaCl concentration of the
             loop of Henle. In this study, we developed a mathematical
             model of the TGF system that represents NaCl transport along
             a short loop of Henle with compliant walls. The proximal
             tubule and the outer-stripe segment of the descending limb
             are assumed to be highly water permeable; the thick
             ascending limb (TAL) is assumed to be water impermeable and
             have active NaCl transport. A bifurcation analysis of the
             TGF model equations was performed by computing parameter
             boundaries, as functions of TGF gain and delay, that
             separate differing model behaviors. The analysis revealed a
             complex parameter region that allows a variety of
             qualitatively different model equations: a regime having one
             stable, time-independent steady-state solution and regimes
             having stable oscillatory solutions of different
             frequencies. A comparison with a previous model, which
             represents only the TAL explicitly and other segments using
             phenomenological relations, indicates that explicit
             representation of the proximal tubule and descending limb of
             the loop of Henle lowers the stability of the TGF system.
             Model simulations also suggest that the onset of limit-cycle
             oscillations results in increases in the time-averaged
             distal NaCl delivery, whereas distal fluid delivery is not
             much affected. © 2013 Springer-Verlag Berlin
             Heidelberg.},
   Doi = {10.1007/s00285-013-0667-5},
   Key = {fds243633}
}

@article{fds320889,
   Author = {Layton, AT},
   Title = {Impacts of Facilitated Urea Transporters on the
             Urine-Concentrating Mechanism in the Rat
             Kidney},
   Journal = {Contemporary Mathematics},
   Volume = {628},
   Pages = {191-208},
   Year = {2014},
   ISBN = {978-0-8218-9850-5},
   url = {http://dx.doi.org/10.1090/conm/628/12518},
   Doi = {10.1090/conm/628/12518},
   Key = {fds320889}
}

@article{fds320890,
   Author = {Ryu, H and Layton, AT},
   Title = {Feedback-Mediated Dynamics in a Model of Coupled Nephrons
             with Compliant Short Loop of Henle},
   Journal = {Contemporary Mathematics},
   Volume = {628},
   Pages = {209-238},
   Year = {2014},
   ISBN = {978-0-8218-9850-5},
   url = {http://dx.doi.org/10.1090/conm/628/12542},
   Doi = {10.1090/conm/628/12542},
   Key = {fds320890}
}

@article{fds320891,
   Author = {Olson, SD and Layton, AT},
   Title = {Simulating Biofluid-Structure Interactions with an Immersed
             Boundary Framework - A Review},
   Journal = {Contemporary Mathematics},
   Volume = {628},
   Pages = {1-36},
   Year = {2014},
   ISBN = {978-0-8218-9850-5},
   url = {http://dx.doi.org/10.1090/conm/628/12545},
   Doi = {10.1090/conm/628/12545},
   Key = {fds320891}
}

@article{fds243628,
   Author = {Li, Y and Williams, SA and Layton, AT},
   Title = {A hybrid immersed interface method for driven stokes flow in
             an elastic tube},
   Journal = {Numerical Mathematics: Theory, Methods and Applications
             (NM-TMA)},
   Volume = {6},
   Number = {4},
   Pages = {600-616},
   Year = {2013},
   Month = {November},
   ISSN = {1004-8979},
   url = {http://dx.doi.org/10.4208/nmtma.2013.1219nm},
   Abstract = {We present a hybrid numerical method for simulating fluid
             flow through a compliant, closed tube, driven by an internal
             source and sink. Fluid is assumed to be highly viscous with
             its motion described by Stokes flow. Model geometry is
             assumed to be axisymmetric, and the governing equations are
             implemented in axisymmetric cylindrical coordinates, which
             capture 3D flow dynamics with only 2D computations. We solve
             the model equations using a hybrid approach: we decompose
             the pressure and velocity fields into parts due to the
             surface forcings and due to the source and sink, with each
             part handled separately by means of an appropriate method.
             Because the singularly-supported surface forcings yield an
             unsmooth solution, that part of the solution is computed
             using the immersed interface method. Jump conditions are
             derived for the axisymmetric cylindrical coordinates. The
             velocity due to the source and sink is calculated along the
             tubular surface using boundary integrals. Numerical results
             are presented that indicate second-order accuracy of the
             method. © 2013 Global-Science Press.},
   Doi = {10.4208/nmtma.2013.1219nm},
   Key = {fds243628}
}

@article{fds320892,
   Author = {Layton, AT and Bankir, L},
   Title = {Impacts of Active Urea Secretion into Pars Recta on Urine
             Concentration and Urea Excretion Rate.},
   Journal = {Physiological Reports},
   Volume = {1},
   Number = {3},
   Pages = {e00034},
   Year = {2013},
   Month = {September},
   url = {http://dx.doi.org/10.1002/phy2.34},
   Abstract = {It has been observed experimentally that early distal
             tubular urea flow exceeds urea delivery by the proximal
             convoluted tubule to the pars recta and loop of Henle.
             Moreover, the fractional excretion of urea in the urine may
             exceed values compatible with the reabsorption known to
             occur in the proximal convoluted tubule in the cortex. A
             likely explanation for these observations is that urea may
             be actively secreted into the pars recta, as proposed in a
             few studies. However, this hypothesis has yet to be
             demonstrated experimentally. In this study, we used a
             mathematical model of the renal medulla of the rat kidney to
             investigate the impacts of active urea secretion in the
             intrarenal handling of urea and in the urine concentrating
             ability. The model represents only the outer and inner
             medullary zones, with the actions taking place in the cortex
             incorporated via boundary conditions. Blood flow in the
             model vasculature is divided into plasma and red blood cell
             compartments. We compared urea flow rates and other related
             model variables without and with the hypothetical active
             urea secretion in the pars recta. The simulation suggests
             that active urea secretion induces a "urea-selective"
             improvement in urine concentrating ability by enhancing the
             efficiency of urea excretion without requiring a higher
             urine flow rate, and with only modest changes in the
             excretion of other solutes. These results should encourage
             experimental studies in order to assess the existence of an
             active urea secretion in the rodent kidney.},
   Doi = {10.1002/phy2.34},
   Key = {fds320892}
}

@article{fds243631,
   Author = {Layton, AT},
   Title = {Mathematical modeling of kidney transport.},
   Journal = {Wiley Interdisciplinary Reviews: Systems Biology and
             Medicine},
   Volume = {5},
   Number = {5},
   Pages = {557-573},
   Year = {2013},
   Month = {September},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/23852667},
   Abstract = {In addition to metabolic waste and toxin excretion, the
             kidney also plays an indispensable role in regulating the
             balance of water, electrolytes, nitrogen, and acid-base. In
             this review, we describe representative mathematical models
             that have been developed to better understand kidney
             physiology and pathophysiology, including the regulation of
             glomerular filtration, the regulation of renal blood flow by
             means of the tubuloglomerular feedback mechanisms and of the
             myogenic mechanism, the urine concentrating mechanism,
             epithelial transport, and regulation of renal oxygen
             transport. We discuss the extent to which these modeling
             efforts have expanded our understanding of renal function in
             both health and disease.},
   Doi = {10.1002/wsbm.1232},
   Key = {fds243631}
}

@article{fds243654,
   Author = {Ryu, H and Layton, AT},
   Title = {Effect of tubular inhomogeneities on feedback-mediated
             dynamics of a model of a thick ascending
             limb.},
   Journal = {Mathematical Medicine and Biology: A Journal of the
             IMA},
   Volume = {30},
   Number = {3},
   Pages = {191-212},
   Year = {2013},
   Month = {September},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/22511507},
   Abstract = {One of the key mechanisms that mediate renal autoregulation
             is the tubuloglomerular feedback (TGF) system, which is a
             negative feedback loop in the kidney that balances
             glomerular filtration with tubular reabsorptive capacity.
             Tubular fluid flow, NaCl concentration and other related
             variables are known to exhibit TGF-mediated oscillations. In
             this study, we used a mathematical model of the thick
             ascending limb (TAL) of a short loop of Henle of the rat
             kidney to study the effects of (i) spatially inhomogeneous
             TAL NaCl active transport rate, (ii) spatially inhomogeneous
             tubular radius and (iii) compliance of the tubular walls on
             TGF-mediated dynamics. A bifurcation analysis of the TGF
             model equations was performed by deriving a characteristic
             equation and finding its roots. Results of the bifurcation
             analysis were validated via numerical simulations of the
             full model equations. Model results suggest that a higher
             TAL NaCl active transport rate or a smaller TAL radius near
             the loop bend gives rise to stable oscillatory solutions at
             sufficiently high TGF gain values, even with zero TGF delay.
             In addition, when the TAL walls are assumed to be compliant,
             the TGF system exhibits a heightened tendency to oscillate,
             a result that is consistent with predictions of a previous
             modelling study.},
   Doi = {10.1093/imammb/dqs020},
   Key = {fds243654}
}

@article{fds320893,
   Author = {Haer-Wigman, L and Linthorst, GE and Sands, JM and Klein, JD and Thai,
             TL and Verhoeven, AJ and van Zwieten, R and Folman, C and Jansweijer,
             MC and Knegt, LC and de Ru, MH and Groothoff, JW and Ludwig, M and Layton,
             AT and Bokenkamp, A},
   Title = {DUPLICATION OF THE UREA TRANSPORTER B GENE (KIDD BLOOD
             GROUP) IN A KINDRED WITH FAMILIAL AZOTEMIA},
   Journal = {Vox Sanguinis},
   Volume = {105},
   Pages = {30-31},
   Year = {2013},
   Month = {June},
   Key = {fds320893}
}

@article{fds243632,
   Author = {Nieves-González, A and Clausen, C and Layton, AT and Layton, HE and Moore, LC},
   Title = {Transport efficiency and workload distribution in a
             mathematical model of the thick ascending
             limb.},
   Journal = {American journal of physiology. Renal physiology},
   Volume = {304},
   Number = {6},
   Pages = {F653-F664},
   Year = {2013},
   Month = {March},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/23097466},
   Abstract = {The thick ascending limb (TAL) is a major NaCl reabsorbing
             site in the nephron. Efficient reabsorption along that
             segment is thought to be a consequence of the establishment
             of a strong transepithelial potential that drives
             paracellular Na(+) uptake. We used a multicell mathematical
             model of the TAL to estimate the efficiency of Na(+)
             transport along the TAL and to examine factors that
             determine transport efficiency, given the condition that TAL
             outflow must be adequately dilute. The TAL model consists of
             a series of epithelial cell models that represent all major
             solutes and transport pathways. Model equations describe
             luminal flows, based on mass conservation and
             electroneutrality constraints. Empirical descriptions of
             cell volume regulation (CVR) and pH control were
             implemented, together with the tubuloglomerular feedback
             (TGF) system. Transport efficiency was calculated as the
             ratio of total net Na(+) transport (i.e., paracellular and
             transcellular transport) to transcellular Na(+) transport.
             Model predictions suggest that 1) the transepithelial Na(+)
             concentration gradient is a major determinant of transport
             efficiency; 2) CVR in individual cells influences the
             distribution of net Na(+) transport along the TAL; 3) CVR
             responses in conjunction with TGF maintain luminal Na(+)
             concentration well above static head levels in the cortical
             TAL, thereby preventing large decreases in transport
             efficiency; and 4) under the condition that the distribution
             of Na(+) transport along the TAL is quasi-uniform, the
             tubular fluid axial Cl(-) concentration gradient near the
             macula densa is sufficiently steep to yield a TGF gain
             consistent with experimental data.},
   Doi = {10.1152/ajprenal.00101.2012},
   Key = {fds243632}
}

@article{fds225252,
   Author = {Sarah D. Olson and Anita T. Layton},
   Title = {Simulating Fluid-Structure Interactions --- A
             Review},
   Journal = {AMS Contemporary Mathematics, Biological Fluid Dynamics:
             Modeling, Computations, and Applications},
   Volume = {628},
   Number = {1-36},
   Year = {2013},
   Key = {fds225252}
}

@article{fds243658,
   Author = {Leiderman, K and Bouzarth, EL and Cortez, R and Layton,
             AT},
   Title = {A regularization method for the numerical solution of
             periodic Stokes flow},
   Journal = {Journal of Computational Physics},
   Volume = {236},
   Number = {1},
   Pages = {187-202},
   Year = {2013},
   ISSN = {0021-9991},
   url = {http://dx.doi.org/10.1016/j.jcp.2012.09.035},
   Abstract = {We introduce a regularization method that gives a smooth
             formulation for the fundamental solution to Stokes flow
             driven by an infinite, triply-periodic array of point
             forces. With this formulation, the velocity at any spatial
             location may be calculated, including at and very near the
             point forces; these locations typically lead to numerical
             difficulties due to the singularity within the Stokeslet
             when using other methods. For computational efficiency, we
             build upon previous methods in which the periodic Stokeslet
             is split into two rapidly decaying sums, one in physical
             space and one in reciprocal, or Fourier, space. We present
             two validation studies of our method. First, we compute the
             drag coefficient for periodic arrays of spheres with a
             variety of concentrations of sphere packings; and second, we
             prescribe a force density onto a periodic array of spheres,
             compute the resulting nearby velocity field, and compare
             these velocities to those computed using an immersed
             boundary method formulation. The drag coefficients computed
             with our method are within 0.63 % of previously published
             values. The velocity field comparison shows a relative error
             of about 0.18 % in the L2-norm. We then apply our numerical
             method to a periodic arrangement of sinusoidal swimmers. By
             systematically varying their spacing in three directions, we
             are able to explore how their spacing affects their
             collective swimming speed. © 2012 Elsevier
             Inc..},
   Doi = {10.1016/j.jcp.2012.09.035},
   Key = {fds243658}
}

@article{fds243629,
   Author = {Sgouralis, I and Layton, AT},
   Title = {Control and modulation of fluid flow in the rat
             kidney},
   Journal = {BULLETIN OF MATHEMATICAL BIOLOGY},
   Volume = {75},
   Pages = {2551-2574},
   Year = {2012},
   Month = {November},
   Key = {fds243629}
}

@article{fds243630,
   Author = {Dantzler, WH and Layton, AT and Layton, HE and Pannabecker,
             TL},
   Title = {Urine concentrating mechanism in the inner medulla: function
             of the thin limbs of Henle’s loops},
   Journal = {Clinical Journal of the American Society of
             Nephrology.},
   Pages = {doi:10.2215/CJN.08750812},
   Year = {2012},
   Month = {August},
   Key = {fds243630}
}

@article{fds304490,
   Author = {Sgouralis, I and Layton, AT},
   Title = {Autoregulation and conduction of vasomotor responses in a
             mathematical model of the rat afferent arteriole.},
   Journal = {American journal of physiology. Renal physiology},
   Volume = {303},
   Number = {2},
   Pages = {F229-F239},
   Year = {2012},
   Month = {July},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/22496414},
   Abstract = {We have formulated a mathematical model for the rat afferent
             arteriole (AA). Our model consists of a series of arteriolar
             smooth muscle cells and endothelial cells, each of which
             represents ion transport, cell membrane potential, and gap
             junction coupling. Cellular contraction and wall mechanics
             are also represented for the smooth muscle cells. Blood flow
             through the AA lumen is described by Poiseuille flow. The AA
             model's representation of the myogenic response is based on
             the hypothesis that changes in hydrostatic pressure induce
             changes in the activity of nonselective cation channels. The
             resulting changes in membrane potential then affect calcium
             influx through changes in the activity of the voltage-gated
             calcium channels, so that vessel diameter decreases with
             increasing pressure values. With this configuration, the
             model AA maintains roughly stable renal blood flow within a
             physiologic range of blood flow pressure. Model simulation
             of vasoconstriction initiated from local stimulation also
             agrees well with findings in the experimental literature,
             notably those of Steinhausen et al. (Steinhausen M, Endlich
             K, Nobiling R, Rarekh N, Schütt F. J Physiol 505: 493-501,
             1997), which indicated that conduction of vasoconstrictive
             response decays more rapidly in the upstream flow direction
             than downstream. The model can be incorporated into models
             of integrated renal hemodynamic regulation.},
   Doi = {10.1152/ajprenal.00589.2011},
   Key = {fds304490}
}

@article{fds243662,
   Author = {Savage, NS and Layton, AT and Lew, DJ},
   Title = {Mechanistic mathematical model of polarity in
             yeast.},
   Journal = {Molecular Biology of the Cell},
   Volume = {23},
   Number = {10},
   Pages = {1998-2013},
   Year = {2012},
   Month = {May},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/22438587},
   Abstract = {The establishment of cell polarity involves
             positive-feedback mechanisms that concentrate polarity
             regulators, including the conserved GTPase Cdc42p, at the
             "front" of the polarized cell. Previous studies in yeast
             suggested the presence of two parallel positive-feedback
             loops, one operating as a diffusion-based system, and the
             other involving actin-directed trafficking of Cdc42p on
             vesicles. F-actin (and hence directed vesicle traffic)
             speeds fluorescence recovery of Cdc42p after photobleaching,
             suggesting that vesicle traffic of Cdc42p contributes to
             polarization. We present a mathematical modeling framework
             that combines previously developed mechanistic
             reaction-diffusion and vesicle-trafficking models.
             Surprisingly, the combined model recapitulated the observed
             effect of vesicle traffic on Cdc42p dynamics even when the
             vesicles did not carry significant amounts of Cdc42p.
             Vesicle traffic reduced the concentration of Cdc42p at the
             front, so that fluorescence recovery mediated by Cdc42p flux
             from the cytoplasm took less time to replenish the bleached
             pool. Simulations in which Cdc42p was concentrated into
             vesicles or depleted from vesicles yielded almost identical
             predictions, because Cdc42p flux from the cytoplasm was
             dominant. These findings indicate that vesicle-mediated
             delivery of Cdc42p is not required to explain the observed
             Cdc42p dynamics, and raise the question of whether such
             Cdc42p traffic actually contributes to polarity
             establishment.},
   Doi = {10.1091/mbc.E11-10-0837},
   Key = {fds243662}
}

@article{fds243663,
   Author = {Layton, AT and Moore, LC and Layton, HE},
   Title = {Signal transduction in a compliant thick ascending
             limb.},
   Journal = {American journal of physiology. Renal physiology},
   Volume = {302},
   Number = {9},
   Pages = {F1188-F1202},
   Year = {2012},
   Month = {May},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/22262482},
   Abstract = {In several previous studies, we used a mathematical model of
             the thick ascending limb (TAL) to investigate nonlinearities
             in the tubuloglomerular feedback (TGF) loop. That model,
             which represents the TAL as a rigid tube, predicts that TGF
             signal transduction by the TAL is a generator of
             nonlinearities: if a sinusoidal oscillation is added to
             constant intratubular fluid flow, the time interval required
             for an element of tubular fluid to traverse the TAL, as a
             function of time, is oscillatory and periodic but not
             sinusoidal. As a consequence, NaCl concentration in tubular
             fluid alongside the macula densa will be nonsinusoidal and
             thus contain harmonics of the original sinusoidal frequency.
             We hypothesized that the complexity found in power spectra
             based on in vivo time series of key TGF variables arises in
             part from those harmonics and that nonlinearities in
             TGF-mediated oscillations may result in increased NaCl
             delivery to the distal nephron. To investigate the
             possibility that a more realistic model of the TAL would
             damp the harmonics, we have conducted new studies in a model
             TAL that has compliant walls and thus a tubular radius that
             depends on transmural pressure. These studies predict that
             compliant TAL walls do not damp, but instead intensify, the
             harmonics. In addition, our results predict that mean TAL
             flow strongly influences the shape of the NaCl concentration
             waveform at the macula densa. This is a consequence of the
             inverse relationship between flow speed and transit time,
             which produces asymmetry between up- and downslopes of the
             oscillation, and the nonlinearity of TAL NaCl absorption at
             low flow rates, which broadens the trough of the oscillation
             relative to the peak. The dependence of waveform shape on
             mean TAL flow may be the source of the variable degree of
             distortion, relative to a sine wave, seen in experimental
             recordings of TGF-mediated oscillations.},
   Doi = {10.1152/ajprenal.00732.2010},
   Key = {fds243663}
}

@article{fds243665,
   Author = {Layton, AT and Gilbert, RL and Pannabecker, TL},
   Title = {Isolated interstitial nodal spaces may facilitate
             preferential solute and fluid mixing in the rat renal inner
             medulla.},
   Journal = {American journal of physiology. Renal physiology},
   Volume = {302},
   Number = {7},
   Pages = {F830-F839},
   Year = {2012},
   Month = {April},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/22160770},
   Abstract = {Recent anatomic findings indicate that in the upper inner
             medulla of the rodent kidney, tubules, and vessels are
             organized around clusters of collecting ducts (CDs). Within
             CD clusters, CDs and some of the ascending vasa recta (AVR)
             and ascending thin limbs (ATLs), when viewed in transverse
             sections, form interstitial nodal spaces, which are arrayed
             at structured intervals throughout the inner medulla. These
             spaces, or microdomains, are bordered on one side by a
             single CD, on the opposite side by one or more ATLs, and on
             the other two sides by AVR. To study the interactions among
             these CDs, ATLs, and AVR, we have developed a mathematical
             compartment model, which simulates steady-state solute
             exchange through the microdomain at a given inner medullary
             level. Fluid in all compartments contains Na(+), Cl(-), urea
             and, in the microdomain, negative fixed charges that
             represent macromolecules (e.g., hyaluronan) balanced by
             Na(+). Fluid entry into AVR is assumed to be driven by
             hydraulic and oncotic pressures. Model results suggest that
             the isolated microdomains facilitate solute and fluid mixing
             among the CDs, ATLs, and AVR, promote water withdrawal from
             CDs, and consequently may play an important role in
             generating the inner medullary osmotic gradient.},
   Doi = {10.1152/ajprenal.00539.2011},
   Key = {fds243665}
}

@article{fds320894,
   Author = {Gilbert, RL and Pannabecker, TL and Layton, AT},
   Title = {Role of interstitial nodal spaces in the urine concentrating
             mechanism of the rat kidney},
   Journal = {The FASEB journal : official publication of the Federation
             of American Societies for Experimental Biology},
   Volume = {26},
   Year = {2012},
   Month = {April},
   Key = {fds320894}
}

@article{fds320895,
   Author = {Pannabecker, TL and Dantzler, WH and Layton, AT},
   Title = {Urine Concentrating Mechanism: Impact of Vascular and
             Tubular Architecture and a Proposed Descending Limb Urea-Na
             Cotransporter},
   Journal = {The FASEB journal : official publication of the Federation
             of American Societies for Experimental Biology},
   Volume = {26},
   Year = {2012},
   Month = {April},
   Key = {fds320895}
}

@article{fds320896,
   Author = {Ryu, H and Layton, AT},
   Title = {Tubular Fluid Oscillations Mediated by Tubuloglomerular
             Feedback in a Short Loop of Henle},
   Journal = {The FASEB journal : official publication of the Federation
             of American Societies for Experimental Biology},
   Volume = {26},
   Year = {2012},
   Month = {April},
   Key = {fds320896}
}

@article{fds320897,
   Author = {Sgouralis, I and Layton, AT},
   Title = {Interactions between Tubuloglomerular Feedback and the
             Myogenic Mechanism of the Afferent Arteriole},
   Journal = {The FASEB journal : official publication of the Federation
             of American Societies for Experimental Biology},
   Volume = {26},
   Year = {2012},
   Month = {April},
   Key = {fds320897}
}

@article{fds243664,
   Author = {Layton, AT and Dantzler, WH and Pannabecker, TL},
   Title = {Urine concentrating mechanism: impact of vascular and
             tubular architecture and a proposed descending limb urea-Na+
             cotransporter.},
   Journal = {American journal of physiology. Renal physiology},
   Volume = {302},
   Number = {5},
   Pages = {F591-F605},
   Year = {2012},
   Month = {March},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/22088433},
   Abstract = {We extended a region-based mathematical model of the renal
             medulla of the rat kidney, previously developed by us, to
             represent new anatomic findings on the vascular architecture
             in the rat inner medulla (IM). In the outer medulla (OM),
             tubules and vessels are organized around tightly packed
             vascular bundles; in the IM, the organization is centered
             around collecting duct clusters. In particular, the model
             represents the separation of descending vasa recta from the
             descending limbs of loops of Henle, and the model represents
             a papillary segment of the descending thin limb that is
             water impermeable and highly urea permeable. Model results
             suggest that, despite the compartmentalization of IM blood
             flow, IM interstitial fluid composition is substantially
             more homogeneous compared with OM. We used the model to
             study medullary blood flow in antidiuresis and the effects
             of vascular countercurrent exchange. We also hypothesize
             that the terminal aquaporin-1 null segment of the long
             descending thin limbs may express a urea-Na(+) or urea-Cl(-)
             cotransporter. As urea diffuses from the urea-rich papillary
             interstitium into the descending thin limb luminal fluid,
             NaCl is secreted via the cotransporter against its
             concentration gradient. That NaCl is then reabsorbed near
             the loop bend, raising the interstitial fluid osmolality and
             promoting water reabsorption from the IM collecting ducts.
             Indeed, the model predicts that the presence of the
             urea-Na(+) or urea- Cl(-) cotransporter facilitates the
             cycling of NaCl within the IM and yields a loop-bend fluid
             composition consistent with experimental
             data.},
   Doi = {10.1152/ajprenal.00263.2011},
   Key = {fds243664}
}

@article{fds243666,
   Author = {Layton, AT and Pham, P and Ryu, H},
   Title = {Signal transduction in a compliant short loop of
             Henle.},
   Journal = {International Journal for Numerical Methods in Biomedical
             Engineering},
   Volume = {28},
   Number = {3},
   Pages = {369-383},
   Year = {2012},
   Month = {March},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/22577511},
   Abstract = {To study the transformation of fluctuations in filtration
             rate into tubular fluid chloride concentration oscillations
             alongside the macula densa, we have developed a mathematical
             model for tubuloglomerular feedback (TGF) signal
             transduction along the pars recta, the descending limb, and
             the thick ascending limb (TAL) of a short-looped nephron.
             The model tubules are assumed to have compliant walls and,
             thus, a tubular radius that depends on the transmural
             pressure difference. Previously, it has been predicted that
             TGF transduction by the TAL is a generator of
             nonlinearities: if a sinusoidal oscillation is added to a
             constant TAL flow rate, then the time required for a fluid
             element to traverse the TAL is oscillatory in time but
             nonsinusoidal. The results from the new model simulations
             presented here predict that TGF transduction by the loop of
             Henle is also, in the same sense, a generator of
             nonlinearities. Thus, this model predicts that oscillations
             in tubular fluid alongside the macula densa will be
             nonsinusoidal and will exhibit harmonics of sinusoidal
             perturbations of pars recta flow. Model results also
             indicate that the loop acts as a low-pass filter in the
             transduction of the TGF signal.},
   Doi = {10.1002/cnm.1475},
   Key = {fds243666}
}

@article{fds204560,
   Author = {Anita T. Layton and Guowei Wei},
   Title = {Editorial: Interface methods for biological and biomedical
             problems},
   Journal = {Int J Numer Methods Biomed Eng},
   Volume = {28},
   Number = {3},
   Editor = {289-290},
   Year = {2012},
   Key = {fds204560}
}

@article{fds243626,
   Author = {Witelski, T and Ambrose, D and Bertozzi, A and Layton, A and Li, Z and Minion, M},
   Title = {Preface: Special issue on fluid dynamics, analysis and
             numerics},
   Journal = {Discrete and Continuous Dynamical Systems - Series
             B},
   Volume = {17},
   Number = {4},
   Pages = {i-ii},
   Year = {2012},
   ISSN = {1531-3492},
   url = {http://dx.doi.org/10.3934/dcdsb.2012.17.4i},
   Doi = {10.3934/dcdsb.2012.17.4i},
   Key = {fds243626}
}

@article{fds243651,
   Author = {Layton, A and Stockie, J and Li, Z and Huang, H},
   Title = {Preface: Special issue on fluid motion driven by immersed
             structures},
   Journal = {Communications in computational physics},
   Volume = {12},
   Number = {2},
   Pages = {i-iii},
   Year = {2012},
   ISSN = {1815-2406},
   Key = {fds243651}
}

@article{fds243653,
   Author = {Layton, AT},
   Title = {A velocity decomposition approach for solving the immersed
             interface problem with Dirichlet boundary
             conditions},
   Journal = {IMA Volume on Natural Locomotion in Fluids and on Surfaces:
             Swimming, Flying, and Sliding, in press},
   Pages = {263-270},
   Year = {2012},
   Key = {fds243653}
}

@article{fds243655,
   Author = {Nieves-Gonzalez, A and Clausen, C and Marcano, M and Layton, AT and Layton, HE and Moore, LC},
   Title = {Fluid dilution and efficiency of Na+ transport in a
             mathematical model of a thick ascending limb
             cell},
   Journal = {American Journal of Physiology---Renal Physiology},
   Volume = {304},
   Number = {F634-F652},
   Year = {2012},
   Key = {fds243655}
}

@article{fds243656,
   Author = {Nieves-Gonzalez, A and Clausen, C and Layton, AT and Layton, HE and Moore, LC},
   Title = {Efficiency and workload distribution in a mathematical model
             of the thick ascending limb},
   Journal = {American Journal of Physiology--Renal Physiology},
   Year = {2012},
   Key = {fds243656}
}

@article{fds243657,
   Author = {Edwards, A and Layton, AT},
   Title = {Impact of nitric oxide-mediated vasodilation on outer
             medullary NaCl transport and oxygenation},
   Journal = {American journal of physiology. Renal physiology},
   Volume = {303},
   Number = {7},
   Pages = {F907-F917},
   Year = {2012},
   ISSN = {0363-6127},
   url = {http://dx.doi.org/10.1152/ajprenal.00055.2012},
   Abstract = {The present study aimed to elucidate the reciprocal
             interactions between oxygen (O2), nitric oxide (NO), and
             superoxide (O2-) and their effects on vascular and tubular
             function in the outer medulla. We expanded our region-based
             model of transport in the rat outer medulla (Edwards A,
             Layton AT. Am J Physiol Renal Physiol 301: F979-F996, 2011)
             to incorporate the effects of NO on descending vasa recta
             (DVR) diameter and blood flow. Our model predicts that the
             segregation of long DVR in the center of vascular bundles,
             away from tubular segments, gives rise to large radial NO
             concentration gradients that in turn result in differential
             regulation of vasoactivity in short and long DVR. The
             relative isolation of long DVR shields them from changes in
             the rate of NaCl reabsorption, and hence from changes in O2
             requirements, by medullary thick ascending limbs (mTALs),
             thereby preserving O2 delivery to the inner medulla. The
             model also predicts that O2- can sufficiently decrease the
             bioavailability of NO in the interbundle region to affect
             the diameter of short DVR, suggesting that the
             experimentally observed effects of O2- on medullary blood
             flow may be at least partly mediated by NO. In addition, our
             results indicate that the tubulovascular cross talk of NO,
             that is, the diffusion of NO produced by mTAL epithelia
             toward adjacent DVR, helps to maintain blood flow and O2
             supply to the interbundle region even under basal
             conditions. NO also acts to preserve local O2 availability
             by inhibiting the rate of active Na+ transport, thereby
             reducing the O2 requirements of mTALs. The dual regulation
             by NO of oxygen supply and demand is predicted to
             significantly attenuate the hypoxic effects of angiotensin
             II. © 2012 the American Physiological Society.},
   Doi = {10.1152/ajprenal.00055.2012},
   Key = {fds243657}
}

@article{fds243659,
   Author = {Sgouralis, I and Layton, AT},
   Title = {Autoregulation and conduction of vasomotor responses in a
             mathematical model of the rat afferent arteriole},
   Journal = {Am J Physiol Renal Physiol},
   Volume = {303},
   Number = {F229-F239},
   Pages = {F229-F239},
   Year = {2012},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/22496414},
   Abstract = {We have formulated a mathematical model for the rat afferent
             arteriole (AA). Our model consists of a series of arteriolar
             smooth muscle cells and endothelial cells, each of which
             represents ion transport, cell membrane potential, and gap
             junction coupling. Cellular contraction and wall mechanics
             are also represented for the smooth muscle cells. Blood flow
             through the AA lumen is described by Poiseuille flow. The AA
             model's representation of the myogenic response is based on
             the hypothesis that changes in hydrostatic pressure induce
             changes in the activity of nonselective cation channels. The
             resulting changes in membrane potential then affect calcium
             influx through changes in the activity of the voltage-gated
             calcium channels, so that vessel diameter decreases with
             increasing pressure values. With this configuration, the
             model AA maintains roughly stable renal blood flow within a
             physiologic range of blood flow pressure. Model simulation
             of vasoconstriction initiated from local stimulation also
             agrees well with findings in the experimental literature,
             notably those of Steinhausen et al. (Steinhausen M, Endlich
             K, Nobiling R, Rarekh N, Schütt F. J Physiol 505: 493-501,
             1997), which indicated that conduction of vasoconstrictive
             response decays more rapidly in the upstream flow direction
             than downstream. The model can be incorporated into models
             of integrated renal hemodynamic regulation.},
   Doi = {10.1152/ajprenal.00589.2011},
   Key = {fds243659}
}

@article{fds243660,
   Author = {Layton, AT},
   Title = {Modeling transport and flow regulatory mechanisms of the
             kidney},
   Journal = {ISRN Biomath},
   Volume = {2012},
   Pages = {ID: 170594, 18 pages},
   Year = {2012},
   Key = {fds243660}
}

@article{fds243661,
   Author = {Li, Y and Layton, AT},
   Title = {Accurate computation of Stokes flow driven by an open
             immersed interface},
   Journal = {Journal of Computational Physics},
   Volume = {231},
   Number = {15},
   Pages = {5195-5215},
   Year = {2012},
   ISSN = {0021-9991},
   url = {http://dx.doi.org/10.1016/j.jcp.2012.04.020},
   Abstract = {We present numerical methods for computing two-dimensional
             Stokes flow driven by forces singularly supported along an
             open, immersed interface. Two second-order accurate methods
             are developed: one for accurately evaluating boundary
             integral solutions at a point, and another for computing
             Stokes solution values on a rectangular mesh. We first
             describe a method for computing singular or nearly singular
             integrals, such as a double layer potential due to sources
             on a curve in the plane, evaluated at a point on or near the
             curve. To improve accuracy of the numerical quadrature, we
             add corrections for the errors arising from discretization,
             which are found by asymptotic analysis. When used to solve
             the Stokes equations with sources on an open, immersed
             interface, the method generates second-order approximations,
             for both the pressure and the velocity, and preserves the
             jumps in the solutions and their derivatives across the
             boundary. We then combine the method with a mesh-based
             solver to yield a hybrid method for computing Stokes
             solutions at N 2 grid points on a rectangular grid.
             Numerical results are presented which exhibit second-order
             accuracy. To demonstrate the applicability of the method, we
             use the method to simulate fluid dynamics induced by the
             beating motion of a cilium. The method preserves the sharp
             jumps in the Stokes solution and their derivatives across
             the immersed boundary. Model results illustrate the distinct
             hydrodynamic effects generated by the effective stroke and
             by the recovery stroke of the ciliary beat cycle. © 2012
             Elsevier Inc.},
   Doi = {10.1016/j.jcp.2012.04.020},
   Key = {fds243661}
}

@article{fds243667,
   Author = {Layton, AT and Beale, JT},
   Title = {A partially implicit hybrid method for computing interface
             motion in stokes flow},
   Journal = {Discrete and Continuous Dynamical Systems - Series
             B},
   Volume = {17},
   Number = {4},
   Pages = {1139-1153},
   Year = {2012},
   ISSN = {1531-3492},
   url = {http://dx.doi.org/10.3934/dcdsb.2012.17.1139},
   Abstract = {We present a partially implicit hybrid method for simulating
             the motion of a stiff interface immersed in Stokes flow, in
             free space or in a rectangular domain with boundary
             conditions. We assume the interface is a closed curve which
             remains in the interior of the computational region. The
             implicit time integration is based on the small-scale
             decomposition approach and does not require the iterative
             solution of a system of nonlinear equations. First-order and
             second-order versions of the time-stepping method are
             derived systematically, and numerical results indicate that
             both methods are substantially more stable than explicit
             methods. At each time level, the Stokes equations are solved
             using a hybrid approach combining nearly singular integrals
             on a band of mesh points near the interface and a mesh-based
             solver. The solutions are second-order accurate in space and
             preserve the jump discontinuities across the interface.
             Finally, the hybrid method can be used as an alternative to
             adaptive mesh refinement to resolve boundary layers that are
             frequently present around a stiff immersed
             interface.},
   Doi = {10.3934/dcdsb.2012.17.1139},
   Key = {fds243667}
}

@article{fds243668,
   Author = {Hou, G and Wang, J and Layton, A},
   Title = {Numerical methods for fluid-structure interaction - A
             review},
   Journal = {Communications in computational physics},
   Volume = {12},
   Number = {2},
   Pages = {337-377},
   Year = {2012},
   ISSN = {1815-2406},
   url = {http://dx.doi.org/10.4208/cicp.291210.290411s},
   Abstract = {The interactions between incompressible fluid flows and
             immersed structures are nonlinear multi-physics phenomena
             that have applications to a wide range of scientific and
             engineering disciplines. In this article, we review
             representative numerical methods based on conforming and
             non-conforming meshes that are currently available for
             computing fluid-structure interaction problems, with an
             emphasis on some of the recent developments in the field. A
             goal is to categorize the selected methods and assess their
             accuracy and efficiency. We discuss challenges faced by
             researchers in this field, and we emphasize the importance
             of interdisciplinary effort for advancing the study in
             fluid-structure interactions. © 2012 Global-Science
             Press.},
   Doi = {10.4208/cicp.291210.290411s},
   Key = {fds243668}
}

@article{fds304488,
   Author = {Layton, AT and Layton, HE},
   Title = {Countercurrent multiplication may not explain the axial
             osmolality gradient in the outer medulla of the rat
             kidney.},
   Journal = {American journal of physiology. Renal physiology},
   Volume = {301},
   Number = {5},
   Pages = {F1047-F1056},
   Year = {2011},
   Month = {November},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/21753076},
   Abstract = {It has become widely accepted that the osmolality gradient
             along the corticomedullary axis of the mammalian outer
             medulla is generated and sustained by a process of
             countercurrent multiplication: active NaCl absorption from
             thick ascending limbs is coupled with the counterflow
             configuration of the descending and ascending limbs of the
             loops of Henle to generate an axial osmolality gradient
             along the outer medulla. However, aspects of anatomic
             structure (e.g., the physical separation of the descending
             limbs of short loops of Henle from contiguous ascending
             limbs), recent physiologic experiments (e.g., those that
             suggest that the thin descending limbs of short loops of
             Henle have a low osmotic water permeability), and
             mathematical modeling studies (e.g., those that predict that
             water-permeable descending limbs of short loops are not
             required for the generation of an axial osmolality gradient)
             suggest that countercurrent multiplication may be an
             incomplete, or perhaps even erroneous, explanation. We
             propose an alternative explanation for the axial osmolality
             gradient: we regard the thick limbs as NaCl sources for the
             surrounding interstitium, and we hypothesize that the
             increasing axial osmolality gradient along the outer medulla
             is primarily sustained by an increasing ratio, as a function
             of increasing medullary depth, of NaCl absorption (from
             thick limbs) to water absorption (from thin descending limbs
             of long loops of Henle and, in antidiuresis, from collecting
             ducts). We further hypothesize that ascending vasa recta
             that are external to vascular bundles will carry, toward the
             cortex, an absorbate that at each medullary level is
             hyperosmotic relative to the adjacent interstitium.},
   Doi = {10.1152/ajprenal.00620.2010},
   Key = {fds304488}
}

@article{fds243675,
   Author = {Layton, AT and Bowen, M and Wen, A and Layton, HE},
   Title = {Feedback-mediated dynamics in a model of coupled nephrons
             with compliant thick ascending limbs.},
   Journal = {Mathematical Biosciences},
   Volume = {230},
   Number = {2},
   Pages = {115-127},
   Year = {2011},
   Month = {April},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/21329704},
   Abstract = {The tubuloglomerular feedback (TGF) system in the kidney, a
             key regulator of glomerular filtration rate, has been shown
             in physiologic experiments in rats to mediate oscillations
             in thick ascending limb (TAL) tubular fluid pressure, flow,
             and NaCl concentration. In spontaneously hypertensive rats,
             TGF-mediated flow oscillations may be highly irregular. We
             conducted a bifurcation analysis of a mathematical model of
             nephrons that are coupled through their TGF systems; the
             TALs of these nephrons are assumed to have compliant tubular
             walls. A characteristic equation was derived for a model of
             two coupled nephrons. Analysis of that characteristic
             equation has revealed a number of parameter regions having
             the potential for differing stable dynamic states. Numerical
             solutions of the full equations for two model nephrons
             exhibit a variety of behaviors in these regions. Also, model
             results suggest that the stability of the TGF system is
             reduced by the compliance of TAL walls and by internephron
             coupling; as a result, the likelihood of the emergence of
             sustained oscillations in tubular fluid pressure and flow is
             increased. Based on information provided by the
             characteristic equation, we identified parameters with which
             the model predicts irregular tubular flow oscillations that
             exhibit a degree of complexity that may help explain the
             emergence of irregular oscillations in spontaneously
             hypertensive rats.},
   Doi = {10.1016/j.mbs.2011.02.004},
   Key = {fds243675}
}

@article{fds320898,
   Author = {Layton, AT},
   Title = {Role of UTB Urea Transporters in the Urine Concentrating
             Mechanism of the Rat Kidney},
   Journal = {The FASEB journal : official publication of the Federation
             of American Societies for Experimental Biology},
   Volume = {25},
   Year = {2011},
   Month = {April},
   Key = {fds320898}
}

@article{fds320899,
   Author = {Nieves-Gonzalez, A and Clausen, C and Marcano, M and Layton, HE and Layton, AT and Moore, LC},
   Title = {Efficiency of sodium transport in a model of the Thick
             Ascending Limb (TAL)},
   Journal = {The FASEB journal : official publication of the Federation
             of American Societies for Experimental Biology},
   Volume = {25},
   Year = {2011},
   Month = {April},
   Key = {fds320899}
}

@article{fds320900,
   Author = {Pannabecker, TL and Layton, AT},
   Title = {Isolated interstitial nodal spaces facilitate preferential
             solute and fluid mixing},
   Journal = {The FASEB journal : official publication of the Federation
             of American Societies for Experimental Biology},
   Volume = {25},
   Year = {2011},
   Month = {April},
   Key = {fds320900}
}

@article{fds320901,
   Author = {Layton, AT and Sgouralis, I and Layton, H and Moore,
             L},
   Title = {Propagation of vasoconstrictive responses in a mathematical
             model of the rat afferent arteriole},
   Journal = {The FASEB journal : official publication of the Federation
             of American Societies for Experimental Biology},
   Volume = {25},
   Year = {2011},
   Month = {April},
   Key = {fds320901}
}

@article{fds320902,
   Author = {Nieves-Gonzalez, A and Clausen, C and Layton, HE and Layton, AT and Moore, LC},
   Title = {Dynamical Properties of the Thick Ascending Limb (TAL): A
             Modeling Study},
   Journal = {The FASEB journal : official publication of the Federation
             of American Societies for Experimental Biology},
   Volume = {25},
   Year = {2011},
   Month = {April},
   Key = {fds320902}
}

@article{fds243674,
   Author = {Chen, J and Sgouralis, I and Moore, LC and Layton, HE and Layton,
             AT},
   Title = {A mathematical model of the myogenic response to systolic
             pressure in the afferent arteriole.},
   Journal = {American journal of physiology. Renal physiology},
   Volume = {300},
   Number = {3},
   Pages = {F669-F681},
   Year = {2011},
   Month = {March},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/21190949},
   Abstract = {Elevations in systolic blood pressure are believed to be
             closely linked to the pathogenesis and progression of renal
             diseases. It has been hypothesized that the afferent
             arteriole (AA) protects the glomerulus from the damaging
             effects of hypertension by sensing increases in systolic
             blood pressure and responding with a compensatory
             vasoconstriction (Loutzenhiser R, Bidani A, Chilton L. Circ
             Res 90: 1316-1324, 2002). To investigate this hypothesis, we
             developed a mathematical model of the myogenic response of
             an AA wall, based on an arteriole model (Gonzalez-Fernandez
             JM, Ermentrout B. Math Biosci 119: 127-167, 1994). The model
             incorporates ionic transport, cell membrane potential,
             contraction of the AA smooth muscle cell, and the mechanics
             of a thick-walled cylinder. The model represents a myogenic
             response based on a pressure-induced shift in the voltage
             dependence of calcium channel openings: with increasing
             transmural pressure, model vessel diameter decreases; and
             with decreasing pressure, vessel diameter increases.
             Furthermore, the model myogenic mechanism includes a
             rate-sensitive component that yields constriction and
             dilation kinetics similar to behaviors observed in vitro. A
             parameter set is identified based on physical dimensions of
             an AA in a rat kidney. Model results suggest that the
             interaction of Ca(2+) and K(+) fluxes mediated by
             voltage-gated and voltage-calcium-gated channels,
             respectively, gives rise to periodicity in the transport of
             the two ions. This results in a time-periodic cytoplasmic
             calcium concentration, myosin light chain phosphorylation,
             and cross-bridge formation with the attending muscle stress.
             Furthermore, the model predicts myogenic responses that
             agree with experimental observations, most notably those
             which demonstrate that the renal AA constricts in response
             to increases in both steady and systolic blood pressures.
             The myogenic model captures these essential functions of the
             renal AA, and it may prove useful as a fundamental component
             in a multiscale model of the renal microvasculature suitable
             for investigations of the pathogenesis of hypertensive renal
             diseases.},
   Doi = {10.1152/ajprenal.00382.2010},
   Key = {fds243674}
}

@article{fds304487,
   Author = {Layton, AT and Savage, NS and Howell, AS and Carroll, SY and Drubin, DG and Lew, DJ},
   Title = {Modeling vesicle traffic reveals unexpected consequences for
             Cdc42p-mediated polarity establishment.},
   Journal = {Current Biology},
   Volume = {21},
   Number = {3},
   Pages = {184-194},
   Year = {2011},
   Month = {February},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/21277209},
   Abstract = {BACKGROUND: Polarization in yeast has been proposed to
             involve a positive feedback loop whereby the polarity
             regulator Cdc42p orients actin cables, which deliver
             vesicles carrying Cdc42p to the polarization site. Previous
             mathematical models treating Cdc42p traffic as a
             membrane-free flux suggested that directed traffic would
             polarize Cdc42p, but it remained unclear whether Cdc42p
             would become polarized without the membrane-free simplifying
             assumption. RESULTS: We present mathematical models that
             explicitly consider stochastic vesicle traffic via
             exocytosis and endocytosis, providing several new insights.
             Our findings suggest that endocytic cargo influences the
             timing of vesicle internalization in yeast. Moreover, our
             models provide quantitative support for the view that
             integral membrane cargo proteins would become polarized by
             directed vesicle traffic given the experimentally determined
             rates of vesicle traffic and diffusion. However, such
             traffic cannot effectively polarize the more rapidly
             diffusing Cdc42p in the model without making additional
             assumptions that seem implausible and lack experimental
             support. CONCLUSIONS: Our findings suggest that
             actin-directed vesicle traffic would perturb, rather than
             reinforce, polarization in yeast.},
   Doi = {10.1016/j.cub.2011.01.012},
   Key = {fds304487}
}

@article{fds304485,
   Author = {Layton, AT},
   Title = {A mathematical model of the urine concentrating mechanism in
             the rat renal medulla. II. Functional implications of
             three-dimensional architecture.},
   Journal = {American journal of physiology. Renal physiology},
   Volume = {300},
   Number = {2},
   Pages = {F372-F384},
   Year = {2011},
   Month = {February},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/21068088},
   Abstract = {In a companion study [Layton AT. A mathematical model of the
             urine concentrating mechanism in the rat renal medulla. I.
             Formulation and base-case results. Am J Physiol Renal
             Physiol. (First published November 10, 2010).
             10.1152/ajprenal.00203.2010] a region-based mathematical
             model was formulated for the urine concentrating mechanism
             in the renal medulla of the rat kidney. In the present
             study, we investigated model sensitivity to some of the
             fundamental structural assumptions. An unexpected finding is
             that the concentrating capability of this region-based model
             falls short of the capability of models that have radially
             homogeneous interstitial fluid at each level of only the
             inner medulla (IM) or of both the outer medulla and IM, but
             are otherwise analogous to the region-based model.
             Nonetheless, model results reveal the functional
             significance of several aspects of tubular segmentation and
             heterogeneity: 1) the exclusion of ascending thin limbs that
             reach into the deep IM from the collecting duct clusters in
             the upper IM promotes urea cycling within the IM; 2) the
             high urea permeability of the lower IM thin limb segments
             allows their tubular fluid urea content to equilibrate with
             the surrounding interstitium; 3) the aquaporin-1-null
             terminal descending limb segments prevent water entry and
             maintain the transepithelial NaCl concentration gradient; 4)
             a higher thick ascending limb Na(+) active transport rate in
             the inner stripe augments concentrating capability without a
             corresponding increase in energy expenditure for transport;
             5) active Na(+) reabsorption from the collecting duct
             elevates its tubular fluid urea concentration. Model
             calculations predict that these aspects of tubular
             segmentation and heterogeneity promote effective urine
             concentrating functions.},
   Doi = {10.1152/ajprenal.00204.2010},
   Key = {fds304485}
}

@article{fds304486,
   Author = {Layton, AT},
   Title = {A mathematical model of the urine concentrating mechanism in
             the rat renal medulla. I. Formulation and base-case
             results.},
   Journal = {American journal of physiology. Renal physiology},
   Volume = {300},
   Number = {2},
   Pages = {F356-F371},
   Year = {2011},
   Month = {February},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/21068086},
   Abstract = {A new, region-based mathematical model of the urine
             concentrating mechanism of the rat renal medulla was used to
             investigate the significance of transport and structural
             properties revealed in anatomic studies. The model simulates
             preferential interactions among tubules and vessels by
             representing concentric regions that are centered on a
             vascular bundle in the outer medulla (OM) and on a
             collecting duct cluster in the inner medulla (IM).
             Particularly noteworthy features of this model include
             highly urea-permeable and water-impermeable segments of the
             long descending limbs and highly urea-permeable ascending
             thin limbs. Indeed, this is the first detailed mathematical
             model of the rat urine concentrating mechanism that
             represents high long-loop urea permeabilities and that
             produces a substantial axial osmolality gradient in the IM.
             That axial osmolality gradient is attributable to the
             increasing urea concentration gradient. The model equations,
             which are based on conservation of solutes and water and on
             standard expressions for transmural transport, were solved
             to steady state. Model simulations predict that the
             interstitial NaCl and urea concentrations in adjoining
             regions differ substantially in the OM but not in the IM. In
             the OM, active NaCl transport from thick ascending limbs, at
             rates inferred from the physiological literature, resulted
             in a concentrating effect such that the intratubular fluid
             osmolality of the collecting duct increases ~2.5 times along
             the OM. As a result of the separation of urea from NaCl and
             the subsequent mixing of that urea and NaCl in the
             interstitium and vasculature of the IM, collecting duct
             fluid osmolality further increases by a factor of ~1.55
             along the IM.},
   Doi = {10.1152/ajprenal.00203.2010},
   Key = {fds304486}
}

@article{fds243669,
   Author = {Bouzarth, EL and Layton, AT and Young, Y-N},
   Title = {Modeling a semi-flexible filament in cellular Stokes flow
             using regularized Stokeslets},
   Journal = {International Journal for Numerical Methods in Biomedical
             Engineering},
   Volume = {27},
   Number = {12},
   Pages = {2021-2034},
   Year = {2011},
   ISSN = {2040-7939},
   url = {http://dx.doi.org/10.1002/cnm.1454},
   Abstract = {Many physical and biological systems involve inextensible
             fibers immersed in a fluid; examples include cilia, polymer
             suspensions, and actin filament transport. In such systems,
             the dynamics of the immersed fibers may play a significant
             role in the observed macroscale fluid dynamics. In this
             study, we simulate the dynamics of an approximately
             inextensible semi-flexible fiber immersed in a
             two-dimensional cellular background flow. The system is
             modeled as an immersed boundary problem with the fluid
             dynamics described using the Stokes equations. The motion of
             the immersed fiber is computed by means of the method of
             regularized Stokeslets, which allows one to calculate fluid
             velocity, pressure, and stress in the Stokes fluid flow
             regime because of a collection of regularized point forces
             without computing fluid velocities on an underlying grid.
             Simulation results show that, for some parameter values, the
             fiber may buckle when approaching a stagnation point. These
             results provide insight into the stretch-coil transition and
             macroscale random walk behavior that have been reported in
             mathematical and experimental literature. © 2011 John Wiley
             & Sons, Ltd.},
   Doi = {10.1002/cnm.1454},
   Key = {fds243669}
}

@article{fds243670,
   Author = {Edwards, A and Layton, AT},
   Title = {Modulation of outer medullary NaCl transport and oxygenation
             by nitric oxide and superoxide},
   Journal = {Am J Physiol Renal Physiol},
   Volume = {301},
   Number = {F979-F996},
   Pages = {F979-F996},
   Year = {2011},
   ISSN = {0363-6127},
   url = {http://dx.doi.org/10.1152/ajprenal.00096.2011},
   Abstract = {We expanded our region- based model of water and solute
             exchanges in the rat outer medulla to incorporate the
             transport of nitric oxide (NO) and superoxide (O 2-) and to
             examine the impact of NO- O 2- interactions on medullary
             thick ascending limb (mTAL) NaCl reabsorption and oxygen
             (O2) consumption, under both physiological and pathological
             conditions. Our results suggest that NaCl transport and the
             concentrating capacity of the outer medulla are
             substantially modulated by basal levels of NO and O 2-.
             Moreover, the effect of each solute on NaCl reabsorption
             cannot be considered in isolation, given the feedback loops
             resulting from three-way interactions between O 2, NO, and O
             2-. Notwithstanding vasoactive effects, our model predicts
             that in the absence of O 2--mediated stimulation of NaCl
             active transport, the outer medullary concentrating capacity
             (evaluated as the collecting duct fluid osmolality at the
             outer-inner medullary junction) would be ~40% lower.
             Conversely, without NO-induced inhibition of NaCl active
             transport, the outer medullary concentrating capacity would
             increase by ~70%, but only if that anaerobic metabolism can
             provide up to half the maximal energy requirements of the
             outer medulla. The model suggests that in addition to
             scavenging NO, O 2- modulates NO levels indirectly via its
             stimulation of mTAL metabolism, leading to reduction of O 2
             as a substrate for NO. When O 2- levels are raised 10-fold,
             as in hypertensive animals, mTAL NaCl reabsorption is
             significantly enhanced, even as the inefficient use of O 2
             exacerbates hypoxia in the outer medulla. Conversely, an
             increase in tubular and vascular flows is predicted to
             substantially reduce mTAL NaCl reabsorption. In conclusion,
             our model suggests that the complex interactions between NO,
             O 2-, and O 2 significantly impact the O 2 balance and NaCl
             reabsorption in the outer medulla. ©2011 the American
             Physiological Society.},
   Doi = {10.1152/ajprenal.00096.2011},
   Key = {fds243670}
}

@article{fds243671,
   Author = {Lei, T and Zhou, L and Layton, AT and Zhou, H and Zhao, X and Bankir, L and Yang, B},
   Title = {Role of thin descending limb urea transport in renal urea
             handling and the urine concentrating mechanism},
   Journal = {American journal of physiology. Renal physiology},
   Volume = {301},
   Number = {6},
   Pages = {F1251-F1259},
   Year = {2011},
   ISSN = {0363-6127},
   url = {http://dx.doi.org/10.1152/ajprenal.00404.2011},
   Abstract = {Urea transporters UT-A2 and UT-B are expressed in epithelia
             of thin descending limb of Henle's loop and in descending
             vasa recta, respectively. To study their role and possible
             interaction in the context of the urine concentration
             mechanism, a UT-A2 and UT-B double knockout (UT-A2/B
             knockout) mouse model was generated by targeted deletion of
             the UT-A2 promoter in embryonic stem cells with UT-B gene
             knockout. The UT-A2/B knockout mice lacked detectable UT-A2
             and UT-B transcripts and proteins and showed normal survival
             and growth. Daily urine output was significantly higher in
             UT-A2/B knockout mice than that in wild-type mice and lower
             than that in UT-B knockout mice. Urine osmolality in UT-A2/B
             knockout mice was intermediate between that in UT-B knockout
             and wild-type mice. The changes in urine osmolality and flow
             rate, plasma and urine urea concentration, as well as
             non-urea solute concentration after an acute urea load or
             chronic changes in protein intake suggested that UT-A2 plays
             a role in the progressive accumulation of urea in the inner
             medulla. These results suggest that in wild-type mice UT-A2
             facilitates urea absorption by urea efflux from the thin
             descending limb of short loops of Henle. Moreover, UT-A2
             deletion in UT-B knockout mice partially remedies the urine
             concentrating defect caused by UT-B deletion, by reducing
             urea loss from the descending limbs to the peripheral
             circulation; instead, urea is returned to the inner medulla
             through the loops of Henle and the collecting ducts. © 2011
             the American Physiological Society.},
   Doi = {10.1152/ajprenal.00404.2011},
   Key = {fds243671}
}

@article{fds243672,
   Author = {Layton, AT and Layton, HE},
   Title = {Countercurrent multiplication may not explain the axial
             osmolality gradient},
   Journal = {Am J Physiol Renal Physiol},
   Volume = {301},
   Number = {5},
   Pages = {F1047-F1056},
   Year = {2011},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/21753076},
   Abstract = {It has become widely accepted that the osmolality gradient
             along the corticomedullary axis of the mammalian outer
             medulla is generated and sustained by a process of
             countercurrent multiplication: active NaCl absorption from
             thick ascending limbs is coupled with the counterflow
             configuration of the descending and ascending limbs of the
             loops of Henle to generate an axial osmolality gradient
             along the outer medulla. However, aspects of anatomic
             structure (e.g., the physical separation of the descending
             limbs of short loops of Henle from contiguous ascending
             limbs), recent physiologic experiments (e.g., those that
             suggest that the thin descending limbs of short loops of
             Henle have a low osmotic water permeability), and
             mathematical modeling studies (e.g., those that predict that
             water-permeable descending limbs of short loops are not
             required for the generation of an axial osmolality gradient)
             suggest that countercurrent multiplication may be an
             incomplete, or perhaps even erroneous, explanation. We
             propose an alternative explanation for the axial osmolality
             gradient: we regard the thick limbs as NaCl sources for the
             surrounding interstitium, and we hypothesize that the
             increasing axial osmolality gradient along the outer medulla
             is primarily sustained by an increasing ratio, as a function
             of increasing medullary depth, of NaCl absorption (from
             thick limbs) to water absorption (from thin descending limbs
             of long loops of Henle and, in antidiuresis, from collecting
             ducts). We further hypothesize that ascending vasa recta
             that are external to vascular bundles will carry, toward the
             cortex, an absorbate that at each medullary level is
             hyperosmotic relative to the adjacent interstitium.},
   Doi = {10.1152/ajprenal.00620.2010},
   Key = {fds243672}
}

@article{fds243673,
   Author = {Dantzler, WH and Pannabecker, TL and Layton, AT and Layton,
             HE},
   Title = {Urine concentrating mechanism in the inner medulla of the
             mammalian kidney: role of three-dimensional
             architecture.},
   Journal = {Acta Physiologica},
   Volume = {202},
   Number = {3},
   Pages = {361-378},
   Year = {2011},
   ISSN = {1748-1716},
   url = {http://dx.doi.org/10.1111/j.1748-1716.2010.02214.x},
   Abstract = {The urine concentrating mechanism in the mammalian renal
             inner medulla (IM) is not understood, although it is
             generally considered to involve countercurrent flows in
             tubules and blood vessels. A possible role for the
             three-dimensional relationships of these tubules and vessels
             in the concentrating process is suggested by recent
             reconstructions from serial sections labelled with
             antibodies to tubular and vascular proteins and mathematical
             models based on these studies. The reconstructions revealed
             that the lower 60% of each descending thin limb (DTL) of
             Henle's loops lacks water channels (aquaporin-1) and osmotic
             water permeability and ascending thin limbs (ATLs) begin
             with a prebend segment of constant length. In the outer zone
             of the IM (i) clusters of coalescing collecting ducts (CDs)
             form organizing motif for loops of Henle and vasa recta;
             (ii) DTLs and descending vasa recta (DVR) are arrayed
             outside CD clusters, whereas ATLs and ascending vasa recta
             (AVR) are uniformly distributed inside and outside clusters;
             (iii) within CD clusters, interstitial nodal spaces are
             formed by a CD on one side, AVR on two sides, and an ATL on
             the fourth side. These spaces may function as mixing
             chambers for urea from CDs and NaCl from ATLs. In the inner
             zone of the IM, cluster organization disappears and half of
             Henle's loops have broad lateral bends wrapped around
             terminal CDs. Mathematical models based on these findings
             and involving solute mixing in the interstitial spaces can
             produce urine slightly more concentrated than that of a
             moderately antidiuretic rat but no higher. © 2010 The
             Authors. Acta Physiologica © 2010 Scandinavian
             Physiological Society.},
   Doi = {10.1111/j.1748-1716.2010.02214.x},
   Key = {fds243673}
}

@article{fds243678,
   Author = {Layton, AT},
   Title = {A mathematical model of the urine concentrating mechanism in
             the rat renal medulla: II. Functional implications of
             three-dimensional architecture},
   Journal = {Am J Physiol Renal Physiol},
   Volume = {300},
   Number = {F372-F384},
   Pages = {F372-F384},
   Year = {2011},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/21068088},
   Abstract = {In a companion study [Layton AT. A mathematical model of the
             urine concentrating mechanism in the rat renal medulla. I.
             Formulation and base-case results. Am J Physiol Renal
             Physiol. (First published November 10, 2010).
             10.1152/ajprenal.00203.2010] a region-based mathematical
             model was formulated for the urine concentrating mechanism
             in the renal medulla of the rat kidney. In the present
             study, we investigated model sensitivity to some of the
             fundamental structural assumptions. An unexpected finding is
             that the concentrating capability of this region-based model
             falls short of the capability of models that have radially
             homogeneous interstitial fluid at each level of only the
             inner medulla (IM) or of both the outer medulla and IM, but
             are otherwise analogous to the region-based model.
             Nonetheless, model results reveal the functional
             significance of several aspects of tubular segmentation and
             heterogeneity: 1) the exclusion of ascending thin limbs that
             reach into the deep IM from the collecting duct clusters in
             the upper IM promotes urea cycling within the IM; 2) the
             high urea permeability of the lower IM thin limb segments
             allows their tubular fluid urea content to equilibrate with
             the surrounding interstitium; 3) the aquaporin-1-null
             terminal descending limb segments prevent water entry and
             maintain the transepithelial NaCl concentration gradient; 4)
             a higher thick ascending limb Na(+) active transport rate in
             the inner stripe augments concentrating capability without a
             corresponding increase in energy expenditure for transport;
             5) active Na(+) reabsorption from the collecting duct
             elevates its tubular fluid urea concentration. Model
             calculations predict that these aspects of tubular
             segmentation and heterogeneity promote effective urine
             concentrating functions.},
   Doi = {10.1152/ajprenal.00204.2010},
   Key = {fds243678}
}

@article{fds243679,
   Author = {Layton, AT},
   Title = {A mathematical model of the urine concentrating mechanism in
             the rat renal medulla: I. Formulation and base-case
             results},
   Journal = {Am J Physiol Renal Physiol},
   Volume = {300},
   Number = {F356-F371},
   Pages = {F356-F371},
   Year = {2011},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/21068086},
   Abstract = {A new, region-based mathematical model of the urine
             concentrating mechanism of the rat renal medulla was used to
             investigate the significance of transport and structural
             properties revealed in anatomic studies. The model simulates
             preferential interactions among tubules and vessels by
             representing concentric regions that are centered on a
             vascular bundle in the outer medulla (OM) and on a
             collecting duct cluster in the inner medulla (IM).
             Particularly noteworthy features of this model include
             highly urea-permeable and water-impermeable segments of the
             long descending limbs and highly urea-permeable ascending
             thin limbs. Indeed, this is the first detailed mathematical
             model of the rat urine concentrating mechanism that
             represents high long-loop urea permeabilities and that
             produces a substantial axial osmolality gradient in the IM.
             That axial osmolality gradient is attributable to the
             increasing urea concentration gradient. The model equations,
             which are based on conservation of solutes and water and on
             standard expressions for transmural transport, were solved
             to steady state. Model simulations predict that the
             interstitial NaCl and urea concentrations in adjoining
             regions differ substantially in the OM but not in the IM. In
             the OM, active NaCl transport from thick ascending limbs, at
             rates inferred from the physiological literature, resulted
             in a concentrating effect such that the intratubular fluid
             osmolality of the collecting duct increases ~2.5 times along
             the OM. As a result of the separation of urea from NaCl and
             the subsequent mixing of that urea and NaCl in the
             interstitium and vasculature of the IM, collecting duct
             fluid osmolality further increases by a factor of ~1.55
             along the IM.},
   Doi = {10.1152/ajprenal.00203.2010},
   Key = {fds243679}
}

@article{fds243680,
   Author = {Layton, AT and Savage, NS and Howell, AS and Carroll, SY and Drubin, DG and Lew, DJ},
   Title = {Modeling vesicle traffic reveals unexpected consequences for
             Cdc42p-mediated polarity establishment},
   Journal = {Curr Biol},
   Volume = {21},
   Number = {3},
   Pages = {1-11},
   Year = {2011},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/21277209},
   Abstract = {BACKGROUND: Polarization in yeast has been proposed to
             involve a positive feedback loop whereby the polarity
             regulator Cdc42p orients actin cables, which deliver
             vesicles carrying Cdc42p to the polarization site. Previous
             mathematical models treating Cdc42p traffic as a
             membrane-free flux suggested that directed traffic would
             polarize Cdc42p, but it remained unclear whether Cdc42p
             would become polarized without the membrane-free simplifying
             assumption. RESULTS: We present mathematical models that
             explicitly consider stochastic vesicle traffic via
             exocytosis and endocytosis, providing several new insights.
             Our findings suggest that endocytic cargo influences the
             timing of vesicle internalization in yeast. Moreover, our
             models provide quantitative support for the view that
             integral membrane cargo proteins would become polarized by
             directed vesicle traffic given the experimentally determined
             rates of vesicle traffic and diffusion. However, such
             traffic cannot effectively polarize the more rapidly
             diffusing Cdc42p in the model without making additional
             assumptions that seem implausible and lack experimental
             support. CONCLUSIONS: Our findings suggest that
             actin-directed vesicle traffic would perturb, rather than
             reinforce, polarization in yeast.},
   Doi = {10.1016/j.cub.2011.01.012},
   Key = {fds243680}
}

@article{fds304489,
   Author = {Edwards, A and Layton, AT},
   Title = {Modulation of outer medullary NaCl transport and oxygenation
             by nitric oxide and superoxide},
   Journal = {American journal of physiology. Renal physiology},
   Volume = {301},
   Number = {5},
   Pages = {F979-F996},
   Year = {2011},
   ISSN = {0363-6127},
   url = {http://dx.doi.org/10.1152/ajprenal.00096.2011},
   Abstract = {We expanded our region- based model of water and solute
             exchanges in the rat outer medulla to incorporate the
             transport of nitric oxide (NO) and superoxide (O 2-) and to
             examine the impact of NO- O 2- interactions on medullary
             thick ascending limb (mTAL) NaCl reabsorption and oxygen
             (O2) consumption, under both physiological and pathological
             conditions. Our results suggest that NaCl transport and the
             concentrating capacity of the outer medulla are
             substantially modulated by basal levels of NO and O 2-.
             Moreover, the effect of each solute on NaCl reabsorption
             cannot be considered in isolation, given the feedback loops
             resulting from three-way interactions between O 2, NO, and O
             2-. Notwithstanding vasoactive effects, our model predicts
             that in the absence of O 2--mediated stimulation of NaCl
             active transport, the outer medullary concentrating capacity
             (evaluated as the collecting duct fluid osmolality at the
             outer-inner medullary junction) would be ~40% lower.
             Conversely, without NO-induced inhibition of NaCl active
             transport, the outer medullary concentrating capacity would
             increase by ~70%, but only if that anaerobic metabolism can
             provide up to half the maximal energy requirements of the
             outer medulla. The model suggests that in addition to
             scavenging NO, O 2- modulates NO levels indirectly via its
             stimulation of mTAL metabolism, leading to reduction of O 2
             as a substrate for NO. When O 2- levels are raised 10-fold,
             as in hypertensive animals, mTAL NaCl reabsorption is
             significantly enhanced, even as the inefficient use of O 2
             exacerbates hypoxia in the outer medulla. Conversely, an
             increase in tubular and vascular flows is predicted to
             substantially reduce mTAL NaCl reabsorption. In conclusion,
             our model suggests that the complex interactions between NO,
             O 2-, and O 2 significantly impact the O 2 balance and NaCl
             reabsorption in the outer medulla. ©2011 the American
             Physiological Society.},
   Doi = {10.1152/ajprenal.00096.2011},
   Key = {fds304489}
}

@article{fds304484,
   Author = {Layton, AT},
   Title = {Feedback-mediated dynamics in a model of a compliant thick
             ascending limb.},
   Journal = {Mathematical Biosciences},
   Volume = {228},
   Number = {2},
   Pages = {185-194},
   Year = {2010},
   Month = {December},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/20934438},
   Abstract = {The tubuloglomerular feedback (TGF) system in the kidney,
             which is a key regulator of filtration rate, has been shown
             in physiologic experiments in rats to mediate oscillations
             in tubular fluid pressure and flow, and in NaCl
             concentration in the tubular fluid of the thick ascending
             limb (TAL). In this study, we developed a mathematical model
             of the TGF system that represents NaCl transport along a TAL
             with compliant walls. The model was used to investigate the
             dynamic behaviors of the TGF system. A bifurcation analysis
             of the TGF model equations was performed by deriving and
             finding roots of the characteristic equation, which arises
             from a linearization of the model equations. Numerical
             simulations of the full model equations were conducted to
             assist in the interpretation of the bifurcation analysis.
             These techniques revealed a complex parameter region that
             allows a variety of qualitatively different model solutions:
             a regime having one stable, time-independent steady-state
             solution; regimes having one stable oscillatory solution
             only; and regimes having multiple possible stable
             oscillatory solutions. Model results suggest that the
             compliance of the TAL walls increases the tendency of the
             model TGF system to oscillate.},
   Doi = {10.1016/j.mbs.2010.10.002},
   Key = {fds304484}
}

@article{fds304483,
   Author = {Chen, J and Edwards, A and Layton, AT},
   Title = {Effects of pH and medullary blood flow on oxygen transport
             and sodium reabsorption in the rat outer
             medulla.},
   Journal = {American journal of physiology. Renal physiology},
   Volume = {298},
   Number = {6},
   Pages = {F1369-F1383},
   Year = {2010},
   Month = {June},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/20335320},
   Abstract = {We used a mathematical model of O(2) transport and the urine
             concentrating mechanism of the outer medulla of the rat
             kidney to study the effects of blood pH and medullary blood
             flow on O(2) availability and Na(+) reabsorption. The model
             predicts that in vivo paracellular Na(+) fluxes across
             medullary thick ascending limbs (mTALs) are small relative
             to transcellular Na(+) fluxes and that paracellular fluxes
             favor Na(+) reabsorption from the lumen along most of the
             mTAL segments. In addition, model results suggest that blood
             pH has a significant impact on O(2) transport and Na(+)
             reabsorption owing to the Bohr effect, according to which a
             lower pH reduces the binding affinity of hemoglobin for
             O(2). Thus our model predicts that the presumed greater
             acidity of blood in the interbundle regions, where mTALs are
             located, relative to that in the vascular bundles,
             facilitates the delivery of O(2) to support the high
             metabolic requirements of the mTALs and raises the
             concentrating capability of the outer medulla. Model results
             also suggest that increases in vascular and tubular flow
             rates result in disproportional, smaller increases in active
             O(2) consumption and mTAL active Na(+) transport, despite
             the higher delivery of O(2) and Na(+). That is, at a
             sufficiently high medullary O(2) supply, O(2) demand in the
             outer medulla does not adjust precisely to changes in O(2)
             delivery.},
   Doi = {10.1152/ajprenal.00572.2009},
   Key = {fds304483}
}

@article{fds243685,
   Author = {Layton, AT and Pannabecker, TL and Dantzler, WH and Layton,
             HE},
   Title = {Hyperfiltration and inner stripe hypertrophy may explain
             findings by Gamble and coworkers.},
   Journal = {American journal of physiology. Renal physiology},
   Volume = {298},
   Number = {4},
   Pages = {F962-F972},
   Year = {2010},
   Month = {April},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/20042460},
   Abstract = {Simulations conducted in a mathematical model were used to
             exemplify the hypothesis that elevated solute concentrations
             and tubular flows at the boundary of the renal outer and
             inner medullas of rats may contribute to increased urine
             osmolalities and urine flow rates. Such elevated quantities
             at that boundary may arise from hyperfiltration and from
             inner stripe hypertrophy, which are correlated with
             increased concentrating activity (Bankir L, Kriz W. Kidney
             Int. 47: 7-24, 1995). The simulations used the region-based
             model for the rat inner medulla that was presented in the
             companion study (Layton AT, Pannabecker TL, Dantzler WH,
             Layton HE. Am J Physiol Renal Physiol 298: F000-F000, 2010).
             The simulations were suggested by experiments which were
             conducted in rat by Gamble et al. (Gamble JL, McKhann CF,
             Butler AM, Tuthill E. Am J Physiol 109: 139-154, 1934) in
             which the ratio of NaCl to urea in the diet was
             systematically varied in eight successive 5-day intervals.
             The simulations predict that changes in boundary conditions
             at the boundary of the outer and inner medulla, accompanied
             by plausible modifications in transport properties of the
             collecting duct system, can significantly increase urine
             osmolality and flow rate. This hyperfiltration-hypertrophy
             hypothesis may explain the finding by Gamble et al. that the
             maximum urine osmolality attained from supplemental feeding
             of urea and NaCl in the eight intervals depends on NaCl
             being the initial predominant solute and on urea being the
             final predominant solute, because urea in sufficient
             quantity appears to stimulate concentrating activity. More
             generally, the hypothesis suggests that high osmolalities
             and urine flow rates may depend, in large part, on adaptive
             modifications of cortical hemodynamics and on outer
             medullary structure and not entirely on an extraordinary
             concentrating capability that is intrinsic to the inner
             medulla.},
   Doi = {10.1152/ajprenal.00250.2009},
   Key = {fds243685}
}

@article{fds243686,
   Author = {Layton, AT and Pannabecker, TL and Dantzler, WH and Layton,
             HE},
   Title = {Functional implications of the three-dimensional
             architecture of the rat renal inner medulla.},
   Journal = {American journal of physiology. Renal physiology},
   Volume = {298},
   Number = {4},
   Pages = {F973-F987},
   Year = {2010},
   Month = {April},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/20053796},
   Abstract = {A new, region-based mathematical model of the urine
             concentrating mechanism of the rat renal inner medulla (IM)
             was used to investigate the significance of transport and
             structural properties revealed in recent studies that
             employed immunohistochemical methods combined with
             three-dimensional computerized reconstruction. The model
             simulates preferential interactions among tubules and
             vessels by representing two concentric regions. The inner
             region, which represents a collecting duct (CD) cluster,
             contains CDs, some ascending thin limbs (ATLs), and some
             ascending vasa recta; the outer region, which represents the
             intercluster region, contains descending thin limbs,
             descending vasa recta, remaining ATLs, and additional
             ascending vasa recta. In the upper portion of the IM, the
             model predicts that interstitial Na(+) and urea
             concentrations (and osmolality) in the CD clusters differ
             significantly from those in the intercluster regions: model
             calculations predict that those CD clusters have higher urea
             concentrations than the intercluster regions, a finding that
             is consistent with a concentrating mechanism that depends
             principally on the mixing of NaCl from ATLs and urea from
             CDs. In the lower IM, the model predicts that limited or
             nearly zero water permeability in descending thin limb
             segments will increase concentrating effectiveness by
             increasing the rate of solute-free water absorption. The
             model predicts that high urea permeabilities in the upper
             portions of ATLs and increased contact areas of longest loop
             bends with CDs both modestly increase concentrating
             capability. A surprising finding is that the concentrating
             capability of this region-based model falls short of the
             capability of a model IM that has radially homogeneous
             interstitial fluid at each level but is otherwise analogous
             to the region-based model.},
   Doi = {10.1152/ajprenal.00249.2009},
   Key = {fds243686}
}

@article{fds320903,
   Author = {Pannabecker, TL and Dantzler, WH and Layton, AT},
   Title = {Urine Concentrating Mechanism: Impact of Vascular and
             Tubular Architecture and a Proposed Descending Limb Urea-Na
             Cotransporter},
   Journal = {The FASEB journal : official publication of the Federation
             of American Societies for Experimental Biology},
   Volume = {24},
   Year = {2010},
   Month = {April},
   Key = {fds320903}
}

@article{fds320904,
   Author = {Gilbert, RL and Pannabecker, TL and Layton, AT},
   Title = {Role of interstitial nodal spaces in the urine concentrating
             mechanism of the rat kidney},
   Journal = {The FASEB journal : official publication of the Federation
             of American Societies for Experimental Biology},
   Volume = {24},
   Year = {2010},
   Month = {April},
   Key = {fds320904}
}

@article{fds320905,
   Author = {Sgouralis, I and Layton, AT},
   Title = {Interactions between Tubuloglomerular Feedback and the
             Myogenic Mechanism of the Afferent Arteriole},
   Journal = {The FASEB journal : official publication of the Federation
             of American Societies for Experimental Biology},
   Volume = {24},
   Year = {2010},
   Month = {April},
   Key = {fds320905}
}

@article{fds320906,
   Author = {Ryu, H and Layton, AT},
   Title = {Tubular Fluid Oscillations Mediated by Tubuloglomerular
             Feedback in a Short Loop of Henle},
   Journal = {The FASEB journal : official publication of the Federation
             of American Societies for Experimental Biology},
   Volume = {24},
   Year = {2010},
   Month = {April},
   Key = {fds320906}
}

@article{fds320907,
   Author = {Edwards, A and Layton, AT},
   Title = {Impact of nitric oxide-mediated vasodilation on outer
             medullary NaCl transport and oxygenation},
   Journal = {The FASEB journal : official publication of the Federation
             of American Societies for Experimental Biology},
   Volume = {24},
   Year = {2010},
   Month = {April},
   Key = {fds320907}
}

@article{fds320908,
   Author = {Layton, HE and Chen, J and Moore, LC and Layton, AT},
   Title = {A mathematical model of the afferent arteriolar smooth
             muscle cell},
   Journal = {The FASEB journal : official publication of the Federation
             of American Societies for Experimental Biology},
   Volume = {24},
   Year = {2010},
   Month = {April},
   Key = {fds320908}
}

@article{fds320909,
   Author = {Nieves-Gonzalez, A and Moore, LC and Clausen, C and Marcano, M and Layton, HE and Layton, AT},
   Title = {Efficiency of sodium transport in the thick ascending
             limb},
   Journal = {The FASEB journal : official publication of the Federation
             of American Societies for Experimental Biology},
   Volume = {24},
   Year = {2010},
   Month = {April},
   Key = {fds320909}
}

@article{fds303546,
   Author = {Hallen, MA and Layton, AT},
   Title = {Expanding the scope of quantitative FRAP
             analysis.},
   Journal = {Journal of Theoretical Biology},
   Volume = {262},
   Number = {2},
   Pages = {295-305},
   Year = {2010},
   Month = {January},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/19836405},
   Abstract = {In this study, new mathematical models were developed for
             analysis of fluorescence recovery after photobleaching
             (FRAP) data to account for features not represented in
             previous analysis: conical photobleaching geometry, spatial
             variations in binding of fluorescent molecules, and directed
             transport of fluorescent molecules. To facilitate
             computations in conical geometry, a fast computational
             method for calculation of fluorescence recovery is
             presented. Two approximations are presented to aid in FRAP
             analysis when binding varies spatially, one applying to
             cases of relatively fast diffusion and slow binding and the
             other to binding of molecules to small cellular structures.
             Numerical results show that using a model that represents
             the influential physical processes and that is formulated in
             the appropriate geometry can substantially improve the
             accuracy of FRAP calculations.},
   Doi = {10.1016/j.jtbi.2009.10.020},
   Key = {fds303546}
}

@article{fds243688,
   Author = {Layton, AT and Edwards, A},
   Title = {Tubuloglomerular feedback signal transduction in a short
             loop of henle.},
   Journal = {Bulletin of Mathematical Biology},
   Volume = {72},
   Number = {1},
   Pages = {34-62},
   Year = {2010},
   Month = {January},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/19657700},
   Abstract = {In previous studies, we used a mathematical model of the
             thick ascending limb (TAL) to investigate nonlinearities in
             the tubuloglomerular feedback (TGF) loop. That model does
             not represent other segments of the nephron, the water, and
             NaCl transport along which may impact fluid flow rate and
             NaCl transport along the TAL. To investigate the extent to
             which those transport processes affect TGF mediation, we
             have developed a mathematical model for TGF signal
             transduction in a short loop nephron. The model combines a
             simple representation of the renal cortex with a
             highly-detailed representation of the outer medulla (OM).
             The OM portion of the model is based on an OM urine
             concentrating mechanism model previously developed by Layton
             and Layton (Am. J. Renal 289:F1346-F1366, 2005a). When
             perturbations are applied to intratubular fluid flow at the
             proximal straight tubule entrance, the present model
             predicts oscillations in fluid flow and solute
             concentrations in the cortical TAL and interstitium, and in
             all tubules, vessels, and interstitium in the OM. Model
             results suggest that TGF signal transduction by the TAL is a
             generator of nonlinearities: if a sinusoidal oscillation is
             added to constant intratubular fluid flow, the time required
             for an element of tubular fluid to traverse the TAL is
             oscillatory, but nonsinusoidal; those results are consistent
             with our previous studies. As a consequence, oscillations in
             NaCl concentration in tubular fluid alongside the macula
             densa (MD) will be nonsinusoidal and contain harmonics of
             the original sinusoidal frequency. Also, the model predicts
             that the oscillations in NaCl concentration at the loop-bend
             fluid are smaller in amplitude than those at the MD, a
             result that further highlights the crucial role of TAL in
             the nonlinear transduction of TGF signal from SNGFR to MD
             NaCl concentration.},
   Doi = {10.1007/s11538-009-9436-4},
   Key = {fds243688}
}

@article{fds243690,
   Author = {Loreto, M and Layton, AT},
   Title = {An optimization study of a mathematical model of the urine
             concentrating mechanism of the rat kidney.},
   Journal = {Mathematical Biosciences},
   Volume = {223},
   Number = {1},
   Pages = {66-78},
   Year = {2010},
   Month = {January},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/19891979},
   Abstract = {The rat kidney's morphological and transepithelial transport
             properties may change in response to different physiologic
             conditions. To better understand those processes, we used a
             non-linear optimization technique to estimate parameter sets
             that maximize key measures that assess the effectiveness and
             efficiency of a mathematical model of the rat urine
             concentrating mechanism (UCM). We considered two related
             measures of UCM effectiveness: the urine-to-plasma
             osmolality (U/P) ratio and free-water absorption rate (FWA).
             The optimization algorithm sought parameter sets that
             separately maximize FWA, maximize U/P with the constraint
             that the predicted urine flow rate is consistent with
             reported experimental value (denoted by (U/P)(rho)), and
             maximize the ratio U/P to the total NaCl active transport
             (TAT) (denoted by (U/P)/TAT). When the principal need of the
             animal is to maximize the impact of its UCM on blood plasma
             osmolality, the kidney likely undergoes changes that
             increase FWA. By selecting parameter values that increase
             model urine flow rate (while maintaining a sufficiently high
             urine osmolality), the optimization algorithm identified a
             set of parameter values that increased FWA by 95.6% above
             base-case efficiency. If, on the other hand, water must be
             preserved, then the animal may seek to optimize U/P instead.
             To study that scenario, the optimization algorithm
             separately sought parameter sets that attained maximum
             (U/P)(rho) and (U/P)/TAT. Those parameter sets increased
             urine osmolality by 55.4% and 44.5%, respectively, above
             base-case value; the outer-medullary concentrating
             capability was increased by 64.6% and 35.5%, respectively,
             above base case; and the inner-medullary concentrating
             capability was increased by 73.1% and 70.8%, respectively,
             above base case. The corresponding urine flow rate and the
             concentrations of NaCl and urea are all within or near
             reported experimental ranges.},
   Doi = {10.1016/j.mbs.2009.10.009},
   Key = {fds243690}
}

@article{fds243642,
   Author = {Marcano, M and Layton, AT and Layton, HE},
   Title = {Maximum urine concentrating capability in a mathematical
             model of the inner medulla of the rat kidney},
   Journal = {Bulletin of Mathematical Biology},
   Volume = {72},
   Number = {2},
   Pages = {314-339},
   Year = {2010},
   ISSN = {0092-8240},
   url = {http://dx.doi.org/10.1007/s11538-009-9448-0},
   Abstract = {In a mathematical model of the urine concentrating mechanism
             of the inner medulla of the rat kidney, a nonlinear
             optimization technique was used to estimate parameter sets
             that maximize the urine-to-plasma osmolality ratio (U/P)
             while maintaining the urine flow rate within a plausible
             physiologic range. The model, which used a central core
             formulation, represented loops of Henle turning at all
             levels of the inner medulla and a composite collecting duct
             (CD). The parameters varied were: water flow and urea
             concentration in tubular fluid entering the descending thin
             limbs and the composite CD at the outer-inner medullary
             boundary; scaling factors for the number of loops of Henle
             and CDs as a function of medullary depth; location and
             increase rate of the urea permeability profile along the CD;
             and a scaling factor for the maximum rate of NaCl transport
             from the CD. The optimization algorithm sought to maximize a
             quantity E that equaled U/P minus a penalty function for
             insufficient urine flow. Maxima of E were sought by changing
             parameter values in the direction in parameter space in
             which E increased. The algorithm attained a maximum E that
             increased urine osmolality and inner medullary concentrating
             capability by 37.5% and 80.2%, respectively, above base-case
             values; the corresponding urine flow rate and the
             concentrations of NaCl and urea were all within or near
             reported experimental ranges. Our results predict that urine
             osmolality is particularly sensitive to three parameters:
             the urea concentration in tubular fluid entering the CD at
             the outer-inner medullary boundary, the location and
             increase rate of the urea permeability profile along the CD,
             and the rate of decrease of the CD population (and thus of
             CD surface area) along the cortico-medullary axis. © 2009
             Society for Mathematical Biology.},
   Doi = {10.1007/s11538-009-9448-0},
   Key = {fds243642}
}

@article{fds243676,
   Author = {Layton, AT},
   Title = {Feedback-mediated dynamics in a model of a compliant thick
             ascending limb},
   Journal = {Math Biosci},
   Volume = {228},
   Number = {185-194},
   Pages = {185-194},
   Year = {2010},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/20934438},
   Abstract = {The tubuloglomerular feedback (TGF) system in the kidney,
             which is a key regulator of filtration rate, has been shown
             in physiologic experiments in rats to mediate oscillations
             in tubular fluid pressure and flow, and in NaCl
             concentration in the tubular fluid of the thick ascending
             limb (TAL). In this study, we developed a mathematical model
             of the TGF system that represents NaCl transport along a TAL
             with compliant walls. The model was used to investigate the
             dynamic behaviors of the TGF system. A bifurcation analysis
             of the TGF model equations was performed by deriving and
             finding roots of the characteristic equation, which arises
             from a linearization of the model equations. Numerical
             simulations of the full model equations were conducted to
             assist in the interpretation of the bifurcation analysis.
             These techniques revealed a complex parameter region that
             allows a variety of qualitatively different model solutions:
             a regime having one stable, time-independent steady-state
             solution; regimes having one stable oscillatory solution
             only; and regimes having multiple possible stable
             oscillatory solutions. Model results suggest that the
             compliance of the TAL walls increases the tendency of the
             model TGF system to oscillate.},
   Doi = {10.1016/j.mbs.2010.10.002},
   Key = {fds243676}
}

@article{fds243677,
   Author = {Wang, J and Layton, A},
   Title = {New numerical methods for Burgers' equation based on
             semi-Lagrangian and modified equation approaches},
   Journal = {Applied Numerical Mathematics},
   Volume = {60},
   Number = {6},
   Pages = {645-657},
   Year = {2010},
   ISSN = {0168-9274},
   url = {http://dx.doi.org/10.1016/j.apnum.2010.03.007},
   Abstract = {In this paper, we develop a class of semi-Lagrangian finite
             difference schemes which are derived by a new algorithm
             based on the modified equation technique; and we apply those
             methods to the Burgers' equation. We show that the overall
             accuracy of the proposed semi-Lagrangian schemes depends on
             two factors: one is the global truncation error which can be
             obtained by the modified equation analysis, the other is a
             generic feature of semi-Lagrangian methods which
             characterizes their non-monotonic dependence on the time
             stepsize. The analytical results are confirmed by numerical
             tests. © 2010 IMACS.},
   Doi = {10.1016/j.apnum.2010.03.007},
   Key = {fds243677}
}

@article{fds243681,
   Author = {Edwards, A and Layton, AT},
   Title = {Nitric oxide and superoxide transport in a cross section of
             the rat outer medulla. II. Reciprocal interactions and
             tubulovascular cross talk},
   Journal = {American journal of physiology. Renal physiology},
   Volume = {299},
   Number = {3},
   Pages = {F634-F647},
   Year = {2010},
   ISSN = {0363-6127},
   url = {http://dx.doi.org/10.1152/ajprenal.00681.2009},
   Abstract = {In a companion study (Edwards A and Layton AT. Am J Physiol
             Renal Physiol. doi:10.1152/ajprenal.00680.2009), we
             developed a mathematical model of nitric oxide (NO),
             superoxide (O2-), and total peroxynitrite (ONOO) transport
             in mid-outer stripe and mid-inner stripe cross sections of
             the rat outer medulla (OM). We examined how the
             three-dimensional architecture of the rat OM, together with
             low medullary oxygen tension (PO2), affects the distribution
             of NO, O2-, and ONOO in the rat OM. In the current study, we
             sought to determine generation rate and permeability values
             that are compatible with measurements of medullary NO
             concentrations and to assess the importance of
             tubulovascular cross talk and NO-O2- interactions under
             physiological conditions. Our results suggest that the main
             determinants of NO concentrations in the rat OM are the rate
             of vascular and tubular NO synthesis under hypoxic
             conditions, and the red blood cell (RBC) permeability to NO
             (PNORBC). The lower the PNORBC, the lower the amount of NO
             that is scavenged by hemoglobin species, and the higher the
             extra-erythrocyte NO concentrations. In addition, our
             results indicate that basal endothelial NO production acts
             to significantly limit NaCl reabsorption across medullary
             thick ascending limbs and to sustain medullary perfusion,
             whereas basal epithelial NO production has a smaller impact
             on NaCl transport and a negligible effect on vascular tone.
             Our model also predicts that O2- consumption by NO
             significantly reduces medullary O2- concentrations, but that
             O2- , when present at subnanomolar concentrations, has a
             small impact on medullary NO bioavailability. Copyright ©
             2010 the American Physiological Society.},
   Doi = {10.1152/ajprenal.00681.2009},
   Key = {fds243681}
}

@article{fds243682,
   Author = {Edwards, A and Layton, AT},
   Title = {Nitric oxide and superoxide transport in a cross section of
             the rat outer medulla. I. Effects of low medullary oxygen
             tension},
   Journal = {American journal of physiology. Renal physiology},
   Volume = {299},
   Number = {3},
   Pages = {F616-F633},
   Year = {2010},
   ISSN = {0363-6127},
   url = {http://dx.doi.org/10.1152/ajprenal.00680.2009},
   Abstract = {To examine the impact of the complex radial organization of
             the rat outer medulla (OM) on the distribution of nitric
             oxide (NO), superoxide (O 2-) and total peroxynitrite
             (ONOO), we developed a mathematical model that simulates the
             transport of those species in a cross section of the rat OM.
             To simulate the preferential interactions among tubules and
             vessels that arise from their relative radial positions in
             the OM, we adopted the region-based approach developed by
             Layton and Layton (Am J Physiol Renal Physiol 289:
             F1346-F1366, 2005). In that approach, the structural
             organization of the OM is represented by means of four
             concentric regions centered on a vascular bundle. The model
             predicts the concentrations of NO, O2-, and ONOO in the
             tubular and vascular lumen, epithelial and endothelial
             cells, red blood cells (RBCs), and interstitial fluid. Model
             results suggest that the large gradients in PO2 from the
             core of the vascular bundle toward its periphery, which stem
             from the segregation of O2-supplying descending vasa recta
             (DVR) within the vascular bundles, in turn generate steep
             radial NO and O2- concentration gradients, since the
             synthesis of both solutes is O2 dependent. Without the
             rate-limiting effects of O2, NO concentration would be
             lowest in the vascular bundle core, that is, the region with
             the highest density of RBCs, which act as a sink for NO. Our
             results also suggest that, under basal conditions, the
             difference in NO concentrations between DVR that reach into
             the inner medulla and those that turn within the OM should
             lead to differences in vasodilation and preferentially
             increase blood flow to the inner medulla. Copyright © 2010
             the American Physiological Society.},
   Doi = {10.1152/ajprenal.00680.2009},
   Key = {fds243682}
}

@article{fds243683,
   Author = {Chen, J and Edwards, A and Layton, AT},
   Title = {Effects of pH and medullary blood flow on oxygen transport
             and sodium reabsorption in the rat outer
             medulla},
   Journal = {Am J Physiol Renal Physiol},
   Volume = {298},
   Number = {F1369 - F1383},
   Pages = {F1369-F1383},
   Year = {2010},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/20335320},
   Abstract = {We used a mathematical model of O(2) transport and the urine
             concentrating mechanism of the outer medulla of the rat
             kidney to study the effects of blood pH and medullary blood
             flow on O(2) availability and Na(+) reabsorption. The model
             predicts that in vivo paracellular Na(+) fluxes across
             medullary thick ascending limbs (mTALs) are small relative
             to transcellular Na(+) fluxes and that paracellular fluxes
             favor Na(+) reabsorption from the lumen along most of the
             mTAL segments. In addition, model results suggest that blood
             pH has a significant impact on O(2) transport and Na(+)
             reabsorption owing to the Bohr effect, according to which a
             lower pH reduces the binding affinity of hemoglobin for
             O(2). Thus our model predicts that the presumed greater
             acidity of blood in the interbundle regions, where mTALs are
             located, relative to that in the vascular bundles,
             facilitates the delivery of O(2) to support the high
             metabolic requirements of the mTALs and raises the
             concentrating capability of the outer medulla. Model results
             also suggest that increases in vascular and tubular flow
             rates result in disproportional, smaller increases in active
             O(2) consumption and mTAL active Na(+) transport, despite
             the higher delivery of O(2) and Na(+). That is, at a
             sufficiently high medullary O(2) supply, O(2) demand in the
             outer medulla does not adjust precisely to changes in O(2)
             delivery.},
   Doi = {10.1152/ajprenal.00572.2009},
   Key = {fds243683}
}

@article{fds243684,
   Author = {Hallen, MA and Layton, AT},
   Title = {Expanding the scope of quantitative FRAP
             analysis},
   Journal = {J. Theor. Biol.},
   Volume = {2},
   Number = {21},
   Pages = {295-305},
   Year = {2010},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/19836405},
   Abstract = {In this study, new mathematical models were developed for
             analysis of fluorescence recovery after photobleaching
             (FRAP) data to account for features not represented in
             previous analysis: conical photobleaching geometry, spatial
             variations in binding of fluorescent molecules, and directed
             transport of fluorescent molecules. To facilitate
             computations in conical geometry, a fast computational
             method for calculation of fluorescence recovery is
             presented. Two approximations are presented to aid in FRAP
             analysis when binding varies spatially, one applying to
             cases of relatively fast diffusion and slow binding and the
             other to binding of molecules to small cellular structures.
             Numerical results show that using a model that represents
             the influential physical processes and that is formulated in
             the appropriate geometry can substantially improve the
             accuracy of FRAP calculations.},
   Doi = {10.1016/j.jtbi.2009.10.020},
   Key = {fds243684}
}

@article{fds243687,
   Author = {Marcano, M and Layton, AT and Layton, HE},
   Title = {Maximum urine concentrating capability for transport
             parameters and urine flow within prescribed
             ranges},
   Journal = {Bull. Math. Biol.},
   Volume = {7},
   Number = {2},
   Pages = {314-339},
   Year = {2010},
   Key = {fds243687}
}

@article{fds243689,
   Author = {Layton, AT and Toyama, Y and Yang, G-Q and Edwards, GS and Kiehart, DP and Venakides, S},
   Title = {Drosophila morphogenesis: tissue force laws and the modeling
             of dorsal closure.},
   Journal = {HFSP Journal},
   Volume = {3},
   Number = {6},
   Pages = {441-460},
   Year = {2009},
   Month = {December},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/20514134},
   Abstract = {Dorsal closure, a stage of Drosophila development, is a
             model system for cell sheet morphogenesis and wound healing.
             During closure, two flanks of epidermal tissue progressively
             advance to reduce the area of the eye-shaped opening in the
             dorsal surface, which contains amnioserosa tissue. To
             simulate the time evolution of the overall shape of the
             dorsal opening, we developed a mathematical model, in which
             contractility and elasticity are manifest in model
             force-producing elements that satisfy force-velocity
             relationships similar to muscle. The action of the elements
             is consistent with the force-producing behavior of actin and
             myosin in cells. The parameters that characterize the
             simulated embryos were optimized by reference to
             experimental observations on wild-type embryos and, to a
             lesser extent, on embryos whose amnioserosa was removed by
             laser surgery and on myospheroid mutant embryos. Simulations
             failed to reproduce the amnioserosa-removal protocol in
             either the elastic or the contractile limit, indicating that
             both elastic and contractile dynamics are essential
             components of the biological force-producing elements. We
             found it was necessary to actively upregulate forces to
             recapitulate both the double and single-canthus nick
             protocols, which did not participate in the optimization of
             parameters, suggesting the existence of additional key
             feedback mechanisms.},
   Doi = {10.2976/1.3266062},
   Key = {fds243689}
}

@article{fds243693,
   Author = {Layton, AT and Layton, HE and Dantzler, WH and Pannabecker,
             TL},
   Title = {The mammalian urine concentrating mechanism: hypotheses and
             uncertainties.},
   Journal = {Physiology (Bethesda, Md.)},
   Volume = {24},
   Pages = {250-256},
   Year = {2009},
   Month = {August},
   ISSN = {1548-9213},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/19675356},
   Abstract = {The urine concentrating mechanism of the mammalian kidney,
             which can produce a urine that is substantially more
             concentrated than blood plasma during periods of water
             deprivation, is one of the enduring mysteries in traditional
             physiology. Owing to the complex lateral and axial
             relationships of tubules and vessels, in both the outer and
             inner medulla, the urine concentrating mechanism may only be
             fully understood in terms of the kidney's three-dimensional
             functional architecture and its implications for
             preferential interactions among tubules and
             vessels.},
   Doi = {10.1152/physiol.00013.2009},
   Key = {fds243693}
}

@article{fds243696,
   Author = {Layton, AT and Moore, LC and Layton, HE},
   Title = {Multistable dynamics mediated by tubuloglomerular feedback
             in a model of coupled nephrons.},
   Journal = {Bulletin of Mathematical Biology},
   Volume = {71},
   Number = {3},
   Pages = {515-555},
   Year = {2009},
   Month = {April},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/19205808},
   Abstract = {To help elucidate the causes of irregular tubular flow
             oscillations found in the nephrons of spontaneously
             hypertensive rats (SHR), we have conducted a bifurcation
             analysis of a mathematical model of two nephrons that are
             coupled through their tubuloglomerular feedback (TGF)
             systems. This analysis was motivated by a previous modeling
             study which predicts that NaCl backleak from a nephron's
             thick ascending limb permits multiple stable oscillatory
             states that are mediated by TGF (Layton et al. in Am. J.
             Physiol. Renal Physiol. 291:F79-F97, 2006); that prediction
             served as the basis for a comprehensive, multifaceted
             hypothesis for the emergence of irregular flow oscillations
             in SHR. However, in that study, we used a characteristic
             equation obtained via linearization from a single-nephron
             model, in conjunction with numerical solutions of the full,
             nonlinear model equations for two and three coupled
             nephrons. In the present study, we have derived a
             characteristic equation for a model of any finite number of
             mutually coupled nephrons having NaCl backleak. Analysis of
             that characteristic equation for the case of two coupled
             nephrons has revealed a number of parameter regions having
             the potential for differing stable dynamic states. Numerical
             solutions of the full equations for two model nephrons
             exhibit a variety of behaviors in these regions. Some
             behaviors exhibit a degree of complexity that is consistent
             with our hypothesis for the emergence of irregular
             oscillations in SHR.},
   Doi = {10.1007/s11538-008-9370-x},
   Key = {fds243696}
}

@article{fds320910,
   Author = {Edwards, A and Chen, J and Layton, AT},
   Title = {Impact of Rat Outer Medullary Architecture on Oxygen
             Distribution},
   Journal = {The FASEB journal : official publication of the Federation
             of American Societies for Experimental Biology},
   Volume = {23},
   Year = {2009},
   Month = {April},
   Key = {fds320910}
}

@article{fds320911,
   Author = {Layton, AT and Moore, LC and Layton, HE},
   Title = {Waveform distortion in TGF-mediated limit-cycle
             oscillations: Effects of TAL flow},
   Journal = {The FASEB journal : official publication of the Federation
             of American Societies for Experimental Biology},
   Volume = {23},
   Year = {2009},
   Month = {April},
   Key = {fds320911}
}

@article{fds243691,
   Author = {Chen, J and Edwards, A and Layton, AT},
   Title = {A mathematical model of O2 transport in the rat
             outer medulla. II. Impact of outer medullary
             architecture},
   Journal = {American journal of physiology. Renal physiology},
   Volume = {297},
   Number = {2},
   Pages = {F537-F548},
   Year = {2009},
   ISSN = {0363-6127},
   url = {http://dx.doi.org/10.1152/ajprenal.90497.2008},
   Abstract = {In the companion study (Am J Physiol Renal Physiol. First
             published April 29, 2009; doi:10.1152/ajprenal.90496.2008),
             we extended the regionbased mathematical model of the
             urine-concentrating mechanism in the rat outer medulla (OM)
             developed by Layton and Layton (Am J Physiol Renal Physiol
             289: F1346-F1366, 2005) to examine the impact of the complex
             structural organization of the OM on O2 transport and
             distribution. In the present study, we investigated the
             sensitivity of predicted PO2 profiles to several parameters
             that characterize the degree of OM regionalization, boundary
             conditions, structural dimensions, transmural transport
             properties, and relative positions and distributions of
             tubules and vessels. Our results suggest that the fraction
             of O2 supplied to descending vasa recta (DVR) that reaches
             the inner medulla, i.e., a measure of the axial PO2 gradient
             in the OM, is insensitive to parameter variations as a
             result of the sequestration of long DVR in the vascular
             bundles. In contrast, O2 distribution among the regions
             surrounding the vascular core strongly depends on the radial
             positions of medullary thick ascending limbs (mTALs)
             relative to the vascular core, the degree of
             regionalization, and the distribution of short DVR along the
             corticomedullary axis. Moreover, if it is assumed that the
             mTAL active Na+ transport rate decreases when mTAL PO2 falls
             below a critical level, O2 availability to mTALs has a
             significant impact on the concentrating capability of the
             model OM. The model also predicts that when the OM undergoes
             hypertrophy, its concentrating capability increases
             significantly only when anaerobic metabolism supports a
             substantial fraction of the mTAL active Na+ transport and is
             otherwise critically reduced by low interstitial and mTAL
             luminal PO2 in a hypertrophied OM. Copyright © 2009 the
             American Physiological Society.},
   Doi = {10.1152/ajprenal.90497.2008},
   Key = {fds243691}
}

@article{fds243692,
   Author = {Chen, J and Layton, AT and Edwards, A},
   Title = {A mathematical model of O2 transport in the rat
             outer medulla. I. Model formulation and baseline
             results},
   Journal = {American journal of physiology. Renal physiology},
   Volume = {297},
   Number = {2},
   Pages = {F517-F536},
   Year = {2009},
   ISSN = {0363-6127},
   url = {http://dx.doi.org/10.1152/ajprenal.90496.2008},
   Abstract = {The mammalian kidney is particularly vulnerable to
             hypoperfusion, because the O2 supply to the renal medulla
             barely exceeds its O2 requirements. In this study, we
             examined the impact of the complex structural organization
             of the rat outer medulla (OM) on O2 distribution. We
             extended the region-based mathematical model of the rat OM
             developed by Layton and Layton (Am J Physiol Renal Physiol
             289: F1346-F1366, 2005) to incorporate the transport of
             RBCs, Hb, and O2. We considered basal cellular O2
             consumption and O2 consumption for active transport of NaCl
             across medullary thick ascending limb epithelia. Our model
             predicts that the structural organization of the OM results
             in significant PO2 gradients in the axial and radial
             directions. The segregation of descending vasa recta, the
             main supply of O2, at the center and immediate periphery of
             the vascular bundles gives rise to large radial differences
             in PO2 between regions, limits O2 reabsorption from long
             descending vasa recta, and helps preserve O2 delivery to the
             inner medulla. Under baseline conditions, significantly more
             O2 is transferred radially between regions by capillary
             flow, i.e., advection, than by diffusion. In agreement with
             experimental observations, our results suggest that 79% of
             the O2 supplied to the medulla is consumed in the OM and
             that medullary thick ascending limbs operate on the brink of
             hypoxia. Copyright © 2009 the American Physiological
             Society.},
   Doi = {10.1152/ajprenal.90496.2008},
   Key = {fds243692}
}

@article{fds243694,
   Author = {Layton, AT},
   Title = {On the efficiency of spectral deferred correction methods
             for time-dependent partial differential equations},
   Journal = {Applied Numerical Mathematics},
   Volume = {59},
   Number = {7},
   Pages = {1629-1643},
   Year = {2009},
   ISSN = {0168-9274},
   url = {http://dx.doi.org/10.1016/j.apnum.2008.11.004},
   Abstract = {Many physical and biological systems involve the
             interactions of two or more processes with widely-differing
             characteristic time scales. Previously, high-order
             semi-implicit and multi-implicit formulations of the
             spectral deferred correction methods (denoted by SISDC and
             MISDC methods, respectively) have been proposed for solving
             partial differential equations arising in such model
             systems. These methods compute a temporally high-order
             approximation by means of a first-order numerical method,
             which solves a series of correction equations to increase
             the temporal order of accuracy of the approximation. MISDC
             methods also allow several fast-evolving processes to be
             handled implicitly but independently, allowing for different
             time steps for each process while avoiding the splitting
             errors present in traditional operator-splitting methods. In
             this study, we propose MISDC methods that use second- and
             third-order integration and splitting methods in the
             prediction steps, and we assess the efficiency of SISDC and
             MISDC methods that are based on those moderate-order
             integration methods. Numerical results indicate that SISDC
             methods using third-order prediction steps are the most
             efficient, but the efficiency of SISDC methods using
             first-order steps improves, particularly in higher spatial
             dimensions, when combined with a "ladder approach" that uses
             a less refined spatial discretization during the initial SDC
             iterations. Among the MISDC methods studied, the one with a
             third-order prediction step is the most efficient for a
             mildly-stiff problem, but the method with a first-order
             prediction step has the least splitting error and thus the
             highest efficiency for a stiff problem. Furthermore, a MISDC
             method using a second-order prediction step with Strang
             splitting generates approximations with large splitting
             errors, compared with methods that use a different
             operator-splitting approach that orders the integration of
             processes according to their relative stiffness. © 2008
             IMACS.},
   Doi = {10.1016/j.apnum.2008.11.004},
   Key = {fds243694}
}

@article{fds243695,
   Author = {Beale, JT and Layton, AT},
   Title = {A velocity decomposition approach for moving interfaces in
             viscous fluids},
   Journal = {Journal of Computational Physics},
   Volume = {228},
   Number = {9},
   Pages = {3358-3367},
   Year = {2009},
   ISSN = {0021-9991},
   url = {http://dx.doi.org/10.1016/j.jcp.2009.01.023},
   Abstract = {We present a second-order accurate method for computing the
             coupled motion of a viscous fluid and an elastic material
             interface with zero thickness. The fluid flow is described
             by the Navier-Stokes equations, with a singular force due to
             the stretching of the moving interface. We decompose the
             velocity into a "Stokes" part and a "regular" part. The
             first part is determined by the Stokes equations and the
             singular interfacial force. The Stokes solution is obtained
             using the immersed interface method, which gives
             second-order accurate values by incorporating known jumps
             for the solution and its derivatives into a finite
             difference method. The regular part of the velocity is given
             by the Navier-Stokes equations with a body force resulting
             from the Stokes part. The regular velocity is obtained using
             a time-stepping method that combines the semi-Lagrangian
             method with the backward difference formula. Because the
             body force is continuous, jump conditions are not necessary.
             For problems with stiff boundary forces, the decomposition
             approach can be combined with fractional time-stepping,
             using a smaller time step to advance the interface quickly
             by Stokes flow, with the velocity computed using boundary
             integrals. The small time steps maintain numerical
             stability, while the overall solution is updated on a larger
             time step to reduce computational cost. © 2009 Elsevier
             Inc. All rights reserved.},
   Doi = {10.1016/j.jcp.2009.01.023},
   Key = {fds243695}
}

@article{fds243697,
   Author = {Layton, AT},
   Title = {Using integral equations and the immersed interface method
             to solve immersed boundary problems with stiff
             forces},
   Journal = {Computers & Fluids},
   Volume = {38},
   Number = {2},
   Pages = {266-272},
   Year = {2009},
   ISSN = {0045-7930},
   url = {http://dx.doi.org/10.1016/j.compfluid.2008.02.003},
   Abstract = {We propose a fast, explicit numerical method for computing
             approximations for the immersed boundary problem in which
             the boundaries that separate the fluid into two regions are
             stiff. In the numerical computations of such problems, one
             frequently has to contend with numerical instability, as the
             stiff immersed boundaries exert large forces on the local
             fluid. When the boundary forces are treated explicitly,
             prohibitively small time-steps may be required to maintain
             numerical stability. On the other hand, when the boundary
             forces are treated implicitly, the restriction on the
             time-step size is reduced, but the solution of a large
             system of coupled non-linear equations may be required. In
             this work, we develop an efficient method that combines an
             integral equation approach with the immersed interface
             method. The present method treats the boundary forces
             explicitly. To reduce computational costs, the method uses
             an operator-splitting approach: large time-steps are used to
             update the non-stiff advection terms, and smaller substeps
             are used to advance the stiff boundary. At each substep, an
             integral equation is computed to yield fluid velocity local
             to the boundary; those velocity values are then used to
             update the boundary configuration. Fluid variables are
             computed over the entire domain, using the immersed
             interface method, only at the end of the large advection
             time-steps. Numerical results suggest that the present
             method compares favorably with an implementation of the
             immersed interface method that employs an explicit
             time-stepping and no fractional stepping. © 2008 Elsevier
             Ltd. All rights reserved.},
   Doi = {10.1016/j.compfluid.2008.02.003},
   Key = {fds243697}
}

@article{fds243699,
   Author = {Wang, J and Layton, A},
   Title = {Numerical simulations of fiber sedimentation in
             Navier-stokes flows},
   Journal = {Communications in computational physics},
   Volume = {5},
   Number = {1},
   Pages = {61-83},
   Year = {2009},
   ISSN = {1815-2406},
   Abstract = {We perform numerical simulations of the sedimentation of
             rigid fibers suspended in a viscous incompressible fluid at
             nonzero Reynolds numbers. The fiber sedimentation system is
             modeled as a two-dimensional immersed boundary problem,
             which naturally accommodates the fluid-particle interactions
             and which allows the simulation of a large number of
             suspending fibers. We study the dynamics of sedimenting
             fibers under a variety of conditions, including differing
             fiber densities, Reynolds numbers, domain boundary
             conditions, etc. Simulation results are compared to
             experimental measurements and numerical results obtained in
             previous studies. © 2009 Global-Science
             Press.},
   Key = {fds243699}
}

@article{fds320912,
   Author = {Layton, HE and Moore, LC and Layton, AT},
   Title = {Tubuloglomerular feedback signal transduction in a model of
             a compliant thick ascending limb},
   Journal = {The FASEB journal : official publication of the Federation
             of American Societies for Experimental Biology},
   Volume = {22},
   Year = {2008},
   Month = {April},
   Key = {fds320912}
}

@article{fds320913,
   Author = {Pannabecker, TL and Dantzler, WH and Layton, AT and Layton,
             HE},
   Title = {Three-dimensional reconstructions of rat renal inner medulla
             suggest two anatomically separated countercurrent mechanisms
             for urine concentration},
   Journal = {The FASEB journal : official publication of the Federation
             of American Societies for Experimental Biology},
   Volume = {22},
   Year = {2008},
   Month = {April},
   Key = {fds320913}
}

@article{fds243698,
   Author = {Pannabecker, TL and Dantzler, WH and Layton, HE and Layton,
             AT},
   Title = {Role of three-dimensional architecture in the urine
             concentrating mechanism of the rat renal inner
             medulla},
   Journal = {American journal of physiology. Renal physiology},
   Volume = {295},
   Number = {5},
   Pages = {F1271-F1285},
   Year = {2008},
   ISSN = {0363-6127},
   url = {http://dx.doi.org/10.1152/ajprenal.90252.2008},
   Abstract = {Recent studies of three-dimensional architecture of rat
             renal inner medulla (IM) and expression of membrane proteins
             associated with fluid and solute transport in nephrons and
             vasculature have revealed structural and transport
             properties that likely impact the IM urine concentrating
             mechanism. These studies have shown that 1) IM descending
             thin limbs (DTLs) have at least two or three functionally
             distinct subsegments; 2) most ascending thin limbs (ATLs)
             and about half the ascending vasa recta (AVR) are arranged
             among clusters of collecting ducts (CDs), which form the
             organizing motif through the first 3-3.5 mm of the IM,
             whereas other ATLs and AVR, along with aquaporin-1-positive
             DTLs and urea transporter B-positive descending vasa recta
             (DVR), are external to the CD clusters; 3) ATLs, AVR, CDs,
             and interstitial cells delimit interstitial microdomains
             within the CD clusters; and 4) many of the longest loops of
             Henle form bends that include subsegments that run
             transversely along CDs that lie in the terminal 500 μm of
             the papilla tip. Based on a more comprehensive understanding
             of three-dimensional IM architecture, we distinguish two
             distinct countercurrent systems in the first 3-3.5 mm of the
             IM (an intra-CD cluster system and an inter-CD cluster
             system) and a third countercurrent system in the final 1.5-2
             mm. Spatial arrangements of loop of Henle subsegments and
             multiple countercurrent systems throughout four distinct
             axial IM zones, as well as our initial mathematical model,
             are consistent with a solute-separation, solute-mixing
             mechanism for concentrating urine in the IM. Copyright ©
             2008 the American Physiological Society.},
   Doi = {10.1152/ajprenal.90252.2008},
   Key = {fds243698}
}

@article{fds243700,
   Author = {Layton, AT},
   Title = {An efficient numerical method for the two-fluid Stokes
             equations with a moving immersed boundary},
   Journal = {Computer Methods in Applied Mechanics and
             Engineering},
   Volume = {197},
   Number = {25-28},
   Pages = {2147-2155},
   Year = {2008},
   ISSN = {0045-7825},
   url = {http://dx.doi.org/10.1016/j.cma.2007.08.018},
   Abstract = {We consider the immersed boundary problem in which the
             boundary separates two very viscous fluids with differing
             viscosities. The moving elastic boundary may exert a force
             on the local fluid. The model solution is obtained using the
             immersed interface method, which computes second-order
             accurate approximations by incorporating known jumps in the
             solution or its derivatives into a finite difference method.
             These jump conditions become coupled when the fluid
             viscosity has a jump across the boundary, and this coupling
             renders the application of the immersed interface method
             challenging. We present a method that first uses boundary
             integral equations to reduce the two-fluid Stokes problem to
             the single-fluid case, and then solves the single-fluid
             problem using the immersed interface method. Using this
             method, we assess, through two numerical examples, how the
             fluid dynamics are affected by differing viscosities in the
             two-fluid regions. We also propose an implicit algorithm and
             a fractional-step algorithm for advancing the boundary
             position. Because both algorithms make use of the integral
             form of the solution, neither one requires the solution of a
             large system of coupled nonlinear equations, as is
             traditionally the case. Numerical results suggest that, for
             sufficiently stiff problems, the fractional time-stepping
             algorithm is the most efficient, in the sense that it allows
             the largest time-interval between subsequent updates of
             global model solutions. © 2007 Elsevier B.V. All rights
             reserved.},
   Doi = {10.1016/j.cma.2007.08.018},
   Key = {fds243700}
}

@article{fds243701,
   Author = {Layton, AT},
   Title = {On the choice of correctors for semi-implicit Picard
             deferred correction methods},
   Journal = {Applied Numerical Mathematics},
   Volume = {58},
   Number = {6},
   Pages = {845-858},
   Year = {2008},
   ISSN = {0168-9274},
   url = {http://dx.doi.org/10.1016/j.apnum.2007.03.003},
   Abstract = {The goal of this study is to assess the implications of the
             choice of correctors for semi-implicit Picard integral
             deferred correction (SIPIDC) methods. The SIPIDC methods
             previously developed compute a high-order approximation by
             first computing a low-order provisional solution using a
             semi-implicit method and then using a first-order
             semi-implicit method to solve a series of correction
             equations, each of which raises the order of accuracy of the
             solution by one. In this study, we examine the efficiency of
             SIPIDC methods that instead use standard second-order
             semi-implicit methods to solve the correction equations. The
             accuracy, efficiency, and stability of the resulting methods
             are compared to previously developed methods, in the context
             of both nonstiff and stiff problems. © 2007
             IMACS.},
   Doi = {10.1016/j.apnum.2007.03.003},
   Key = {fds243701}
}

@article{fds243705,
   Author = {Layton, AT},
   Title = {Role of UTB urea transporters in the urine concentrating
             mechanism of the rat kidney.},
   Journal = {Bulletin of Mathematical Biology},
   Volume = {69},
   Number = {3},
   Pages = {887-929},
   Year = {2007},
   Month = {April},
   ISSN = {0092-8240},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/17265123},
   Abstract = {A mathematical model of the renal medulla of the rat kidney
             was used to investigate urine concentrating mechanism
             function in animals lacking the UTB urea transporter. The
             UTB transporter is believed to mediate countercurrent urea
             exchange between descending vasa recta (DVR) and ascending
             vasa recta (AVR) by facilitating urea transport across DVR
             endothelia. The model represents the outer medulla (OM) and
             inner medulla (IM), with the actions of the cortex
             incorporated via boundary conditions. Blood flow in the
             model vasculature is divided into plasma and red blood cell
             compartments. In the base-case model configuration tubular
             dimensions and transport parameters are based on, or
             estimated from, experimental measurements or
             immunohistochemical evidence in wild-type rats. The
             base-case model configuration generated an osmolality
             gradient along the cortico-medullary axis that is consistent
             with measurements from rats in a moderately antidiuretic
             state. When expression of UTB was eliminated in the model,
             model results indicated that, relative to wild-type, the OM
             cortico-medullary osmolality gradient and the net urea flow
             through the OM were little affected by absence of UTB
             transporter. However, because urea transfer from AVR to DVR
             was much reduced, urea trapping by countercurrent exchange
             was significantly compromised. Consequently, urine urea
             concentration and osmolality were decreased by 12% and 8.9%
             from base case, respectively, with most of the reduction
             attributable to the impaired IM concentrating mechanism.
             These results indicate that the in vivo urine concentrating
             defect in knockout mouse, reported by Yang et al. (J Biol
             Chem 277(12), 10633-10637, 2002), is not attributable to an
             OM concentrating mechanism defect, but that reduced urea
             trapping by long vasa recta plays a significant role in
             compromising the concentrating mechanism of the IM.
             Moreover, model results are in general agreement with the
             explanation of knockout renal function proposed by Yang et
             al.},
   Doi = {10.1007/s11538-005-9030-3},
   Key = {fds243705}
}

@article{fds320914,
   Author = {Marcano, M and Layton, AT and Layton, HE},
   Title = {Maximum urine concentrating capability for transport
             parameters and urine flow within prescribed
             ranges},
   Journal = {The FASEB journal : official publication of the Federation
             of American Societies for Experimental Biology},
   Volume = {21},
   Number = {6},
   Pages = {A905-A905},
   Year = {2007},
   Month = {April},
   Key = {fds320914}
}

@article{fds320915,
   Author = {Layton, HE and Layton, AT and Moore, LC},
   Title = {A mechanism for the generation of harmonics in oscillations
             mediated by tubuloglomerular feedback},
   Journal = {The FASEB journal : official publication of the Federation
             of American Societies for Experimental Biology},
   Volume = {21},
   Number = {6},
   Pages = {A828-A828},
   Year = {2007},
   Month = {April},
   Key = {fds320915}
}

@article{fds243704,
   Author = {Layton, AT and Minion, ML},
   Title = {Implications of the choice of predictors for semi-implicit
             Picard Integral deferred correction methods},
   Journal = {Comm. Appl. Math. Comp. Sci.},
   Volume = {2},
   Number = {1},
   Pages = {1-34},
   Year = {2007},
   Key = {fds243704}
}

@article{fds243707,
   Author = {Layton, AT and Moore, LC and Layton, HE},
   Title = {Multistability in tubuloglomerular feedback and spectral
             complexity in spontaneously hypertensive
             rats.},
   Journal = {American Journal of Physiology: Renal Physiology},
   Volume = {291},
   Number = {1},
   Pages = {F79-F97},
   Year = {2006},
   Month = {July},
   ISSN = {1931-857X},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/16204416},
   Abstract = {Single-nephron proximal tubule pressure in spontaneously
             hypertensive rats (SHR) can exhibit highly irregular
             oscillations similar to deterministic chaos. We used a
             mathematical model of tubuloglomerular feedback (TGF) to
             investigate potential sources of the irregular oscillations
             and the corresponding complex power spectra in SHR. A
             bifurcation analysis of the TGF model equations, for nonzero
             thick ascending limb (TAL) NaCl permeability, was performed
             by finding roots of the characteristic equation, and
             numerical simulations of model solutions were conducted to
             assist in the interpretation of the analysis. These
             techniques revealed four parameter regions, consistent with
             TGF gain and delays in SHR, where multiple stable model
             solutions are possible: 1) a region having one stable,
             time-independent steady-state solution; 2) a region having
             one stable oscillatory solution only, of frequency f1; 3) a
             region having one stable oscillatory solution only, of
             frequency f2, which is approximately equal to 2f1; and 4) a
             region having two possible stable oscillatory solutions, of
             frequencies f1 and f2. In addition, we conducted simulations
             in which TAL volume was assumed to vary as a function of
             time and simulations in which two or three nephrons were
             assumed to have coupled TGF systems. Four potential sources
             of spectral complexity in SHR were identified: 1)
             bifurcations that permit switching between different stable
             oscillatory modes, leading to multiple spectral peaks and
             their respective harmonic peaks; 2) sustained lability in
             delay parameters, leading to broadening of peaks and of
             their harmonics; 3) episodic, but abrupt, lability in delay
             parameters, leading to multiple peaks and their harmonics;
             and 4) coupling of small numbers of nephrons, leading to
             multiple peaks and their harmonics. We conclude that the TGF
             system in SHR may exhibit multistability and that the
             complex power spectra of the irregular TGF fluctuations in
             this strain may be explained by switching between multiple
             dynamic modes, temporal variation in TGF parameters, and
             nephron coupling.},
   Doi = {10.1152/ajprenal.00048.2005},
   Key = {fds243707}
}

@article{fds320916,
   Author = {Marcano, M and Layton, AT and Layton, HE},
   Title = {Estimation of collecting duct parameters for maximum urine
             concentrating capability in a mathematical model of the rat
             inner medulla},
   Journal = {The FASEB journal : official publication of the Federation
             of American Societies for Experimental Biology},
   Volume = {20},
   Number = {5},
   Pages = {A1224-A1224},
   Year = {2006},
   Month = {March},
   Key = {fds320916}
}

@article{fds320917,
   Author = {Moore, LC and Siu, KL and Layton, AT and Layton, HE and Chon,
             KH},
   Title = {Evidence for multi-stability of the tubuloglomerular
             feedback system in spontaneously-hypertensive rats
             (SHR)},
   Journal = {The FASEB journal : official publication of the Federation
             of American Societies for Experimental Biology},
   Volume = {20},
   Number = {4},
   Pages = {A762-A762},
   Year = {2006},
   Month = {March},
   Key = {fds320917}
}

@article{fds320918,
   Author = {Layton, AT and Moore, LC and Layton, HE},
   Title = {Dynamics in coupled nephrons may contribute to irregular
             flow oscillations in spontaneously hypertensive
             rats},
   Journal = {The FASEB journal : official publication of the Federation
             of American Societies for Experimental Biology},
   Volume = {20},
   Number = {4},
   Pages = {A759-A759},
   Year = {2006},
   Month = {March},
   Key = {fds320918}
}

@article{fds243639,
   Author = {Layton, AT and Christara, CC and Jackson, KR},
   Title = {Quadratic spline methods for the shallow water equations on
             the sphere: Galerkin},
   Journal = {Mathematics and Computers in Simulation},
   Volume = {71},
   Number = {3},
   Pages = {175-186},
   Year = {2006},
   ISSN = {0378-4754},
   url = {http://dx.doi.org/10.1016/j.matcom.2004.10.008},
   Abstract = {Currently in most global meteorological applications,
             low-order finite difference or finite element methods, or
             the spectral transform method are used. The spectral
             transform method, which yields high-order approximations,
             requires Legendre transforms. The Legendre transforms have a
             computational complexity of O ( N3 ), where N is the number
             of subintervals in one dimension, and thus render the
             spectral transform method unscalable. In this study, we
             present an alternative numerical method for solving the
             shallow water equations (SWEs) on a sphere in spherical
             coordinates. In this implementation, the SWEs are
             discretized in time using the two-level semi-Lagrangian
             semi-implicit method, and in space on staggered grids using
             the quadratic spline Galerkin method. We show that, when
             applied to a simplified version of the SWEs, the method
             yields a neutrally stable solution for the meteorologically
             significant Rossby waves. Moreover, we demonstrate that the
             Helmholtz equation arising from the discretization and
             solution of the SWEs should be derived algebraically rather
             than analytically, in order for the method to be stable with
             respect to the Rossby waves. These results are verified
             numerically using Boyd's equatorial wave equations [J.P.
             Boyd, Equatorial solitary waves. Part I. Rossby solitons, J.
             Phys. Oceanogr. 10 (1980) 1699-1717] with initial conditions
             chosen to generate a soliton. © 2006.},
   Doi = {10.1016/j.matcom.2004.10.008},
   Key = {fds243639}
}

@article{fds243640,
   Author = {Layton, AT and Christara, CC and Jackson, KR},
   Title = {Quadratic spline methods for the shallow water equations on
             the sphere: Collocation},
   Journal = {Mathematics and Computers in Simulation},
   Volume = {71},
   Number = {3},
   Pages = {187-205},
   Year = {2006},
   ISSN = {0378-4754},
   url = {http://dx.doi.org/10.1016/j.matcom.2004.10.009},
   Abstract = {In this study, we present numerical methods, based on the
             optimal quadratic spline collocation (OQSC) methods, for
             solving the shallow water equations (SWEs) in spherical
             coordinates. The error associated with quadratic spline
             interpolation is fourth order locally at certain points and
             third order globally, but the standard quadratic spline
             collocation methods generate only second-order
             approximations. In contrast, the OQSC methods generate
             approximations of the same order as quadratic spline
             interpolation. In the one-step OQSC method, the discrete
             differential operators are perturbed to eliminate low-order
             error terms, and a high-order approximation is computed
             using the perturbed operators. In the two-step OQSC method,
             a second-order approximation is generated first, using the
             standard formulation, and then a high-order approximation is
             computed in a second phase by perturbing the right sides of
             the equations appropriately. In this implementation, the
             SWEs are discretized in time using the semi-Lagrangian
             semi-implicit method, and in space using the OQSC methods.
             The resulting methods are efficient and yield stable and
             accurate representation of the meteorologically important
             Rossby waves. Moreover, by adopting the Arakawa C-type grid,
             the methods also faithfully capture the group velocity of
             inertia-gravity waves. © 2006.},
   Doi = {10.1016/j.matcom.2004.10.009},
   Key = {fds243640}
}

@article{fds243702,
   Author = {Layton, AT},
   Title = {Modeling water transport across elastic boundaries using an
             explicit jump method},
   Journal = {SIAM Journal on Scientific Computing},
   Volume = {28},
   Number = {6},
   Pages = {2189-2207},
   Year = {2006},
   ISSN = {1064-8275},
   url = {http://dx.doi.org/10.1137/050642198},
   Abstract = {A mathematical model is presented to simulate water and
             solute transport in a highly viscous fluid with a
             water-permeable, elastic immersed membrane. In this model,
             fluid motion is described by Stokes flow, whereas water
             fluxes across the membrane are driven by transmural pressure
             and solute concentration differences. The elastic forces,
             arising from the membrane being distorted from its relaxed
             configuration, and the transmembrane water fluxes introduce
             into model solutions discontinuities across the membrane.
             Such discontinuities are faithfully captured using a
             second-order explicit jump method [A. Mayo, SIAM J. Numer.
             Anal., 21 (1984), pp. 285-299], in which jumps in the
             solution and its derivatives are incorporated into a
             finite-difference scheme. Numerical results suggest that the
             method exhibits desirable volume accuracy and mass
             conservation. © 2006 Society for Industrial and Applied
             Mathematics.},
   Doi = {10.1137/050642198},
   Key = {fds243702}
}

@article{fds243703,
   Author = {Beale, JT and Layton, AT},
   Title = {On the accuracy of finite difference methods for elliptic
             problems with interfaces},
   Journal = {Commun. Appl. Math. Comput. Sci.},
   Volume = {1},
   Number = {1},
   Pages = {91-119},
   Year = {2006},
   url = {http://www.math.duke.edu/faculty/beale/papers/alayton.pdf},
   Key = {fds243703}
}

@article{fds243706,
   Author = {Marcano, M and Layton, AT and Layton, HE},
   Title = {An optimization algorithm for a distributed-loop model of an
             avian urine concentrating mechanism},
   Journal = {Bulletin of Mathematical Biology},
   Volume = {68},
   Number = {7},
   Pages = {1625-1660},
   Year = {2006},
   ISSN = {0092-8240},
   url = {http://dx.doi.org/10.1007/s11538-006-9087-1},
   Abstract = {To better understand how the avian kidney's morphological
             and transepithelial transport properties affect the urine
             concentrating mechanism (UCM), an inverse problem was solved
             for a mathematical model of the quail UCM. In this model, a
             continuous, monotonically decreasing population distribution
             of tubes, as a function of medullary length, was used to
             represent the loops of Henle, which reach to varying levels
             along the avian medullary cones. A measure of concentrating
             mechanism efficiency - the ratio of the free-water
             absorption rate (FWA) to the total NaCl active transport
             rate (TAT) - was optimized by varying a set of parameters
             within bounds suggested by physiological experiments. Those
             parameters include transepithelial transport properties of
             renal tubules, length of the prebend enlargement of the
             descending limb (DL), DL and collecting duct (CD) inflows,
             plasma Na+ concentration, length of the cortical thick
             ascending limbs, central core solute diffusivity, and
             population distribution of loops of Henle and of CDs along
             the medullary cone. By selecting parameter values that
             increase urine flow rate (while maintaining a sufficiently
             high urine-to-plasma osmolality ratio (U/P)) and that reduce
             TAT, the optimization algorithm identified a set of
             parameter values that increased efficiency by ∼60% above
             base-case efficiency. Thus, higher efficiency can be
             achieved by increasing urine flow rather than increasing
             U/P. The algorithm also identified a set of parameters that
             reduced efficiency by ∼70% via the production of a urine
             having near-plasma osmolality at near-base-case TAT. In
             separate studies, maximum efficiency was evaluated as
             selected parameters were varied over large ranges. Shorter
             cones were found to be more efficient than longer ones, and
             an optimal loop of Henle distribution was found that is
             consistent with experimental findings. © Society for
             Mathematical Biology 2006.},
   Doi = {10.1007/s11538-006-9087-1},
   Key = {fds243706}
}

@article{fds243708,
   Author = {Layton, AT and Christara, CC and Jackson, KR},
   Title = {Optimal quadratic spline collocation methods for the shallow
             water equations on the sphere},
   Journal = {Math. Comput. Simul.},
   Volume = {71},
   Number = {3},
   Pages = {187-205},
   Year = {2006},
   Key = {fds243708}
}

@article{fds243709,
   Author = {Layton, AT and Christara, CC and Jackson, KR},
   Title = {Quadratic spline Galerkin method for the shallow water
             equations on the sphere},
   Journal = {Math. Comput. Simul.},
   Volume = {71},
   Number = {3},
   Pages = {175-186},
   Year = {2006},
   Key = {fds243709}
}

@article{fds243710,
   Author = {Thomas, SR and Layton, AT and Layton, HE and Moore,
             LC},
   Title = {Kidney modeling: Status and perspectives},
   Journal = {Proceedings of the Institute of Electrical and Electronics
             Engineers (IEEE)},
   Volume = {94},
   Number = {4},
   Pages = {740-752},
   Year = {2006},
   ISSN = {0018-9219},
   url = {http://dx.doi.org/10.1109/JPROC.2006.871770},
   Abstract = {Mathematical models have played an essential role in
             elucidating various functions of the kidney, including the
             mechanism by which the avion and mammalian kidney can
             produce a urine that is more concentrated than blood plasma,
             quasi-isosmotic reabsorption along the proximal tubule, and
             the control and regulation of glomerular filtration by the
             myogenic and tubuloglomerular feedback mechanisms. This
             review includes a brief description of relevant renal
             physiology, a summary of the contributions of mathematical
             models at various levels and describes our recent work
             toward the Renal Physiome. © 2006 IEEE.},
   Doi = {10.1109/JPROC.2006.871770},
   Key = {fds243710}
}

@article{fds243711,
   Author = {Layton, AT and Layton, HE},
   Title = {A region-based mathematical model of the urine concentrating
             mechanism in the rat outer medulla. I. Formulation and
             base-case results.},
   Journal = {American Journal of Physiology: Renal Physiology},
   Volume = {289},
   Number = {6},
   Pages = {F1346-F1366},
   Year = {2005},
   Month = {December},
   ISSN = {1931-857X},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/15914776},
   Abstract = {We have developed a highly detailed mathematical model for
             the urine concentrating mechanism (UCM) of the rat kidney
             outer medulla (OM). The model simulates preferential
             interactions among tubules and vessels by representing four
             concentric regions that are centered on a vascular bundle;
             tubules and vessels, or fractions thereof, are assigned to
             anatomically appropriate regions. Model parameters, which
             are based on the experimental literature, include
             transepithelial transport properties of short descending
             limbs inferred from immunohistochemical localization
             studies. The model equations, which are based on
             conservation of solutes and water and on standard
             expressions for transmural transport, were solved to steady
             state. Model simulations predict significantly differing
             interstitial NaCl and urea concentrations in adjoining
             regions. Active NaCl transport from thick ascending limbs
             (TALs), at rates inferred from the physiological literature,
             resulted in model osmolality profiles along the OM that are
             consistent with tissue slice experiments. TAL luminal NaCl
             concentrations at the corticomedullary boundary are
             consistent with tubuloglomerular feedback function. The
             model exhibited solute exchange, cycling, and sequestration
             patterns (in tubules, vessels, and regions) that are
             generally consistent with predictions in the physiological
             literature, including significant urea addition from long
             ascending vasa recta to inner-stripe short descending limbs.
             In a companion study (Layton AT and Layton HE. Am J Physiol
             Renal Physiol 289: F1367-F1381, 2005), the impact of model
             assumptions, medullary anatomy, and tubular segmentation on
             the UCM was investigated by means of extensive parameter
             studies.},
   Doi = {10.1152/ajprenal.00346.2003},
   Key = {fds243711}
}

@article{fds243712,
   Author = {Layton, AT and Layton, HE},
   Title = {A region-based mathematical model of the urine concentrating
             mechanism in the rat outer medulla. II. Parameter
             sensitivity and tubular inhomogeneity.},
   Journal = {American Journal of Physiology: Renal Physiology},
   Volume = {289},
   Number = {6},
   Pages = {F1367-F1381},
   Year = {2005},
   Month = {December},
   ISSN = {1931-857X},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/15914775},
   Abstract = {In a companion study (Layton AT and Layton HE. Am J Physiol
             Renal Physiol 289: F1346-F1366, 2005), a region-based
             mathematical model was formulated for the urine
             concentrating mechanism (UCM) in the outer medulla (OM) of
             the rat kidney. In the present study, we quantified the
             sensitivity of that model to several structural assumptions,
             including the degree of regionalization and the degree of
             inclusion of short descending limbs (SDLs) in the vascular
             bundles of the inner stripe (IS). Also, we quantified model
             sensitivity to several parameters that have not been well
             characterized in the experimental literature, including
             boundary conditions, short vasa recta distribution, and
             ascending vasa recta (AVR) solute permeabilities. These
             studies indicate that regionalization elevates the
             osmolality of the fluid delivered into the inner medulla via
             the collecting ducts; that model predictions are not
             significantly sensitive to boundary conditions; and that
             short vasa recta distribution and AVR permeabilities
             significantly impact concentrating capability. Moreover, we
             investigated, in the context of the UCM, the functional
             significance of several aspects of tubular segmentation and
             heterogeneity: SDL segments in the IS that are likely to be
             impermeable to water but highly permeable to urea; a prebend
             segment of SDLs that may be functionally like thick
             ascending limb (TAL); differing IS and outer stripe Na(+)
             active transport rates in TAL; and potential active urea
             secretion into the proximal straight tubules. Model
             calculations predict that these aspects of tubular of
             segmentation and heterogeneity generally enhance solute
             cycling or promote effective UCM function.},
   Doi = {10.1152/ajprenal.00347.2003},
   Key = {fds243712}
}

@article{fds243714,
   Author = {Layton, AT},
   Title = {Role of structural organization in the urine concentrating
             mechanism of an avian kidney.},
   Journal = {Mathematical Biosciences},
   Volume = {197},
   Number = {2},
   Pages = {211-230},
   Year = {2005},
   Month = {October},
   ISSN = {0025-5564},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/16135372},
   Abstract = {The organization of tubules and blood vessels in the quail
             medullary cone is highly structured. This structural
             organization may result in preferential interactions among
             tubules and vessels, interactions that may enhance urine
             concentrating capability. In this study, we formulate a
             model framework for the urine concentrating mechanism of the
             quail kidney. The model simulates preferential interactions
             among renal tubules by representing two concentric cores and
             by specifying the fractions of tubules assigned to each of
             the concentric cores. The model equations are based on
             standard expressions for transmural transport and on solute
             and water conservation. Model results suggest that the
             preferential interactions among tubules enhance the urine
             concentration capacity of short medullary cones by reducing
             the diluting effect of the descending limbs on the region of
             the interstitium where the collecting ducts are located;
             however, the effects on longer cones are
             unclear.},
   Doi = {10.1016/j.mbs.2005.07.004},
   Key = {fds243714}
}

@article{fds320919,
   Author = {Marcano, M and Layton, AT and Layton, HE},
   Title = {An optimization algorithm for a model of the urine
             concentrating mechanism in rat inner medulla},
   Journal = {The FASEB journal : official publication of the Federation
             of American Societies for Experimental Biology},
   Volume = {19},
   Number = {4},
   Pages = {A150-A150},
   Year = {2005},
   Month = {March},
   Key = {fds320919}
}

@article{fds320920,
   Author = {Layton, AT and Layton, HE},
   Title = {A mathematical model of the urine concentrating mechanism of
             the inner medulla of the chinchilla kidney},
   Journal = {The FASEB journal : official publication of the Federation
             of American Societies for Experimental Biology},
   Volume = {19},
   Number = {4},
   Pages = {A149-A149},
   Year = {2005},
   Month = {March},
   Key = {fds320920}
}

@article{fds243713,
   Author = {Layton, AT and Minion, ML},
   Title = {Implications of the choice of quadrature nodes for Picard
             Integral deferred correction methods},
   Journal = {BIT},
   Volume = {45},
   Number = {2},
   Pages = {341-373},
   Year = {2005},
   url = {http://dx.doi.org/10.1007/s10543-005-0016-1},
   Abstract = {This paper concerns a class of deferred correction methods
             recently developed for initial value ordinary differential
             equations; such methods are based on a Picard integral form
             of the correction equation. These methods divide a given
             timestep [t n ,t n+1] into substeps, and use function values
             computed at these substeps to approximate the Picard
             integral by means of a numerical quadrature. The main
             purpose of this paper is to present a detailed analysis of
             the implications of the location of quadrature nodes on the
             accuracy and stability of the overall method. Comparisons
             between Gauss-Legendre, Gauss-Lobatto, Gauss-Radau, and
             uniformly spaced points are presented. Also, for a given set
             of quadrature nodes, quadrature rules may be formulated that
             include or exclude function values computed at the left-hand
             endpoint t n . Quadrature rules that do not depend on the
             left-hand endpoint (which are referred to as right-hand
             quadrature rules) are shown to lead to L(α)-stable implicit
             methods with α≈π/2. The semi-implicit analog of this
             property is also discussed. Numerical results suggest that
             the use of uniform quadrature nodes, as opposed to nodes
             based on Gaussian quadratures, does not significantly affect
             the stability or accuracy of these methods for orders less
             than ten. In contrast, a study of the reduction of order for
             stiff equations shows that when uniform quadrature nodes are
             used in conjunction with a right-hand quadrature rule, the
             form and extent of order-reduction changes considerably.
             Specifically, a reduction of order to script O sign(ε2) is
             observed for uniform nodes as opposed to script O
             sign(εΔt) for non-uniform nodes, where Δt denotes the
             time step and ε a stiffness parameter such that ε→0
             corresponds to the problem becoming increasingly stiff. ©
             Springer 2005.},
   Doi = {10.1007/s10543-005-0016-1},
   Key = {fds243713}
}

@article{fds243715,
   Author = {Layton, AT},
   Title = {A methodology for tracking solute distribution in
             mathematical models of the kidney},
   Journal = {J. Biol. Sys.},
   Volume = {13},
   Number = {4},
   Pages = {1-21},
   Year = {2005},
   ISSN = {0218-3390},
   url = {http://dx.doi.org/10.1142/S0218339005001598},
   Abstract = {The goal of this study is to develop a methodology for
             tracking the distribution of filtered solute in mathematical
             models of the urine concentrating mechanism. Investigation
             of intrarenal solute distribution, and its cycling by way of
             counter-current exchange and preferential tubular
             interactions, may yield new insights into fundamental
             principles of concentrating mechanism function. Our method
             is implemented in a dynamic formulation of a central core
             model that represents renal tubules in both the cortex and
             the medulla. Axial solute diffusion is represented in
             intratubular flows and in the central core. By representing
             the fate of solute originally belonging to a marked bolus,
             we obtain the distribution of that solute as a function of
             time. In addition, we characterize the residence time of
             that solute by computing the portion of that solute
             remaining in the model system as a function of time. Because
             precise mass conservation is of particular importance in
             solute tracking, our numerical approach is based on the
             second-order Godunov method, which, by construction, is
             mass-conserving and accurately represents steep gradients
             and discontinuities in solute concentrations and tubular
             properties. © World Scientific Publishing
             Company.},
   Doi = {10.1142/S0218339005001598},
   Key = {fds243715}
}

@article{fds304481,
   Author = {Layton, AT and Minion, ML},
   Title = {Implications of the choice of quadrature nodes for Picard
             integral deferred corrections methods for ordinary
             differential equations},
   Journal = {BIT Numerical Mathematics},
   Volume = {45},
   Number = {2},
   Pages = {341-373},
   Year = {2005},
   url = {http://dx.doi.org/10.1007/s10543-005-0016-1},
   Abstract = {This paper concerns a class of deferred correction methods
             recently developed for initial value ordinary differential
             equations; such methods are based on a Picard integral form
             of the correction equation. These methods divide a given
             timestep [t n ,t n+1] into substeps, and use function values
             computed at these substeps to approximate the Picard
             integral by means of a numerical quadrature. The main
             purpose of this paper is to present a detailed analysis of
             the implications of the location of quadrature nodes on the
             accuracy and stability of the overall method. Comparisons
             between Gauss-Legendre, Gauss-Lobatto, Gauss-Radau, and
             uniformly spaced points are presented. Also, for a given set
             of quadrature nodes, quadrature rules may be formulated that
             include or exclude function values computed at the left-hand
             endpoint t n . Quadrature rules that do not depend on the
             left-hand endpoint (which are referred to as right-hand
             quadrature rules) are shown to lead to L(α)-stable implicit
             methods with α≈π/2. The semi-implicit analog of this
             property is also discussed. Numerical results suggest that
             the use of uniform quadrature nodes, as opposed to nodes
             based on Gaussian quadratures, does not significantly affect
             the stability or accuracy of these methods for orders less
             than ten. In contrast, a study of the reduction of order for
             stiff equations shows that when uniform quadrature nodes are
             used in conjunction with a right-hand quadrature rule, the
             form and extent of order-reduction changes considerably.
             Specifically, a reduction of order to script O sign(ε2) is
             observed for uniform nodes as opposed to script O
             sign(εΔt) for non-uniform nodes, where Δt denotes the
             time step and ε a stiffness parameter such that ε→0
             corresponds to the problem becoming increasingly stiff. ©
             Springer 2005.},
   Doi = {10.1007/s10543-005-0016-1},
   Key = {fds304481}
}

@article{fds304482,
   Author = {Layton, AT},
   Title = {A methodology for tracking solute distribution in a
             mathematical model of the kidney},
   Journal = {Journal of Biological Systems},
   Volume = {13},
   Number = {4},
   Pages = {399-419},
   Year = {2005},
   ISSN = {0218-3390},
   url = {http://dx.doi.org/10.1142/S0218339005001598},
   Abstract = {The goal of this study is to develop a methodology for
             tracking the distribution of filtered solute in mathematical
             models of the urine concentrating mechanism. Investigation
             of intrarenal solute distribution, and its cycling by way of
             counter-current exchange and preferential tubular
             interactions, may yield new insights into fundamental
             principles of concentrating mechanism function. Our method
             is implemented in a dynamic formulation of a central core
             model that represents renal tubules in both the cortex and
             the medulla. Axial solute diffusion is represented in
             intratubular flows and in the central core. By representing
             the fate of solute originally belonging to a marked bolus,
             we obtain the distribution of that solute as a function of
             time. In addition, we characterize the residence time of
             that solute by computing the portion of that solute
             remaining in the model system as a function of time. Because
             precise mass conservation is of particular importance in
             solute tracking, our numerical approach is based on the
             second-order Godunov method, which, by construction, is
             mass-conserving and accurately represents steep gradients
             and discontinuities in solute concentrations and tubular
             properties. © World Scientific Publishing
             Company.},
   Doi = {10.1142/S0218339005001598},
   Key = {fds304482}
}

@article{fds320921,
   Author = {Layton, AT and Pannabecker, TL and Dantzler, WH and Layton,
             HE},
   Title = {Effects of structural organization on the urine
             concentrating mechanism of the rat kidney},
   Journal = {The FASEB journal : official publication of the Federation
             of American Societies for Experimental Biology},
   Volume = {18},
   Number = {5},
   Pages = {A1021-A1021},
   Year = {2004},
   Month = {March},
   Key = {fds320921}
}

@article{fds24336,
   Author = {Anita T. Layton},
   Title = {Conservative multi-implicit integral deferred correction
             methods with adaptive mesh refinement},
   Journal = {Proceedings of the 12th Annual Conference of the CFD Society
             of Canada},
   Year = {2004},
   Key = {fds24336}
}

@article{fds243716,
   Author = {Layton, AT and Pannabecker, TL and Dantzler, WH and Layton,
             HE},
   Title = {Two modes for concentrating urine in rat inner
             medulla},
   Journal = {American Journal of Physiology - Renal Physiology},
   Volume = {287},
   Number = {4 56-4},
   Pages = {F816-F839},
   Year = {2004},
   url = {http://dx.doi.org/10.1152/ajprenal.00398.2003},
   Abstract = {We used a mathematical model of the urine concentrating
             mechanism of rat inner medulla (IM) to investigate the
             implications of experimental studies in which
             immunohistochemical methods were combined with
             three-dimensional computerized reconstruction of renal
             tubules. The mathematical model represents a distribution of
             loops of Henle with loop bends at all levels of the IM, and
             the vasculature is represented by means of the central core
             assumption. Based on immunohistochemical evidence,
             descending limb portions that reach into the papilla are
             assumed to be only moderately water permeable or to be water
             impermeable, and only prebend segments and ascending thin
             limbs are assumed to be NaCl permeable. Model studies
             indicate that this configuration favors the targeted
             delivery of NaCl to loop bends, where a favorable gradient,
             sustained by urea absorption from collecting ducts, promotes
             NaCl absorption. We identified two model modes that produce
             a significant axial osmolality gradient. One mode, suggested
             by preliminary immunohistochemical findings, assumes that
             aquaporin-1-null portions of loops of Henle that reach into
             the papilla have very low urea permeability. The other mode,
             suggested by perfused tubule experiments from the
             literature, assumes that these same portions of loops of
             Henle have very high urea permeabilities. Model studies were
             conducted to determine the sensitivity of these modes to
             parameter choices. Model results are compared with extant
             tissue-slice and micropuncture studies.},
   Doi = {10.1152/ajprenal.00398.2003},
   Key = {fds243716}
}

@article{fds243717,
   Author = {Layton, AT and Minion, ML},
   Title = {Conservative multi-implicit spectral deferred correction
             methods for reacting gas dynamics},
   Journal = {Journal of Computational Physics},
   Volume = {194},
   Number = {2},
   Pages = {697-715},
   Year = {2004},
   url = {http://dx.doi.org/10.1016/j.jcp.2003.09.010},
   Abstract = {In most models of reacting gas dynamics, the characteristic
             time scales of chemical reactions are much shorter than the
             hydrodynamic and diffusive time scales, rendering the
             reaction part of the model equations stiff. Moreover,
             non-linear forcings may introduce into the solutions sharp
             gradients or shocks, the robust behavior and correct
             propagation of which require the use of specialized spatial
             discretization procedures. This study presents high-order
             conservative methods for the temporal integration of model
             equations of reacting flows. By means of a method of lines
             discretization on the flux difference form of the equations,
             these methods compute approximations to the cell-averaged or
             finite-volume solution. The temporal discretization is based
             on a multi-implicit generalization of spectral deferred
             correction methods. The advection term is integrated
             explicitly, and the diffusion and reaction terms are treated
             implicitly but independently, with the splitting errors
             reduced via the spectral deferred correction procedure. To
             reduce computational cost, different time steps may be used
             to integrate processes with widely-differing time scales.
             Numerical results show that the conservative nature of the
             methods allows a robust representation of discontinuities
             and sharp gradients; the results also demonstrate the
             expected convergence rates for the methods of orders three,
             four, and five for smooth problems. © 2003 Elsevier Inc.
             All rights reserved.},
   Doi = {10.1016/j.jcp.2003.09.010},
   Key = {fds243717}
}

@article{fds320922,
   Author = {Layton, HE and Layton, AT},
   Title = {Impaired countercurrent exchange in a mathematical model of
             a urine concentrating mechanism lacking UT-B urea
             transporter.},
   Journal = {Journal of the American Society of Nephrology :
             JASN},
   Volume = {14},
   Pages = {76A-76A},
   Year = {2003},
   Month = {November},
   Key = {fds320922}
}

@article{fds320923,
   Author = {Layton, AT and Layton, HE},
   Title = {A method for tracking solute distribution in mathematical
             models of the urine concentrating mechanism
             (UCM)},
   Journal = {The FASEB journal : official publication of the Federation
             of American Societies for Experimental Biology},
   Volume = {17},
   Number = {4},
   Pages = {A485-A485},
   Year = {2003},
   Month = {March},
   Key = {fds320923}
}

@article{fds24337,
   Author = {Anita T. Layton},
   Title = {High-order operator-splitting methods for reacting gas
             dynamics},
   Journal = {Proceedings of the 11th Annual Conference of the CFD Society
             of Canada},
   Year = {2003},
   Key = {fds24337}
}

@article{fds24338,
   Author = {Anita T. Layton},
   Title = {A two-time-level semi-Lagrangian semi-implicit double
             Fourier method},
   Journal = {Proceedings of the Workshop on Current Development in
             Shallow Water Models on the Sphere},
   Year = {2003},
   Key = {fds24338}
}

@article{fds243718,
   Author = {Layton, AT and Layton, HE},
   Title = {A region-based model framework for the rat urine
             concentrating mechanism},
   Journal = {Bull. Math. Biol.},
   Volume = {65},
   Number = {6},
   Pages = {859-901},
   Year = {2003},
   url = {http://dx.doi.org/10.1016/S0092-8240(03)00045-4},
   Abstract = {The highly structured organization of tubules and blood
             vessels in the outer medulla of the mammalian kidney is
             believed to result in preferential interactions among
             tubules and vessels; such interactions may promote solute
             cycling and enhance urine concentrating capability. In this
             study, we formulate a new model framework for the urine
             concentrating mechanism in the outer medulla of the rat
             kidney. The model simulates preferential interactions among
             tubules and vessels by representing two concentric regions
             and by specifying the fractions of tubules and vessels
             assigned to each of the regions. The model equations are
             based on standard expressions for transmural transport and
             on solute and water conservation. Model equations, which are
             derived in dynamic form, are solved to obtain steady-state
             solutions by means of a stable and efficient numerical
             method, based on the semi-Lagrangian semi-implicit method
             and on Newton's method. In this application, the
             computational cost scales as [IPQ] (N2), where N is the
             number of spatial subintervals along the medulla. We present
             representative solutions and show that the method generates
             approximations that are second-order accurate in space and
             that exhibit mass conservation. © 2003 Society for
             Mathematical Biology. Published by Elsevier Ltd. All rights
             reserved.},
   Doi = {10.1016/S0092-8240(03)00045-4},
   Key = {fds243718}
}

@article{fds243719,
   Author = {Bourlioux, A and Layton, AT and Minion, ML},
   Title = {High-order multi-implicit spectral deferred correction
             methods for problems of reactive flow},
   Journal = {Journal of Computational Physics},
   Volume = {189},
   Number = {2},
   Pages = {651-675},
   Year = {2003},
   url = {http://dx.doi.org/10.1016/S0021-9991(03)00251-1},
   Abstract = {Models for reacting flow are typically based on
             advection-diffusion-reaction (A-D-R) partial differential
             equations. Many practical cases correspond to situations
             where the relevant time scales associated with each of the
             three sub-processes can be widely different, leading to
             disparate time-step requirements for robust and accurate
             time-integration. in particular, interesting regimes in
             combustion correspond to systems in which diffusion and
             reaction are much faster processes than advection. The
             numerical strategy introduced in this paper is a general
             procedure to account for this time-scale disparity. The
             proposed methods are high-order multi-implicit
             generalizations of spectral deferred correction methods
             (MISDC methods), constructed for the temporal integration of
             A-D-R equations. Spectral deferred correction methods
             compute a high-order approximation to the solution of a
             differential equation by using a simple, low-order numerical
             method to solve a series of correction equations, each of
             which increases the order of accuracy of the approximation.
             The key feature of MISDC methods is their flexibility in
             handling several sub-processes implicitly but independently,
             while avoiding the splitting errors present in traditional
             operator-splitting methods and also allowing for different
             time steps for each process. The stability, accuracy, and
             efficiency of MISDC methods are first analyzed using a
             linear model problem and the results are compared to
             semi-implicit spectral deferred correction methods.
             Furthermore, numerical tests on simplified reacting flows
             demonstrate the expected convergence rates for MISDC methods
             of orders three, four, and five. The gain in efficiency by
             independently controlling the sub-process time steps is
             illustrated for nonlinear problems, where reaction and
             diffusion are much stiffer than advection. Although the
             paper focuses on this specific time-scales ordering, the
             generalization to any ordering combination is
             straightforward. © 2003 Elsevier Science B.V. All rights
             reserved.},
   Doi = {10.1016/S0021-9991(03)00251-1},
   Key = {fds243719}
}

@article{fds243720,
   Author = {Layton, AT and Spotz, WF},
   Title = {A semi-Lagrangian double Fourier method for the shallow
             water equations on the sphere},
   Journal = {Journal of Computational Physics},
   Volume = {189},
   Number = {1},
   Pages = {180-196},
   Year = {2003},
   url = {http://dx.doi.org/10.1016/S0021-9991(03)00207-9},
   Abstract = {We describe a numerical method, based on the semi-Lagrangian
             semi-implicit approach, for solving the shallow water
             equations (SWEs) in spherical coordinates. The most popular
             spatial discretization method used in global atmospheric
             models is currently the spectral transform method, which
             generates high-order numerical solutions and provides an
             elegant solution to the pole problems induced by a spherical
             coordinate system. However, the standard spherical harmonic
             spectral transform method requires associated Legendre
             transforms, which for problems with resolutions of current
             interest, have a computational complexity of O(N3), where N
             is the number of spatial subintervals in one dimension.
             Thus, the double Fourier spectral method, which uses
             trigonometric series, may be a viable alternative. The
             advantage of the double Fourier method is that fast Fourier
             transforms, which have a computational complexity of O(N2
             log N), can be used in both the longitudinal and latitudinal
             directions. In this implementation, the SWEs are discretized
             in time by means of the three-time-level semi-Lagrangian
             semi-implicit method, which integrates along fluid
             trajectories and allows large time steps while maintaining
             stability. Numerical results for the standard SWEs test
             suite are presented to demonstrate the stability and
             accuracy of the method. © 2003 Elsevier Science B.V. All
             rights reserved.},
   Doi = {10.1016/S0021-9991(03)00207-9},
   Key = {fds243720}
}

@article{fds243721,
   Author = {Layton, AT},
   Title = {A semi-Lagrangian collocation method for the shallow water
             equations on the sphere},
   Journal = {SIAM Journal on Scientific Computing},
   Volume = {24},
   Number = {4},
   Pages = {1433-1449},
   Year = {2003},
   ISSN = {1064-8275},
   url = {http://dx.doi.org/10.1137/S1064827501395021},
   Abstract = {In this paper, we describe a numerical method for solving
             the shallow water equations (SWEs) in spherical coordinates.
             The most popular spatial discretization method used in
             global atmospheric models is currently the spectral
             transform method, which generates high-order numerical
             solutions and provides an elegant solution to the pole
             problems induced by a spherical coordinate system. However,
             the spectral transform method requires Legendre transforms,
             which have a computational complexity of script O sign(N 3),
             where N is the number of subintervals in one spatial
             dimension. Thus, high-order finite element methods may be a
             viable alternative. In this implementation, the SWEs are
             discretized in time using the three-level semi-Lagrangian
             semi-implicit method and in space using the cubic spline
             collocation method. Numerical results for the standard SWEs
             test suite [D. L. Williamson et al., J. Comput. Phys., 102
             (1992), pp. 211-224] are presented to demonstrate the
             stability and accuracy of the method. When compared to a
             previously applied Eulerian-based method, our method
             generates solutions with comparable accuracy while allowing
             larger timesteps and thus lower computational
             cost.},
   Doi = {10.1137/S1064827501395021},
   Key = {fds243721}
}

@article{fds243722,
   Author = {Layton, AT and Layton, HE},
   Title = {An efficient numerical method for distributed-loop models of
             the urine concentrating mechanism},
   Journal = {Mathematical Biosciences},
   Volume = {181},
   Number = {2},
   Pages = {111-132},
   Year = {2003},
   url = {http://dx.doi.org/10.1016/S0025-5564(02)00176-1},
   Abstract = {In this study we describe an efficient numerical method,
             based on the semi-Lagrangian (SL) semi-implicit (SI) method
             and Newton's method, for obtaining steady-state (SS)
             solutions of equations arising in distributed-loop models of
             the urine concentrating mechanism. Dynamic formulations of
             these models contain large systems of coupled hyperbolic
             partial differential equations (PDEs). The SL method
             advances the solutions of these PDEs in time by integrating
             backward along flow trajectories, thus allowing large time
             steps while maintaining stability. The SI approach controls
             stiffness arising from transtubular transport terms by
             averaging these terms in time along flow trajectories. An
             approximate SS solution of a dynamic formulation obtained
             via the SLSI method can be used as an initial guess for a
             Newton-type solver, which rapidly converges to a highly
             accurate numerical approximation to the solution of the
             ordinary differential equations that arise in the
             corresponding SS model formulation. In general, it is
             difficult to specify a priori for a Newton-type solver an
             initial guess that falls within the radius of convergence;
             however, the initial guess generated by solving the dynamic
             formulation via the SLSI method can be made sufficiently
             close to the SS solution to avoid numerical instability. The
             combination of the SLSI method and the Newton-type solver
             generates stable and accurate solutions with substantially
             reduced computation times, when compared to previously
             applied dynamic methods. © 2003 Elsevier Science Inc. All
             rights reserved.},
   Doi = {10.1016/S0025-5564(02)00176-1},
   Key = {fds243722}
}

@article{fds304480,
   Author = {Layton, AT and Layton, HE},
   Title = {A region-based model framework for the rat urine
             concentrating mechanism},
   Journal = {Bulletin of Mathematical Biology},
   Volume = {65},
   Number = {5},
   Pages = {859-901},
   Year = {2003},
   url = {http://dx.doi.org/10.1016/S0092-8240(03)00045-4},
   Abstract = {The highly structured organization of tubules and blood
             vessels in the outer medulla of the mammalian kidney is
             believed to result in preferential interactions among
             tubules and vessels; such interactions may promote solute
             cycling and enhance urine concentrating capability. In this
             study, we formulate a new model framework for the urine
             concentrating mechanism in the outer medulla of the rat
             kidney. The model simulates preferential interactions among
             tubules and vessels by representing two concentric regions
             and by specifying the fractions of tubules and vessels
             assigned to each of the regions. The model equations are
             based on standard expressions for transmural transport and
             on solute and water conservation. Model equations, which are
             derived in dynamic form, are solved to obtain steady-state
             solutions by means of a stable and efficient numerical
             method, based on the semi-Lagrangian semi-implicit method
             and on Newton's method. In this application, the
             computational cost scales as [IPQ] (N2), where N is the
             number of spatial subintervals along the medulla. We present
             representative solutions and show that the method generates
             approximations that are second-order accurate in space and
             that exhibit mass conservation. © 2003 Society for
             Mathematical Biology. Published by Elsevier Ltd. All rights
             reserved.},
   Doi = {10.1016/S0092-8240(03)00045-4},
   Key = {fds304480}
}

@article{fds320924,
   Author = {Layton, AT and Moore, LC and Layton, HE},
   Title = {Internephron coupling may contribute to emergence of
             irregular oscillations mediated by tubuloglomerular
             feedback.},
   Journal = {Journal of the American Society of Nephrology :
             JASN},
   Volume = {13},
   Pages = {333A-333A},
   Year = {2002},
   Month = {September},
   Key = {fds320924}
}

@article{fds320925,
   Author = {Layton, AT and Layton, HE},
   Title = {A mathematical model of the urine concentrating mechanism in
             the outer medulla of the rat kidney},
   Journal = {The FASEB journal : official publication of the Federation
             of American Societies for Experimental Biology},
   Volume = {16},
   Number = {4},
   Pages = {A51-A51},
   Year = {2002},
   Month = {March},
   Key = {fds320925}
}

@article{fds243723,
   Author = {Layton, AT and Layton, HE},
   Title = {A numerical method for renal models that represent tubules
             with abrupt changes in membrane properties},
   Journal = {J. Math. Biol.},
   Volume = {45},
   Number = {5},
   Pages = {549-567},
   Year = {2002},
   ISSN = {0303-6812},
   url = {http://dx.doi.org/10.1007/s00285-002-0166-6},
   Abstract = {The urine concentrating mechanism of mammals and birds
             depends on a counterflow configuration of thousands of
             nearly parallel tubules in the medulla of the kidney. Along
             the course of a renal tubule, cell type may change abruptly,
             resulting in abrupt changes in the physical characteristics
             and transmural transport properties of the tubule. A
             mathematical model that faithfully represents these abrupt
             changes will have jump discontinuities in model parameters.
             Without proper treatment, such discontinuities may cause
             unrealistic transmural fluxes and introduce suboptimal
             spatial convergence in the numerical solution to the model
             equations. In this study, we show how to treat discontinuous
             parameters in the context of a previously developed
             numerical method that is based on the semi-Lagrangian
             semi-implicit method and Newton's method. The numerical
             solutions have physically plausible fluxes at the
             discontinuities and the solutions converge at second order,
             as is appropriate for the method. © Springer-Verlag
             2002.},
   Doi = {10.1007/s00285-002-0166-6},
   Key = {fds243723}
}

@article{fds243724,
   Author = {Layton, AT and Panne, MVD},
   Title = {A numerically efficient and stable algorithm for animating
             water waves},
   Journal = {The Visual Computer},
   Volume = {18},
   Number = {1},
   Pages = {41-53},
   Year = {2002},
   ISSN = {0178-2789},
   url = {http://dx.doi.org/10.1007/s003710100131},
   Abstract = {Water motion can be realistically captured by physically
             based fluid models. We begin by presenting a survey on fluid
             simulation models that are based on fluid dynamics
             equations, from the most comprehensive Navier-Stokes
             equations to the simple wave equation. We then present a
             model that is based on the two-dimensional shallow water
             equations. The equations are integrated by a novel numerical
             method - the implicit semi-Lagrangian integration scheme -
             which allows large timesteps while maintaining stability,
             and which is described in detail in this paper. Gentle wave
             motions, the superposition of waves, drifting objects, and
             obstacles and boundaries of various shapes can be
             efficiently simulated with this model.},
   Doi = {10.1007/s003710100131},
   Key = {fds243724}
}

@article{fds243725,
   Author = {Layton, AT and Layton, HE},
   Title = {A semi-Lagrangian semi-implicit numerical method for models
             of the urine concentrating mechanism},
   Journal = {SIAM J. Sci. Comput.},
   Volume = {23},
   Number = {5},
   Pages = {1528-1548},
   Year = {2002},
   ISSN = {1064-8275},
   url = {http://dx.doi.org/10.1137/S1064827500381781},
   Abstract = {Mathematical models of the urine concentrating mechanism
             consist of large systems of coupled differential equations.
             The numerical methods that have usually been used to solve
             the steady-state formulation of these equations involve
             implicit Newton-type solvers that are limited by numerical
             instability attributed to transient flow reversal. Dynamic
             numerical methods, which solve the dynamic formulation of
             the equations by means of a direction-sensitive time
             integration until a steady state is reached, are stable in
             the presence of transient flow reversal. However, when an
             explicit, Eulerian-based dynamic method is used,
             prohibitively small time steps may be required owing to the
             CFL condition and the stiffness of the problem. In this
             report, we describe a semi-Lagrangian semi-implicit (SLSI)
             method for solving the system of hyperbolic partial
             differential equations that arises in the dynamic
             formulation. The semi-Lagrangian scheme advances the
             solution in time by integrating backward along flow
             trajectories, thus allowing large time steps while
             maintaining stability. The semi-implicit approach controls
             stiffness by averaging transtubular transport terms in time
             along flow trajectories. For sufficiently refined spatial
             grids, the SLSI method computes stable and accurate
             solutions with substantially reduced computation
             costs.},
   Doi = {10.1137/S1064827500381781},
   Key = {fds243725}
}

@article{fds243726,
   Author = {Layton, AT},
   Title = {Cubic spline collocation method for the shallow water
             equations on the sphere},
   Journal = {Journal of Computational Physics},
   Volume = {179},
   Number = {2},
   Pages = {578-592},
   Year = {2002},
   ISSN = {0021-9991},
   url = {http://dx.doi.org/10.1006/jcph.2002.7075},
   Abstract = {Spatial discretization schemes commonly used in global
             meteorological applications are currently limited to
             spectral methods or low-order finite-difference/finite-element
             methods. The spectral transform method, which yields
             high-order approximations, requires Legendre transforms,
             which have a computational complexity of O(N3), where N is
             the number of subintervals in one dimension. Thus,
             high-order finite-element methods may be a viable
             alternative to spectral methods. In this study, we present a
             new numerical method for solving the shallow water equations
             (SWE) in spherical coordinates. In this implementation, the
             SWE are discretized in time with the semi-implicit leapfrog
             method, and in space with the cubic spline collocation
             method on a skipped latitude-longitude grid. Numerical
             results for the Williamson et al. SWE test cases [D. L.
             Williamson, J. B. Blake, J. J. Hack, R. Jakob, and P. N.
             Swarztrauber, J. Comput. Phys. 102, 211 (1992)] are
             presented to demonstrate the stability and accuracy of the
             method. Results are also shown for an efficiency comparison
             between this method and a similar method in which spatial
             discretization is done on a uniform latitude-longitude grid.
             © 2002 Elsevier Science (USA).},
   Doi = {10.1006/jcph.2002.7075},
   Key = {fds243726}
}

@article{fds304478,
   Author = {Layton, AT and Layton, HE},
   Title = {A semi-lagrangian semi-implicit numerical method for models
             of the urine concentrating mechanism},
   Journal = {SIAM Journal on Scientific Computing},
   Volume = {23},
   Number = {5},
   Pages = {1526-1548},
   Year = {2002},
   ISSN = {1064-8275},
   url = {http://dx.doi.org/10.1137/S1064827500381781},
   Abstract = {Mathematical models of the urine concentrating mechanism
             consist of large systems of coupled differential equations.
             The numerical methods that have usually been used to solve
             the steady-state formulation of these equations involve
             implicit Newton-type solvers that are limited by numerical
             instability attributed to transient flow reversal. Dynamic
             numerical methods, which solve the dynamic formulation of
             the equations by means of a direction-sensitive time
             integration until a steady state is reached, are stable in
             the presence of transient flow reversal. However, when an
             explicit, Eulerian-based dynamic method is used,
             prohibitively small time steps may be required owing to the
             CFL condition and the stiffness of the problem. In this
             report, we describe a semi-Lagrangian semi-implicit (SLSI)
             method for solving the system of hyperbolic partial
             differential equations that arises in the dynamic
             formulation. The semi-Lagrangian scheme advances the
             solution in time by integrating backward along flow
             trajectories, thus allowing large time steps while
             maintaining stability. The semi-implicit approach controls
             stiffness by averaging transtubular transport terms in time
             along flow trajectories. For sufficiently refined spatial
             grids, the SLSI method computes stable and accurate
             solutions with substantially reduced computation
             costs.},
   Doi = {10.1137/S1064827500381781},
   Key = {fds304478}
}

@article{fds304479,
   Author = {Layton, AT and Layton, HE},
   Title = {A numerical method for renal models that represent tubules
             with abrupt changes in membrane properties},
   Journal = {Journal of Mathematical Biology},
   Volume = {45},
   Number = {6},
   Pages = {549-567},
   Year = {2002},
   ISSN = {0303-6812},
   url = {http://dx.doi.org/10.1007/s00285-002-0166-6},
   Abstract = {The urine concentrating mechanism of mammals and birds
             depends on a counterflow configuration of thousands of
             nearly parallel tubules in the medulla of the kidney. Along
             the course of a renal tubule, cell type may change abruptly,
             resulting in abrupt changes in the physical characteristics
             and transmural transport properties of the tubule. A
             mathematical model that faithfully represents these abrupt
             changes will have jump discontinuities in model parameters.
             Without proper treatment, such discontinuities may cause
             unrealistic transmural fluxes and introduce suboptimal
             spatial convergence in the numerical solution to the model
             equations. In this study, we show how to treat discontinuous
             parameters in the context of a previously developed
             numerical method that is based on the semi-Lagrangian
             semi-implicit method and Newton's method. The numerical
             solutions have physically plausible fluxes at the
             discontinuities and the solutions converge at second order,
             as is appropriate for the method. © Springer-Verlag
             2002.},
   Doi = {10.1007/s00285-002-0166-6},
   Key = {fds304479}
}

@article{fds24339,
   Author = {Anita W. Tam},
   Title = {A two-time-level semi-quadratic spline Galerkin method for
             the shallow water equations},
   Journal = {Proceedings of the 8th Annual Conference of the CFD Society
             of Canada},
   Year = {2000},
   Key = {fds24339}
}


%% Papers Accepted   
@article{fds320880,
   Author = {Layton, AT and Vallon, V and Edwards, A},
   Title = {Predicted consequences of diabetes and SGLT inhibition on
             transport and oxygen consumption along a rat
             nephron.},
   Journal = {American Journal of Physiology: Renal Physiology},
   Volume = {310},
   Number = {11},
   Pages = {F1269-F1283},
   Year = {2016},
   Month = {June},
   url = {http://dx.doi.org/10.1152/ajprenal.00543.2015},
   Abstract = {Diabetes increases the reabsorption of Na(+) (TNa) and
             glucose via the sodium-glucose cotransporter SGLT2 in the
             early proximal tubule (S1-S2 segments) of the renal cortex.
             SGLT2 inhibitors enhance glucose excretion and lower
             hyperglycemia in diabetes. We aimed to investigate how
             diabetes and SGLT2 inhibition affect TNa and sodium
             transport-dependent oxygen consumption [Formula: see text]
             along the whole nephron. To do so, we developed a
             mathematical model of water and solute transport from the
             Bowman space to the papillary tip of a superficial nephron
             of the rat kidney. Model simulations indicate that, in the
             nondiabetic kidney, acute and chronic SGLT2 inhibition
             enhances active TNa in all nephron segments, thereby raising
             [Formula: see text] by 5-12% in the cortex and medulla.
             Diabetes increases overall TNa and [Formula: see text] by
             ∼50 and 100%, mainly because it enhances glomerular
             filtration rate (GFR) and transport load. In diabetes, acute
             and chronic SGLT2 inhibition lowers [Formula: see text] in
             the cortex by ∼30%, due to GFR reduction that lowers
             proximal tubule active TNa, but raises [Formula: see text]
             in the medulla by ∼7%. In the medulla specifically,
             chronic SGLT2 inhibition is predicted to increase [Formula:
             see text] by 26% in late proximal tubules (S3 segments), by
             2% in medullary thick ascending limbs (mTAL), and by 9 and
             21% in outer and inner medullary collecting ducts (OMCD and
             IMCD), respectively. Additional blockade of SGLT1 in S3
             segments enhances glucose excretion, reduces [Formula: see
             text] by 33% in S3 segments, and raises [Formula: see text]
             by <1% in mTAL, OMCD, and IMCD. In summary, the model
             predicts that SGLT2 blockade in diabetes lowers cortical
             [Formula: see text] and raises medullary [Formula: see
             text], particularly in S3 segments.},
   Doi = {10.1152/ajprenal.00543.2015},
   Key = {fds320880}
}

@article{fds320881,
   Author = {Liu, R and Layton, AT},
   Title = {Modeling the effects of positive and negative feedback in
             kidney blood flow control.},
   Journal = {Mathematical Biosciences},
   Volume = {276},
   Pages = {8-18},
   Year = {2016},
   Month = {June},
   url = {http://dx.doi.org/10.1016/j.mbs.2016.02.007},
   Abstract = {Blood flow in the mammalian kidney is tightly autoregulated.
             One of the important autoregulation mechanisms is the
             myogenic response, which is activated by perturbations in
             blood pressure along the afferent arteriole. Another is the
             tubuloglomerular feedback, which is a negative feedback that
             responds to variations in tubular fluid [Cl(-)] at the
             macula densa.(1) When initiated, both the myogenic response
             and the tubuloglomerular feedback adjust the afferent
             arteriole muscle tone. A third mechanism is the connecting
             tubule glomerular feedback, which is a positive feedback
             mechanism located at the connecting tubule, downstream of
             the macula densa. The connecting tubule glomerular feedback
             is much less well studied. The goal of this study is to
             investigate the interactions among these feedback mechanisms
             and to better understand the effects of their interactions.
             To that end, we have developed a mathematical model of
             solute transport and blood flow control in the rat kidney.
             The model represents the myogenic response, tubuloglomerular
             feedback, and connecting tubule glomerular feedback. By
             conducting a bifurcation analysis, we studied the stability
             of the system under a range of physiologically-relevant
             parameters. The bifurcation results were confirmed by means
             of a comparison with numerical simulations. Additionally, we
             conducted numerical simulations to test the hypothesis that
             the interactions between the tubuloglomerular feedback and
             the connecting tubule glomerular feedback may give rise to a
             yet-to-be-explained low-frequency oscillation that has been
             observed in experimental records.},
   Doi = {10.1016/j.mbs.2016.02.007},
   Key = {fds320881}
}

@article{fds303024,
   Author = {Anita T. Layton and Aurelie Edwards},
   Title = {Introduction to mathematical modeling of blood flow control
             in the kidney},
   Booktitle = {AWM proceedings for NIMBioS WS for Women in Mathematical
             Biology},
   Year = {2015},
   Key = {fds303024}
}

@article{fds227201,
   Author = {Veronica Ciocanel and Tracy L. Stepien and Aur´elie Edwards and Anita T. Layton},
   Title = {Modeling autoregulation of the afferent arteriole of the rat
             kidney},
   Journal = {AWM proceedings for NIMBioS WS for Women in Mathematical
             Biology, in press},
   Year = {2015},
   Key = {fds227201}
}

@article{fds227202,
   Author = {Ioannis Sgouralis and Anita T. Layton},
   Title = {Modeling blood flow and oxygenation in a diabetic rat
             kidney},
   Booktitle = {AWM proceedings for NIMBioS WS for Women in Mathematical
             Biology, in press},
   Year = {2015},
   Key = {fds227202}
}

@article{fds227058,
   Author = {Gregory J. Herschlag and Jian-Guo Liu and Anita T.
             Layton},
   Title = {An exact solution for Stokes flow in an infinite channel
             with permeable walls},
   Journal = {SIAM Appl Math, in press},
   Year = {2015},
   Key = {fds227058}
}

@article{fds226985,
   Author = {Tal Burt and Douglas C. Rouse and Kihak Lee and Huali Wu and Anita T.
             Layton and Thomas C. Hawk and Douglas H. Weitzel and Bennett B. Chin and Michael Cohen-Wolkowiez and Shein-Chung Chow and Robert J.
             Noveck},
   Title = {Intra-arterial microdosing (IAM), a novel drug development
             approach,proof of concept in rodents},
   Journal = {CPT: Pharmacometrics and Systems Pharmacology, in
             press},
   Year = {2015},
   Key = {fds226985}
}

@article{fds226210,
   Author = {Ioannis Sgouralis and Anita T. Layton},
   Title = {Conduction of feedback-mediated signal in a computational
             model of coupled nephron},
   Journal = {Med Math Biol, in press},
   Year = {2014},
   Key = {fds226210}
}


%% Papers Submitted   
@article{fds320879,
   Author = {Sgouralis, I and Evans, RG and Layton, AT},
   Title = {Renal medullary and urinary oxygen tension during
             cardiopulmonary bypass in the rat.},
   Journal = {Mathematical Medicine and Biology: A Journal of the
             IMA},
   Volume = {34},
   Number = {3},
   Pages = {313-333},
   Year = {2017},
   Month = {September},
   url = {http://dx.doi.org/10.1093/imammb/dqw010},
   Abstract = {Renal hypoxia could result from a mismatch in renal oxygen
             supply and demand, particularly in the renal medulla.
             Medullary hypoxic damage is believed to give rise to acute
             kidney injury, which is a prevalent complication of cardiac
             surgery performed on cardiopulmonary bypass (CPB). To
             determine the mechanisms that could lead to medullary
             hypoxia during CPB in the rat kidney, we developed a
             mathematical model which incorporates (i) autoregulation of
             renal blood flow and glomerular filtration rate, (ii)
             detailed oxygen transport and utilization in the renal
             medulla and (iii) oxygen transport along the ureter. Within
             the outer medulla, the lowest interstitial tissue P$_{\rm
             O2}$, which is an indicator of renal hypoxia, is predicted
             near the thick ascending limbs. Interstitial tissue P$_{\rm
             O2}$ exhibits a general decrease along the inner medullary
             axis, but urine P$_{\rm O2}$ increases significantly along
             the ureter. Thus, bladder urinary P$_{\rm O2}$ is predicted
             to be substantially higher than medullary P$_{\rm O2}$. The
             model is used to identify the phase of cardiac surgery
             performed on CPB that is associated with the highest risk
             for hypoxic kidney injury. Simulation results indicate that
             the outer medulla's vulnerability to hypoxic injury depends,
             in part, on the extent to which medullary blood flow is
             autoregulated. With imperfect medullary blood flow
             autoregulation, the model predicts that the rewarming phase
             of CPB, in which medullary blood flow is low but medullary
             oxygen consumption remains high, is the phase in which the
             kidney is most likely to suffer hypoxic injury.},
   Doi = {10.1093/imammb/dqw010},
   Key = {fds320879}
}

@article{fds320882,
   Author = {Chen, Y and Fry, BC and Layton, AT},
   Title = {Modeling Glucose Metabolism in the Kidney.},
   Journal = {Bulletin of Mathematical Biology},
   Volume = {78},
   Number = {6},
   Pages = {1318-1336},
   Year = {2016},
   Month = {June},
   url = {http://dx.doi.org/10.1007/s11538-016-0188-7},
   Abstract = {The mammalian kidney consumes a large amount of energy to
             support the reabsorptive work it needs to excrete metabolic
             wastes and to maintain homeostasis. Part of that energy is
             supplied via the metabolism of glucose. To gain insights
             into the transport and metabolic processes in the kidney, we
             have developed a detailed model of the renal medulla of the
             rat kidney. The model represents water and solute flows,
             transmural fluxes, and biochemical reactions in the luminal
             fluid of the nephrons and vessels. In particular, the model
             simulates the metabolism of oxygen and glucose. Using that
             model, we have identified parameters concerning glucose
             transport and basal metabolism that yield predicted blood
             glucose concentrations that are consistent with experimental
             measurements. The model predicts substantial axial gradients
             in blood glucose levels along various medullary structures.
             Furthermore, the model predicts that in the inner medulla,
             owing to the relatively limited blood flow and low tissue
             oxygen tension, anaerobic metabolism of glucose
             dominates.},
   Doi = {10.1007/s11538-016-0188-7},
   Key = {fds320882}
}

@article{fds320883,
   Author = {Nganguia, H and Young, Y-N and Layton, AT and Lai, M-C and Hu,
             W-F},
   Title = {Electrohydrodynamics of a viscous drop with
             inertia.},
   Journal = {Physical review. E},
   Volume = {93},
   Number = {5},
   Pages = {053114},
   Year = {2016},
   Month = {May},
   url = {http://dx.doi.org/10.1103/physreve.93.053114},
   Abstract = {Most of the existing numerical and theoretical
             investigations on the electrohydrodynamics of a viscous drop
             have focused on the creeping Stokes flow regime, where
             nonlinear inertia effects are neglected. In this work we
             study the inertia effects on the electrodeformation of a
             viscous drop under a DC electric field using a novel
             second-order immersed interface method. The inertia effects
             are quantified by the Ohnesorge number Oh, and the electric
             field is characterized by an electric capillary number
             Ca_{E}. Below the critical Ca_{E}, small to moderate
             electric field strength gives rise to steady equilibrium
             drop shapes. We found that, at a fixed Ca_{E}, inertia
             effects induce larger deformation for an oblate drop than a
             prolate drop, consistent with previous results in the
             literature. Moreover, our simulations results indicate that
             inertia effects on the equilibrium drop deformation are
             dictated by the direction of normal electric stress on the
             drop interface: Larger drop deformation is found when the
             normal electric stress points outward, and smaller drop
             deformation is found otherwise. To our knowledge, such
             inertia effects on the equilibrium drop deformation has not
             been reported in the literature. Above the critical Ca_{E},
             no steady equilibrium drop deformation can be found, and
             often the drop breaks up into a number of daughter droplets.
             In particular, our Navier-Stokes simulations show that, for
             the parameters we use, (1) daughter droplets are larger in
             the presence of inertia, (2) the drop deformation evolves
             more rapidly compared to creeping flow, and (3) complex
             distribution of electric stresses for drops with inertia
             effects. Our results suggest that normal electric pressure
             may be a useful tool in predicting drop pinch-off in oblate
             deformations.},
   Doi = {10.1103/physreve.93.053114},
   Key = {fds320883}
}

@article{fds320884,
   Author = {Sgouralis, I and Maroulas, V and Layton, AT},
   Title = {Transfer Function Analysis of Dynamic Blood Flow Control in
             the Rat Kidney.},
   Journal = {Bulletin of Mathematical Biology},
   Volume = {78},
   Number = {5},
   Pages = {923-960},
   Year = {2016},
   Month = {May},
   url = {http://dx.doi.org/10.1007/s11538-016-0168-y},
   Abstract = {Renal blood flow is regulated by the myogenic response (MR)
             and tubuloglomerular feedback (TGF). Both mechanisms
             function to buffer not only steady pressure perturbations
             but also transient ones. In this study, we develop two
             models of renal autoregulation-a comprehensive model and a
             simplified model-and use them to analyze the individual
             contributions of MR and TGF in buffering transient pressure
             perturbations. Both models represent a single nephron of a
             rat kidney together with the associated vasculature. The
             comprehensive model includes detailed representation of the
             vascular properties and cellular processes. In contrast, the
             simplified model represents a minimal set of key processes.
             To assess the degree to which fluctuations in renal
             perfusion pressure at different frequencies are attenuated,
             we derive a transfer function for each model. The transfer
             functions of both models predict resonance at 45 and
             180 mHz, which are associated with TGF and MR,
             respectively, effective autoregulation below [Formula: see
             text]100 mHz, and amplification of pressure perturbations
             above [Formula: see text]200 mHz. The predictions are in
             good agreement with experimental findings.},
   Doi = {10.1007/s11538-016-0168-y},
   Key = {fds320884}
}

@article{fds227194,
   Author = {Gregory Herschlag and Jian-Guo Liu and Anita T.
             Layton},
   Title = {Optimal reservoir conditions for fluid extraction through
             permeable walls in the viscous limit},
   Journal = {Phys Fluids, submitted},
   Year = {2015},
   Key = {fds227194}
}

@article{fds226368,
   Author = {Anita T. Layton},
   Title = {Tracking the distribution of a solute bolus in the rat
             kidney},
   Booktitle = {AWM proceedings for NIMBioS WS for Women in Mathematical
             Biology, submitted},
   Year = {2015},
   Key = {fds226368}
}

@article{fds207970,
   Author = {Gabor E. Linthorst and Lonneke Haer-Wigman and Jeff M. Sands and Janet D. Klein and Tiffany L. Thai and Arthur J. Verhoeven and Rob
             van Zwieten, Maaike C. Jansweijer and Alida C. Knegt and Minke H.
             de Ru and Jaap W. Groothoff and Michael Ludwig and Anita T. Layton and Arend Bökenkamp},
   Title = {Familial azotemia caused by a duplication of the UT-B
             transporter},
   Journal = {J Am Soc Nephrol, submitted},
   Year = {2012},
   Key = {fds207970}
}

 

dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320