%% 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}, 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}, Volume = {79}, Number = {11}, Pages = {2512-2533}, Year = {2017}, Month = {November}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, Doi = {10.4208/cicp.171014.270315a}, Key = {fds300275} } @article{fds320184, Author = {Burt, T and Wu, H and Layton, A and Rouse, D and Chin, B and Hawk, T and Weitzel, D and Cohen-Wolkowiez, M and Chow, S and Noveck, R}, 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}, Doi = {10.1016/j.clinthera.2015.05.122}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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 O_{2}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}, 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 O_{2}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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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}, 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} }