%%
@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 = {25122533},
Year = {2017},
Month = {November},
url = {http://dx.doi.org/10.1007/s1153801703386},
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/s1153801703386},
Key = {fds329189}
}
@article{fds328946,
Author = {Burt, T and Noveck, RJ and MacLeod, DB and Layton, AT and Rowland, M and Lappin, G},
Title = {IntraTarget 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 = {337350},
Year = {2017},
Month = {September},
url = {http://dx.doi.org/10.1111/cts.12464},
Doi = {10.1111/cts.12464},
Key = {fds328946}
}
@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 = {313333},
Year = {2017},
Month = {September},
url = {http://dx.doi.org/10.1093/imammb/dqw010},
Abstract = {Renal hypoxia could result from a mismatch in renal oxygen
supply and demand, particularly in the renal medulla.
Medullary hypoxic damage is believed to give rise to acute
kidney injury, which is a prevalent complication of cardiac
surgery performed on cardiopulmonary bypass (CPB). To
determine the mechanisms that could lead to medullary
hypoxia during CPB in the rat kidney, we developed a
mathematical model which incorporates (i) autoregulation of
renal blood flow and glomerular filtration rate, (ii)
detailed oxygen transport and utilization in the renal
medulla and (iii) oxygen transport along the ureter. Within
the outer medulla, the lowest interstitial tissue P$_{\rm
O2}$, which is an indicator of renal hypoxia, is predicted
near the thick ascending limbs. Interstitial tissue P$_{\rm
O2}$ exhibits a general decrease along the inner medullary
axis, but urine P$_{\rm O2}$ increases significantly along
the ureter. Thus, bladder urinary P$_{\rm O2}$ is predicted
to be substantially higher than medullary P$_{\rm O2}$. The
model is used to identify the phase of cardiac surgery
performed on CPB that is associated with the highest risk
for hypoxic kidney injury. Simulation results indicate that
the outer medulla's vulnerability to hypoxic injury depends,
in part, on the extent to which medullary blood flow is
autoregulated. With imperfect medullary blood flow
autoregulation, the model predicts that the rewarming phase
of CPB, in which medullary blood flow is low but medullary
oxygen consumption remains high, is the phase in which the
kidney is most likely to suffer hypoxic injury.},
Doi = {10.1093/imammb/dqw010},
Key = {fds320879}
}
@article{fds328036,
Author = {Chen, Y and Sullivan, JC and Edwards, A and Layton,
AT},
Title = {Sexspecific 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 = {F174F183},
Year = {2017},
Month = {August},
url = {http://dx.doi.org/10.1152/ajprenal.00482.2016},
Abstract = {The goals of this study were to 1) develop a computational
model of solute transport and oxygenation in the kidney of
the female spontaneously hypertensive rat (SHR), and 2)
apply that model to investigate sex differences in nitric
oxide (NO) levels in SHR and their effects on medullary
oxygenation and oxidative stress. To accomplish these goals,
we first measured NO synthase (NOS) 1 and NOS3 protein
expression levels in total renal microvessels of male and
female SHR. We found that the expression of both NOS1 and
NOS3 is higher in the renal vasculature of females compared
with males. To predict the implications of that finding on
medullary oxygenation and oxidative stress levels, we
developed a detailed computational model of the female SHR
kidney. The model was based on a published male kidney model
and represents solute transport and the biochemical
reactions among O2, NO, and superoxide ([Formula: see text])
in the renal medulla. Model simulations conducted using both
male and female SHR kidney models predicted significant
radial gradients in interstitial fluid oxygen tension (Po2)
and NO and [Formula: see text] concentration in the outer
medulla and upper inner medulla. The models also predicted
that increases in endothelial NOgenerating 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 = {F199F209},
Year = {2017},
Month = {August},
url = {http://dx.doi.org/10.1152/ajprenal.00018.2017},
Abstract = {Removal of renal mass stimulates anatomical and functional
adaptations in the surviving nephrons, including elevations
in singlenephron 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 5/6nephrectomized (5/6NX) rat. Model
simulations indicate that nephrectomyinduced 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 5/6NX models predict urine flow and urinary Na+ and K+
excretions that are similar to sham levels. The models
predict that, in the UNX and 5/6NX 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 5/6NX 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 5/6NX
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 = {116129},
Year = {2017},
Month = {July},
url = {http://dx.doi.org/10.1016/j.mbs.2017.04.008},
Abstract = {The metabolism of glucose provides most of the ATP required
for energydependent 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 = {F671F672},
Year = {2017},
Month = {April},
url = {http://dx.doi.org/10.1152/ajprenal.00648.2016},
Doi = {10.1152/ajprenal.00648.2016},
Key = {fds325778}
}
@article{fds323660,
Author = {Jiang, T and Li, Y and Layton, AT and Wang, W and Sun, Y and Li, M and Zhou,
H and Yang, B},
Title = {Generation and phenotypic analysis of mice lacking all urea
transporters.},
Journal = {Kidney international},
Volume = {91},
Number = {2},
Pages = {338351},
Year = {2017},
Month = {February},
url = {http://dx.doi.org/10.1016/j.kint.2016.09.017},
Abstract = {Urea transporters (UT) are a family of transmembrane
ureaselective 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 allUTknockout
mice. Daily urine output was nearly 3.5fold higher, with
significantly lower urine osmolality in allUTknockout mice
than that in wildtype mice. AllUTknockout 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 UTknockout
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 ureaselective
urineconcentrating 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 = {F1217F1229},
Year = {2016},
Month = {December},
url = {http://dx.doi.org/10.1152/ajprenal.00294.2016},
Abstract = {Sodium and its associated anions are the major determinant
of extracellular fluid volume, and the reabsorption of Na+
by the kidney plays a crucial role in longterm 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 bumetanidesensitive Na+K+2Cl transporter
(NKCC2), the Na+Cl cotransporter (NCC), and the
amiloridesensitive 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 ). Wholekidney 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 wholekidney 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 wholekidney 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 wholekidney
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 = {F1378F1390},
Year = {2016},
Month = {December},
url = {http://dx.doi.org/10.1152/ajprenal.00293.2016},
Abstract = {The goal of this study was to investigate water and solute
transport, with a focus on sodium transport (TNa) and
metabolism along individual nephron segments under differing
physiological and pathophysiological conditions. To
accomplish this goal, we developed a computational model of
solute transport and oxygen consumption (QO2 ) along
different nephron populations of a rat kidney. The model
represents detailed epithelial and paracellular transport
processes along both the superficial and juxtamedullary
nephrons, with the loop of Henle of each model nephron
extending to differing depths of the inner medulla. We used
the model to assess how changes in TNa may alter QO2 in
different nephron segments and how shifting the TNa sites
alters overall kidney QO2 Under baseline conditions, the
model predicted a whole kidney TNa/QO2 , which denotes the
number of moles of Na+ reabsorbed per moles of O2 consumed,
of ∼15, with TNa efficiency predicted to be significantly
greater in cortical nephron segments than in medullary
segments. The TNa/QO2 ratio was generally similar among the
superficial and juxtamedullary nephron segments, except for
the proximal tubule, where TNa/QO2 was ∼20% higher in
superficial nephrons, due to the larger luminal flow along
the juxtamedullary proximal tubules and the resulting
higher, flowinduced transcellular transport. Moreover, the
model predicted that an increase in singlenephron
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
flowinduced 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 = {R532R544},
Year = {2016},
Month = {September},
url = {http://dx.doi.org/10.1152/ajpregu.00195.2016},
Abstract = {Oxygen tension (Po2) of urine in the bladder could be used
to monitor risk of acute kidney injury if it varies with
medullary Po2 Therefore, we examined this relationship and
characterized oxygen diffusion across walls of the ureter
and bladder in anesthetized rabbits. A computational model
was then developed to predict medullary Po2 from bladder
urine Po2 Both intravenous infusion of [Phe(2),Ile(3),Orn(8)]vasopressin
and infusion of N(G)nitrolarginine reduced urinary Po2
and medullary Po2 (817%), 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 (withinrabbit r(2) = 0.870.90). 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
(0.10.5 ml/min for a single kidney), a change in bladder
urine Po2 explains 1050% 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 realtime 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 = {F162F165},
Year = {2016},
Month = {July},
url = {http://dx.doi.org/10.1152/ajprenal.00228.2016},
Abstract = {The availability of oxygen in renal tissue is determined by
the complex interactions among a host of processes,
including renal blood flow, glomerular filtration,
arterialtovenous 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{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 = {F1269F1283},
Year = {2016},
Month = {June},
url = {http://dx.doi.org/10.1152/ajprenal.00543.2015},
Abstract = {Diabetes increases the reabsorption of Na(+) (TNa) and
glucose via the sodiumglucose cotransporter SGLT2 in the
early proximal tubule (S1S2 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
transportdependent 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 512% 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 = {818},
Year = {2016},
Month = {June},
url = {http://dx.doi.org/10.1016/j.mbs.2016.02.007},
Abstract = {Blood flow in the mammalian kidney is tightly autoregulated.
One of the important autoregulation mechanisms is the
myogenic response, which is activated by perturbations in
blood pressure along the afferent arteriole. Another is the
tubuloglomerular feedback, which is a negative feedback that
responds to variations in tubular fluid [Cl()] at the
macula densa.(1) When initiated, both the myogenic response
and the tubuloglomerular feedback adjust the afferent
arteriole muscle tone. A third mechanism is the connecting
tubule glomerular feedback, which is a positive feedback
mechanism located at the connecting tubule, downstream of
the macula densa. The connecting tubule glomerular feedback
is much less well studied. The goal of this study is to
investigate the interactions among these feedback mechanisms
and to better understand the effects of their interactions.
To that end, we have developed a mathematical model of
solute transport and blood flow control in the rat kidney.
The model represents the myogenic response, tubuloglomerular
feedback, and connecting tubule glomerular feedback. By
conducting a bifurcation analysis, we studied the stability
of the system under a range of physiologicallyrelevant
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
yettobeexplained lowfrequency oscillation that has been
observed in experimental records.},
Doi = {10.1016/j.mbs.2016.02.007},
Key = {fds320881}
}
@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 = {13181336},
Year = {2016},
Month = {June},
url = {http://dx.doi.org/10.1007/s1153801601887},
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/s1153801601887},
Key = {fds320882}
}
@article{fds320883,
Author = {Nganguia, H and Young, YN and Layton, AT and Lai, MC and Hu,
WF},
Title = {Electrohydrodynamics of a viscous drop with
inertia.},
Journal = {Physical review. E},
Volume = {93},
Number = {5},
Pages = {053114},
Year = {2016},
Month = {May},
url = {http://dx.doi.org/10.1103/physreve.93.053114},
Abstract = {Most of the existing numerical and theoretical
investigations on the electrohydrodynamics of a viscous drop
have focused on the creeping Stokes flow regime, where
nonlinear inertia effects are neglected. In this work we
study the inertia effects on the electrodeformation of a
viscous drop under a DC electric field using a novel
secondorder 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 NavierStokes 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 pinchoff 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 = {923960},
Year = {2016},
Month = {May},
url = {http://dx.doi.org/10.1007/s115380160168y},
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 autoregulationa comprehensive model and a
simplified modeland 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/s115380160168y},
Key = {fds320884}
}
@article{fds320180,
Author = {Herschlag, G and Liu, JG and Layton, AT},
Title = {Fluid extraction across pumping and permeable walls in the
viscous limit},
Journal = {Physics of Fluids},
Volume = {28},
Number = {4},
Pages = {041902041902},
Year = {2016},
Month = {April},
url = {http://dx.doi.org/10.1063/1.4946005},
Doi = {10.1063/1.4946005},
Key = {fds320180}
}
@article{fds320885,
Author = {Sgouralis, I and Layton, AT},
Title = {Conduction of feedbackmediated signal in a computational
model of coupled nephrons.},
Journal = {Mathematical Medicine and Biology: A Journal of the
IMA},
Volume = {33},
Number = {1},
Pages = {87106},
Year = {2016},
Month = {March},
url = {http://dx.doi.org/10.1093/imammb/dqv005},
Abstract = {The nephron in the kidney regulates its fluid flow by
several autoregulatory mechanisms. Two primary mechanisms
are the myogenic response and the tubuloglomerular feedback
(TGF). The myogenic response is a property of the
preglomerular 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 preglomerular vasculature.
To better understand the conduction of these signals along
the preglomerular 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
TGFmediated flow oscillations. Simulation results suggest
that reduced gapjunctional conductances may yield stronger
internephron TGF coupling and highly irregular TGFmediated
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 nitricoxidemediated vasodilation and oxidative
stress on renal medullary oxygenation: a modeling
study.},
Journal = {American Journal of Physiology: Renal Physiology},
Volume = {310},
Number = {3},
Pages = {F237F247},
Year = {2016},
Month = {February},
url = {http://dx.doi.org/10.1152/ajprenal.00334.2015},
Abstract = {The goal of this study was to investigate the effects of
nitric oxide (NO)mediated vasodilation in preventing
medullary hypoxia, as well as the likely pathways by which
superoxide (O2()) conversely enhances medullary hypoxia. To
do so, we expanded a previously developed mathematical model
of solute transport in the renal medulla that accounts for
the reciprocal interactions among oxygen (O2), NO, and O2()
to include the vasoactive effects of NO on medullary
descending vasa recta. The model represents the radial
organization of the vessels and tubules, centered around
vascular bundles in the outer medulla and collecting ducts
in the inner medulla. Model simulations suggest that NO
helps to prevent medullary hypoxia both by inducing
vasodilation of the descending vasa recta (thus increasing
O2 supply) and by reducing the active sodium transport rate
(thus reducing O2 consumption). That is, the vasodilative
properties of NO significantly contribute to maintaining
sufficient medullary oxygenation. The model further predicts
that a reduction in tubular transport efficiency (i.e., the
ratio of active sodium transport per O2 consumption) is the
main factor by which increased O2() levels lead to hypoxia,
whereas hyperfiltration is not a likely pathway to medullary
hypoxia due to oxidative stress. Finally, our results
suggest that further increasing the radial separation
between vessels and tubules would reduce the diffusion of NO
towards descending vasa recta in the inner medulla, thereby
diminishing its vasoactive effects therein and reducing O2
delivery to the papillary tip.},
Doi = {10.1152/ajprenal.00334.2015},
Key = {fds320886}
}
@article{fds320181,
Author = {Xie, L and Layton, AT and Wang, N and Larson, PEZ and Zhang, JL and Lee,
VS and Liu, C and Johnson, GA},
Title = {Dynamic contrastenhanced quantitative susceptibility
mapping with ultrashort echo time MRI for evaluating renal
function.},
Journal = {American Journal of Physiology: Renal Physiology},
Volume = {310},
Number = {2},
Pages = {F174F182},
Year = {2016},
Month = {January},
url = {http://dx.doi.org/10.1152/ajprenal.00351.2015},
Abstract = {Dynamic contrastenhanced (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 17wk course (3, 5, 7, 9, 13,
17 wk of age). We conclude that the UTEbased 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 CohenWolkowiez, M and Chow, SC and Noveck, RJ},
Title = {Intraarterial Microdosing: A Novel Drug Development
Approach, ProofofConcept PET Study in Rats.},
Journal = {Journal of nuclear medicine : official publication, Society
of Nuclear Medicine},
Volume = {56},
Number = {11},
Pages = {17931799},
Year = {2015},
Month = {November},
url = {http://dx.doi.org/10.2967/jnumed.115.160986},
Abstract = {Intraarterial microdosing (IAM) is a novel drug development
approach combining intraarterial drug delivery and
microdosing. We aimed to demonstrate that IAM leads to
target exposure similar to that of systemic fulldose
administration but with minimal systemic exposure. IAM could
enable the safe, inexpensive, and early study of novel drugs
at the firstinhuman 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 60min
(18)FFDG uptake PET imaging of ipsilateral and
contralateral leg muscles (lateral gastrocnemius) and
systemic muscles (spinotrapezius). The (18)FFDG 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)FFDG slope
analysis found no difference between IAM and systemic
fulldose 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, 0.0230.058;
P = 0.0052). The pharmacokinetics/pharmacodynamics data were
used to identify model parameters that describe membrane
insulin binding and glucoseinsulin 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 wholebody 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 CohenWolkowiez, M and Chow, SC and Noveck, RJ},
Title = {Intraarterial Microdosing: A Novel Drug Development
Approach, ProofofConcept PET Study in Rats},
Journal = {Journal of nuclear medicine : official publication, Society
of Nuclear Medicine},
Volume = {56},
Number = {11},
Pages = {17931799},
Year = {2015},
Month = {November},
url = {http://dx.doi.org/10.2967/jnumed.115.160986},
Doi = {10.2967/jnumed.115.160986},
Key = {fds320183}
}
@article{fds300274,
Author = {Layton, AT and Edwards, A},
Title = {Predicted effects of nitric oxide and superoxide on the
vasoactivity of the afferent arteriole.},
Journal = {American Journal of Physiology: Renal Physiology},
Volume = {309},
Number = {8},
Pages = {F708F719},
Year = {2015},
Month = {October},
ISSN = {1931857X},
url = {http://dx.doi.org/10.1152/ajprenal.00187.2015},
Abstract = {We expanded a published mathematical model of an afferent
arteriole smooth muscle cell in rat kidney (Edwards A,
Layton, AT. Am J Physiol Renal Physiol 306: F34F48, 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 pressureinduced increases in O(2)()
production, O(2)()mediated regulation of Ltype 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, YN and Layton, AT and Hu, WF and Lai,
MC},
Title = {An Immersed Interface Method for Axisymmetric
Electrohydrodynamic Simulations in Stokes
flow},
Journal = {Communications in computational physics},
Volume = {18},
Number = {02},
Pages = {429449},
Year = {2015},
Month = {August},
ISSN = {18152406},
url = {http://dx.doi.org/10.4208/cicp.171014.270315a},
Doi = {10.4208/cicp.171014.270315a},
Key = {fds300275}
}
@article{fds320184,
Author = {Burt, T and Wu, H and Layton, A and Rouse, D and Chin, B and Hawk, T and Weitzel, D and CohenWolkowiez, M and Chow, S and Noveck,
R},
Title = {IntraArterial Microdosing (IAM), a novel Drug development
approach, proof of concept in Rats},
Journal = {Clinical Therapeutics},
Volume = {37},
Number = {8},
Pages = {e40e41},
Year = {2015},
Month = {August},
url = {http://dx.doi.org/10.1016/j.clinthera.2015.05.122},
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 = {820},
Year = {2015},
Month = {June},
ISSN = {00255564},
url = {http://dx.doi.org/10.1016/j.mbs.2015.02.016},
Abstract = {In addition to the excretion of metabolic waste and toxin,
the kidney plays an indispensable role in regulating the
balance of water, electrolyte, acidbase, 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 = {F1343F1357},
Year = {2015},
Month = {June},
ISSN = {1931857X},
url = {http://dx.doi.org/10.1152/ajprenal.00007.2015},
Abstract = {The objective of this study was to investigate how
physiological, pharmacological, and pathological conditions
that alter sodium reabsorption (TNa) in the proximal tubule
affect oxygen consumption (QO2 ) and Na(+) transport
efficiency (TNa/QO2 ). To do so, we expanded a mathematical
model of solute transport in the proximal tubule of the rat
kidney. The model represents compliant S1, S2, and S3
segments and accounts for their specific apical and
basolateral transporters. Sodium is reabsorbed
transcellularly, via apical Na(+)/H(+) exchangers (NHE) and
Na(+)glucose (SGLT) cotransporters, and paracellularly. Our
results suggest that TNa/QO2 is 80% higher in S3 than in
S1S2 segments, due to the greater contribution of the
passive paracellular pathway to TNa in the former segment.
Inhibition of NHE or NaKATPase 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
S1S2 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 = {F951F955},
Year = {2015},
Month = {May},
ISSN = {1931857X},
url = {http://dx.doi.org/10.1152/ajprenal.00008.2015},
Abstract = {It has been long known that the kidney plays an essential
role in the control of body fluids and blood pressure and
that impairment of renal function may lead to the
development of diseases such as hypertension (Guyton AC,
Coleman TG, Granger Annu Rev Physiol 34: 1346, 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 = {F967F980},
Year = {2015},
Month = {May},
ISSN = {1931857X},
url = {http://dx.doi.org/10.1152/ajprenal.00600.2014},
Abstract = {The goal of this study was to investigate the reciprocal
interactions among oxygen (O2), nitric oxide (NO), and
superoxide (O2 ()) and their effects on medullary
oxygenation and urinary output. To accomplish that goal, we
developed a detailed mathematical model of solute transport
in the renal medulla of the rat kidney. The model represents
the radial organization of the renal tubules and vessels,
which centers around the vascular bundles in the outer
medulla and around clusters of collecting ducts in the inner
medulla. Model simulations yield significant radial
gradients in interstitial fluid oxygen tension (Po2) and NO
and O2 () concentration in the OM and upper IM. In the deep
inner medulla, interstitial fluid concentrations become much
more homogeneous, as the radial organization of tubules and
vessels is not distinguishable. The model further predicts
that due to the nonlinear interactions among O2, NO, and O2
(), the effects of NO and O2 () on sodium transport,
osmolality, and medullary oxygenation cannot be gleaned by
considering each solute's effect in isolation. An additional
simulation suggests that a sufficiently large reduction in
tubular transport efficiency may be the key contributing
factor, more so than oxidative stress alone, to
hypertensioninduced medullary hypoxia. Moreover, model
predictions suggest that urine Po2 could serve as a
biomarker for medullary hypoxia and a predictor of the risk
for hospitalacquired 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 = {169179},
Year = {2015},
Month = {May},
url = {http://dx.doi.org/10.1016/j.mbs.2015.02.015},
Abstract = {Renal blood flow is maintained within a narrow window by a
set of intrinsic autoregulatory mechanisms. Here, a
mathematical model of renal hemodynamics control in the rat
kidney is used to understand the interactions between two
major renal autoregulatory mechanisms: the myogenic response
and tubuloglomerular feedback. A bifurcation analysis of the
model equations is performed to assess the effects of the
delay and sensitivity of the feedback system and the time
constants governing the response of vessel diameter and
smooth muscle tone. The results of the bifurcation analysis
are verified using numerical simulations of the full
nonlinear model. Both the analytical and numerical results
predict the generation of limit cycle oscillations under
certain physiologically relevant conditions, as observed in
vivo.},
Doi = {10.1016/j.mbs.2015.02.015},
Key = {fds320887}
}
@article{fds320888,
Author = {Sgouralis, I and Evans, RG and Gardiner, BS and Smith, JA and Fry, BC and Layton, AT},
Title = {Renal hemodynamics, function, and oxygenation during cardiac
surgery performed on cardiopulmonary bypass: a modeling
study.},
Journal = {Physiological Reports},
Volume = {3},
Number = {1},
Year = {2015},
Month = {January},
url = {http://dx.doi.org/10.14814/phy2.12260},
Abstract = {Acute kidney injury, a prevalent complication of cardiac
surgery performed on cardiopulmonary bypass (CPB), is
thought to be driven partly by hypoxic damage in the renal
medulla. To determine the causes of medullary hypoxia during
CPB, we modeled its impact on renal hemodynamics and
function, and thus oxygen delivery and consumption in the
renal medulla. The model incorporates autoregulation of
renal blood flow and glomerular filtration rate and the
utilization of oxygen for tubular transport. The model
predicts that renal medullary oxygen delivery and
consumption are reduced by a similar magnitude during the
hypothermic (down to 28°C) phase of CPB. Thus, the
fractional extraction of oxygen in the medulla, an index of
hypoxia, is increased only by 58% from baseline. However,
during the rewarming phase (up to 37°C), oxygen consumption
by the medullary thick ascending limb increases 2.3fold but
medullary oxygen delivery increases only by 33%.
Consequently, the fractional extraction of oxygen in the
medulla is increased 2.7fold 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 = {2015June},
Year = {2015},
Month = {January},
ISBN = {9781450335638},
Key = {fds299957}
}
@article{fds320185,
Author = {Herschlag, G and Liu, JG 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 = {22462267},
Year = {2015},
Month = {January},
url = {http://dx.doi.org/10.1137/140995854},
Doi = {10.1137/140995854},
Key = {fds320185}
}
@article{fds227194,
Author = {Gregory Herschlag and JianGuo 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{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 JianGuo 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{fds226446,
Author = {Anita T. Layton},
Title = {Mathematical physiology},
Booktitle = {Princeton Companion to Applied Mathematics},
Editor = {Nicholas J. Higham},
Year = {2015},
ISBN = {9780691150390},
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 = {5573},
Booktitle = {The IMA Volumes in Mathematics and its Applications:
Applications of Dynamical Systems in Biology and
Medicine},
Year = {2015},
Key = {fds226967}
}
@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 CohenWolkowiez and SheinChung Chow and Robert J.
Noveck},
Title = {Intraarterial 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{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{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 = {6876},
Year = {2014},
Month = {December},
ISSN = {00255564},
url = {http://dx.doi.org/10.1016/j.mbs.2014.09.009},
Abstract = {We have developed a highly detailed mathematical model of
oxygen transport in a cross section of the upper inner
medulla of the rat kidney. The model is used to study the
impact of the structured organization of nephrons and
vessels revealed in anatomic studies, in which descending
vasa recta are found to lie distant from clusters of
collecting ducts. Specifically, we formulated a
twodimensional 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,
Threedimensional architecture of inner medullary vasa
recta, Am. J. Physiol. Renal Physiol. 290 (2006)
F1355F1366). 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 = {F649F655},
Year = {2014},
Month = {September},
ISSN = {1931857X},
url = {http://dx.doi.org/10.1152/ajprenal.00276.2014},
Abstract = {Renal medullary function is characterized by
corticopapillary concentration gradients of various
molecules. One example is the generally decreasing axial
gradient in oxygen tension (Po2). Another example, found in
animals in the antidiuretic state, is a generally increasing
axial solute gradient, consisting mostly of NaCl and urea.
This osmolality gradient, which plays a principal role in
the urine concentrating mechanism, is generally considered
to involve countercurrent multiplication and countercurrent
exchange, although the underlying mechanism is not fully
understood. Radial oxygen and solute gradients in the
transverse dimension of the medullary parenchyma have been
hypothesized to occur, although strong experimental evidence
in support of these gradients remains lacking. This review
considers anatomic features of the renal medulla that may
impact the formation and maintenance of oxygen and solute
gradients. A better understanding of medullary architecture
is essential for more clearly defining the
compartmenttocompartment 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 threedimensional architecture on
oxygen transport.},
Journal = {American Journal of Physiology: Renal Physiology},
Volume = {307},
Number = {3},
Pages = {F263F272},
Year = {2014},
Month = {August},
ISSN = {1931857X},
url = {http://dx.doi.org/10.1152/ajprenal.00149.2014},
Abstract = {We have developed a highly detailed mathematical model of
solute transport in the renal medulla of the rat kidney to
study the impact of the structured organization of nephrons
and vessels revealed in anatomic studies. The model
represents the arrangement of tubules around a vascular
bundle in the outer medulla and around a collecting duct
cluster in the upper inner medulla. Model simulations yield
marked gradients in intrabundle and interbundle interstitial
fluid oxygen tension (PO2), NaCl concentration, and
osmolality in the outer medulla, owing to the vigorous
active reabsorption of NaCl by the thick ascending limbs. In
the inner medulla, where the thin ascending limbs do not
mediate significant active NaCl transport, interstitial
fluid composition becomes much more homogeneous with respect
to NaCl, urea, and osmolality. Nonetheless, a substantial
PO2 gradient remains, owing to the relatively high oxygen
demand of the inner medullary collecting ducts. Perhaps more
importantly, the model predicts that in the absence of the
threedimensional 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
threedimensional 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 = {F137F146},
Year = {2014},
Month = {July},
ISSN = {1931857X},
url = {http://dx.doi.org/10.1152/ajprenal.00158.2014},
Abstract = {This study aims to understand the extent to which modulation
of the Na(+)K(+)2Cl() cotransporter NKCC2 differential
splicing affects NaCl delivery to the macula densa. NaCl
absorption by the thick ascending limb and macula densa
cells is mediated by apical NKCC2. A recent study has
indicated that differential splicing of NKCC2 is modulated
by dietary salt (Schieβl IM, Rosenauer A, Kattler V, Minuth
WW, Oppermann M, Castrop H. Am J Physiol Renal Physiol 305:
F1139F1148, 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: F525F542, 2010).
The macula densa model predicts a 27.4 and 13.1mV
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 NKCC2A to NKCC2B
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 lowsalt 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 = {F1357F1371},
Year = {2014},
Month = {June},
ISSN = {1931857X},
url = {http://dx.doi.org/10.1152/ajprenal.00649.2013},
Abstract = {A mathematical model of renal hemodynamics was used to
assess the individual contributions of the tubuloglomerular
feedback (TGF) mechanism and the myogenic response to
glomerular filtration rate regulation in the rat kidney. The
model represents an afferent arteriole segment, glomerular
filtration, and a short loop of Henle. The afferent
arteriole model exhibits myogenic response, which is
activated by hydrostatic pressure variations to induce
changes in membrane potential and vascular muscle tone. The
tubule model predicts tubular fluid and Cl() transport.
Macula densa Cl() concentration is sensed as the signal for
TGF, which acts to constrict or dilate the afferent
arteriole. With this configuration, the model afferent
arteriole maintains stable glomerular filtration rate within
a physiologic range of perfusion pressure (80180 mmHg). The
contribution of TGF to overall autoregulation is significant
only within a narrow band of perfusion pressure values
(80110 mmHg). Model simulations of ramplike 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: 22532262, 2001), which
indicate that changes in vascular conductance are markedly
sensitive to pressure velocity. That asymmetric response is
attributed to the ratedependent kinetics of the myogenic
mechanism. Moreover, simulations of renal autoregulation in
diabetes mellitus predict that, due to the impairment of the
voltagegated Ca(2+) channels of the afferent arteriole
smooth muscle cells, the perfusion pressure range in which
singlenephron 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 = {F952F969},
Year = {2014},
Month = {May},
ISSN = {1931857X},
url = {http://dx.doi.org/10.1152/ajprenal.00500.2013},
Abstract = {We have developed a whole kidney model of the urine
concentrating mechanism and renal autoregulation. The model
represents the tubuloglomerular feedback (TGF) and myogenic
mechanisms, which together affect the resistance of the
afferent arteriole and thus glomerular filtration rate. TGF
is activated by fluctuations in macula densa [Cl()] and the
myogefnic mechanism by changes in hydrostatic pressure. The
model was used to investigate the relative contributions of
medullary blood flow autoregulation and inhibition of
transport in the proximal convoluted tubule to pressure
natriuresis in both diuresis and antidiuresis. The model
predicts that medullary blood flow autoregulation, which
only affects the interstitial solute composition in the
model, has negligible influence on the rate of NaCl
excretion. However, it exerts a significant effect on urine
flow, particularly in the antidiuretic kidney. This suggests
that interstitial washout has significant implications for
the maintenance of hydration status but little direct
bearing on salt excretion, and that medullary blood flow may
only play a signaling role for stimulating a
pressurenatriuresis 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
(NMTMA)},
Volume = {7},
Number = {4},
Pages = {555574},
Year = {2014},
Month = {January},
ISSN = {10048979},
url = {http://dx.doi.org/10.4208/nmtma.2014.1303si},
Abstract = {©2014 GlobalScience 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 NavierStokes 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 secondorder 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 NavierStokes equations with a continuous body
force, is regular. The equations describing the remainder
part are discretized in time using the semiLagrangian
approach, and then solved using a pressurefree projection
method. Numerical results indicate that the computed overall
solution is secondorder accurate in space, and the velocity
is secondorder 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 = {SubCellular Biochemistry},
Volume = {73},
Pages = {3143},
Booktitle = {Urea Transporters},
Publisher = {Springer},
Editor = {Baoxue Yang},
Year = {2014},
Month = {January},
ISSN = {03060225},
url = {http://dx.doi.org/10.1007/9789401793438_3},
Abstract = {Mathematical modeling techniques have been useful in
providing insights into biological systems, including the
kidney. This article considers some of the mathematical
models that concern urea transport in the kidney. Modeling
simulations have been conducted to investigate, in the
context of urea cycling and urine concentration, the effects
of hypothetical active urea secretion into pars recta.
Simulation results suggest that active urea secretion
induces a "ureaselective" 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 = {10.1007/9789401793438_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 = {F34F48},
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
pressureinduced changes in the activity of nonselective
cation channels. Our model predicts spontaneous vasomotion
at physiological luminal pressures and KCl and
diltiazeminduced diameter changes comparable to
experimental findings. The timeperiodic 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 voltageactivated Ltype
channels; blocking sarco/endoplasmic reticulum Ca(2+) pumps,
ryanodine receptors (RyR), KCa, ClCa, or Ltype channels
abolishes these oscillations. Our results indicate that the
profile of the myogenic response is also strongly dependent
on the conductance of ClCa and Ltype 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 Ltype 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:
13161324, 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 = {10231049},
Year = {2014},
Month = {January},
ISSN = {03036812},
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 outerstripe 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, timeindependent steadystate 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 limitcycle
oscillations results in increases in the timeaveraged
distal NaCl delivery, whereas distal fluid delivery is not
much affected. © 2013 SpringerVerlag Berlin
Heidelberg.},
Doi = {10.1007/s0028501306675},
Key = {fds243633}
}
@article{fds226210,
Author = {Ioannis Sgouralis and Anita T. Layton},
Title = {Conduction of feedbackmediated signal in a computational
model of coupled nephron},
Journal = {Med Math Biol, in press},
Year = {2014},
Key = {fds226210}
}
@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}
}
@article{fds320889,
Author = {Layton, AT},
Title = {Impacts of Facilitated Urea Transporters on the
UrineConcentrating Mechanism in the Rat
Kidney},
Journal = {Contemporary Mathematics},
Volume = {628},
Pages = {191208},
Year = {2014},
ISBN = {9780821898505},
url = {http://dx.doi.org/10.1090/conm/628/12518},
Doi = {10.1090/conm/628/12518},
Key = {fds320889}
}
@article{fds320890,
Author = {Ryu, H and Layton, AT},
Title = {FeedbackMediated Dynamics in a Model of Coupled Nephrons
with Compliant Short Loop of Henle},
Journal = {Contemporary Mathematics},
Volume = {628},
Pages = {209238},
Year = {2014},
ISBN = {9780821898505},
url = {http://dx.doi.org/10.1090/conm/628/12542},
Doi = {10.1090/conm/628/12542},
Key = {fds320890}
}
@article{fds320891,
Author = {Olson, SD and Layton, AT},
Title = {Simulating BiofluidStructure Interactions with an Immersed
Boundary Framework  A Review},
Journal = {Contemporary Mathematics},
Volume = {628},
Pages = {136},
Year = {2014},
ISBN = {9780821898505},
url = {http://dx.doi.org/10.1090/conm/628/12545},
Doi = {10.1090/conm/628/12545},
Key = {fds320891}
}
@article{fds243628,
Author = {Li, Y and Williams, SA and Layton, AT},
Title = {A hybrid immersed interface method for driven stokes flow in
an elastic tube},
Journal = {Numerical Mathematics: Theory, Methods and Applications
(NMTMA)},
Volume = {6},
Number = {4},
Pages = {600616},
Year = {2013},
Month = {November},
ISSN = {10048979},
url = {http://dx.doi.org/10.4208/nmtma.2013.1219nm},
Abstract = {We present a hybrid numerical method for simulating fluid
flow through a compliant, closed tube, driven by an internal
source and sink. Fluid is assumed to be highly viscous with
its motion described by Stokes flow. Model geometry is
assumed to be axisymmetric, and the governing equations are
implemented in axisymmetric cylindrical coordinates, which
capture 3D flow dynamics with only 2D computations. We solve
the model equations using a hybrid approach: we decompose
the pressure and velocity fields into parts due to the
surface forcings and due to the source and sink, with each
part handled separately by means of an appropriate method.
Because the singularlysupported 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 secondorder accuracy of the
method. © 2013 GlobalScience Press.},
Doi = {10.4208/nmtma.2013.1219nm},
Key = {fds243628}
}
@article{fds320892,
Author = {Layton, AT and Bankir, L},
Title = {Impacts of Active Urea Secretion into Pars Recta on Urine
Concentration and Urea Excretion Rate.},
Journal = {Physiological Reports},
Volume = {1},
Number = {3},
Pages = {e00034},
Year = {2013},
Month = {September},
url = {http://dx.doi.org/10.1002/phy2.34},
Abstract = {It has been observed experimentally that early distal
tubular urea flow exceeds urea delivery by the proximal
convoluted tubule to the pars recta and loop of Henle.
Moreover, the fractional excretion of urea in the urine may
exceed values compatible with the reabsorption known to
occur in the proximal convoluted tubule in the cortex. A
likely explanation for these observations is that urea may
be actively secreted into the pars recta, as proposed in a
few studies. However, this hypothesis has yet to be
demonstrated experimentally. In this study, we used a
mathematical model of the renal medulla of the rat kidney to
investigate the impacts of active urea secretion in the
intrarenal handling of urea and in the urine concentrating
ability. The model represents only the outer and inner
medullary zones, with the actions taking place in the cortex
incorporated via boundary conditions. Blood flow in the
model vasculature is divided into plasma and red blood cell
compartments. We compared urea flow rates and other related
model variables without and with the hypothetical active
urea secretion in the pars recta. The simulation suggests
that active urea secretion induces a "ureaselective"
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 = {557573},
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 acidbase. 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 feedbackmediated
dynamics of a model of a thick ascending
limb.},
Journal = {Mathematical Medicine and Biology: A Journal of the
IMA},
Volume = {30},
Number = {3},
Pages = {191212},
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 TGFmediated 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
TGFmediated 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 = {HaerWigman, 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 = {3031},
Year = {2013},
Month = {June},
Key = {fds320893}
}
@article{fds243632,
Author = {NievesGonzález, 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 = {F653F664},
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 quasiuniform, 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 FluidStructure Interactions  A
Review},
Journal = {AMS Contemporary Mathematics, Biological Fluid Dynamics:
Modeling, Computations, and Applications},
Volume = {628},
Number = {136},
Year = {2013},
Key = {fds225252}
}
@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}
}
@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 = {187202},
Year = {2013},
ISSN = {00219991},
url = {http://dx.doi.org/10.1016/j.jcp.2012.09.035},
Abstract = {We introduce a regularization method that gives a smooth
formulation for the fundamental solution to Stokes flow
driven by an infinite, triplyperiodic 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 L2norm. 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 = {25512574},
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 = {F229F239},
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 voltagegated
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: 493501,
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 = {19982013},
Year = {2012},
Month = {May},
url = {http://www.ncbi.nlm.nih.gov/pubmed/22438587},
Abstract = {The establishment of cell polarity involves
positivefeedback 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 positivefeedback
loops, one operating as a diffusionbased system, and the
other involving actindirected trafficking of Cdc42p on
vesicles. Factin (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
reactiondiffusion and vesicletrafficking 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 vesiclemediated
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.E11100837},
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 = {F1188F1202},
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
TGFmediated 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 TGFmediated 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 = {F830F839},
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 steadystate 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 UreaNa
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 ureaNa+
cotransporter.},
Journal = {American journal of physiology. Renal physiology},
Volume = {302},
Number = {5},
Pages = {F591F605},
Year = {2012},
Month = {March},
url = {http://www.ncbi.nlm.nih.gov/pubmed/22088433},
Abstract = {We extended a regionbased 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 aquaporin1 null segment of the long
descending thin limbs may express a ureaNa(+) or ureaCl()
cotransporter. As urea diffuses from the urearich 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
ureaNa(+) or urea Cl() cotransporter facilitates the
cycling of NaCl within the IM and yields a loopbend 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 = {369383},
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 shortlooped 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 lowpass filter in the
transduction of the TGF signal.},
Doi = {10.1002/cnm.1475},
Key = {fds243666}
}
@article{fds207970,
Author = {Gabor E. Linthorst and Lonneke HaerWigman 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 UTB
transporter},
Journal = {J Am Soc Nephrol, submitted},
Year = {2012},
Key = {fds207970}
}
@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}
}
@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 = {289290},
Year = {2012},
Key = {fds204560}
}
@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}
}
@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 = {iii},
Year = {2012},
ISSN = {15313492},
url = {http://dx.doi.org/10.3934/dcdsb.2012.17.4i},
Doi = {10.3934/dcdsb.2012.17.4i},
Key = {fds243626}
}
@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 = {289290},
Year = {2012},
ISSN = {20407939},
url = {http://dx.doi.org/10.1002/cnm.2477},
Doi = {10.1002/cnm.2477},
Key = {fds243650}
}
@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 = {iiii},
Year = {2012},
ISSN = {18152406},
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 = {263270},
Year = {2012},
Key = {fds243653}
}
@article{fds243655,
Author = {NievesGonzalez, 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 PhysiologyRenal Physiology},
Volume = {304},
Number = {F634F652},
Year = {2012},
Key = {fds243655}
}
@article{fds243656,
Author = {NievesGonzalez, 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 PhysiologyRenal Physiology},
Year = {2012},
Key = {fds243656}
}
@article{fds243657,
Author = {Edwards, A and Layton, AT},
Title = {Impact of nitric oxidemediated vasodilation on outer
medullary NaCl transport and oxygenation},
Journal = {American journal of physiology. Renal physiology},
Volume = {303},
Number = {7},
Pages = {F907F917},
Year = {2012},
ISSN = {03636127},
url = {http://dx.doi.org/10.1152/ajprenal.00055.2012},
Abstract = {The present study aimed to elucidate the reciprocal
interactions between oxygen (O2), nitric oxide (NO), and
superoxide (O2) and their effects on vascular and tubular
function in the outer medulla. We expanded our regionbased
model of transport in the rat outer medulla (Edwards A,
Layton AT. Am J Physiol Renal Physiol 301: F979F996, 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 = {F229F239},
Pages = {F229F239},
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 voltagegated
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: 493501,
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 = {51955215},
Year = {2012},
ISSN = {00219991},
url = {http://dx.doi.org/10.1016/j.jcp.2012.04.020},
Abstract = {We present numerical methods for computing twodimensional
Stokes flow driven by forces singularly supported along an
open, immersed interface. Two secondorder 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 secondorder 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 meshbased
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 secondorder
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 = {11391153},
Year = {2012},
ISSN = {15313492},
url = {http://dx.doi.org/10.3934/dcdsb.2012.17.1139},
Abstract = {We present a partially implicit hybrid method for simulating
the motion of a stiff interface immersed in Stokes flow, in
free space or in a rectangular domain with boundary
conditions. We assume the interface is a closed curve which
remains in the interior of the computational region. The
implicit time integration is based on the smallscale
decomposition approach and does not require the iterative
solution of a system of nonlinear equations. Firstorder and
secondorder versions of the timestepping 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 meshbased
solver. The solutions are secondorder 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 fluidstructure interaction  A
review},
Journal = {Communications in computational physics},
Volume = {12},
Number = {2},
Pages = {337377},
Year = {2012},
ISSN = {18152406},
url = {http://dx.doi.org/10.4208/cicp.291210.290411s},
Abstract = {The interactions between incompressible fluid flows and
immersed structures are nonlinear multiphysics 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
nonconforming meshes that are currently available for
computing fluidstructure 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
fluidstructure interactions. © 2012 GlobalScience
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 = {F1047F1056},
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
waterpermeable 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 = {Feedbackmediated dynamics in a model of coupled nephrons
with compliant thick ascending limbs.},
Journal = {Mathematical Biosciences},
Volume = {230},
Number = {2},
Pages = {115127},
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,
TGFmediated 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 = {NievesGonzalez, 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 = {NievesGonzalez, 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 = {F669F681},
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: 13161324, 2002). To investigate this hypothesis, we
developed a mathematical model of the myogenic response of
an AA wall, based on an arteriole model (GonzalezFernandez
JM, Ermentrout B. Math Biosci 119: 127167, 1994). The model
incorporates ionic transport, cell membrane potential,
contraction of the AA smooth muscle cell, and the mechanics
of a thickwalled cylinder. The model represents a myogenic
response based on a pressureinduced 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
ratesensitive 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
voltagegated and voltagecalciumgated channels,
respectively, gives rise to periodicity in the transport of
the two ions. This results in a timeperiodic cytoplasmic
calcium concentration, myosin light chain phosphorylation,
and crossbridge 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
Cdc42pmediated polarity establishment.},
Journal = {Current Biology},
Volume = {21},
Number = {3},
Pages = {184194},
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
membranefree flux suggested that directed traffic would
polarize Cdc42p, but it remained unclear whether Cdc42p
would become polarized without the membranefree 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
actindirected 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
threedimensional architecture.},
Journal = {American journal of physiology. Renal physiology},
Volume = {300},
Number = {2},
Pages = {F372F384},
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 basecase results. Am J Physiol Renal
Physiol. (First published November 10, 2010).
10.1152/ajprenal.00203.2010] a regionbased 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 regionbased 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 regionbased 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 aquaporin1null
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 basecase
results.},
Journal = {American journal of physiology. Renal physiology},
Volume = {300},
Number = {2},
Pages = {F356F371},
Year = {2011},
Month = {February},
url = {http://www.ncbi.nlm.nih.gov/pubmed/21068086},
Abstract = {A new, regionbased 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 ureapermeable and waterimpermeable segments of the
long descending limbs and highly ureapermeable ascending
thin limbs. Indeed, this is the first detailed mathematical
model of the rat urine concentrating mechanism that
represents high longloop 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, YN},
Title = {Modeling a semiflexible filament in cellular Stokes flow
using regularized Stokeslets},
Journal = {International Journal for Numerical Methods in Biomedical
Engineering},
Volume = {27},
Number = {12},
Pages = {20212034},
Year = {2011},
ISSN = {20407939},
url = {http://dx.doi.org/10.1002/cnm.1454},
Abstract = {Many physical and biological systems involve inextensible
fibers immersed in a fluid; examples include cilia, polymer
suspensions, and actin filament transport. In such systems,
the dynamics of the immersed fibers may play a significant
role in the observed macroscale fluid dynamics. In this
study, we simulate the dynamics of an approximately
inextensible semiflexible fiber immersed in a
twodimensional 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 stretchcoil 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 = {F979F996},
Pages = {F979F996},
Year = {2011},
ISSN = {03636127},
url = {http://dx.doi.org/10.1152/ajprenal.00096.2011},
Abstract = {We expanded our region based model of water and solute
exchanges in the rat outer medulla to incorporate the
transport of nitric oxide (NO) and superoxide (O 2) and to
examine the impact of NO O 2 interactions on medullary
thick ascending limb (mTAL) NaCl reabsorption and oxygen
(O2) consumption, under both physiological and pathological
conditions. Our results suggest that NaCl transport and the
concentrating capacity of the outer medulla are
substantially modulated by basal levels of NO and O 2.
Moreover, the effect of each solute on NaCl reabsorption
cannot be considered in isolation, given the feedback loops
resulting from threeway interactions between O 2, NO, and O
2. Notwithstanding vasoactive effects, our model predicts
that in the absence of O 2mediated stimulation of NaCl
active transport, the outer medullary concentrating capacity
(evaluated as the collecting duct fluid osmolality at the
outerinner medullary junction) would be ~40% lower.
Conversely, without NOinduced 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 10fold,
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 = {F1251F1259},
Year = {2011},
ISSN = {03636127},
url = {http://dx.doi.org/10.1152/ajprenal.00404.2011},
Abstract = {Urea transporters UTA2 and UTB 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 UTA2 and UTB double knockout (UTA2/B
knockout) mouse model was generated by targeted deletion of
the UTA2 promoter in embryonic stem cells with UTB gene
knockout. The UTA2/B knockout mice lacked detectable UTA2
and UTB transcripts and proteins and showed normal survival
and growth. Daily urine output was significantly higher in
UTA2/B knockout mice than that in wildtype mice and lower
than that in UTB knockout mice. Urine osmolality in UTA2/B
knockout mice was intermediate between that in UTB knockout
and wildtype mice. The changes in urine osmolality and flow
rate, plasma and urine urea concentration, as well as
nonurea solute concentration after an acute urea load or
chronic changes in protein intake suggested that UTA2 plays
a role in the progressive accumulation of urea in the inner
medulla. These results suggest that in wildtype mice UTA2
facilitates urea absorption by urea efflux from the thin
descending limb of short loops of Henle. Moreover, UTA2
deletion in UTB knockout mice partially remedies the urine
concentrating defect caused by UTB 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 = {F1047F1056},
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
waterpermeable 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 threedimensional
architecture.},
Journal = {Acta Physiologica},
Volume = {202},
Number = {3},
Pages = {361378},
Year = {2011},
ISSN = {17481716},
url = {http://dx.doi.org/10.1111/j.17481716.2010.02214.x},
Abstract = {The urine concentrating mechanism in the mammalian renal
inner medulla (IM) is not understood, although it is
generally considered to involve countercurrent flows in
tubules and blood vessels. A possible role for the
threedimensional 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 (aquaporin1) 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.17481716.2010.02214.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
threedimensional architecture},
Journal = {Am J Physiol Renal Physiol},
Volume = {300},
Number = {F372F384},
Pages = {F372F384},
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 basecase results. Am J Physiol Renal
Physiol. (First published November 10, 2010).
10.1152/ajprenal.00203.2010] a regionbased 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 regionbased 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 regionbased 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 aquaporin1null
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 basecase
results},
Journal = {Am J Physiol Renal Physiol},
Volume = {300},
Number = {F356F371},
Pages = {F356F371},
Year = {2011},
url = {http://www.ncbi.nlm.nih.gov/pubmed/21068086},
Abstract = {A new, regionbased 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 ureapermeable and waterimpermeable segments of the
long descending limbs and highly ureapermeable ascending
thin limbs. Indeed, this is the first detailed mathematical
model of the rat urine concentrating mechanism that
represents high longloop 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
Cdc42pmediated polarity establishment},
Journal = {Curr Biol},
Volume = {21},
Number = {3},
Pages = {111},
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
membranefree flux suggested that directed traffic would
polarize Cdc42p, but it remained unclear whether Cdc42p
would become polarized without the membranefree 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
actindirected 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 = {F979F996},
Year = {2011},
ISSN = {03636127},
url = {http://dx.doi.org/10.1152/ajprenal.00096.2011},
Abstract = {We expanded our region based model of water and solute
exchanges in the rat outer medulla to incorporate the
transport of nitric oxide (NO) and superoxide (O 2) and to
examine the impact of NO O 2 interactions on medullary
thick ascending limb (mTAL) NaCl reabsorption and oxygen
(O2) consumption, under both physiological and pathological
conditions. Our results suggest that NaCl transport and the
concentrating capacity of the outer medulla are
substantially modulated by basal levels of NO and O 2.
Moreover, the effect of each solute on NaCl reabsorption
cannot be considered in isolation, given the feedback loops
resulting from threeway interactions between O 2, NO, and O
2. Notwithstanding vasoactive effects, our model predicts
that in the absence of O 2mediated stimulation of NaCl
active transport, the outer medullary concentrating capacity
(evaluated as the collecting duct fluid osmolality at the
outerinner medullary junction) would be ~40% lower.
Conversely, without NOinduced 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 10fold,
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 = {Feedbackmediated dynamics in a model of a compliant thick
ascending limb.},
Journal = {Mathematical Biosciences},
Volume = {228},
Number = {2},
Pages = {185194},
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, timeindependent steadystate
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 = {F1369F1383},
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 = {F962F972},
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: 724, 1995). The simulations used the regionbased
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: F000F000, 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: 139154, 1934) in
which the ratio of NaCl to urea in the diet was
systematically varied in eight successive 5day 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 hyperfiltrationhypertrophy
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 threedimensional
architecture of the rat renal inner medulla.},
Journal = {American journal of physiology. Renal physiology},
Volume = {298},
Number = {4},
Pages = {F973F987},
Year = {2010},
Month = {April},
url = {http://www.ncbi.nlm.nih.gov/pubmed/20053796},
Abstract = {A new, regionbased 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
threedimensional 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 solutefree 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 regionbased 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 regionbased 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 UreaNa
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 oxidemediated 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 = {NievesGonzalez, 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 = {295305},
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 = {3462},
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
highlydetailed 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:F1346F1366, 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 loopbend
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/s1153800994364},
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 = {6678},
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
nonlinear 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 urinetoplasma
osmolality (U/P) ratio and freewater 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
basecase 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
basecase value; the outermedullary concentrating
capability was increased by 64.6% and 35.5%, respectively,
above base case; and the innermedullary 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 = {314339},
Year = {2010},
ISSN = {00928240},
url = {http://dx.doi.org/10.1007/s1153800994480},
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 urinetoplasma 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 outerinner 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 basecase
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 outerinner 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 corticomedullary axis. © 2009
Society for Mathematical Biology.},
Doi = {10.1007/s1153800994480},
Key = {fds243642}
}
@article{fds243676,
Author = {Layton, AT},
Title = {Feedbackmediated dynamics in a model of a compliant thick
ascending limb},
Journal = {Math Biosci},
Volume = {228},
Number = {185194},
Pages = {185194},
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, timeindependent steadystate
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
semiLagrangian and modified equation approaches},
Journal = {Applied Numerical Mathematics},
Volume = {60},
Number = {6},
Pages = {645657},
Year = {2010},
ISSN = {01689274},
url = {http://dx.doi.org/10.1016/j.apnum.2010.03.007},
Abstract = {In this paper, we develop a class of semiLagrangian 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 semiLagrangian 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 semiLagrangian methods which
characterizes their nonmonotonic 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 = {F634F647},
Year = {2010},
ISSN = {03636127},
url = {http://dx.doi.org/10.1152/ajprenal.00681.2009},
Abstract = {In a companion study (Edwards A and Layton AT. Am J Physiol
Renal Physiol. doi:10.1152/ajprenal.00680.2009), we
developed a mathematical model of nitric oxide (NO),
superoxide (O2), and total peroxynitrite (ONOO) transport
in midouter stripe and midinner stripe cross sections of
the rat outer medulla (OM). We examined how the
threedimensional 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 NOO2 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
extraerythrocyte 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 = {F616F633},
Year = {2010},
ISSN = {03636127},
url = {http://dx.doi.org/10.1152/ajprenal.00680.2009},
Abstract = {To examine the impact of the complex radial organization of
the rat outer medulla (OM) on the distribution of nitric
oxide (NO), superoxide (O 2) and total peroxynitrite
(ONOO), we developed a mathematical model that simulates the
transport of those species in a cross section of the rat OM.
To simulate the preferential interactions among tubules and
vessels that arise from their relative radial positions in
the OM, we adopted the regionbased approach developed by
Layton and Layton (Am J Physiol Renal Physiol 289:
F1346F1366, 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 O2supplying 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
ratelimiting 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 = {F1369F1383},
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 = {295305},
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 = {314339},
Year = {2010},
Key = {fds243687}
}
@article{fds243689,
Author = {Layton, AT and Toyama, Y and Yang, GQ 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 = {441460},
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 eyeshaped 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
forceproducing elements that satisfy forcevelocity
relationships similar to muscle. The action of the elements
is consistent with the forceproducing behavior of actin and
myosin in cells. The parameters that characterize the
simulated embryos were optimized by reference to
experimental observations on wildtype 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 amnioserosaremoval protocol in
either the elastic or the contractile limit, indicating that
both elastic and contractile dynamics are essential
components of the biological forceproducing elements. We
found it was necessary to actively upregulate forces to
recapitulate both the double and singlecanthus 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 = {250256},
Year = {2009},
Month = {August},
ISSN = {15489213},
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 threedimensional
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 = {515555},
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:F79F97, 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 singlenephron
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/s115380089370x},
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 TGFmediated limitcycle
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 = {F537F548},
Year = {2009},
ISSN = {03636127},
url = {http://dx.doi.org/10.1152/ajprenal.90497.2008},
Abstract = {In the companion study (Am J Physiol Renal Physiol. First
published April 29, 2009; doi:10.1152/ajprenal.90496.2008),
we extended the regionbased mathematical model of the
urineconcentrating mechanism in the rat outer medulla (OM)
developed by Layton and Layton (Am J Physiol Renal Physiol
289: F1346F1366, 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 = {F517F536},
Year = {2009},
ISSN = {03636127},
url = {http://dx.doi.org/10.1152/ajprenal.90496.2008},
Abstract = {The mammalian kidney is particularly vulnerable to
hypoperfusion, because the O2 supply to the renal medulla
barely exceeds its O2 requirements. In this study, we
examined the impact of the complex structural organization
of the rat outer medulla (OM) on O2 distribution. We
extended the regionbased mathematical model of the rat OM
developed by Layton and Layton (Am J Physiol Renal Physiol
289: F1346F1366, 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 timedependent partial differential equations},
Journal = {Applied Numerical Mathematics},
Volume = {59},
Number = {7},
Pages = {16291643},
Year = {2009},
ISSN = {01689274},
url = {http://dx.doi.org/10.1016/j.apnum.2008.11.004},
Abstract = {Many physical and biological systems involve the
interactions of two or more processes with widelydiffering
characteristic time scales. Previously, highorder
semiimplicit and multiimplicit 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 highorder
approximation by means of a firstorder numerical method,
which solves a series of correction equations to increase
the temporal order of accuracy of the approximation. MISDC
methods also allow several fastevolving processes to be
handled implicitly but independently, allowing for different
time steps for each process while avoiding the splitting
errors present in traditional operatorsplitting methods. In
this study, we propose MISDC methods that use second and
thirdorder integration and splitting methods in the
prediction steps, and we assess the efficiency of SISDC and
MISDC methods that are based on those moderateorder
integration methods. Numerical results indicate that SISDC
methods using thirdorder prediction steps are the most
efficient, but the efficiency of SISDC methods using
firstorder 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
thirdorder prediction step is the most efficient for a
mildlystiff problem, but the method with a firstorder
prediction step has the least splitting error and thus the
highest efficiency for a stiff problem. Furthermore, a MISDC
method using a secondorder prediction step with Strang
splitting generates approximations with large splitting
errors, compared with methods that use a different
operatorsplitting 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 = {33583367},
Year = {2009},
ISSN = {00219991},
url = {http://dx.doi.org/10.1016/j.jcp.2009.01.023},
Abstract = {We present a secondorder 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 NavierStokes 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
secondorder 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 NavierStokes equations with a body force resulting
from the Stokes part. The regular velocity is obtained using
a timestepping method that combines the semiLagrangian
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 timestepping,
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 = {266272},
Year = {2009},
ISSN = {00457930},
url = {http://dx.doi.org/10.1016/j.compfluid.2008.02.003},
Abstract = {We propose a fast, explicit numerical method for computing
approximations for the immersed boundary problem in which
the boundaries that separate the fluid into two regions are
stiff. In the numerical computations of such problems, one
frequently has to contend with numerical instability, as the
stiff immersed boundaries exert large forces on the local
fluid. When the boundary forces are treated explicitly,
prohibitively small timesteps may be required to maintain
numerical stability. On the other hand, when the boundary
forces are treated implicitly, the restriction on the
timestep size is reduced, but the solution of a large
system of coupled nonlinear 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 operatorsplitting approach: large timesteps are used to
update the nonstiff 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
timesteps. Numerical results suggest that the present
method compares favorably with an implementation of the
immersed interface method that employs an explicit
timestepping 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
Navierstokes flows},
Journal = {Communications in computational physics},
Volume = {5},
Number = {1},
Pages = {6183},
Year = {2009},
ISSN = {18152406},
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 twodimensional immersed boundary problem,
which naturally accommodates the fluidparticle 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 GlobalScience
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 = {Threedimensional 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 threedimensional architecture in the urine
concentrating mechanism of the rat renal inner
medulla},
Journal = {American journal of physiology. Renal physiology},
Volume = {295},
Number = {5},
Pages = {F1271F1285},
Year = {2008},
ISSN = {03636127},
url = {http://dx.doi.org/10.1152/ajprenal.90252.2008},
Abstract = {Recent studies of threedimensional 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 33.5 mm of the IM,
whereas other ATLs and AVR, along with aquaporin1positive
DTLs and urea transporter Bpositive 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 threedimensional IM architecture, we distinguish two
distinct countercurrent systems in the first 33.5 mm of the
IM (an intraCD cluster system and an interCD cluster
system) and a third countercurrent system in the final 1.52
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 soluteseparation, solutemixing
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 twofluid Stokes
equations with a moving immersed boundary},
Journal = {Computer Methods in Applied Mechanics and
Engineering},
Volume = {197},
Number = {2528},
Pages = {21472155},
Year = {2008},
ISSN = {00457825},
url = {http://dx.doi.org/10.1016/j.cma.2007.08.018},
Abstract = {We consider the immersed boundary problem in which the
boundary separates two very viscous fluids with differing
viscosities. The moving elastic boundary may exert a force
on the local fluid. The model solution is obtained using the
immersed interface method, which computes secondorder
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 twofluid Stokes problem to
the singlefluid case, and then solves the singlefluid
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
twofluid regions. We also propose an implicit algorithm and
a fractionalstep 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 timestepping
algorithm is the most efficient, in the sense that it allows
the largest timeinterval 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 semiimplicit Picard
deferred correction methods},
Journal = {Applied Numerical Mathematics},
Volume = {58},
Number = {6},
Pages = {845858},
Year = {2008},
ISSN = {01689274},
url = {http://dx.doi.org/10.1016/j.apnum.2007.03.003},
Abstract = {The goal of this study is to assess the implications of the
choice of correctors for semiimplicit Picard integral
deferred correction (SIPIDC) methods. The SIPIDC methods
previously developed compute a highorder approximation by
first computing a loworder provisional solution using a
semiimplicit method and then using a firstorder
semiimplicit 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 secondorder
semiimplicit 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 = {887929},
Year = {2007},
Month = {April},
ISSN = {00928240},
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 basecase model configuration tubular
dimensions and transport parameters are based on, or
estimated from, experimental measurements or
immunohistochemical evidence in wildtype rats. The
basecase model configuration generated an osmolality
gradient along the corticomedullary 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 wildtype, the OM
corticomedullary 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), 1063310637, 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/s1153800590303},
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 = {A905A905},
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 = {A828A828},
Year = {2007},
Month = {April},
Key = {fds320915}
}
@article{fds243704,
Author = {Layton, AT and Minion, ML},
Title = {Implications of the choice of predictors for semiimplicit
Picard Integral deferred correction methods},
Journal = {Comm. Appl. Math. Comp. Sci.},
Volume = {2},
Number = {1},
Pages = {134},
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 = {F79F97},
Year = {2006},
Month = {July},
ISSN = {1931857X},
url = {http://www.ncbi.nlm.nih.gov/pubmed/16204416},
Abstract = {Singlenephron 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,
timeindependent steadystate 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 = {A1224A1224},
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 multistability of the tubuloglomerular
feedback system in spontaneouslyhypertensive rats
(SHR)},
Journal = {The FASEB journal : official publication of the Federation
of American Societies for Experimental Biology},
Volume = {20},
Number = {4},
Pages = {A762A762},
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 = {A759A759},
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 = {175186},
Year = {2006},
ISSN = {03784754},
url = {http://dx.doi.org/10.1016/j.matcom.2004.10.008},
Abstract = {Currently in most global meteorological applications,
loworder finite difference or finite element methods, or
the spectral transform method are used. The spectral
transform method, which yields highorder 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 twolevel semiLagrangian
semiimplicit 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) 16991717] 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 = {187205},
Year = {2006},
ISSN = {03784754},
url = {http://dx.doi.org/10.1016/j.matcom.2004.10.009},
Abstract = {In this study, we present numerical methods, based on the
optimal quadratic spline collocation (OQSC) methods, for
solving the shallow water equations (SWEs) in spherical
coordinates. The error associated with quadratic spline
interpolation is fourth order locally at certain points and
third order globally, but the standard quadratic spline
collocation methods generate only secondorder
approximations. In contrast, the OQSC methods generate
approximations of the same order as quadratic spline
interpolation. In the onestep OQSC method, the discrete
differential operators are perturbed to eliminate loworder
error terms, and a highorder approximation is computed
using the perturbed operators. In the twostep OQSC method,
a secondorder approximation is generated first, using the
standard formulation, and then a highorder 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 semiLagrangian
semiimplicit 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 Ctype grid,
the methods also faithfully capture the group velocity of
inertiagravity 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 = {21892207},
Year = {2006},
ISSN = {10648275},
url = {http://dx.doi.org/10.1137/050642198},
Abstract = {A mathematical model is presented to simulate water and
solute transport in a highly viscous fluid with a
waterpermeable, 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
secondorder explicit jump method [A. Mayo, SIAM J. Numer.
Anal., 21 (1984), pp. 285299], in which jumps in the
solution and its derivatives are incorporated into a
finitedifference 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 = {91119},
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 distributedloop model of an
avian urine concentrating mechanism},
Journal = {Bulletin of Mathematical Biology},
Volume = {68},
Number = {7},
Pages = {16251660},
Year = {2006},
ISSN = {00928240},
url = {http://dx.doi.org/10.1007/s1153800690871},
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 freewater
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 urinetoplasma osmolality ratio (U/P)) and that reduce
TAT, the optimization algorithm identified a set of
parameter values that increased efficiency by ∼60% above
basecase 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 nearplasma osmolality at nearbasecase 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/s1153800690871},
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 = {187205},
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 = {175186},
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 = {740752},
Year = {2006},
ISSN = {00189219},
url = {http://dx.doi.org/10.1109/JPROC.2006.871770},
Abstract = {Mathematical models have played an essential role in
elucidating various functions of the kidney, including the
mechanism by which the avion and mammalian kidney can
produce a urine that is more concentrated than blood plasma,
quasiisosmotic 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 regionbased mathematical model of the urine concentrating
mechanism in the rat outer medulla. I. Formulation and
basecase results.},
Journal = {American Journal of Physiology: Renal Physiology},
Volume = {289},
Number = {6},
Pages = {F1346F1366},
Year = {2005},
Month = {December},
ISSN = {1931857X},
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 innerstripe short descending limbs.
In a companion study (Layton AT and Layton HE. Am J Physiol
Renal Physiol 289: F1367F1381, 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 regionbased 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 = {F1367F1381},
Year = {2005},
Month = {December},
ISSN = {1931857X},
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: F1346F1366, 2005), a regionbased
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 = {211230},
Year = {2005},
Month = {October},
ISSN = {00255564},
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 = {A150A150},
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 = {A149A149},
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 = {341373},
Year = {2005},
url = {http://dx.doi.org/10.1007/s1054300500161},
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 GaussLegendre, GaussLobatto, GaussRadau, 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 lefthand
endpoint t n . Quadrature rules that do not depend on the
lefthand endpoint (which are referred to as righthand
quadrature rules) are shown to lead to L(α)stable implicit
methods with α≈π/2. The semiimplicit 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 righthand quadrature rule, the
form and extent of orderreduction 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 nonuniform 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/s1054300500161},
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 = {121},
Year = {2005},
ISSN = {02183390},
url = {http://dx.doi.org/10.1142/S0218339005001598},
Abstract = {The goal of this study is to develop a methodology for
tracking the distribution of filtered solute in mathematical
models of the urine concentrating mechanism. Investigation
of intrarenal solute distribution, and its cycling by way of
countercurrent 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
secondorder Godunov method, which, by construction, is
massconserving 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 = {341373},
Year = {2005},
url = {http://dx.doi.org/10.1007/s1054300500161},
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 GaussLegendre, GaussLobatto, GaussRadau, 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 lefthand
endpoint t n . Quadrature rules that do not depend on the
lefthand endpoint (which are referred to as righthand
quadrature rules) are shown to lead to L(α)stable implicit
methods with α≈π/2. The semiimplicit 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 righthand quadrature rule, the
form and extent of orderreduction 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 nonuniform 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/s1054300500161},
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 = {399419},
Year = {2005},
ISSN = {02183390},
url = {http://dx.doi.org/10.1142/S0218339005001598},
Abstract = {The goal of this study is to develop a methodology for
tracking the distribution of filtered solute in mathematical
models of the urine concentrating mechanism. Investigation
of intrarenal solute distribution, and its cycling by way of
countercurrent 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
secondorder Godunov method, which, by construction, is
massconserving 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 = {A1021A1021},
Year = {2004},
Month = {March},
Key = {fds320921}
}
@article{fds24336,
Author = {Anita T. Layton},
Title = {Conservative multiimplicit 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 = {4 564},
Pages = {F816F839},
Year = {2004},
url = {http://dx.doi.org/10.1152/ajprenal.00398.2003},
Abstract = {We used a mathematical model of the urine concentrating
mechanism of rat inner medulla (IM) to investigate the
implications of experimental studies in which
immunohistochemical methods were combined with
threedimensional 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
aquaporin1null 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
tissueslice and micropuncture studies.},
Doi = {10.1152/ajprenal.00398.2003},
Key = {fds243716}
}
@article{fds243717,
Author = {Layton, AT and Minion, ML},
Title = {Conservative multiimplicit spectral deferred correction
methods for reacting gas dynamics},
Journal = {Journal of Computational Physics},
Volume = {194},
Number = {2},
Pages = {697715},
Year = {2004},
url = {http://dx.doi.org/10.1016/j.jcp.2003.09.010},
Abstract = {In most models of reacting gas dynamics, the characteristic
time scales of chemical reactions are much shorter than the
hydrodynamic and diffusive time scales, rendering the
reaction part of the model equations stiff. Moreover,
nonlinear 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 highorder
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 cellaveraged or
finitevolume solution. The temporal discretization is based
on a multiimplicit 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 widelydiffering 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 UTB urea
transporter.},
Journal = {Journal of the American Society of Nephrology :
JASN},
Volume = {14},
Pages = {76A76A},
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 = {A485A485},
Year = {2003},
Month = {March},
Key = {fds320923}
}
@article{fds24337,
Author = {Anita T. Layton},
Title = {Highorder operatorsplitting 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 twotimelevel semiLagrangian semiimplicit 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 regionbased model framework for the rat urine
concentrating mechanism},
Journal = {Bull. Math. Biol.},
Volume = {65},
Number = {6},
Pages = {859901},
Year = {2003},
url = {http://dx.doi.org/10.1016/S00928240(03)000454},
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 steadystate
solutions by means of a stable and efficient numerical
method, based on the semiLagrangian semiimplicit 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 secondorder accurate in space and
that exhibit mass conservation. © 2003 Society for
Mathematical Biology. Published by Elsevier Ltd. All rights
reserved.},
Doi = {10.1016/S00928240(03)000454},
Key = {fds243718}
}
@article{fds243719,
Author = {Bourlioux, A and Layton, AT and Minion, ML},
Title = {Highorder multiimplicit spectral deferred correction
methods for problems of reactive flow},
Journal = {Journal of Computational Physics},
Volume = {189},
Number = {2},
Pages = {651675},
Year = {2003},
url = {http://dx.doi.org/10.1016/S00219991(03)002511},
Abstract = {Models for reacting flow are typically based on
advectiondiffusionreaction (ADR) partial differential
equations. Many practical cases correspond to situations
where the relevant time scales associated with each of the
three subprocesses can be widely different, leading to
disparate timestep requirements for robust and accurate
timeintegration. 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 timescale disparity. The
proposed methods are highorder multiimplicit
generalizations of spectral deferred correction methods
(MISDC methods), constructed for the temporal integration of
ADR equations. Spectral deferred correction methods
compute a highorder approximation to the solution of a
differential equation by using a simple, loworder 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 subprocesses implicitly but independently,
while avoiding the splitting errors present in traditional
operatorsplitting 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
semiimplicit 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 subprocess time steps is
illustrated for nonlinear problems, where reaction and
diffusion are much stiffer than advection. Although the
paper focuses on this specific timescales ordering, the
generalization to any ordering combination is
straightforward. © 2003 Elsevier Science B.V. All rights
reserved.},
Doi = {10.1016/S00219991(03)002511},
Key = {fds243719}
}
@article{fds243720,
Author = {Layton, AT and Spotz, WF},
Title = {A semiLagrangian double Fourier method for the shallow
water equations on the sphere},
Journal = {Journal of Computational Physics},
Volume = {189},
Number = {1},
Pages = {180196},
Year = {2003},
url = {http://dx.doi.org/10.1016/S00219991(03)002079},
Abstract = {We describe a numerical method, based on the semiLagrangian
semiimplicit 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 highorder 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 threetimelevel semiLagrangian
semiimplicit 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/S00219991(03)002079},
Key = {fds243720}
}
@article{fds243721,
Author = {Layton, AT},
Title = {A semiLagrangian collocation method for the shallow water
equations on the sphere},
Journal = {SIAM Journal on Scientific Computing},
Volume = {24},
Number = {4},
Pages = {14331449},
Year = {2003},
ISSN = {10648275},
url = {http://dx.doi.org/10.1137/S1064827501395021},
Abstract = {In this paper, we describe a numerical method for solving
the shallow water equations (SWEs) in spherical coordinates.
The most popular spatial discretization method used in
global atmospheric models is currently the spectral
transform method, which generates highorder 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, highorder finite element methods may be a
viable alternative. In this implementation, the SWEs are
discretized in time using the threelevel semiLagrangian
semiimplicit 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. 211224] are presented to demonstrate the
stability and accuracy of the method. When compared to a
previously applied Eulerianbased 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 distributedloop models of
the urine concentrating mechanism},
Journal = {Mathematical Biosciences},
Volume = {181},
Number = {2},
Pages = {111132},
Year = {2003},
url = {http://dx.doi.org/10.1016/S00255564(02)001761},
Abstract = {In this study we describe an efficient numerical method,
based on the semiLagrangian (SL) semiimplicit (SI) method
and Newton's method, for obtaining steadystate (SS)
solutions of equations arising in distributedloop 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
Newtontype 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 Newtontype 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 Newtontype 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/S00255564(02)001761},
Key = {fds243722}
}
@article{fds304480,
Author = {Layton, AT and Layton, HE},
Title = {A regionbased model framework for the rat urine
concentrating mechanism},
Journal = {Bulletin of Mathematical Biology},
Volume = {65},
Number = {5},
Pages = {859901},
Year = {2003},
url = {http://dx.doi.org/10.1016/S00928240(03)000454},
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 steadystate
solutions by means of a stable and efficient numerical
method, based on the semiLagrangian semiimplicit 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 secondorder accurate in space and
that exhibit mass conservation. © 2003 Society for
Mathematical Biology. Published by Elsevier Ltd. All rights
reserved.},
Doi = {10.1016/S00928240(03)000454},
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 = {333A333A},
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 = {A51A51},
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 = {549567},
Year = {2002},
ISSN = {03036812},
url = {http://dx.doi.org/10.1007/s0028500201666},
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 semiLagrangian
semiimplicit 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. © SpringerVerlag
2002.},
Doi = {10.1007/s0028500201666},
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 = {4153},
Year = {2002},
ISSN = {01782789},
url = {http://dx.doi.org/10.1007/s003710100131},
Abstract = {Water motion can be realistically captured by physically
based fluid models. We begin by presenting a survey on fluid
simulation models that are based on fluid dynamics
equations, from the most comprehensive NavierStokes
equations to the simple wave equation. We then present a
model that is based on the twodimensional shallow water
equations. The equations are integrated by a novel numerical
method  the implicit semiLagrangian 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 semiLagrangian semiimplicit numerical method for models
of the urine concentrating mechanism},
Journal = {SIAM J. Sci. Comput.},
Volume = {23},
Number = {5},
Pages = {15281548},
Year = {2002},
ISSN = {10648275},
url = {http://dx.doi.org/10.1137/S1064827500381781},
Abstract = {Mathematical models of the urine concentrating mechanism
consist of large systems of coupled differential equations.
The numerical methods that have usually been used to solve
the steadystate formulation of these equations involve
implicit Newtontype 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 directionsensitive time
integration until a steady state is reached, are stable in
the presence of transient flow reversal. However, when an
explicit, Eulerianbased 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 semiLagrangian semiimplicit (SLSI)
method for solving the system of hyperbolic partial
differential equations that arises in the dynamic
formulation. The semiLagrangian scheme advances the
solution in time by integrating backward along flow
trajectories, thus allowing large time steps while
maintaining stability. The semiimplicit 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 = {578592},
Year = {2002},
ISSN = {00219991},
url = {http://dx.doi.org/10.1006/jcph.2002.7075},
Abstract = {Spatial discretization schemes commonly used in global
meteorological applications are currently limited to
spectral methods or loworder finitedifference/finiteelement
methods. The spectral transform method, which yields
highorder approximations, requires Legendre transforms,
which have a computational complexity of O(N3), where N is
the number of subintervals in one dimension. Thus,
highorder finiteelement 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 semiimplicit leapfrog
method, and in space with the cubic spline collocation
method on a skipped latitudelongitude 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 latitudelongitude grid.
© 2002 Elsevier Science (USA).},
Doi = {10.1006/jcph.2002.7075},
Key = {fds243726}
}
@article{fds304478,
Author = {Layton, AT and Layton, HE},
Title = {A semilagrangian semiimplicit numerical method for models
of the urine concentrating mechanism},
Journal = {SIAM Journal on Scientific Computing},
Volume = {23},
Number = {5},
Pages = {15261548},
Year = {2002},
ISSN = {10648275},
url = {http://dx.doi.org/10.1137/S1064827500381781},
Abstract = {Mathematical models of the urine concentrating mechanism
consist of large systems of coupled differential equations.
The numerical methods that have usually been used to solve
the steadystate formulation of these equations involve
implicit Newtontype 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 directionsensitive time
integration until a steady state is reached, are stable in
the presence of transient flow reversal. However, when an
explicit, Eulerianbased 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 semiLagrangian semiimplicit (SLSI)
method for solving the system of hyperbolic partial
differential equations that arises in the dynamic
formulation. The semiLagrangian scheme advances the
solution in time by integrating backward along flow
trajectories, thus allowing large time steps while
maintaining stability. The semiimplicit 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 = {549567},
Year = {2002},
ISSN = {03036812},
url = {http://dx.doi.org/10.1007/s0028500201666},
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 semiLagrangian
semiimplicit 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. © SpringerVerlag
2002.},
Doi = {10.1007/s0028500201666},
Key = {fds304479}
}
@article{fds24339,
Author = {Anita W. Tam},
Title = {A twotimelevel semiquadratic 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}
}
