%% Books
@book{fds10275,
Author = {Harold E. Layton and Alan M. Weinstein},
Title = {Membrane Transport and Renal Physiology},
Journal = {(The IMA Volumes in Mathematics and its Applications, Volume
129) New York: SpringerVerlag, 2002},
Key = {fds10275}
}
%% Papers Published
@article{fds342141,
Author = {Layton, AT and Layton, HE},
Title = {A computational model of epithelial solute and water
transport along a human nephron.},
Journal = {Plos Computational Biology},
Volume = {15},
Number = {2},
Pages = {e1006108},
Year = {2019},
Month = {February},
url = {http://dx.doi.org/10.1371/journal.pcbi.1006108},
Abstract = {We have developed the first computational model of solute
and water transport from Bowman space to the papillary tip
of the nephron of a human kidney. The nephron is represented
as a tubule lined by a layer of epithelial cells, with
apical and basolateral transporters that vary according to
cell type. The model is formulated for steady state, and
consists of a large system of coupled ordinary differential
equations and algebraic equations. Model solution describes
luminal fluid flow, hydrostatic pressure, luminal fluid
solute concentrations, cytosolic solute concentrations,
epithelial membrane potential, and transcellular and
paracellular fluxes. We found that if we assume that the
transporter density and permeabilities are taken to be the
same between the human and rat nephrons (with the exception
of a glucose transporter along the proximal tubule and the
H+pump along the collecting duct), the model yields
segmental deliveries and urinary excretion of volume and key
solutes that are consistent with human data. The model
predicted that the human nephron exhibits glomerulotubular
balance, such that proximal tubular Na+ reabsorption varies
proportionally to the singlenephron glomerular filtration
rate. To simulate the action of a novel diabetic treatment,
we inhibited the Na+glucose cotransporter 2 (SGLT2) along
the proximal convoluted tubule. Simulation results predicted
that the segment's Na+ reabsorption decreased significantly,
resulting in natriuresis and osmotic diuresis.},
Doi = {10.1371/journal.pcbi.1006108},
Key = {fds342141}
}
@article{fds287294,
Author = {Layton, HE and Pitman, EB},
Title = {A dynamic numerical method for models of renal
tubules},
Journal = {Bulletin of Mathematical Biology},
Volume = {56},
Number = {3},
Pages = {547565},
Year = {1994},
ISSN = {00928240},
url = {http://dx.doi.org/10.1007/BF02460470},
Abstract = {We show that an explicit method for solving hyperbolic
partial differential equations can be applied to a model of
a renal tubule to obtain both dynamic and steadystate
solutions. Appropriate implementation of this method
eliminates numerical instability arising from reversal of
intratubular flow direction. To obtain secondorder
convergence in space and time, we employ the recently
developed ENO (Essentially NonOscillatory) methodology. We
present examples of computed flows and concentration
profiles in representative model contexts. Finally, we
indicate briefly how model tubules may be coupled to
construct largescale simulations of the renal counterflow
system. © 1994 Elsevier Science Ltd.},
Doi = {10.1007/BF02460470},
Key = {fds287294}
}
@article{fds287296,
Author = {Layton, HE and Pitman, EB and Knepper, MA},
Title = {A Dynamic Numerical Method for Models of the Urine
Concentrating Mechanism},
Journal = {Siam Journal on Applied Mathematics},
Volume = {55},
Number = {5},
Pages = {13901418},
Publisher = {Society for Industrial & Applied Mathematics
(SIAM)},
Year = {1995},
Month = {October},
url = {http://dx.doi.org/10.1137/s0036139993252864},
Abstract = {Dynamic models of the urine concentrating mechanism consist
of large systems of hyperbolic partial differential
equations, with stiff source terms, coupled with fluid
conservation relations. Efforts to solve these equations
numerically with explicit methods have been frustrated by
numerical instability and by long computation times. As a
consequence, most models have been reformulated as
steadystate boundary value problems, which have usually
been solved by an adaptation of Newton's method.
Nonetheless, difficulties arise in finding conditions that
lead to stable convergence, especially when the very large
membrane permeabilities measured in experiments are used. In
this report, an explicit method, previously introduced to
solve the model equations of a single renal tubule, is
extended to solve a largescale model of the urine
concentrating mechanism. This explicit method tracks
concentration profiles in the upwind direction and thereby
avoids instability arising from flow reversal. To attain
secondorder convergence in space and time, the recently
developed ENO (essentially nonoscillatory) methodology is
implemented. The method described here, which has been
rendered practical for renal models by the emergence of
desktop workstations, is adaptable to various medullary
geometries and permits the inclusion of experimentally
measured permeabilities. This report describes an
implementation of the method, makes comparisons with results
obtained previously by a different method, and presents an
example calculation using some recently measured membrane
properties.},
Doi = {10.1137/s0036139993252864},
Key = {fds287296}
}
@article{fds8947,
Author = {Layton, H. E. and E. Bruce Pitman and Mark A.
Knepper},
Title = {A dynamic numerical method for models of the urine
concentrating mechanism},
Journal = {SIAM Journal on Applied Mathematics 55(5): 13901418,
October, 1995.},
Key = {fds8947}
}
@article{fds287333,
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 = {fds287333}
}
@article{fds10382,
Author = {Layton, Anita T. and Harold E. Layton},
Title = {A numerical method for renal models that represent abrupt
changes in tubular properties},
Journal = {Journal of Mathematical Biology 45(5): 549567,
2002.},
Key = {fds10382}
}
@article{fds287317,
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 = {fds287317}
}
@article{fds10277,
Author = {Pitman, E. Bruce and Roman M. Zaritski and Leon C. Moore and Harold E. Layton},
Title = {A reduced model for nephron flow dynamics mediated by
tubuloglomerular feedback},
Journal = {In: Membrane Transport and Renal Physiology, The IMA Volumes
in Mathematics and its Applications, Volume 129, edited by
Harold E. Layton and Alan M. Weinstein. New York:
SpringerVerlag, pp. 345364, 2002.},
Key = {fds10277}
}
@article{fds287321,
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 = {fds287321}
}
@article{fds287322,
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 = {fds287322}
}
@article{fds287319,
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 = {fds287319}
}
@article{fds287316,
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},
Publisher = {Society for Industrial & Applied Mathematics
(SIAM)},
Year = {2002},
Month = {December},
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 = {fds287316}
}
@article{fds287277,
Author = {Sands, JM and Layton, HE},
Title = {Advances in understanding the urineconcentrating
mechanism.},
Journal = {Annual Review of Physiology},
Volume = {76},
Pages = {387409},
Year = {2014},
Month = {January},
ISSN = {00664278},
url = {http://dx.doi.org/10.1146/annurevphysiol021113170350},
Abstract = {The renal medulla produces concentrated urine through the
generation of an osmotic gradient that progressively
increases from the corticomedullary boundary to the inner
medullary tip. In the outer medulla, the osmolality gradient
arises principally from vigorous active transport of NaCl,
without accompanying water, from the thick ascending limbs
of short and longlooped nephrons. In the inner medulla,
the source of the osmotic gradient has not been identified.
Recently, there have been important advances in our
understanding of key components of the urineconcentrating
mechanism, including (a) better understanding of the
regulation of water, urea, and sodium transport proteins;
(b) better resolution of the anatomical relationships in the
medulla; and (c) improvements in mathematical modeling of
the urineconcentrating mechanism. Continued experimental
investigation of signaling pathways regulating
transepithelial transport, both in normal animals and in
knockout mice, and incorporation of the resulting
information into mathematical simulations may help to more
fully elucidate the mechanism for concentrating urine in the
inner medulla.},
Doi = {10.1146/annurevphysiol021113170350},
Key = {fds287277}
}
@article{fds287310,
Author = {Layton, HE},
Title = {Advective transport of nitric oxide in a mathematical model
of the afferent arteriole},
Journal = {American Journal of Physiology Renal Physiology},
Volume = {284},
Number = {5 535},
Pages = {F1080F1096},
Year = {2003},
Month = {May},
Abstract = {Endotheliumderived nitric oxide (NO) is thought to be
shortlived in blood because of rapid removal from plasma,
mainly by binding to Hb. The extent to which removal limits
NO advection is unclear, especially for blood flow in the
renal afferent arteriole (AA), which has a transit time of
330 ms. A mathematical model of AA fluid dynamics and
myogenic response that includes NO diffusion, advection,
degradation, and vasorelaxant action was used to estimate NO
advective transport. Model simulations indicate that
advective transport of locally produced NO is sufficient to
yield physiologically significant NO concentrations along
much of the AA. Advective transport is insensitive to NO
scavenging by Hb because the NOHb binding rate is slow
relative to AA transit time. Hence, plasma NO concentration
near the vessel wall is influenced by both diffusion from
endothelial cells and advection from upstream sites.
Simulations also suggest that NO advection may constitute a
mechanism to stabilize arteriolar flow in response to a
localized vasoconstriction accompanied by enhanced NO
release.},
Key = {fds287310}
}
@article{fds287318,
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 = {fds287318}
}
@article{fds287311,
Author = {MarcanoVelázquez, M and Layton, HE},
Title = {An inverse algorithm for a mathematical model of an avian
urine concentrating mechanism},
Journal = {Bulletin of Mathematical Biology},
Volume = {65},
Number = {4},
Pages = {665691},
Year = {2003},
url = {http://dx.doi.org/10.1016/S00928240(03)000296},
Abstract = {A nonlinear optimization technique, in conjunction with a
singlenephron, singlesolute mathematical model of the
quail urine concentrating mechanism, was used to estimate
parameter sets that optimize a measure of concentrating
mechanism efficiency, viz., the ratio of the freewater
absorption rate to the total NaCl active transport rate. The
optimization algorithm, which is independent of the
numerical method used to solve the model equations, runs in
a few minutes on a 1000 MHz desktop computer. The parameters
varied were: tubular permeabilities to water and solute;
maximum active solute transport rates of the ascending limb
of Henle and the collecting duct (CD); length of the prebend
enlargement (PBE) of the descending limb; fractional solute
delivery to the CD; solute concentration of tubular fluid
entering the CD at the corticomedullary boundary; and rate
of exponential CD population decrease along the medullary
cone. Using a basecase parameter set and parameter bounds
suggested by physiologic experiments, the optimization
algorithm identified a maximumefficiency set of parameter
values that increased efficiency by 40% above basecase
efficiency; a minimumefficiency set reduced efficiency by
about 41%. When maximumefficiency parameter values were
computed as medullary length varied over the physiologic
range, the PBE was found to make up 88% of a short medullary
cone but only 8% of a long medullary cone. © 2003 Society
for Mathematical Biology. Published by Elsevier Science Ltd.
All rights reserved.},
Doi = {10.1016/S00928240(03)000296},
Key = {fds287311}
}
@article{fds287325,
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},
Month = {October},
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 approximately
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 approximately 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.},
Doi = {10.1007/s1153800690871},
Key = {fds287325}
}
@article{fds287288,
Author = {Layton, HE and Pitman, EB and Moore, LC},
Title = {Bifurcation analysis of TGFmediated oscillations in
SNGFR},
Journal = {American Journal of Physiology Renal Physiology},
Volume = {261},
Number = {5 305},
Pages = {F904F919},
Year = {1991},
Month = {December},
Abstract = {Recent micropuncture studies in rats have demonstrated the
existence of oscillatory states in nephron filtration
mediated by tubuloglomerular feedback (TGF). We develop a
minimal mathematical model of the TGF system, consisting of
a firstorder hyperbolic partial differential equation
describing thick ascending limb (TAL) NaCl reabsorption and
an empirical feedback relation. An analytic bifurcation
analysis of this model provides fundamental insight into how
oscillatory states depend on the physiological parameters of
the model. In the special case of no solute backleak in the
TAL, the emergence of oscillations explicitly depends on two
nondimensional parameters. The first corresponds to the
delay time of the TGF response across the juxtaglomerular
apparatus, and the second corresponds to the product of the
slope of the TGF response curve at the steadystate
operating point and the space derivative of the steadystate
NaCl concentration profile in the TAL at the macula densa.
Numerical calculations for the case without TAL backleak are
consistent with this result. Numerical simulation of the
more general case with TAL backleak shows that the
bifurcation analysis still provides useful predictions
concerning nephron dynamics. With typical parameter values,
the analysis predicts that the TGF system will be in an
oscillatory state. However, the system is near enough to the
boundary of the nonoscillatory region so that small changes
in parameter values could result in nonoscillatory behavior.
Copyright © 1991 the american physiological
society.},
Key = {fds287288}
}
@article{fds9596,
Author = {Layton, H. E.},
Title = {Concentrating urine in the inner medulla of the
kidney},
Journal = {Comments on Theoretical Biology 1(3): 179196,
1989.},
Key = {fds9596}
}
@article{fds9604,
Author = {Jamison, Rex L. and Dennis R. Roy and Harold E.
Layton},
Title = {Countercurrent mechanism and its regulation},
Journal = {Chapter 7 in Clinical Disturbances of Water Metabolism,
edited by D. W. Seldin and G. Giebisch. New York: Raven
Press, 1993, p. 119156. (This chapter is an abridgment of
the 1992 chapter by the same authors.)},
Key = {fds9604}
}
@article{fds9601,
Author = {Roy, Dennis R., Jr. and Harold E. Layton and Rex L.
Jamison},
Title = {Countercurrent mechanism and its regulation},
Journal = {Chapter 45 in The Kidney: Physiology and Pathophysiology
(second edition), edited by D. W. Seldin and G. Giebisch.
New York: Raven Press, 1992, p. 16491692.},
Key = {fds9601}
}
@article{fds208186,
Author = {Anita T. Layton and Harold E. Layton},
Title = {Countercurrent multiplication may not explain the axial
osmolality gradient in the outer medulla of the rat
kidney},
Journal = {American Journal of PhysiologyRenal Physiology 301:
F1047F1056},
Year = {2011},
Month = {October},
Key = {fds208186}
}
@article{fds287334,
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 = {fds287334}
}
@article{fds9866,
Author = {Zaritski, Roman M. and E. Bruce Pitman and Harold E. Layton and Leon C. Moore},
Title = {Coupling a tubuloglomerular feedback nephron model with a
myogenic afferent arteriole model},
Journal = {In: Computing and Information Technologies (Proceedings of
the International Conference on Computing and Information
Technologies, Montclair State University, Upper Montclair,
NJ, USA, 12 October 2001), edited by George Antoniou and
Dorothy Deremer. World Scientific Publishing Co. Pte. Ltd.,
2001, p. 5562.},
Key = {fds9866}
}
@article{fds287287,
Author = {Layton, HE},
Title = {Distributed loops of Henle in a central core model of the
renal medulla: Where should the solute come
out?},
Journal = {Mathematical and Computer Modelling},
Volume = {14},
Number = {C},
Pages = {533537},
Publisher = {Elsevier BV},
Year = {1990},
Month = {January},
ISSN = {08957177},
url = {http://dx.doi.org/10.1016/08957177(90)90239J},
Abstract = {In the mammalian kidney the number of loops of Henle
decreases as a function of medullary depth. The role of this
decreasing loop population was studied in a steadystate,
central core model of the renal inner medulla under simple
assumptions: there is no axial diffusion in the central
core; the osmolalities in the central core, the descending
limbs, and the collecting ducts are equal at each medullary
level; and the concentration gradient is generated through
the reabsorption of solute from the waterimpermeable
ascending limbs. A continuous approximation to the loop
distribution in rats was based on experimental data. When
solute is transported from the ascending limbs with a
spatially uniform transport rate, similar in magnitude to
the transport rate from the thick ascending limbs of the
outer medulla, a moderate gradient is generated in the inner
medulla. A steeper gradient, however, is generated by a
transport rate that is largest near the turns in the loops,
but which is scaled so that the total solute transport is
unchanged. When loop distributions that decrease more slowly
than those found in rats are used in the model,
concentrating capability is decreased for both
transportrate assumptions. These results indicate that the
conclusions reached in an earlier study under less accurate
physiological assumptions also hold in a central core model.
© 1990.},
Doi = {10.1016/08957177(90)90239J},
Key = {fds287287}
}
@article{fds287289,
Author = {Layton, HE and Davies, JM},
Title = {Distributed solute and water reabsorption in a central core
model of the renal medulla},
Journal = {Mathematical Biosciences},
Volume = {116},
Number = {2},
Pages = {169196},
Year = {1993},
ISSN = {00255564},
url = {http://dx.doi.org/10.1016/00255564(93)90065I},
Abstract = {In this model study we investigate the dependence of urine
concentrating capability on the spatial distribution of
solute and water reabsorption from Henle's loops. Within the
context of model assumptions, urine concentrating capability
is increased by exponential decline in loop population as a
function of medullary depth and by solute efflux localized
near loop bends, in accordance with earlier, but less
comprehensive, studies. Further, we find that
waterimpermeable prebend enlargements of the descending
limb may release urine concentrating capacity that would
Otherwise be needed to concentrate the fluid flowing in the
prebend enlargements. Calculations reported here suggest
that without some distributed features, even vigorous net
active transport of solute from the ascending limbs of the
inner medulla would not be sufficient to explain the large
concentration gradients generated by some mammals. We
consider the significance of distributed reabsorption for
the operation of the concentrating mechanisms of the
mammalian inner medulla, the mammalian outer medulla, and
the avian medullary cone. © 1993.},
Doi = {10.1016/00255564(93)90065I},
Key = {fds287289}
}
@article{fds287282,
Author = {Layton, HE},
Title = {Distribution of Henle's loops may enhance urine
concentrating capability},
Journal = {Biophysical Journal},
Volume = {49},
Number = {5},
Pages = {10331040},
Year = {1986},
url = {http://dx.doi.org/10.1016/S00063495(86)837316},
Doi = {10.1016/S00063495(86)837316},
Key = {fds287282}
}
@article{fds9606,
Author = {Pitman, E. Bruce and H. E. Layton and Leon C.
Moore},
Title = {Dynamic flow in the nephron: filtered delay in the TGF
pathway},
Journal = {in Fluid Dynamics in Biology: Proceedings of the
AMSIMSSIAM Joint Research Conference, July 1991, Edited by
Angela Cheer and C. P. van Dam, appearing as Contemporary
Mathematics (American Mathematical Society) 141: 317336,
1993.},
Key = {fds9606}
}
@article{fds287312,
Author = {Oldson, DR and Moore, LC and Layton, HE},
Title = {Effect of sustained flow perturbations on stability and
compensation of tubuloglomerular feedback},
Journal = {American Journal of Physiology Renal Physiology},
Volume = {285},
Number = {5 545},
Pages = {F972F989},
Year = {2003},
Month = {November},
Abstract = {A mathematical model previously formulated by us predicts
that limitcycle oscillations (LCO) in nephron flow are
mediated by tubuloglomerular feedback (TGF) and that the LCO
arise from a bifurcation that depends heavily on the
feedback gain magnitude, γ, and on its relationship to a
theoretically determined critical value of gain, γc. In
this study, we used that model to show how sustained
perturbations in proximal tubule flow, a common experimental
maneuver, can initiate or terminate LCO by changing the
values of γ and γc, thus changing the sign of γ  γc.
This result may help explain experiments in which
intratubular pressure oscillations were initiated by the
sustained introduction or removal of fluid from the proximal
tubule (Leyssac PP and Baumbach L. Acta Physiol Scand 117:
415419, 1983). In addition, our model predicts that, for a
range of TGF sensitivities, sustained perturbations that
initiate or terminate LCO can yield substantial and abrupt
changes in both distal NaCl delivery and NaCl delivery
compensation, changes that may play an important role in the
response to physiological challenge.},
Key = {fds287312}
}
@article{fds287340,
Author = {BuduGrajdeanu, P and Moore, LC and Layton, HE},
Title = {Effect of tubular inhomogeneities on filter properties of
thick ascending limb of Henle's loop. Mathematical
Biosciences 209(2): 564592, 2007},
Journal = {Mathematical Biosciences},
Year = {2007},
Month = {October},
Key = {fds287340}
}
@article{fds287314,
Author = {BuduGrajdeanu, P and Moore, LC and Layton, HE},
Title = {Effect of tubular inhomogeneities on filter properties of
thick ascending limb of Henle's loop.},
Journal = {Mathematical Biosciences},
Volume = {209},
Number = {2},
Pages = {564592},
Year = {2007},
Month = {October},
ISSN = {00255564},
url = {http://www.ncbi.nlm.nih.gov/pubmed/17499314},
Abstract = {We used a simple mathematical model of rat thick ascending
limb (TAL) of the loop of Henle to predict the impact of
spatially inhomogeneous NaCl permeability, spatially
inhomogeneous NaCl active transport, and spatially
inhomogeneous tubular radius on luminal NaCl concentration
when sustained, sinusoidal perturbations were superimposed
on steadystate TAL flow. A mathematical model previously
devised by us that used homogeneous TAL transport and fixed
TAL radius predicted that such perturbations result in TAL
luminal fluid NaCl concentration profiles that are standing
waves. That study also predicted that nodes in NaCl
concentration occur at the end of the TAL when the tubular
fluid transit time equals the period of a periodic
perturbation, and that, for nonnodal periods, sinusoidal
perturbations generate nonsinusoidal oscillations (and thus
a series of harmonics) in NaCl concentration at the TAL end.
In the present study we find that the inhomogeneities
transform the standing waves and their associated nodes into
approximate standing waves and approximate nodes. The impact
of inhomogeneous NaCl permeability is small. However, for
inhomogeneous active transport or inhomogeneous radius, the
oscillations for nonnodal periods tend to be less
sinusoidal and more distorted than in the homogeneous case
and to thus have stronger harmonics. Both the homogeneous
and nonhomogeneous cases predict that the TAL, in its
transduction of flow oscillations into concentration
oscillations, acts as a lowpass filter, but the
inhomogeneities result in a less effective filter that has
accentuated nonlinearities.},
Doi = {10.1016/j.mbs.2007.03.007},
Key = {fds287314}
}
@article{fds287337,
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 = {fds287337}
}
@article{fds9592,
Author = {Layton, H. E.},
Title = {Energy advantage of countercurrent oxygen exchange in fish
gills},
Journal = {Journal of Theoretical Biology 125: 307316,
1987.},
Key = {fds9592}
}
@article{fds287283,
Author = {Layton, HE},
Title = {Energy advantage of countercurrent oxygen transfer in fish
gills},
Journal = {Journal of Theoretical Biology},
Volume = {125},
Number = {3},
Pages = {307316},
Publisher = {Elsevier BV},
Year = {1987},
Month = {April},
ISSN = {00225193},
url = {http://dx.doi.org/10.1016/S00225193(87)800620},
Abstract = {A steadystate, onedimensional mathematical model for
oxygen transfer in fish gills suggests that under conditions
permitting adequate oxygen uptake, the uptake advantage of a
countercurrent configuration over a cocurrent
configuration is small, given otherwise identical gills,
fluid fluxes, and afferent fluid oxygen tensions. The in
vivo uptake advantage of a countercurrent fish, compared to
a hypothetical cocurrent fish, is estimated from published
data on oxygen uptake of three fish species (Chaenocephalus
aceratus, Salmo gairdneri, Scyliorhinus stellaris) and found
to range from 3 to 17%. However, heuristic calculations
assuming Poiseuille flow suggest that a cocurrent fish
would expend more than 46% additional power for respiration
to compensate for a 10% uptake advantage enjoyed by an
otherwise identical countercurrent fish. Thus the
importance of countercurrent oxygen transfer may lie
primarily in its energy economy rather than in the magnitude
of the uptake advantage. © 1987 Academic Press Inc.
(London) Ltd.},
Doi = {10.1016/S00225193(87)800620},
Key = {fds287283}
}
@article{fds287285,
Author = {Layton, HE},
Title = {Existence and uniqueness of solutions to a mathematical
model of the urine concentrating mechanism},
Journal = {Mathematical Biosciences},
Volume = {84},
Number = {2},
Pages = {197210},
Publisher = {Elsevier BV},
Year = {1987},
Month = {January},
ISSN = {00255564},
url = {http://dx.doi.org/10.1016/00255564(87)900927},
Abstract = {This paper establishes some results for the existence and
uniqueness of solutions to a previously published
mathematical model of the mammalian urine concentrating
mechanism [H.E. Layton, Distribution of Henle's loops may
enhance urine concentrating capability, Biophys. J.
49:10331040 (1986)]. In particular, the contraction mapping
principle is used to show that for sufficiently small and
sufficiently large values of a positive parameter β there
exist unique solutions to the model, whether it be endowed
with firstorder kinetics or MichaelisMenten kinetics.
Large or small β corresponds to large or small rates of
active transport of NaCl from the ascending limbs. The
Schauder principle is used to show that there exist
solutions to the model for physiologically reasonable
reabsorption kinetics, including firstorder and
MichaelisMenten kinetics for all values of β. ©
1987.},
Doi = {10.1016/00255564(87)900927},
Key = {fds287285}
}
@article{fds208184,
Author = {Anita T. Layton and Matthew Bowen and Amy Wen and Harold E.
Layton},
Title = {Feedbackmediated dynamics in a model of coupled nephrons
with compliant thick ascending limbs},
Journal = {Mathematical Biosciences Vol. 230: 115127},
Year = {2010},
Month = {December},
Key = {fds208184}
}
@article{fds287332,
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 = {fds287332}
}
@article{fds287313,
Author = {Pitman, EB and Zaritski, RM and Kesseler, KJ and Moore, LC and Layton,
HE},
Title = {Feedbackmediated dynamics in two coupled
nephrons},
Journal = {Bulletin of Mathematical Biology},
Volume = {66},
Number = {6},
Pages = {14631492},
Year = {2004},
url = {http://dx.doi.org/10.1016/j.bulm.2004.01.006},
Abstract = {Previously, we developed a dynamic model for the
tubuloglomerular feedback (TGF) system in a single,
shortlooped nephron of the mammalian kidney. In that model,
a semilinear hyperbolic partial differential equation was
used to represent two fundamental processes of solute
transport in the nephron's thick ascending limb (TAL):
chloride advection by fluid flow along the TAL lumen and
transepithelial chloride transport from the lumen to the
interstitium. An empirical function and a time delay were
used to relate glomerular filtration rate to the chloride
concentration at the macula densa of the TAL. Analysis of
the model equations indicated that stable limitcycle
oscillations (LCO) in nephron fluid flow and chloride
concentration can emerge for sufficiently large feedback
gain magnitude and time delay. In this study, the
singlenephron model was extended to two nephrons, which
were coupled through their filtration rates. Explicit
analytical conditions were obtained for bifurcation loci
corresponding to two special cases: (1) identical time
delays but differing feedback gains, and (2) identical gains
but differing delays. Similar to the case of a single
nephron, our analysis indicates that stable LCO can emerge
in coupled nephrons for sufficiently large gains and delays.
However, these LCO may emerge at lower values of the
feedback gain, relative to a single (i.e., uncoupled)
nephron, or at shorter delays, provided the delays are
sufficiently close. These results suggest that, in vivo, if
two nephrons are sufficiently similar, then coupling will
tend to increase the likelihood of LCO. © 2004 Society for
Mathematical Biology. Published by Elsevier Ltd. All rights
reserved.},
Doi = {10.1016/j.bulm.2004.01.006},
Key = {fds287313}
}
@article{fds287304,
Author = {Arthurs, KM and Moore, LC and Pitman, EB and Layton,
HE},
Title = {Flow regulation in afferent arterioles following vascular
injury},
Journal = {Faseb Journal},
Volume = {11},
Number = {3},
Pages = {A82},
Year = {1997},
Month = {December},
ISSN = {08926638},
Abstract = {A mathematical model was used to investigate the role of the
vasodilator nitric oxide (NO) in the regulation of renal
afferent arteriole (AA) segmental resistance (SR) following
vascular injury. The AA was modeled as a twodimensional
elasticcontractile boundary immersed in a fluid domain. The
immersed boundary method was used to quantify the
interaction between the fluid and the model AA walls. The
model includes a representation of the AA's myogenic
response; the convection, diffusion, and degradation of NO;
and the relaxation of the model AA walls in response to NO
concentration. A focal constriction that reduced flow by ca.
20% was used to simulate vascular injury. In the absence of
NO, this focal constriction increased SR, indicating that
the myogenic response alone is insufficient to return
downstream resistance to its preconstricted value. However,
the inclusion of NO released from the injury site, as
indicated in the experimental literature, caused sufficient
dilation downstream to return SR to its preconstricted
value. These simulations suggest that even though NO decays
rapidly, it may have important nonlocal effects. The model
provides a new tool for investigating the quantitative
contributions of microvascular regulatory
mechanisms.},
Key = {fds287304}
}
@article{fds287338,
Author = {NievesGonzález, A and Clausen, C and Marcano, M and Layton, AT and Layton, HE and Moore, LC},
Title = {Fluid dilution and efficiency of Na(+) transport in a
mathematical model of a thick ascending limb
cell.},
Journal = {American Journal of Physiology. Renal Physiology},
Volume = {304},
Number = {6},
Pages = {F634F652},
Year = {2013},
Month = {March},
url = {http://dx.doi.org/10.1152/ajprenal.00100.2012},
Abstract = {Thick ascending limb (TAL) cells are capable of reducing
tubular fluid Na(+) concentration to as low as ~25 mM, and
yet they are thought to transport Na(+) efficiently owing to
passive paracellular Na(+) absorption. Transport efficiency
in the TAL is of particular importance in the outer medulla
where O(2) availability is limited by low blood flow. We
used a mathematical model of a TAL cell to estimate the
efficiency of Na(+) transport and to examine how tubular
dilution and cell volume regulation influence transport
efficiency. The TAL cell model represents 13 major solutes
and the associated transporters and channels; model
equations are based on mass conservation and
electroneutrality constraints. We analyzed TAL transport in
cells with conditions relevant to the inner stripe of the
outer medulla, the corticomedullary junction, and the
distal cortical TAL. At each location Na(+) transport
efficiency was computed as functions of changes in luminal
NaCl concentration ([NaCl]), [K(+)], [NH(4)(+)], junctional
Na(+) permeability, and apical K(+) permeability. Na(+)
transport efficiency was calculated as the ratio of total
net Na(+) transport to transcellular Na(+) transport.
Transport efficiency is predicted to be highest at the
corticomedullary boundary where the transepithelial Na(+)
gradient is the smallest. Transport efficiency is lowest in
the cortex where luminal [NaCl] approaches static
head.},
Doi = {10.1152/ajprenal.00100.2012},
Key = {fds287338}
}
@article{fds338525,
Author = {Li, Q and McDonough, AA and Layton, HE and Layton,
AT},
Title = {Functional implications of sexual dimorphism of transporter
patterns along the rat proximal tubule: modeling and
analysis.},
Journal = {American Journal of Physiology. Renal Physiology},
Volume = {315},
Number = {3},
Pages = {F692F700},
Year = {2018},
Month = {September},
url = {http://dx.doi.org/10.1152/ajprenal.00171.2018},
Abstract = {The goal of this study is to investigate the functional
implications of the sexual dimorphism in transporter
patterns along the proximal tubule. To do so, we have
developed sexspecific computational models of solute and
water transport in the proximal convoluted tubule of the rat
kidney. The models account for the sex differences in
expression levels of the apical and basolateral
transporters, in singlenephron glomerular filtration rate,
and in tubular dimensions. Model simulations predict that
70.6 and 38.7% of the filtered volume is reabsorbed by the
proximal tubule of the male and female rat kidneys,
respectively. The lower fractional volume reabsorption in
females can be attributed to their smaller transport area
and lower aquaporin1 expression level. The latter also
results in a larger contribution of the paracellular pathway
to water transport. Correspondingly similar fractions (70.9
and 39.2%) of the filtered Na+ are reabsorbed by the male
and female proximal tubule models, respectively. The lower
fractional Na+ reabsorption in females is due primarily to
their smaller transport area and lower Na+/H+ exchanger
isoform 3 and claudin2 expression levels. Notably, unlike
most Na+ transporters, whose expression levels are lower in
females, Na+glucose cotransporter 2 (SGLT2) expression
levels are 2.5fold higher in females. Model simulations
suggest that the higher SGLT2 expression in females may
compensate for their lower tubular transport area to achieve
a hyperglycemic tolerance similar to that of
males.},
Doi = {10.1152/ajprenal.00171.2018},
Key = {fds338525}
}
@article{fds287330,
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 = {fds287330}
}
@article{fds9605,
Author = {Knepper, M. A. and C.L. Chou and H. E. Layton},
Title = {How is urine concentrated by the inner medulla?},
Journal = {In: Moving Points in Nephrology, edited by E. Bourke, N. P.
Mallick, and V. E. Pollak, appearing as Contributions to
Nephrology, Vol. 102, pp. 144160, S. Karger, Basel,
1993.},
Key = {fds9605}
}
@article{fds287290,
Author = {Knepper, MA and Chou, CL and Layton, HE},
Title = {How is urine concentrated by the renal inner
medulla?},
Journal = {Contributions to nephrology},
Volume = {102},
Pages = {144160},
Year = {1993},
Key = {fds287290}
}
@article{fds287331,
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 = {fds287331}
}
@article{fds287297,
Author = {Layton, HE and Pitman, EB and Moore, LC},
Title = {Instantaneous and steadystate gains in the tubuloglomerular
feedback system},
Journal = {American Journal of Physiology Renal Physiology},
Volume = {268},
Number = {1 371},
Pages = {F163F174},
Year = {1995},
Month = {January},
Abstract = {The load of water and solute entering each nephron of the
mammalian kidney is regulated by the tubuloglomerular
feedback (TGF) mechanism, a negative feedback loop.
Experiments in rats have shown that key variables of this
feedback system may exhibit TGFmediated oscillations.
Mathematical modeling studies have shown that the
openfeedbackloop gain is a crucial parameter for
determining whether oscillations will emerge. However, two
different formulations of this gain have been used. The
first is the steadystate gain, a readily measurable
quantity corresponding to the steadystate reduction in
singlenephron glomerular filtration rate (SNGFR) subsequent
to a sustained increase in ascending limb flow rate. The
second is an instantaneous gain, a variable arising from
theoretical considerations corresponding to the maximum
reduction in SNGFR resulting from an instantaneous shift of
the ascending limb flow column, with the assumption that the
SNGFR response is also instantaneous. Here we show by an
analytic argument how the steadystate and instantaneous
openfeedbackloop gains for the ascending limb are related.
In the case of no solute backleak into the ascending limb,
the two formulations of gain are equivalent; however, in the
presence of solute backleak, the instantaneous gain is
larger in magnitude than the steadystate gain. With typical
physiological parameters for the rat, calculations with a
model previously devised by us show that the gains differ by
510%. Hence, experimental measurements of the steadystate
gain may provide useful lower bound estimates of the
instantaneous gain of the feedback system in the normal rat.
However, the gains may diverge significantly in
pathophysiological states where ascending limb transport is
compromised by abnormally high NaCl permeability.},
Key = {fds287297}
}
@article{fds318292,
Author = {Layton, HE and Pitman, EB and Moore, LC},
Title = {Instantaneous and steadystate gains in the tubuloglomerular
feedback system.},
Journal = {The American Journal of Physiology},
Volume = {268},
Number = {1 Pt 2},
Pages = {F163F174},
Year = {1995},
Month = {January},
url = {http://dx.doi.org/10.1152/ajprenal.1995.268.1.f163},
Abstract = {The load of water and solute entering each nephron of the
mammalian kidney is regulated by the tubuloglomerular
feedback (TGF) mechanism, a negative feedback loop.
Experiments in rats have shown that key variables of this
feedback system may exhibit TGFmediated oscillations.
Mathematical modeling studies have shown that the
openfeedbackloop gain is a crucial parameter for
determining whether oscillations will emerge. However, two
different formulations of this gain have been used. The
first is the steadystate gain, a readily measurable
quantity corresponding to the steadystate reduction in
singlenephron glomerular filtration rate (SNGFR) subsequent
to a sustained increased in ascending limb flow rate. The
second is an instantaneous gain, a variable arising from
theoretical considerations corresponding to the maximum
reduction in SNGFR resulting from an instantaneous shift of
the ascending limb flow column, with the assumption that the
SNGFR response is also instantaneous. Here we show by an
analytic argument how the steadystate and instantaneous
openfeedbackloop gains for the ascending limb are related.
In the case of no solute backleak into the ascending limb,
the two formulations of gain are equivalent; however, in the
presence of solute backleak, the instantaneous gain is
larger in magnitude than the steadystate gain. With typical
physiological parameters for the rat, calculations with a
model previously devised by us show that the gains differ by
510%. Hence, experimental measurements of the steadystate
gain may provide useful lowerbound estimates of the
instantaneous gain of the feedback system in the normal rat.
However, the gains may diverge significantly in
pathophysiological states where ascending limb transport is
compromised by abnormally high NaCl permeability.},
Doi = {10.1152/ajprenal.1995.268.1.f163},
Key = {fds318292}
}
@article{fds287324,
Author = {Thomas, SR and Layton, AT and Layton, HE and Moore,
LC},
Title = {Kidney modeling: Status and perspectives},
Journal = {Proceedings of the Ieee},
Volume = {94},
Number = {4},
Pages = {740752},
Publisher = {Institute of Electrical and Electronics Engineers
(IEEE)},
Year = {2006},
Month = {April},
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 = {fds287324}
}
@article{fds287308,
Author = {Layton, HE and Pitman, EB and Moore, LC},
Title = {Limitcycle oscillations and tubuloglomerular feedback
regulation of distal sodium delivery.},
Journal = {American Journal of Physiology. Renal Physiology},
Volume = {278},
Number = {2},
Pages = {F287F301},
Year = {2000},
Month = {February},
ISSN = {03636127},
url = {http://dx.doi.org/10.1152/ajprenal.2000.278.2.f287},
Abstract = {A mathematical model was used to evaluate the potential
effects of limitcycle oscillations (LCO) on
tubuloglomerular feedback (TGF) regulation of fluid and
sodium delivery to the distal tubule. In accordance with
linear systems theory, simulations of steadystate responses
to infinitesimal perturbations in singlenephron glomerular
filtration rate (SNGFR) show that TGF regulatory ability
(assessed as TGF compensation) increases with TGF gain
magnitude gamma when gamma is less than the critical value
gamma(c), the value at which LCO emerge in tubular fluid
flow and NaCl concentration at the macula densa. When gamma
> gamma(c) and LCO are present, TGF compensation is reduced
for both infinitesimal and finite perturbations in SNGFR,
relative to the compensation that could be achieved in the
absence of LCO. Maximal TGF compensation occurs when gamma
approximately gamma(c). Even in the absence of
perturbations, LCO increase timeaveraged sodium delivery to
the distal tubule, while fluid delivery is little changed.
These effects of LCO are consequences of nonlinear elements
in the TGF system. Because increased distal sodium delivery
may increase the rate of sodium excretion, these simulations
suggest that LCO enhance sodium excretion.},
Doi = {10.1152/ajprenal.2000.278.2.f287},
Key = {fds287308}
}
@article{fds287298,
Author = {Pitman, EB and Layton, HE},
Title = {Mass conservation in a dynamic numerical method for a model
of the urine concentrating mechanism},
Journal = {Zamm Zeitschrift Für Angewandte Mathematik Und
Mechanik},
Volume = {76},
Number = {SUPPL. 4},
Pages = {4548},
Year = {1996},
Month = {December},
ISSN = {00442267},
Abstract = {Dynamic models of the urine concentrating mechanism consist
of large systems of hyperbolic partial differential
equations (PDEs), expressing solute conservation, coupled to
ordinary differential equations (ODEs) for water
conservation. Most numerical methods reformulate these
equations in the steadystate, yielding boundaryvalue
systems of stiff ODEs, which are usually solved by some
variant of Newton's method. We have developed an explicit,
secondorder numerical method for solving the dynamic
PDEODE system. The method is robust and easily adapted to
different renal architectures. Moreover, as we show here,
when the method is used in a largescale simulation of the
renal medulla, the asymptotic steadystate exhibits
secondorder spatial convergence in solute and water mass
flows.},
Key = {fds287298}
}
@article{fds287309,
Author = {Layton, HE and Davies, JM and Casotti, G and Braun,
EJ},
Title = {Mathematical model of an avian urine concentrating
mechanism.},
Journal = {American Journal of Physiology. Renal Physiology},
Volume = {279},
Number = {6},
Pages = {F1139F1160},
Year = {2000},
Month = {December},
ISSN = {03636127},
url = {http://dx.doi.org/10.1152/ajprenal.2000.279.6.f1139},
Abstract = {A mathematical model was used to investigate how
concentrated urine is produced within the medullary cones of
the quail kidney. Model simulations were consistent with a
concentrating mechanism based on singlesolute
countercurrent multiplication and on NaCl cycling from
ascending to descending limbs of loops of Henle. The model
predicted a urinetoplasma (U/P) osmolality ratio of
approximately 2.26, a value consistent with maximum avian
U/P osmolality ratios. Active NaCl transport from descending
limb prebend thick segments contributed 70% of concentrating
capability. NaCl entry and water extraction provided 80 and
20%, respectively, of the concentrating effect in descending
limb flow. Parameter studies indicated that urine osmolality
is sensitive to the rate of fluid entry into descending
limbs and collecting ducts at the cone base. Parameter
studies also indicated that the energetic cost of
concentrating urine is sensitive to loop of Henle population
as a function of medullary depth: as the fraction of loops
reaching the cone tip increased above anatomic values, urine
osmolality increased only marginally, and, ultimately, urine
osmolality decreased.},
Doi = {10.1152/ajprenal.2000.279.6.f1139},
Key = {fds287309}
}
@article{fds290485,
Author = {Layton, HE and Casotti, G and Davies, JM and Braun,
EJ},
Title = {Mathematical model of avian urine concentrating
mechanism},
Journal = {Faseb Journal},
Volume = {11},
Number = {3},
Pages = {A9},
Year = {1997},
Month = {December},
ISSN = {08926638},
Abstract = {A mathematical model of the avian urine concentrating
mechanism was used to investigate how concentrating
capability depends on morphological and tubular transport
parameters. In the bird, urine is concentrated in the
medullary cones, subunits of the kidney that contain
countercurrent multiplier systems. The collecting ducts and
loops of Henle of a single medullary cone were modeled as
interacting flowtubes; the interstitium and vasculature
were represented by a central core (CC). The model included
active transport of NaCl from thick ascending and prebend
thick descending limbs into the CC and passive diffusion of
NaCl from the CC into thin descending limbs. Simulations
conducted with parameters based on experimental measurements
produced urinetoplasma osmolality ratios of about 1.7,
consistent with experimentally measured osmolalities. Active
NaCl transport from the descending limb prebend segment was
found to contribute about 35% of this concentrating
capability. In addition, simulations indicated that
concentrating capability is highly sensitive to
loopofHenle population as a function of medullary
depth.},
Key = {fds290485}
}
@article{fds10278,
Author = {Layton, Harold E.},
Title = {Mathematical models of the mammalian urine concentrating
mechanism},
Journal = {In: Membrane Transport and Renal Physiology, The IMA Volumes
in Mathematics and Its Applications, Volume 129, edited by
Harold E. Layton and Alan M. Weinstein. New York,
SpringerVerlag, pp. 233272, 2002.},
Key = {fds10278}
}
@article{fds172982,
Author = {Mariano Marcano and Anita T. Layton and Harold E.
Layton},
Title = {Maximum urine concentrating capability for transport
parameters and urine flow within prescribed
ranges},
Journal = {Bulletin of Mathematical Biology 72:314339,
2010},
Year = {2010},
Month = {April},
Key = {fds172982}
}
@article{fds287329,
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 = {fds287329}
}
@article{fds287307,
Author = {Arthurs, KM and Moore, LC and Peskin, CS and Pitman, EB and Layton,
HE},
Title = {Modeling arteriolar flow and mass transport using the
immersed boundary method},
Journal = {Journal of Computational Physics},
Volume = {147},
Number = {2},
Pages = {402440},
Publisher = {Elsevier BV},
Year = {1998},
Month = {December},
url = {http://dx.doi.org/10.1006/jcph.1998.6097},
Abstract = {Flow in arterioles is determined by a number of interacting
factors, including perfusion pressure, neural stimulation,
vasoactive substances, the intrinsic contractility of
arteriolar walls, and wall shear stress. We have developed a
twodimensional model of arteriolar fluid flow and mass
transport. The model includes a phenomenological
representation of the myogenic response of the arteriolar
wall, in which an increase in perfusion pressure stimulates
vasoconstriction. The model also includes the release,
advection, diffusion, degradation, and dilatory action of
nitric oxide (NO), a potent, but shortlived, vasodilatory
agent. Parameters for the model were taken primarily from
the experimental literature of the rat renal afferent
arteriole. Solutions to the incompressible NavierStokes
equations were approximated by means of a splitting that
used upwind differencing for the inertial term and a
spectral method for the viscous term and incompressibility
condition. The immersed boundary method was used to include
the forces arising from the arteriolar walls. The advection
of NO was computed by means of a highorder fluxcorrected
transport scheme; the diffusion of NO was computed by a
spectral solver. Simulations demonstrated the efficacy of
the numerical methods employed, and grid refinement studies
confirmed anticipated firstorder temporal convergence and
demonstrated secondorder spatial convergence in key
quantities. By providing information about the effective
width of the immersed boundary and sheer stress magnitude
near that boundary, the grid refinement studies indicate the
degree of spatial refinement required for quantitatively
reliable simulations. Owing to the dominating effect of NO
advection, relative to degradation and diffusion,
simulations indicate that NO has the capacity to produce
dilation along the entire length of the arteriole. © 1998
Academic Press.},
Doi = {10.1006/jcph.1998.6097},
Key = {fds287307}
}
@article{fds287323,
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 = {fds287323}
}
@article{fds287327,
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 = {fds287327}
}
@article{fds287281,
Author = {Layton, HE},
Title = {Nephron distribution enhances concentrating
capability},
Journal = {Federation Proceedings},
Volume = {44},
Number = {6},
Pages = {No.8773},
Year = {1985},
Month = {January},
Key = {fds287281}
}
@article{fds287302,
Author = {Layton, HE and Pitman, EB and Moore, LC},
Title = {Nonlinear filter properties of the thick ascending
limb},
Journal = {American Journal of Physiology Renal Physiology},
Volume = {273},
Number = {4 424},
Pages = {F625F634},
Year = {1997},
Month = {October},
ISSN = {03636127},
Abstract = {A mathematical model was used to investigate the filter
properties of the thick ascending limb (TAL), that is, the
response of TAL luminal NaCl concentration to oscillations
in tubular fluid flow. For the special case of no
transtubular NaCl backleak and for spatially homogeneous
transport parameters, the model predicts that NaCl
concentration in intratubular fluid at each location along
the TAL depends only on the fluid transit time up the TAL to
that location. This exact mathematical result has four
important consequences: 1) when a sinusoidal component is
added to steadystate TAL flow, the NaCl concentration at
the macula densa (MD) undergoes oscillations that are
bounded by a range interval envelope with magnitude that
decreases as a function of oscillatory frequency; 2) the
frequency response within the range envelope exhibits nodes
at those frequencies where the oscillatory flow has a
transit time to the MD that equals the steadystate fluid
transit time (this nodal structure arises from the
establishment of standing waves in luminal concentration,
relative to the steadystate concentration profile, along
the length of the TAL); 3) for any dynamically changing but
positive TAL flow rate, the luminal TAL NaCl concentration
profile along the TAL decreases monotonically as a function
of TAL length; and 4) sinusoidal oscillations in TAL flow,
except at nodal frequencies, result in nonsinusoidal
oscillations in NaCl concentration at the MD. Numerical
calculations that include NaCl backleak exhibit solutions
with these same four properties. For parameters in the
physiological range, the first few nodes in the frequency
response curve are separated by antinodes of significant
amplitude, and the nodes arise at frequencies well below the
frequency of respiration in rat. Therefore, the nodal
structure and nonsinusoidal oscillations should be
detectable in experiments, and they may influence the
dynamic behavior of the tubuloglomerular feedback
system.},
Key = {fds287302}
}
@article{fds340683,
Author = {Layton, HE and Pitman, EB and Moore, LC},
Title = {Nonlinear filter properties of the thick ascending
limb.},
Journal = {The American Journal of Physiology},
Volume = {273},
Number = {4 Pt 2},
Pages = {F625F634},
Year = {1997},
Month = {October},
Abstract = {A mathematical model was used to investigate the filter
properties of the thick ascending limb (TAL), that is, the
response of TAL luminal NaCl concentration to oscillations
in tubular fluid flow. For the special case of no
transtubular NaCl backleak and for spatially homogeneous
transport parameters, the model predicts that NaCl
concentration in intratubular fluid at each location along
the TAL depends only on the fluid transit time up the TAL to
that location. This exact mathematical result has four
important consequences: 1) when a sinusoidal component is
added to steadystate TAL flow, the NaCl concentration at
the macula densa (MD) undergoes oscillations that are
bounded by a range interval envelope with magnitude that
decreases as a function of oscillatory frequency; 2) the
frequency response within the range envelope exhibits nodes
at those frequencies where the oscillatory flow has a
transit time to the MD that equals the steadystate fluid
transit time (this nodal structure arises from the
establishment of standing waves in luminal concentration,
relative to the steadystate concentration profile, along
the length of the TAL); 3) for any dynamically changing but
positive TAL flow rate, the luminal TAL NaCl concentration
profile along the TAL decreases monotonically as a function
of TAL length; and 4) sinusoidal oscillations in TAL flow,
except at nodal frequencies, result in nonsinusoidal
oscillations in NaCl concentration at the MD. Numerical
calculations that include NaCl backleak exhibit solutions
with these same four properties. For parameters in the
physiological range, the first few nodes in the frequency
response curve are separated by antinodes of significant
amplitude, and the nodes arise at frequencies well below the
frequency of respiration in rat. Therefore, the nodal
structure and nonsinusoidal oscillations should be
detectable in experiments, and they may influence the
dynamic behavior of the tubuloglomerular feedback
system.},
Key = {fds340683}
}
@article{fds287292,
Author = {Pitman, EB and Layton, HE and Moore, LC},
Title = {Numerical simulation of propagating concentration profiles
in renal tubules},
Journal = {Bulletin of Mathematical Biology},
Volume = {56},
Number = {3},
Pages = {567586},
Year = {1994},
ISSN = {00928240},
url = {http://dx.doi.org/10.1007/BF02460471},
Abstract = {Methoddependent mechanisms that may affect dynamic
numerical solutions of a hyperbolic partial differential
equation that models concentration profiles in renal tubules
are described. Some numerical methods that have been applied
to the equation are summarized, and ways by which the
methods may misrepresent true solutions are analysed.
Comparison of these methods demonstrates the need for
thoughtful application of computational mathematics when
simulating complicated timedependent phenomena. © 1994
Elsevier Science Ltd.},
Doi = {10.1007/BF02460471},
Key = {fds287292}
}
@article{fds287286,
Author = {Layton, HE and Pitman, EB},
Title = {Oscillations in a simple model of tubuloglomerular
feedback},
Journal = {Annual International Conference of the Ieee Engineering in
Medicine and Biology Proceedings},
Number = {pt 3},
Pages = {987988},
Year = {1990},
Month = {December},
Abstract = {The tubuloglomerular feedback (TGF) system regulates the
fluid and solute load in each nephron of the mammalian
kidney. The authors obtain a necessary condition for
sustained oscillations in a simple mathematical model for
the TGF loop. This model consists of a hyperbolic partial
differential equation representing the chloride
concentration in the thick ascending limb and an empirical
function describing the feedback response of the
juxtaglomerular apparatus. A bifurcation analysis shows that
critical parameters are the time delay, the slope of the
empirical feedback relation at the steady state, and the
steadystate space derivative of the chloride concentration
at the macula densa.},
Key = {fds287286}
}
@article{fds287295,
Author = {Layton, HE and Knepper, MA and Chou, CL},
Title = {Permeability criteria for effective function of passive
countercurrent multiplier.},
Journal = {The American Journal of Physiology},
Volume = {270},
Number = {1 Pt 2},
Pages = {F920},
Year = {1996},
Month = {January},
ISSN = {00029513},
url = {http://dx.doi.org/10.1152/ajprenal.1996.270.1.f9},
Abstract = {The urine concentrating effect of the mammalian renal inner
medulla has been attributed to countercurrent multiplication
of a transepithelial osmotic difference arising from passive
absorption of NaCl from thin ascending limbs of long loops
of Henle. This study assesses, both mathematically and
experimentally, whether the permeability criteria for
effective function of this passive hypothesis are consistent
with transport properties measured in long loops of Henle of
chinchilla. Mathematical simulations incorporating loop of
Henle transepithelial permeabilities idealized for the
passive hypothesis generated a steep inner medullary osmotic
gradient, confirming the fundamental feasibility of the
passive hypothesis. However, when permeabilities measured in
chinchilla were used, no inner medullary gradient was
generated. A key parameter in the apparent failure of the
passive hypothesis is the longloop descending limb (LDL)
urea permeability, which must be small to prevent
significant transepithelial urea flux into inner medullary
LDL. Consequently, experiments in isolated perfused thin LDL
were conducted to determine whether the urea permeability
may be lower under conditions more nearly resembling those
in the inner medulla. LDL segments were dissected from
3070% of the distance along the inner medullary axis of the
chinchilla kidney. The factors tested were NaCl
concentration (125400 mM in perfusate and bath), urea
concentration (5500 mM in perfusate and bath), calcium
concentration (28 mM in perfusate and bath), and protamine
concentration (300 micrograms/ml in perfusate). None of
these factors significantly altered the measured urea
permeability, which exceeded 20 x 10(5) cm/s for all
conditions. Simulation results show that this moderately
high urea permeability in LDL is an order of magnitude too
high for effective operation of the passive countercurrent
multiplier.},
Doi = {10.1152/ajprenal.1996.270.1.f9},
Key = {fds287295}
}
@article{fds287306,
Author = {Layton, HE and Pitman, EB and Moore, LC},
Title = {Potential natriuretic effects of limitcycle oscillations
mediated by tubuloglomerular feedback},
Journal = {Faseb Journal},
Volume = {12},
Number = {4},
Pages = {A108},
Year = {1998},
ISSN = {08926638},
Abstract = {Previously, we used a mathematical model to show that
limitcycle oscillations in nephron water and NaCl flow
emerge when tubuloglomerular feedback (TGF) gain magnitude
γ exceeds a critical value γc ≈ 3.5. Here, we used the
model to investigate the effect of oscillations on the
ability of TGF to regulate water and NaCl delivery to the
distal nephron. For γ < γc, the TGF system, if
transiently perturbed, returned to a steadystate in which
distal delivery of water and NaCl was independent of γ.
Moreover, feedback compensation for infinitesimal sustained
perturbations agreed well with the predictions of linear
systems theory (LST). However, for γ > γc, as the
system tended to a limit cycle, two phenomena emerged.
First, as γ increased from γc to 10, timeaveraged NaCl
delivery increased 3.7% above steadystate delivery, whereas
water delivery deviated from the steadystate by < 0.5%.
Second, for γ > γc, feedback compensation was reduced
up to 21%, in comparison with the predictions of LST. Hence,
these studies suggest that the emergence of TGF oscillations
increases distal NaCl delivery and limits regulatory
ability, effects that tend to enhance sodium
excretion.},
Key = {fds287306}
}
@article{fds287326,
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},
Month = {November},
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 microm
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.},
Doi = {10.1152/ajprenal.90252.2008},
Key = {fds287326}
}
@article{fds287336,
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 = {fds287336}
}
@article{fds287299,
Author = {Layton, HE and Pitman, EB and Moore, LC},
Title = {Spectral properties of the TGF pathway},
Journal = {Zamm Zeitschrift Für Angewandte Mathematik Und
Mechanik},
Volume = {76},
Number = {SUPPL. 4},
Pages = {3335},
Year = {1996},
Month = {December},
ISSN = {00442267},
Abstract = {The tubuloglomerular feedback (TGF) mechanism regulates the
rate of fluid and solute entry into the nephrons, the
functional units of the kidney. Experiments in rats have
shown that key variables in the TGF pathway may exhibit a
regular, sustained oscillation, of frequency ∼35 mHz;
further experiments have revealed substantial spectral
complexity, of unknown etiology, up to 500 mHz, in blood
flow through the associated vasculature. We have previously
published a simple mathematical model of the TGF pathway
that predicts the lowfrequency oscillation. Here we report
additional analysis of the model that suggests that the
spectral complexity in the 50500 mHz range arises, at least
in part, from intrinsic properties of the TGF
pathway.},
Key = {fds287299}
}
@article{fds287301,
Author = {Layton, HE and Pitman, EB and Moore, LC},
Title = {Spectral properties of the thick ascending
limb},
Journal = {Faseb Journal},
Volume = {10},
Number = {3},
Pages = {A547},
Year = {1996},
Month = {December},
ISSN = {08926638},
Abstract = {We used explicit calculations and numerical analysis to
investigate spectral properties of NaCl transport in a
mathematical model of the thick ascending limb (TAL) and
tubuloglomerular feedback (TGF) mechanism. Explicit
calculations predict that when the period of an oscillation
in TAL luminal fluid flow evenly divides the steadystate
fluid transit time of TAL, then the NaCl concentration in
flow past the macula densa (MD ) maintains a value nearly
equal to the steadystate concentration, i.e., there is a
node at the MD. Oscillations with periods about halfway
between nodal periods produce oscillations in NaCl
concentration with locally maximal amplitude at the MD,
i.e., they produce antinodes. These spectral properties were
further evaluated by perturbing TAL model flow with
broadband forcing and computing power spectra from numerical
solutions of the closedloop TGF signal. In cases where
feedback gain is less than that required for emergence of a
sustained oscillation, the spectra are dominated by the
spectral structure of the TAL. Published measurements of
power spectra of glomerular blood flow have characteristics
consistent with the predicted spectral properties of the
TAL.},
Key = {fds287301}
}
@article{fds287305,
Author = {Layton, HE and Pitman, EB and Moore, LC},
Title = {Spectral properties of the tubuloglomerular feedback
system},
Journal = {American Journal of Physiology Renal Physiology},
Volume = {273},
Number = {4 424},
Pages = {F635F649},
Year = {1997},
ISSN = {03636127},
Abstract = {A simple mathematical model was used to investigate the
spectral properties of the tubuloglomerular feedback (TGF)
system. A perturbation, consisting of smallamplitude
broadband forcing, was applied to simulated thick ascending
limb (TAL) flow, and the resulting spectral response of the
TGF pathway was assessed by computing a power spectrum from
resulting TGF regulated TAL flow. Power spectra were
computed for both open and closed feedbackloop cases.
Openfeedbackloop power spectra are consistent with a
mathematical analysis that predicts a nodal pattern in TAL
frequency response, with nodes corresponding to frequencies
where oscillatory flow has a TAL transit time that equals
the steadystate fluid transit time. Closed feedbackloop
spectra are dominated by the openloop spectral response,
provided that γ, the magnitude of feedback gain is less
than the critical value γ(c) required for emergence of a
sustained TGFmediated oscillation. For γ exceeding γ(c),
closedloop spectra have peaks corresponding to the
fundamental frequency of the TGFmediated oscillation and
its harmonics. The harmonics, expressed in a nonsinusoidal
waveform for tubular flow, are introduced by nonlinear
elements of the TGF pathway, notably TAL transit time and
the TGF response curve. The effect of transit time on the
flow waveform leads to crests that are broader than troughs
and to an asymmetry in the magnitudes of increasing and
decreasing slopes. For feedback gain magnitude that is
sufficiently large, the TGF response curve tends to give a
square waveshape to the waveform. Published waveforms and
power spectra of in vivo TGF oscillations have features
consistent with the predictions of this analysis.},
Key = {fds287305}
}
@article{fds287303,
Author = {Pitman, EB and Zaritski, R and Moore, LC and Layton,
HE},
Title = {TGFmediated bifurcation in two coupled nephrons},
Journal = {Faseb Journal},
Volume = {11},
Number = {3},
Pages = {A85},
Year = {1997},
Month = {December},
ISSN = {08926638},
Abstract = {Experiments have found synchronized oscillations of 2050
mHz in proximal tubule flow in nephrons identified as
arising from the same cortical radial artery (CRA). We use
explicit analysis and numerical studies to investigate the
properties, of a simple mathematical model that includes a
representation of two nephrons arising from the same CRA.
The model includes a representation of ascending limb
dynamics, tubuloglomerular feedback (TGF). and vascular
coupling between the nephrons. As in singlenephron models,
analysis shows that increasing the gain of the TGF loop
beyond a critical value, or increasing the signal delay time
at the macula densa, destabilizes a timeindependent model
solution and leads to sustained TGFmediated oscillations in
tubular flow. Analysis and numerical studies indicate that
sustained oscillations in one nephron may induce sustained
oscillations in the second nephron. For a physiologically
relevant parameter range, the amplitude of the oscillations
varies, with a long period, exemplifying the dynamics of
"beats"' that arises in weakly coupled oscillators.},
Key = {fds287303}
}
@article{fds287328,
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 = {fds287328}
}
@article{fds287315,
Author = {Sands, JM and Layton, HE},
Title = {The Physiology of Urinary Concentration: An
Update},
Journal = {Seminars in Nephrology},
Volume = {29},
Number = {3},
Pages = {178195},
Year = {2009},
ISSN = {02709295},
url = {http://dx.doi.org/10.1016/j.semnephrol.2009.03.008},
Abstract = {The renal medulla produces concentrated urine through the
generation of an osmotic gradient extending from the
corticomedullary boundary to the inner medullary tip. This
gradient is generated in the outer medulla by the
countercurrent multiplication of a comparatively small
transepithelial difference in osmotic pressure. This small
difference, called a single effect, arises from active NaCl
reabsorption from thick ascending limbs, which dilutes
ascending limb flow relative to flow in vessels and other
tubules. In the inner medulla, the gradient may also be
generated by the countercurrent multiplication of a single
effect, but the single effect has not been definitively
identified. There have been important recent advances in our
understanding of key components of the urine concentrating
mechanism. In particular, the identification and
localization of key transport proteins for water, urea, and
sodium, the elucidation of the role and regulation of
osmoprotective osmolytes, better resolution of the
anatomical relationships in the medulla, and improvements in
mathematic modeling of the urine concentrating mechanism.
Continued experimental investigation of transepithelial
transport and its regulation, both in normal animals and in
knockout mice, and incorporation of the resulting
information into mathematic simulations, may help to more
fully elucidate the inner medullary urine concentrating
mechanism. © 2009 Elsevier Inc. All rights
reserved.},
Doi = {10.1016/j.semnephrol.2009.03.008},
Key = {fds287315}
}
@article{fds287276,
Author = {Sands, JM and Mount, DB and Layton, HE},
Title = {The physiology of water homeostasis},
Pages = {128},
Booktitle = {Core Concepts in the Disorders of Fluid, Electrolytes and
AcidBase Balance},
Publisher = {Springer US},
Year = {2013},
Month = {November},
ISBN = {1461437695},
url = {http://dx.doi.org/10.1007/9781461437703_1},
Abstract = {© 2013 Springer Science+Business Media New York. All rights
are reserved. Water is the most abundant constituent in the
body. Vasopressin secretion, water ingestion, and the renal
concentrating mechanism collaborate to maintain human body
fluid osmolality nearly constant. Abnormalities in these
processes cause hyponatremia, hypernatremia, and polyuria.
The primary hormonal control of renal water excretion is by
vasopressin (also named antidiuretic hormone). Thirst and
vasopressin release from the posterior pituitary are under
the control of osmoreceptive neurons in the central nervous
system. The kidney maintains blood plasma osmolality and
sodium concentration nearly constant by means of mechanisms
that independently regulate water and sodium excretion. The
renal medulla produces concentrated urine through the
generation of an osmotic gradient extending from the
corticomedullary boundary to the inner medullary tip. This
gradient is generated in the outer medulla by the
countercurrent multiplication of a comparatively small
transepithelial difference in osmotic pressure. This small
difference, called a single effect, arises from active NaCl
reabsorption from thick ascending limbs, which dilutes
ascending limb flow relative to flow in vessels and other
tubules. In the inner medulla, the gradient may also be
generated by the countercurrent multiplication of a single
effect, but the single effect has not been definitively
identified. Continued experimental investigation and
incorporation of the resulting information into mathematic
simulations may help to more fully elucidate the inner
medullary urine concentrating mechanism.},
Doi = {10.1007/9781461437703_1},
Key = {fds287276}
}
@article{fds208190,
Author = {Jeff M. Sands and David B. Mount and Harold E.
Layton},
Title = {The physiology of water homeostasis},
Booktitle = {Core Concepts in the Disorders of Fluids, Electrolytes, and
AcidBase Balance},
Publisher = {Springer},
Editor = {David B. Mount and Ajay Singh and Mo Sayegh},
Year = {2012},
Month = {August},
Key = {fds208190}
}
@article{fds287278,
Author = {Sands, JM and Layton, HE},
Title = {The Urine Concentrating Mechanism and Urea
Transporters},
Volume = {1},
Pages = {14631510},
Publisher = {Elsevier},
Year = {2013},
url = {http://dx.doi.org/10.1016/b9780123814623.000434},
Doi = {10.1016/b9780123814623.000434},
Key = {fds287278}
}
@article{fds208188,
Author = {Jeff M. Sands and Harold E. Layton},
Title = {The urine concentrating mechanism and urea
transporters},
Series = {5th Edition},
Booktitle = {Seldin and Giebische's The Kidney: Physiology and
Pathophysiology},
Publisher = {Elsevier/Academic Press},
Editor = {Robert Alphern and Orson Moe and Michaeal Caplan},
Year = {2010},
Month = {October},
Key = {fds208188}
}
@article{fds287279,
Author = {Sands, JM and Layton, HE},
Title = {The Urine Concentrating Mechanism and Urea
Transporters},
Series = {4th Edition},
Pages = {11431178},
Booktitle = {The Kidney: Physiology and Pathophysiology},
Publisher = {Elsevier},
Address = {New York},
Editor = {Robert J. Alpern and Steven C. Hebert},
Year = {2008},
url = {http://dx.doi.org/10.1016/b9780120884889.500437},
Doi = {10.1016/b9780120884889.500437},
Key = {fds287279}
}
@article{fds287280,
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 = {fds287280}
}
@article{fds323465,
Author = {Pitman, EB and Layton, HE},
Title = {Tubuloglomerular feedback in a dynamic nephron},
Journal = {Communications on Pure and Applied Mathematics},
Volume = {42},
Number = {6},
Pages = {759787},
Year = {1989},
Month = {September},
url = {http://dx.doi.org/10.1002/cpa.3160420604},
Doi = {10.1002/cpa.3160420604},
Key = {fds323465}
}
@article{fds287320,
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},
Pages = {F816F839},
Year = {2004},
Month = {October},
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 = {fds287320}
}
@article{fds287284,
Author = {Layton, HE},
Title = {Urea transport in a distributed loop model of the
urineconcentrating mechanism.},
Journal = {The American Journal of Physiology},
Volume = {258},
Number = {4 Pt 2},
Pages = {F1110F1124},
Year = {1990},
Month = {April},
url = {http://dx.doi.org/10.1152/ajprenal.1990.258.4.f1110},
Abstract = {Continuously distributed loops of Henle were used in a
central core model of the rat kidney's urineconcentrating
mechanism to investigate the importance of overlapping loops
for three different modes of urea transport in the long
loops of Henle: 1) ureaimpermeable loops, 2) ureapermeable
loops (as indicated by perfused tubule experiments), and 3)
loops with ureapermeable descending limbs and active urea
transport out of thin ascending limbs. Mode 1 produces high
papillary tip osmolality in accordance with tissue slice
experiments, but the relative contribution of urea to the
osmolality of the central core and the long descending limbs
is below experimental measurements. Mode 2 generates no
significant osmolality increase in the inner medulla, in
agreement with other model studies. Mode 3 produces high
papillary tip osmolality with a substantial contribution of
urea to the osmolality of the core and the descending limbs,
which is more in accordance with experiments. The results
suggest that 1) overlapping loops may produce a cascade
effect that contributes to the inner medullary concentrating
mechanism and that 2) new experiments are needed to more
certainly ascertain the urea transport characteristics of
the thin ascending limbs.},
Doi = {10.1152/ajprenal.1990.258.4.f1110},
Key = {fds287284}
}
@article{fds9607,
Author = {Chou, ChungLin and Mark A. Knepper and H. E.
Layton},
Title = {Urinary concentrating mechanism: role of the inner
medulla},
Journal = {Seminars in Nephrology 13(2): 168181, 1993.},
Key = {fds9607}
}
@article{fds287291,
Author = {Chou, CL and Knepper, MA and Layton, HE},
Title = {Urinary concentrating mechanism: The role of the inner
medulla},
Journal = {Seminars in Nephrology},
Volume = {13},
Number = {2},
Pages = {168181},
Year = {1993},
Key = {fds287291}
}
@article{fds9654,
Author = {Sands, Jeff M. and Harold E. Layton},
Title = {Urine concentrating mechanism and its regulation},
Journal = {Chapter 45 in: The Kidney: Physiology and Pathophysiology
(third edition), edited by D. W. Seldin and G. Giebisch.
Philadelphia: Lippincott Williams & Wilkins, 2000, p.
11751216.},
Key = {fds9654}
}
@article{fds287335,
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 = {fds287335}
}
@article{fds208189,
Author = {Jeff M. Sands and Harold E. Layton and Robert A.
Fenton},
Title = {Urine concentration and dilution},
Booktitle = {Brenner and Rector's THE KIDNEY, 9th Edition},
Publisher = {Saunders},
Editor = {Alan S. L. Yu},
Year = {2009},
Month = {September},
Key = {fds208189}
}
@article{fds287339,
Author = {Dantzler, WH and Layton, AT and Layton, HE and Pannabecker,
TL},
Title = {Urineconcentrating mechanism in the inner medulla: function
of the thin limbs of the loops of Henle.},
Journal = {Clinical Journal of the American Society of Nephrology :
Cjasn},
Volume = {9},
Number = {10},
Pages = {17811789},
Year = {2014},
Month = {October},
url = {http://dx.doi.org/10.2215/CJN.08750812},
Abstract = {The ability of mammals to produce urine hyperosmotic to
plasma requires the generation of a gradient of increasing
osmolality along the medulla from the corticomedullary
junction to the papilla tip. Countercurrent multiplication
apparently establishes this gradient in the outer medulla,
where there is substantial transepithelial reabsorption of
NaCl from the waterimpermeable thick ascending limbs of the
loops of Henle. However, this process does not establish the
much steeper osmotic gradient in the inner medulla, where
there are no thick ascending limbs of the loops of Henle and
the waterimpermeable ascending thin limbs lack active
transepithelial transport of NaCl or any other solute. The
mechanism generating the osmotic gradient in the inner
medulla remains an unsolved mystery, although it is
generally considered to involve countercurrent flows in the
tubules and vessels. A possible role for the
threedimensional interactions between these inner medullary
tubules and vessels in the concentrating process is
suggested by creation of physiologic models that depict the
threedimensional relationships of tubules and vessels and
their solute and water permeabilities in rat kidneys and by
creation of mathematical models based on biologic phenomena.
The current mathematical model, which incorporates
experimentally determined or estimated solute and water
flows through clearly defined tubular and interstitial
compartments, predicts a urine osmolality in good agreement
with that observed in moderately antidiuretic rats. The
current model provides substantially better predictions than
previous models; however, the current model still fails to
predict urine osmolalities of maximally concentrating
rats.},
Doi = {10.2215/CJN.08750812},
Key = {fds287339}
}
