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Publications of Harold Layton    :chronological  alphabetical  combined listing:

%% 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: Springer-Verlag, 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 single-nephron 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{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 = {F692-F700},
   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 sex-specific 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 single-nephron 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 aquaporin-1 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 claudin-2 expression levels. Notably, unlike
             most Na+ transporters, whose expression levels are lower in
             females, Na+-glucose cotransporter 2 (SGLT2) expression
             levels are 2.5-fold 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{fds287339,
   Author = {Dantzler, WH and Layton, AT and Layton, HE and Pannabecker,
             TL},
   Title = {Urine-concentrating mechanism in the inner medulla: function
             of the thin limbs of the loops of Henle.},
   Journal = {Clinical Journal of the American Society of Nephrology :
             Cjasn},
   Volume = {9},
   Number = {10},
   Pages = {1781-1789},
   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 water-impermeable 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 water-impermeable 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
             three-dimensional interactions between these inner medullary
             tubules and vessels in the concentrating process is
             suggested by creation of physiologic models that depict the
             three-dimensional 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}
}

@article{fds287277,
   Author = {Sands, JM and Layton, HE},
   Title = {Advances in understanding the urine-concentrating
             mechanism.},
   Journal = {Annual Review of Physiology},
   Volume = {76},
   Pages = {387-409},
   Year = {2014},
   Month = {January},
   ISSN = {0066-4278},
   url = {http://dx.doi.org/10.1146/annurev-physiol-021113-170350},
   Abstract = {The renal medulla produces concentrated urine through the
             generation of an osmotic gradient that progressively
             increases from the cortico-medullary 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 long-looped 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 urine-concentrating
             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 urine-concentrating 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/annurev-physiol-021113-170350},
   Key = {fds287277}
}

@article{fds287276,
   Author = {Sands, JM and Mount, DB and Layton, HE},
   Title = {The physiology of water homeostasis},
   Pages = {1-28},
   Booktitle = {Core Concepts in the Disorders of Fluid, Electrolytes and
             Acid-Base Balance},
   Publisher = {Springer US},
   Year = {2013},
   Month = {November},
   ISBN = {1461437695},
   url = {http://dx.doi.org/10.1007/978-1-4614-3770-3_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
             cortico-medullary 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 = {10.1007/978-1-4614-3770-3_1},
   Key = {fds287276}
}

@article{fds287280,
   Author = {Nieves-González, A and Clausen, C and Layton, AT and Layton, HE and Moore, LC},
   Title = {Transport efficiency and workload distribution in a
             mathematical model of the thick ascending
             limb.},
   Journal = {American Journal of Physiology. Renal Physiology},
   Volume = {304},
   Number = {6},
   Pages = {F653-F664},
   Year = {2013},
   Month = {March},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/23097466},
   Abstract = {The thick ascending limb (TAL) is a major NaCl reabsorbing
             site in the nephron. Efficient reabsorption along that
             segment is thought to be a consequence of the establishment
             of a strong transepithelial potential that drives
             paracellular Na(+) uptake. We used a multicell mathematical
             model of the TAL to estimate the efficiency of Na(+)
             transport along the TAL and to examine factors that
             determine transport efficiency, given the condition that TAL
             outflow must be adequately dilute. The TAL model consists of
             a series of epithelial cell models that represent all major
             solutes and transport pathways. Model equations describe
             luminal flows, based on mass conservation and
             electroneutrality constraints. Empirical descriptions of
             cell volume regulation (CVR) and pH control were
             implemented, together with the tubuloglomerular feedback
             (TGF) system. Transport efficiency was calculated as the
             ratio of total net Na(+) transport (i.e., paracellular and
             transcellular transport) to transcellular Na(+) transport.
             Model predictions suggest that 1) the transepithelial Na(+)
             concentration gradient is a major determinant of transport
             efficiency; 2) CVR in individual cells influences the
             distribution of net Na(+) transport along the TAL; 3) CVR
             responses in conjunction with TGF maintain luminal Na(+)
             concentration well above static head levels in the cortical
             TAL, thereby preventing large decreases in transport
             efficiency; and 4) under the condition that the distribution
             of Na(+) transport along the TAL is quasi-uniform, the
             tubular fluid axial Cl(-) concentration gradient near the
             macula densa is sufficiently steep to yield a TGF gain
             consistent with experimental data.},
   Doi = {10.1152/ajprenal.00101.2012},
   Key = {fds287280}
}

@article{fds287338,
   Author = {Nieves-González, 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 = {F634-F652},
   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 cortico-medullary 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
             cortico-medullary 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{fds287278,
   Author = {Sands, JM and Layton, HE},
   Title = {The Urine Concentrating Mechanism and Urea
             Transporters},
   Volume = {1},
   Pages = {1463-1510},
   Publisher = {Elsevier},
   Year = {2013},
   url = {http://dx.doi.org/10.1016/b978-0-12-381462-3.00043-4},
   Doi = {10.1016/b978-0-12-381462-3.00043-4},
   Key = {fds287278}
}

@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
             Acid-Base Balance},
   Publisher = {Springer},
   Editor = {David B. Mount and Ajay Singh and Mo Sayegh},
   Year = {2012},
   Month = {August},
   Key = {fds208190}
}

@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 = {F1188-F1202},
   Year = {2012},
   Month = {May},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/22262482},
   Abstract = {In several previous studies, we used a mathematical model of
             the thick ascending limb (TAL) to investigate nonlinearities
             in the tubuloglomerular feedback (TGF) loop. That model,
             which represents the TAL as a rigid tube, predicts that TGF
             signal transduction by the TAL is a generator of
             nonlinearities: if a sinusoidal oscillation is added to
             constant intratubular fluid flow, the time interval required
             for an element of tubular fluid to traverse the TAL, as a
             function of time, is oscillatory and periodic but not
             sinusoidal. As a consequence, NaCl concentration in tubular
             fluid alongside the macula densa will be nonsinusoidal and
             thus contain harmonics of the original sinusoidal frequency.
             We hypothesized that the complexity found in power spectra
             based on in vivo time series of key TGF variables arises in
             part from those harmonics and that nonlinearities in
             TGF-mediated oscillations may result in increased NaCl
             delivery to the distal nephron. To investigate the
             possibility that a more realistic model of the TAL would
             damp the harmonics, we have conducted new studies in a model
             TAL that has compliant walls and thus a tubular radius that
             depends on transmural pressure. These studies predict that
             compliant TAL walls do not damp, but instead intensify, the
             harmonics. In addition, our results predict that mean TAL
             flow strongly influences the shape of the NaCl concentration
             waveform at the macula densa. This is a consequence of the
             inverse relationship between flow speed and transit time,
             which produces asymmetry between up- and downslopes of the
             oscillation, and the nonlinearity of TAL NaCl absorption at
             low flow rates, which broadens the trough of the oscillation
             relative to the peak. The dependence of waveform shape on
             mean TAL flow may be the source of the variable degree of
             distortion, relative to a sine wave, seen in experimental
             recordings of TGF-mediated oscillations.},
   Doi = {10.1152/ajprenal.00732.2010},
   Key = {fds287336}
}

@article{fds287337,
   Author = {Nieves-Gonzalez, A and Clausen, C and Layton, AT and Layton, HE and Moore, LC},
   Title = {Efficiency and workload distribution in a mathematical model
             of the thick ascending limb},
   Journal = {American Journal of Physiology--Renal Physiology},
   Year = {2012},
   Key = {fds287337}
}

@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 = {F1047-F1056},
   Year = {2011},
   Month = {November},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/21753076},
   Abstract = {It has become widely accepted that the osmolality gradient
             along the corticomedullary axis of the mammalian outer
             medulla is generated and sustained by a process of
             countercurrent multiplication: active NaCl absorption from
             thick ascending limbs is coupled with the counterflow
             configuration of the descending and ascending limbs of the
             loops of Henle to generate an axial osmolality gradient
             along the outer medulla. However, aspects of anatomic
             structure (e.g., the physical separation of the descending
             limbs of short loops of Henle from contiguous ascending
             limbs), recent physiologic experiments (e.g., those that
             suggest that the thin descending limbs of short loops of
             Henle have a low osmotic water permeability), and
             mathematical modeling studies (e.g., those that predict that
             water-permeable descending limbs of short loops are not
             required for the generation of an axial osmolality gradient)
             suggest that countercurrent multiplication may be an
             incomplete, or perhaps even erroneous, explanation. We
             propose an alternative explanation for the axial osmolality
             gradient: we regard the thick limbs as NaCl sources for the
             surrounding interstitium, and we hypothesize that the
             increasing axial osmolality gradient along the outer medulla
             is primarily sustained by an increasing ratio, as a function
             of increasing medullary depth, of NaCl absorption (from
             thick limbs) to water absorption (from thin descending limbs
             of long loops of Henle and, in antidiuresis, from collecting
             ducts). We further hypothesize that ascending vasa recta
             that are external to vascular bundles will carry, toward the
             cortex, an absorbate that at each medullary level is
             hyperosmotic relative to the adjacent interstitium.},
   Doi = {10.1152/ajprenal.00620.2010},
   Key = {fds287334}
}

@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 Physiology--Renal Physiology 301:
             F1047-F1056},
   Year = {2011},
   Month = {October},
   Key = {fds208186}
}

@article{fds287332,
   Author = {Layton, AT and Bowen, M and Wen, A and Layton, HE},
   Title = {Feedback-mediated dynamics in a model of coupled nephrons
             with compliant thick ascending limbs.},
   Journal = {Mathematical Biosciences},
   Volume = {230},
   Number = {2},
   Pages = {115-127},
   Year = {2011},
   Month = {April},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/21329704},
   Abstract = {The tubuloglomerular feedback (TGF) system in the kidney, a
             key regulator of glomerular filtration rate, has been shown
             in physiologic experiments in rats to mediate oscillations
             in thick ascending limb (TAL) tubular fluid pressure, flow,
             and NaCl concentration. In spontaneously hypertensive rats,
             TGF-mediated flow oscillations may be highly irregular. We
             conducted a bifurcation analysis of a mathematical model of
             nephrons that are coupled through their TGF systems; the
             TALs of these nephrons are assumed to have compliant tubular
             walls. A characteristic equation was derived for a model of
             two coupled nephrons. Analysis of that characteristic
             equation has revealed a number of parameter regions having
             the potential for differing stable dynamic states. Numerical
             solutions of the full equations for two model nephrons
             exhibit a variety of behaviors in these regions. Also, model
             results suggest that the stability of the TGF system is
             reduced by the compliance of TAL walls and by internephron
             coupling; as a result, the likelihood of the emergence of
             sustained oscillations in tubular fluid pressure and flow is
             increased. Based on information provided by the
             characteristic equation, we identified parameters with which
             the model predicts irregular tubular flow oscillations that
             exhibit a degree of complexity that may help explain the
             emergence of irregular oscillations in spontaneously
             hypertensive rats.},
   Doi = {10.1016/j.mbs.2011.02.004},
   Key = {fds287332}
}

@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 = {F669-F681},
   Year = {2011},
   Month = {March},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/21190949},
   Abstract = {Elevations in systolic blood pressure are believed to be
             closely linked to the pathogenesis and progression of renal
             diseases. It has been hypothesized that the afferent
             arteriole (AA) protects the glomerulus from the damaging
             effects of hypertension by sensing increases in systolic
             blood pressure and responding with a compensatory
             vasoconstriction (Loutzenhiser R, Bidani A, Chilton L. Circ
             Res 90: 1316-1324, 2002). To investigate this hypothesis, we
             developed a mathematical model of the myogenic response of
             an AA wall, based on an arteriole model (Gonzalez-Fernandez
             JM, Ermentrout B. Math Biosci 119: 127-167, 1994). The model
             incorporates ionic transport, cell membrane potential,
             contraction of the AA smooth muscle cell, and the mechanics
             of a thick-walled cylinder. The model represents a myogenic
             response based on a pressure-induced shift in the voltage
             dependence of calcium channel openings: with increasing
             transmural pressure, model vessel diameter decreases; and
             with decreasing pressure, vessel diameter increases.
             Furthermore, the model myogenic mechanism includes a
             rate-sensitive component that yields constriction and
             dilation kinetics similar to behaviors observed in vitro. A
             parameter set is identified based on physical dimensions of
             an AA in a rat kidney. Model results suggest that the
             interaction of Ca(2+) and K(+) fluxes mediated by
             voltage-gated and voltage-calcium-gated channels,
             respectively, gives rise to periodicity in the transport of
             the two ions. This results in a time-periodic cytoplasmic
             calcium concentration, myosin light chain phosphorylation,
             and cross-bridge formation with the attending muscle stress.
             Furthermore, the model predicts myogenic responses that
             agree with experimental observations, most notably those
             which demonstrate that the renal AA constricts in response
             to increases in both steady and systolic blood pressures.
             The myogenic model captures these essential functions of the
             renal AA, and it may prove useful as a fundamental component
             in a multiscale model of the renal microvasculature suitable
             for investigations of the pathogenesis of hypertensive renal
             diseases.},
   Doi = {10.1152/ajprenal.00382.2010},
   Key = {fds287333}
}

@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 three-dimensional
             architecture.},
   Journal = {Acta Physiologica},
   Volume = {202},
   Number = {3},
   Pages = {361-378},
   Year = {2011},
   ISSN = {1748-1716},
   url = {http://dx.doi.org/10.1111/j.1748-1716.2010.02214.x},
   Abstract = {The urine concentrating mechanism in the mammalian renal
             inner medulla (IM) is not understood, although it is
             generally considered to involve countercurrent flows in
             tubules and blood vessels. A possible role for the
             three-dimensional relationships of these tubules and vessels
             in the concentrating process is suggested by recent
             reconstructions from serial sections labelled with
             antibodies to tubular and vascular proteins and mathematical
             models based on these studies. The reconstructions revealed
             that the lower 60% of each descending thin limb (DTL) of
             Henle's loops lacks water channels (aquaporin-1) and osmotic
             water permeability and ascending thin limbs (ATLs) begin
             with a prebend segment of constant length. In the outer zone
             of the IM (i) clusters of coalescing collecting ducts (CDs)
             form organizing motif for loops of Henle and vasa recta;
             (ii) DTLs and descending vasa recta (DVR) are arrayed
             outside CD clusters, whereas ATLs and ascending vasa recta
             (AVR) are uniformly distributed inside and outside clusters;
             (iii) within CD clusters, interstitial nodal spaces are
             formed by a CD on one side, AVR on two sides, and an ATL on
             the fourth side. These spaces may function as mixing
             chambers for urea from CDs and NaCl from ATLs. In the inner
             zone of the IM, cluster organization disappears and half of
             Henle's loops have broad lateral bends wrapped around
             terminal CDs. Mathematical models based on these findings
             and involving solute mixing in the interstitial spaces can
             produce urine slightly more concentrated than that of a
             moderately antidiuretic rat but no higher. © 2010 The
             Authors. Acta Physiologica © 2010 Scandinavian
             Physiological Society.},
   Doi = {10.1111/j.1748-1716.2010.02214.x},
   Key = {fds287335}
}

@article{fds208184,
   Author = {Anita T. Layton and Matthew Bowen and Amy Wen and Harold E.
             Layton},
   Title = {Feedback-mediated dynamics in a model of coupled nephrons
             with compliant thick ascending limbs},
   Journal = {Mathematical Biosciences Vol. 230: 115-127},
   Year = {2010},
   Month = {December},
   Key = {fds208184}
}

@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{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 72:314-339,
             2010},
   Year = {2010},
   Month = {April},
   Key = {fds172982}
}

@article{fds287330,
   Author = {Layton, AT and Pannabecker, TL and Dantzler, WH and Layton,
             HE},
   Title = {Functional implications of the three-dimensional
             architecture of the rat renal inner medulla.},
   Journal = {American Journal of Physiology. Renal Physiology},
   Volume = {298},
   Number = {4},
   Pages = {F973-F987},
   Year = {2010},
   Month = {April},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/20053796},
   Abstract = {A new, region-based mathematical model of the urine
             concentrating mechanism of the rat renal inner medulla (IM)
             was used to investigate the significance of transport and
             structural properties revealed in recent studies that
             employed immunohistochemical methods combined with
             three-dimensional computerized reconstruction. The model
             simulates preferential interactions among tubules and
             vessels by representing two concentric regions. The inner
             region, which represents a collecting duct (CD) cluster,
             contains CDs, some ascending thin limbs (ATLs), and some
             ascending vasa recta; the outer region, which represents the
             intercluster region, contains descending thin limbs,
             descending vasa recta, remaining ATLs, and additional
             ascending vasa recta. In the upper portion of the IM, the
             model predicts that interstitial Na(+) and urea
             concentrations (and osmolality) in the CD clusters differ
             significantly from those in the intercluster regions: model
             calculations predict that those CD clusters have higher urea
             concentrations than the intercluster regions, a finding that
             is consistent with a concentrating mechanism that depends
             principally on the mixing of NaCl from ATLs and urea from
             CDs. In the lower IM, the model predicts that limited or
             nearly zero water permeability in descending thin limb
             segments will increase concentrating effectiveness by
             increasing the rate of solute-free water absorption. The
             model predicts that high urea permeabilities in the upper
             portions of ATLs and increased contact areas of longest loop
             bends with CDs both modestly increase concentrating
             capability. A surprising finding is that the concentrating
             capability of this region-based model falls short of the
             capability of a model IM that has radially homogeneous
             interstitial fluid at each level but is otherwise analogous
             to the region-based model.},
   Doi = {10.1152/ajprenal.00249.2009},
   Key = {fds287330}
}

@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 = {F962-F972},
   Year = {2010},
   Month = {April},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/20042460},
   Abstract = {Simulations conducted in a mathematical model were used to
             exemplify the hypothesis that elevated solute concentrations
             and tubular flows at the boundary of the renal outer and
             inner medullas of rats may contribute to increased urine
             osmolalities and urine flow rates. Such elevated quantities
             at that boundary may arise from hyperfiltration and from
             inner stripe hypertrophy, which are correlated with
             increased concentrating activity (Bankir L, Kriz W. Kidney
             Int. 47: 7-24, 1995). The simulations used the region-based
             model for the rat inner medulla that was presented in the
             companion study (Layton AT, Pannabecker TL, Dantzler WH,
             Layton HE. Am J Physiol Renal Physiol 298: F000-F000, 2010).
             The simulations were suggested by experiments which were
             conducted in rat by Gamble et al. (Gamble JL, McKhann CF,
             Butler AM, Tuthill E. Am J Physiol 109: 139-154, 1934) in
             which the ratio of NaCl to urea in the diet was
             systematically varied in eight successive 5-day intervals.
             The simulations predict that changes in boundary conditions
             at the boundary of the outer and inner medulla, accompanied
             by plausible modifications in transport properties of the
             collecting duct system, can significantly increase urine
             osmolality and flow rate. This hyperfiltration-hypertrophy
             hypothesis may explain the finding by Gamble et al. that the
             maximum urine osmolality attained from supplemental feeding
             of urea and NaCl in the eight intervals depends on NaCl
             being the initial predominant solute and on urea being the
             final predominant solute, because urea in sufficient
             quantity appears to stimulate concentrating activity. More
             generally, the hypothesis suggests that high osmolalities
             and urine flow rates may depend, in large part, on adaptive
             modifications of cortical hemodynamics and on outer
             medullary structure and not entirely on an extraordinary
             concentrating capability that is intrinsic to the inner
             medulla.},
   Doi = {10.1152/ajprenal.00250.2009},
   Key = {fds287331}
}

@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 = {314-339},
   Year = {2010},
   ISSN = {0092-8240},
   url = {http://dx.doi.org/10.1007/s11538-009-9448-0},
   Abstract = {In a mathematical model of the urine concentrating mechanism
             of the inner medulla of the rat kidney, a nonlinear
             optimization technique was used to estimate parameter sets
             that maximize the urine-to-plasma osmolality ratio (U/P)
             while maintaining the urine flow rate within a plausible
             physiologic range. The model, which used a central core
             formulation, represented loops of Henle turning at all
             levels of the inner medulla and a composite collecting duct
             (CD). The parameters varied were: water flow and urea
             concentration in tubular fluid entering the descending thin
             limbs and the composite CD at the outer-inner medullary
             boundary; scaling factors for the number of loops of Henle
             and CDs as a function of medullary depth; location and
             increase rate of the urea permeability profile along the CD;
             and a scaling factor for the maximum rate of NaCl transport
             from the CD. The optimization algorithm sought to maximize a
             quantity E that equaled U/P minus a penalty function for
             insufficient urine flow. Maxima of E were sought by changing
             parameter values in the direction in parameter space in
             which E increased. The algorithm attained a maximum E that
             increased urine osmolality and inner medullary concentrating
             capability by 37.5% and 80.2%, respectively, above base-case
             values; the corresponding urine flow rate and the
             concentrations of NaCl and urea were all within or near
             reported experimental ranges. Our results predict that urine
             osmolality is particularly sensitive to three parameters:
             the urea concentration in tubular fluid entering the CD at
             the outer-inner medullary boundary, the location and
             increase rate of the urea permeability profile along the CD,
             and the rate of decrease of the CD population (and thus of
             CD surface area) along the cortico-medullary axis. © 2009
             Society for Mathematical Biology.},
   Doi = {10.1007/s11538-009-9448-0},
   Key = {fds287329}
}

@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{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 = {250-256},
   Year = {2009},
   Month = {August},
   ISSN = {1548-9213},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/19675356},
   Abstract = {The urine concentrating mechanism of the mammalian kidney,
             which can produce a urine that is substantially more
             concentrated than blood plasma during periods of water
             deprivation, is one of the enduring mysteries in traditional
             physiology. Owing to the complex lateral and axial
             relationships of tubules and vessels, in both the outer and
             inner medulla, the urine concentrating mechanism may only be
             fully understood in terms of the kidney's three-dimensional
             functional architecture and its implications for
             preferential interactions among tubules and
             vessels.},
   Doi = {10.1152/physiol.00013.2009},
   Key = {fds287328}
}

@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 = {515-555},
   Year = {2009},
   Month = {April},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/19205808},
   Abstract = {To help elucidate the causes of irregular tubular flow
             oscillations found in the nephrons of spontaneously
             hypertensive rats (SHR), we have conducted a bifurcation
             analysis of a mathematical model of two nephrons that are
             coupled through their tubuloglomerular feedback (TGF)
             systems. This analysis was motivated by a previous modeling
             study which predicts that NaCl backleak from a nephron's
             thick ascending limb permits multiple stable oscillatory
             states that are mediated by TGF (Layton et al. in Am. J.
             Physiol. Renal Physiol. 291:F79-F97, 2006); that prediction
             served as the basis for a comprehensive, multifaceted
             hypothesis for the emergence of irregular flow oscillations
             in SHR. However, in that study, we used a characteristic
             equation obtained via linearization from a single-nephron
             model, in conjunction with numerical solutions of the full,
             nonlinear model equations for two and three coupled
             nephrons. In the present study, we have derived a
             characteristic equation for a model of any finite number of
             mutually coupled nephrons having NaCl backleak. Analysis of
             that characteristic equation for the case of two coupled
             nephrons has revealed a number of parameter regions having
             the potential for differing stable dynamic states. Numerical
             solutions of the full equations for two model nephrons
             exhibit a variety of behaviors in these regions. Some
             behaviors exhibit a degree of complexity that is consistent
             with our hypothesis for the emergence of irregular
             oscillations in SHR.},
   Doi = {10.1007/s11538-008-9370-x},
   Key = {fds287327}
}

@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 = {178-195},
   Year = {2009},
   ISSN = {0270-9295},
   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
             cortico-medullary 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
             knock-out 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{fds287326,
   Author = {Pannabecker, TL and Dantzler, WH and Layton, HE and Layton,
             AT},
   Title = {Role of three-dimensional architecture in the urine
             concentrating mechanism of the rat renal inner
             medulla.},
   Journal = {American Journal of Physiology. Renal Physiology},
   Volume = {295},
   Number = {5},
   Pages = {F1271-F1285},
   Year = {2008},
   Month = {November},
   ISSN = {0363-6127},
   url = {http://dx.doi.org/10.1152/ajprenal.90252.2008},
   Abstract = {Recent studies of three-dimensional architecture of rat
             renal inner medulla (IM) and expression of membrane proteins
             associated with fluid and solute transport in nephrons and
             vasculature have revealed structural and transport
             properties that likely impact the IM urine concentrating
             mechanism. These studies have shown that 1) IM descending
             thin limbs (DTLs) have at least two or three functionally
             distinct subsegments; 2) most ascending thin limbs (ATLs)
             and about half the ascending vasa recta (AVR) are arranged
             among clusters of collecting ducts (CDs), which form the
             organizing motif through the first 3-3.5 mm of the IM,
             whereas other ATLs and AVR, along with aquaporin-1-positive
             DTLs and urea transporter B-positive descending vasa recta
             (DVR), are external to the CD clusters; 3) ATLs, AVR, CDs,
             and interstitial cells delimit interstitial microdomains
             within the CD clusters; and 4) many of the longest loops of
             Henle form bends that include subsegments that run
             transversely along CDs that lie in the terminal 500 microm
             of the papilla tip. Based on a more comprehensive
             understanding of three-dimensional IM architecture, we
             distinguish two distinct countercurrent systems in the first
             3-3.5 mm of the IM (an intra-CD cluster system and an
             inter-CD cluster system) and a third countercurrent system
             in the final 1.5-2 mm. Spatial arrangements of loop of Henle
             subsegments and multiple countercurrent systems throughout
             four distinct axial IM zones, as well as our initial
             mathematical model, are consistent with a solute-separation,
             solute-mixing mechanism for concentrating urine in the
             IM.},
   Doi = {10.1152/ajprenal.90252.2008},
   Key = {fds287326}
}

@article{fds287279,
   Author = {Sands, JM and Layton, HE},
   Title = {The Urine Concentrating Mechanism and Urea
             Transporters},
   Series = {4th Edition},
   Pages = {1143-1178},
   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/b978-012088488-9.50043-7},
   Doi = {10.1016/b978-012088488-9.50043-7},
   Key = {fds287279}
}

@article{fds287314,
   Author = {Budu-Grajdeanu, 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 = {564-592},
   Year = {2007},
   Month = {October},
   ISSN = {0025-5564},
   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 steady-state 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 non-nodal periods, sinusoidal
             perturbations generate non-sinusoidal 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 non-nodal periods tend to be less
             sinusoidal and more distorted than in the homogeneous case
             and to thus have stronger harmonics. Both the homogeneous
             and non-homogeneous cases predict that the TAL, in its
             transduction of flow oscillations into concentration
             oscillations, acts as a low-pass filter, but the
             inhomogeneities result in a less effective filter that has
             accentuated non-linearities.},
   Doi = {10.1016/j.mbs.2007.03.007},
   Key = {fds287314}
}

@article{fds287340,
   Author = {Budu-Grajdeanu, 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): 564-592, 2007},
   Journal = {Mathematical Biosciences},
   Year = {2007},
   Month = {October},
   Key = {fds287340}
}

@article{fds287325,
   Author = {Marcano, M and Layton, AT and Layton, HE},
   Title = {An optimization algorithm for a distributed-loop model of an
             avian urine concentrating mechanism.},
   Journal = {Bulletin of Mathematical Biology},
   Volume = {68},
   Number = {7},
   Pages = {1625-1660},
   Year = {2006},
   Month = {October},
   ISSN = {0092-8240},
   url = {http://dx.doi.org/10.1007/s11538-006-9087-1},
   Abstract = {To better understand how the avian kidney's morphological
             and transepithelial transport properties affect the urine
             concentrating mechanism (UCM), an inverse problem was solved
             for a mathematical model of the quail UCM. In this model, a
             continuous, monotonically decreasing population distribution
             of tubes, as a function of medullary length, was used to
             represent the loops of Henle, which reach to varying levels
             along the avian medullary cones. A measure of concentrating
             mechanism efficiency - the ratio of the free-water
             absorption rate (FWA) to the total NaCl active transport
             rate (TAT) - was optimized by varying a set of parameters
             within bounds suggested by physiological experiments. Those
             parameters include transepithelial transport properties of
             renal tubules, length of the prebend enlargement of the
             descending limb (DL), DL and collecting duct (CD) inflows,
             plasma Na(+) concentration, length of the cortical thick
             ascending limbs, central core solute diffusivity, and
             population distribution of loops of Henle and of CDs along
             the medullary cone. By selecting parameter values that
             increase urine flow rate (while maintaining a sufficiently
             high urine-to-plasma osmolality ratio (U/P)) and that reduce
             TAT, the optimization algorithm identified a set of
             parameter values that increased efficiency by approximately
             60% above base-case efficiency. Thus, higher efficiency can
             be achieved by increasing urine flow rather than increasing
             U/P. The algorithm also identified a set of parameters that
             reduced efficiency by approximately 70% via the production
             of a urine having near-plasma osmolality at near-base-case
             TAT. In separate studies, maximum efficiency was evaluated
             as selected parameters were varied over large ranges.
             Shorter cones were found to be more efficient than longer
             ones, and an optimal loop of Henle distribution was found
             that is consistent with experimental findings.},
   Doi = {10.1007/s11538-006-9087-1},
   Key = {fds287325}
}

@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 = {F79-F97},
   Year = {2006},
   Month = {July},
   ISSN = {1931-857X},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/16204416},
   Abstract = {Single-nephron proximal tubule pressure in spontaneously
             hypertensive rats (SHR) can exhibit highly irregular
             oscillations similar to deterministic chaos. We used a
             mathematical model of tubuloglomerular feedback (TGF) to
             investigate potential sources of the irregular oscillations
             and the corresponding complex power spectra in SHR. A
             bifurcation analysis of the TGF model equations, for nonzero
             thick ascending limb (TAL) NaCl permeability, was performed
             by finding roots of the characteristic equation, and
             numerical simulations of model solutions were conducted to
             assist in the interpretation of the analysis. These
             techniques revealed four parameter regions, consistent with
             TGF gain and delays in SHR, where multiple stable model
             solutions are possible: 1) a region having one stable,
             time-independent steady-state solution; 2) a region having
             one stable oscillatory solution only, of frequency f1; 3) a
             region having one stable oscillatory solution only, of
             frequency f2, which is approximately equal to 2f1; and 4) a
             region having two possible stable oscillatory solutions, of
             frequencies f1 and f2. In addition, we conducted simulations
             in which TAL volume was assumed to vary as a function of
             time and simulations in which two or three nephrons were
             assumed to have coupled TGF systems. Four potential sources
             of spectral complexity in SHR were identified: 1)
             bifurcations that permit switching between different stable
             oscillatory modes, leading to multiple spectral peaks and
             their respective harmonic peaks; 2) sustained lability in
             delay parameters, leading to broadening of peaks and of
             their harmonics; 3) episodic, but abrupt, lability in delay
             parameters, leading to multiple peaks and their harmonics;
             and 4) coupling of small numbers of nephrons, leading to
             multiple peaks and their harmonics. We conclude that the TGF
             system in SHR may exhibit multistability and that the
             complex power spectra of the irregular TGF fluctuations in
             this strain may be explained by switching between multiple
             dynamic modes, temporal variation in TGF parameters, and
             nephron coupling.},
   Doi = {10.1152/ajprenal.00048.2005},
   Key = {fds287323}
}

@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 = {740-752},
   Publisher = {Institute of Electrical and Electronics Engineers
             (IEEE)},
   Year = {2006},
   Month = {April},
   ISSN = {0018-9219},
   url = {http://dx.doi.org/10.1109/JPROC.2006.871770},
   Abstract = {Mathematical models have played an essential role in
             elucidating various functions of the kidney, including the
             mechanism by which the avion and mammalian kidney can
             produce a urine that is more concentrated than blood plasma,
             quasi-isosmotic reabsorption along the proximal tubule, and
             the control and regulation of glomerular filtration by the
             myogenic and tubuloglomerular feedback mechanisms. This
             review includes a brief description of relevant renal
             physiology, a summary of the contributions of mathematical
             models at various levels and describes our recent work
             toward the Renal Physiome. © 2006 IEEE.},
   Doi = {10.1109/JPROC.2006.871770},
   Key = {fds287324}
}

@article{fds287321,
   Author = {Layton, AT and Layton, HE},
   Title = {A region-based mathematical model of the urine concentrating
             mechanism in the rat outer medulla. I. Formulation and
             base-case results.},
   Journal = {American Journal of Physiology. Renal Physiology},
   Volume = {289},
   Number = {6},
   Pages = {F1346-F1366},
   Year = {2005},
   Month = {December},
   ISSN = {1931-857X},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/15914776},
   Abstract = {We have developed a highly detailed mathematical model for
             the urine concentrating mechanism (UCM) of the rat kidney
             outer medulla (OM). The model simulates preferential
             interactions among tubules and vessels by representing four
             concentric regions that are centered on a vascular bundle;
             tubules and vessels, or fractions thereof, are assigned to
             anatomically appropriate regions. Model parameters, which
             are based on the experimental literature, include
             transepithelial transport properties of short descending
             limbs inferred from immunohistochemical localization
             studies. The model equations, which are based on
             conservation of solutes and water and on standard
             expressions for transmural transport, were solved to steady
             state. Model simulations predict significantly differing
             interstitial NaCl and urea concentrations in adjoining
             regions. Active NaCl transport from thick ascending limbs
             (TALs), at rates inferred from the physiological literature,
             resulted in model osmolality profiles along the OM that are
             consistent with tissue slice experiments. TAL luminal NaCl
             concentrations at the corticomedullary boundary are
             consistent with tubuloglomerular feedback function. The
             model exhibited solute exchange, cycling, and sequestration
             patterns (in tubules, vessels, and regions) that are
             generally consistent with predictions in the physiological
             literature, including significant urea addition from long
             ascending vasa recta to inner-stripe short descending limbs.
             In a companion study (Layton AT and Layton HE. Am J Physiol
             Renal Physiol 289: F1367-F1381, 2005), the impact of model
             assumptions, medullary anatomy, and tubular segmentation on
             the UCM was investigated by means of extensive parameter
             studies.},
   Doi = {10.1152/ajprenal.00346.2003},
   Key = {fds287321}
}

@article{fds287322,
   Author = {Layton, AT and Layton, HE},
   Title = {A region-based mathematical model of the urine concentrating
             mechanism in the rat outer medulla. II. Parameter
             sensitivity and tubular inhomogeneity.},
   Journal = {American Journal of Physiology. Renal Physiology},
   Volume = {289},
   Number = {6},
   Pages = {F1367-F1381},
   Year = {2005},
   Month = {December},
   ISSN = {1931-857X},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/15914775},
   Abstract = {In a companion study (Layton AT and Layton HE. Am J Physiol
             Renal Physiol 289: F1346-F1366, 2005), a region-based
             mathematical model was formulated for the urine
             concentrating mechanism (UCM) in the outer medulla (OM) of
             the rat kidney. In the present study, we quantified the
             sensitivity of that model to several structural assumptions,
             including the degree of regionalization and the degree of
             inclusion of short descending limbs (SDLs) in the vascular
             bundles of the inner stripe (IS). Also, we quantified model
             sensitivity to several parameters that have not been well
             characterized in the experimental literature, including
             boundary conditions, short vasa recta distribution, and
             ascending vasa recta (AVR) solute permeabilities. These
             studies indicate that regionalization elevates the
             osmolality of the fluid delivered into the inner medulla via
             the collecting ducts; that model predictions are not
             significantly sensitive to boundary conditions; and that
             short vasa recta distribution and AVR permeabilities
             significantly impact concentrating capability. Moreover, we
             investigated, in the context of the UCM, the functional
             significance of several aspects of tubular segmentation and
             heterogeneity: SDL segments in the IS that are likely to be
             impermeable to water but highly permeable to urea; a prebend
             segment of SDLs that may be functionally like thick
             ascending limb (TAL); differing IS and outer stripe Na(+)
             active transport rates in TAL; and potential active urea
             secretion into the proximal straight tubules. Model
             calculations predict that these aspects of tubular of
             segmentation and heterogeneity generally enhance solute
             cycling or promote effective UCM function.},
   Doi = {10.1152/ajprenal.00347.2003},
   Key = {fds287322}
}

@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 = {F816-F839},
   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
             three-dimensional computerized reconstruction of renal
             tubules. The mathematical model represents a distribution of
             loops of Henle with loop bends at all levels of the IM, and
             the vasculature is represented by means of the central core
             assumption. Based on immunohistochemical evidence,
             descending limb portions that reach into the papilla are
             assumed to be only moderately water permeable or to be water
             impermeable, and only prebend segments and ascending thin
             limbs are assumed to be NaCl permeable. Model studies
             indicate that this configuration favors the targeted
             delivery of NaCl to loop bends, where a favorable gradient,
             sustained by urea absorption from collecting ducts, promotes
             NaCl absorption. We identified two model modes that produce
             a significant axial osmolality gradient. One mode, suggested
             by preliminary immunohistochemical findings, assumes that
             aquaporin-1-null portions of loops of Henle that reach into
             the papilla have very low urea permeability. The other mode,
             suggested by perfused tubule experiments from the
             literature, assumes that these same portions of loops of
             Henle have very high urea permeabilities. Model studies were
             conducted to determine the sensitivity of these modes to
             parameter choices. Model results are compared with extant
             tissue-slice and micropuncture studies.},
   Doi = {10.1152/ajprenal.00398.2003},
   Key = {fds287320}
}

@article{fds287313,
   Author = {Pitman, EB and Zaritski, RM and Kesseler, KJ and Moore, LC and Layton,
             HE},
   Title = {Feedback-mediated dynamics in two coupled
             nephrons},
   Journal = {Bulletin of Mathematical Biology},
   Volume = {66},
   Number = {6},
   Pages = {1463-1492},
   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,
             short-looped nephron of the mammalian kidney. In that model,
             a semi-linear 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 limit-cycle
             oscillations (LCO) in nephron fluid flow and chloride
             concentration can emerge for sufficiently large feedback
             gain magnitude and time delay. In this study, the
             single-nephron 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{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 54-5},
   Pages = {F972-F989},
   Year = {2003},
   Month = {November},
   Abstract = {A mathematical model previously formulated by us predicts
             that limit-cycle 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:
             415-419, 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{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 53-5},
   Pages = {F1080-F1096},
   Year = {2003},
   Month = {May},
   Abstract = {Endothelium-derived nitric oxide (NO) is thought to be
             short-lived 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
             3-30 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 NO-Hb 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{fds287311,
   Author = {Marcano-Velázquez, 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 = {665-691},
   Year = {2003},
   url = {http://dx.doi.org/10.1016/S0092-8240(03)00029-6},
   Abstract = {A nonlinear optimization technique, in conjunction with a
             single-nephron, single-solute 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 free-water
             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 cortico-medullary boundary; and rate
             of exponential CD population decrease along the medullary
             cone. Using a base-case parameter set and parameter bounds
             suggested by physiologic experiments, the optimization
             algorithm identified a maximum-efficiency set of parameter
             values that increased efficiency by 40% above base-case
             efficiency; a minimum-efficiency set reduced efficiency by
             about 41%. When maximum-efficiency 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/S0092-8240(03)00029-6},
   Key = {fds287311}
}

@article{fds287318,
   Author = {Layton, AT and Layton, HE},
   Title = {An efficient numerical method for distributed-loop models of
             the urine concentrating mechanism},
   Journal = {Mathematical Biosciences},
   Volume = {181},
   Number = {2},
   Pages = {111-132},
   Year = {2003},
   url = {http://dx.doi.org/10.1016/S0025-5564(02)00176-1},
   Abstract = {In this study we describe an efficient numerical method,
             based on the semi-Lagrangian (SL) semi-implicit (SI) method
             and Newton's method, for obtaining steady-state (SS)
             solutions of equations arising in distributed-loop models of
             the urine concentrating mechanism. Dynamic formulations of
             these models contain large systems of coupled hyperbolic
             partial differential equations (PDEs). The SL method
             advances the solutions of these PDEs in time by integrating
             backward along flow trajectories, thus allowing large time
             steps while maintaining stability. The SI approach controls
             stiffness arising from transtubular transport terms by
             averaging these terms in time along flow trajectories. An
             approximate SS solution of a dynamic formulation obtained
             via the SLSI method can be used as an initial guess for a
             Newton-type solver, which rapidly converges to a highly
             accurate numerical approximation to the solution of the
             ordinary differential equations that arise in the
             corresponding SS model formulation. In general, it is
             difficult to specify a priori for a Newton-type solver an
             initial guess that falls within the radius of convergence;
             however, the initial guess generated by solving the dynamic
             formulation via the SLSI method can be made sufficiently
             close to the SS solution to avoid numerical instability. The
             combination of the SLSI method and the Newton-type solver
             generates stable and accurate solutions with substantially
             reduced computation times, when compared to previously
             applied dynamic methods. © 2003 Elsevier Science Inc. All
             rights reserved.},
   Doi = {10.1016/S0025-5564(02)00176-1},
   Key = {fds287318}
}

@article{fds287319,
   Author = {Layton, AT and Layton, HE},
   Title = {A region-based model framework for the rat urine
             concentrating mechanism},
   Journal = {Bulletin of Mathematical Biology},
   Volume = {65},
   Number = {5},
   Pages = {859-901},
   Year = {2003},
   url = {http://dx.doi.org/10.1016/S0092-8240(03)00045-4},
   Abstract = {The highly structured organization of tubules and blood
             vessels in the outer medulla of the mammalian kidney is
             believed to result in preferential interactions among
             tubules and vessels; such interactions may promote solute
             cycling and enhance urine concentrating capability. In this
             study, we formulate a new model framework for the urine
             concentrating mechanism in the outer medulla of the rat
             kidney. The model simulates preferential interactions among
             tubules and vessels by representing two concentric regions
             and by specifying the fractions of tubules and vessels
             assigned to each of the regions. The model equations are
             based on standard expressions for transmural transport and
             on solute and water conservation. Model equations, which are
             derived in dynamic form, are solved to obtain steady-state
             solutions by means of a stable and efficient numerical
             method, based on the semi-Lagrangian semi-implicit method
             and on Newton's method. In this application, the
             computational cost scales as [IPQ] (N2), where N is the
             number of spatial subintervals along the medulla. We present
             representative solutions and show that the method generates
             approximations that are second-order accurate in space and
             that exhibit mass conservation. © 2003 Society for
             Mathematical Biology. Published by Elsevier Ltd. All rights
             reserved.},
   Doi = {10.1016/S0092-8240(03)00045-4},
   Key = {fds287319}
}

@article{fds287316,
   Author = {Layton, AT and Layton, HE},
   Title = {A semi-lagrangian semi-implicit numerical method for models
             of the urine concentrating mechanism},
   Journal = {Siam Journal on Scientific Computing},
   Volume = {23},
   Number = {5},
   Pages = {1526-1548},
   Publisher = {Society for Industrial & Applied Mathematics
             (SIAM)},
   Year = {2002},
   Month = {December},
   ISSN = {1064-8275},
   url = {http://dx.doi.org/10.1137/S1064827500381781},
   Abstract = {Mathematical models of the urine concentrating mechanism
             consist of large systems of coupled differential equations.
             The numerical methods that have usually been used to solve
             the steady-state formulation of these equations involve
             implicit Newton-type solvers that are limited by numerical
             instability attributed to transient flow reversal. Dynamic
             numerical methods, which solve the dynamic formulation of
             the equations by means of a direction-sensitive time
             integration until a steady state is reached, are stable in
             the presence of transient flow reversal. However, when an
             explicit, Eulerian-based dynamic method is used,
             prohibitively small time steps may be required owing to the
             CFL condition and the stiffness of the problem. In this
             report, we describe a semi-Lagrangian semi-implicit (SLSI)
             method for solving the system of hyperbolic partial
             differential equations that arises in the dynamic
             formulation. The semi-Lagrangian scheme advances the
             solution in time by integrating backward along flow
             trajectories, thus allowing large time steps while
             maintaining stability. The semi-implicit approach controls
             stiffness by averaging transtubular transport terms in time
             along flow trajectories. For sufficiently refined spatial
             grids, the SLSI method computes stable and accurate
             solutions with substantially reduced computation
             costs.},
   Doi = {10.1137/S1064827500381781},
   Key = {fds287316}
}

@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 = {549-567},
   Year = {2002},
   ISSN = {0303-6812},
   url = {http://dx.doi.org/10.1007/s00285-002-0166-6},
   Abstract = {The urine concentrating mechanism of mammals and birds
             depends on a counterflow configuration of thousands of
             nearly parallel tubules in the medulla of the kidney. Along
             the course of a renal tubule, cell type may change abruptly,
             resulting in abrupt changes in the physical characteristics
             and transmural transport properties of the tubule. A
             mathematical model that faithfully represents these abrupt
             changes will have jump discontinuities in model parameters.
             Without proper treatment, such discontinuities may cause
             unrealistic transmural fluxes and introduce suboptimal
             spatial convergence in the numerical solution to the model
             equations. In this study, we show how to treat discontinuous
             parameters in the context of a previously developed
             numerical method that is based on the semi-Lagrangian
             semi-implicit method and Newton's method. The numerical
             solutions have physically plausible fluxes at the
             discontinuities and the solutions converge at second order,
             as is appropriate for the method. © Springer-Verlag
             2002.},
   Doi = {10.1007/s00285-002-0166-6},
   Key = {fds287317}
}

@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 = {F1139-F1160},
   Year = {2000},
   Month = {December},
   ISSN = {0363-6127},
   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 single-solute
             countercurrent multiplication and on NaCl cycling from
             ascending to descending limbs of loops of Henle. The model
             predicted a urine-to-plasma (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{fds287308,
   Author = {Layton, HE and Pitman, EB and Moore, LC},
   Title = {Limit-cycle oscillations and tubuloglomerular feedback
             regulation of distal sodium delivery.},
   Journal = {American Journal of Physiology. Renal Physiology},
   Volume = {278},
   Number = {2},
   Pages = {F287-F301},
   Year = {2000},
   Month = {February},
   ISSN = {0363-6127},
   url = {http://dx.doi.org/10.1152/ajprenal.2000.278.2.f287},
   Abstract = {A mathematical model was used to evaluate the potential
             effects of limit-cycle oscillations (LCO) on
             tubuloglomerular feedback (TGF) regulation of fluid and
             sodium delivery to the distal tubule. In accordance with
             linear systems theory, simulations of steady-state responses
             to infinitesimal perturbations in single-nephron 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 time-averaged 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{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 = {402-440},
   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
             two-dimensional 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 short-lived, vasodilatory
             agent. Parameters for the model were taken primarily from
             the experimental literature of the rat renal afferent
             arteriole. Solutions to the incompressible Navier-Stokes
             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 high-order flux-corrected
             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 first-order temporal convergence and
             demonstrated second-order 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{fds287306,
   Author = {Layton, HE and Pitman, EB and Moore, LC},
   Title = {Potential natriuretic effects of limit-cycle oscillations
             mediated by tubuloglomerular feedback},
   Journal = {Faseb Journal},
   Volume = {12},
   Number = {4},
   Pages = {A108},
   Year = {1998},
   ISSN = {0892-6638},
   Abstract = {Previously, we used a mathematical model to show that
             limit-cycle 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 steady-state 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, time-averaged NaCl
             delivery increased 3.7% above steady-state delivery, whereas
             water delivery deviated from the steady-state 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{fds287303,
   Author = {Pitman, EB and Zaritski, R and Moore, LC and Layton,
             HE},
   Title = {TGF-mediated bifurcation in two coupled nephrons},
   Journal = {Faseb Journal},
   Volume = {11},
   Number = {3},
   Pages = {A85},
   Year = {1997},
   Month = {December},
   ISSN = {0892-6638},
   Abstract = {Experiments have found synchronized oscillations of 20-50
             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 feed-back (TGF). and vascular
             coupling between the nephrons. As in single-nephron 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 time-independent model
             solution and leads to sustained TGF-mediated 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{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 = {0892-6638},
   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 two-dimensional
             elastic-contractile 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 non-local effects. The model
             provides a new tool for investigating the quantitative
             contributions of microvascular regulatory
             mechanisms.},
   Key = {fds287304}
}

@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 = {0892-6638},
   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 flow-tubes; 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 urine-to-plasma 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
             loop-of-Henle population as a function of medullary
             depth.},
   Key = {fds290485}
}

@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 42-4},
   Pages = {F625-F634},
   Year = {1997},
   Month = {October},
   ISSN = {0363-6127},
   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 steady-state 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 steady-state fluid
             transit time (this nodal structure arises from the
             establishment of standing waves in luminal concentration,
             relative to the steady-state 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 = {F625-F634},
   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 steady-state 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 steady-state fluid
             transit time (this nodal structure arises from the
             establishment of standing waves in luminal concentration,
             relative to the steady-state 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{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 42-4},
   Pages = {F635-F649},
   Year = {1997},
   ISSN = {0363-6127},
   Abstract = {A simple mathematical model was used to investigate the
             spectral properties of the tubuloglomerular feedback (TGF)
             system. A perturbation, consisting of small-amplitude
             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- feedback-loop cases.
             Open-feedback-loop 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 steady-state fluid transit time. Closed- feedback-loop
             spectra are dominated by the open-loop spectral response,
             provided that γ, the magnitude of feedback gain is less
             than the critical value γ(c) required for emergence of a
             sustained TGF-mediated oscillation. For γ exceeding γ(c),
             closed-loop spectra have peaks corresponding to the
             fundamental frequency of the TGF-mediated 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{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 = {45-48},
   Year = {1996},
   Month = {December},
   ISSN = {0044-2267},
   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 steady-state, yielding boundary-value
             systems of stiff ODEs, which are usually solved by some
             variant of Newton's method. We have developed an explicit,
             second-order numerical method for solving the dynamic
             PDE-ODE system. The method is robust and easily adapted to
             different renal architectures. Moreover, as we show here,
             when the method is used in a large-scale simulation of the
             renal medulla, the asymptotic steady-state exhibits
             second-order spatial convergence in solute and water mass
             flows.},
   Key = {fds287298}
}

@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 = {33-35},
   Year = {1996},
   Month = {December},
   ISSN = {0044-2267},
   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 low-frequency oscillation. Here we report
             additional analysis of the model that suggests that the
             spectral complexity in the 50-500 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 = {0892-6638},
   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 steady-state
             fluid transit time of TAL, then the NaCl concentration in
             flow past the macula densa (MD ) maintains a value nearly
             equal to the steady-state concentration, i.e., there is a
             node at the MD. Oscillations with periods about half-way
             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 closed-loop 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{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 = {F9-20},
   Year = {1996},
   Month = {January},
   ISSN = {0002-9513},
   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 long-loop 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
             30-70% of the distance along the inner medullary axis of the
             chinchilla kidney. The factors tested were NaCl
             concentration (125-400 mM in perfusate and bath), urea
             concentration (5-500 mM in perfusate and bath), calcium
             concentration (2-8 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{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 = {1390-1418},
   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
             steady-state 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 large-scale 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
             second-order convergence in space and time, the recently
             developed ENO (essentially non-oscillatory) 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{fds287297,
   Author = {Layton, HE and Pitman, EB and Moore, LC},
   Title = {Instantaneous and steady-state gains in the tubuloglomerular
             feedback system},
   Journal = {American Journal of Physiology Renal Physiology},
   Volume = {268},
   Number = {1 37-1},
   Pages = {F163-F174},
   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 TGF-mediated oscillations.
             Mathematical modeling studies have shown that the
             open-feedback-loop 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 steady-state gain, a readily measurable
             quantity corresponding to the steady-state reduction in
             single-nephron 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 steady-state and instantaneous
             open-feedback-loop 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 steady-state gain. With typical
             physiological parameters for the rat, calculations with a
             model previously devised by us show that the gains differ by
             5-10%. Hence, experimental measurements of the steady-state
             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 steady-state gains in the tubuloglomerular
             feedback system.},
   Journal = {The American Journal of Physiology},
   Volume = {268},
   Number = {1 Pt 2},
   Pages = {F163-F174},
   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 TGF-mediated oscillations.
             Mathematical modeling studies have shown that the
             open-feedback-loop 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 steady-state gain, a readily measurable
             quantity corresponding to the steady-state reduction in
             single-nephron 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 steady-state and instantaneous
             open-feedback-loop 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 steady-state gain. With typical
             physiological parameters for the rat, calculations with a
             model previously devised by us show that the gains differ by
             5-10%. Hence, experimental measurements of the steady-state
             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.},
   Doi = {10.1152/ajprenal.1995.268.1.f163},
   Key = {fds318292}
}

@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 = {567-586},
   Year = {1994},
   ISSN = {0092-8240},
   url = {http://dx.doi.org/10.1007/BF02460471},
   Abstract = {Method-dependent 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 time-dependent phenomena. © 1994
             Elsevier Science Ltd.},
   Doi = {10.1007/BF02460471},
   Key = {fds287292}
}

@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 = {547-565},
   Year = {1994},
   ISSN = {0092-8240},
   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 steady-state
             solutions. Appropriate implementation of this method
             eliminates numerical instability arising from reversal of
             intratubular flow direction. To obtain second-order
             convergence in space and time, we employ the recently
             developed ENO (Essentially Non-Oscillatory) 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 large-scale simulations of the renal counterflow
             system. © 1994 Elsevier Science Ltd.},
   Doi = {10.1007/BF02460470},
   Key = {fds287294}
}

@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 = {169-196},
   Year = {1993},
   ISSN = {0025-5564},
   url = {http://dx.doi.org/10.1016/0025-5564(93)90065-I},
   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
             water-impermeable 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 = {10.1016/0025-5564(93)90065-I},
   Key = {fds287289}
}

@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 = {144-160},
   Year = {1993},
   Key = {fds287290}
}

@article{fds287291,
   Author = {Chou, C-L 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 = {168-181},
   Year = {1993},
   Key = {fds287291}
}

@article{fds287288,
   Author = {Layton, HE and Pitman, EB and Moore, LC},
   Title = {Bifurcation analysis of TGF-mediated oscillations in
             SNGFR},
   Journal = {American Journal of Physiology Renal Physiology},
   Volume = {261},
   Number = {5 30-5},
   Pages = {F904-F919},
   Year = {1991},
   Month = {December},
   Abstract = {Recent micropuncture studies in rats have dem-onstrated 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 first-order 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 steady-state
             operating point and the space derivative of the steady-state
             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{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 = {987-988},
   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
             steady-state space derivative of the chloride concentration
             at the macula densa.},
   Key = {fds287286}
}

@article{fds287284,
   Author = {Layton, HE},
   Title = {Urea transport in a distributed loop model of the
             urine-concentrating mechanism.},
   Journal = {The American Journal of Physiology},
   Volume = {258},
   Number = {4 Pt 2},
   Pages = {F1110-F1124},
   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 urine-concentrating
             mechanism to investigate the importance of overlapping loops
             for three different modes of urea transport in the long
             loops of Henle: 1) urea-impermeable loops, 2) urea-permeable
             loops (as indicated by perfused tubule experiments), and 3)
             loops with urea-permeable 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{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 = {533-537},
   Publisher = {Elsevier BV},
   Year = {1990},
   Month = {January},
   ISSN = {0895-7177},
   url = {http://dx.doi.org/10.1016/0895-7177(90)90239-J},
   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 steady-state,
             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 water-impermeable
             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
             transport-rate 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 = {10.1016/0895-7177(90)90239-J},
   Key = {fds287287}
}

@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 = {759-787},
   Year = {1989},
   Month = {September},
   url = {http://dx.doi.org/10.1002/cpa.3160420604},
   Doi = {10.1002/cpa.3160420604},
   Key = {fds323465}
}

@article{fds287283,
   Author = {Layton, HE},
   Title = {Energy advantage of counter-current oxygen transfer in fish
             gills},
   Journal = {Journal of Theoretical Biology},
   Volume = {125},
   Number = {3},
   Pages = {307-316},
   Publisher = {Elsevier BV},
   Year = {1987},
   Month = {April},
   ISSN = {0022-5193},
   url = {http://dx.doi.org/10.1016/S0022-5193(87)80062-0},
   Abstract = {A steady-state, one-dimensional mathematical model for
             oxygen transfer in fish gills suggests that under conditions
             permitting adequate oxygen uptake, the uptake advantage of a
             counter-current configuration over a co-current
             configuration is small, given otherwise identical gills,
             fluid fluxes, and afferent fluid oxygen tensions. The in
             vivo uptake advantage of a counter-current fish, compared to
             a hypothetical co-current 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 co-current fish
             would expend more than 46% additional power for respiration
             to compensate for a 10% uptake advantage enjoyed by an
             otherwise identical counter-current fish. Thus the
             importance of counter-current 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/S0022-5193(87)80062-0},
   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 = {197-210},
   Publisher = {Elsevier BV},
   Year = {1987},
   Month = {January},
   ISSN = {0025-5564},
   url = {http://dx.doi.org/10.1016/0025-5564(87)90092-7},
   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.
             49:1033-1040 (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 first-order kinetics or Michaelis-Menten 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 first-order and
             Michaelis-Menten kinetics for all values of β. ©
             1987.},
   Doi = {10.1016/0025-5564(87)90092-7},
   Key = {fds287285}
}

@article{fds287282,
   Author = {Layton, HE},
   Title = {Distribution of Henle's loops may enhance urine
             concentrating capability},
   Journal = {Biophysical Journal},
   Volume = {49},
   Number = {5},
   Pages = {1033-1040},
   Year = {1986},
   url = {http://dx.doi.org/10.1016/S0006-3495(86)83731-6},
   Doi = {10.1016/S0006-3495(86)83731-6},
   Key = {fds287282}
}

@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{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): 549-567,
             2002.},
   Key = {fds10382}
}

@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:
             Springer-Verlag, pp. 345-364, 2002.},
   Key = {fds10277}
}

@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,
             Springer-Verlag, pp. 233-272, 2002.},
   Key = {fds10278}
}

@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. 55-62.},
   Key = {fds9866}
}

@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.
             1175-1216.},
   Key = {fds9654}
}

@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): 1390-1418,
             October, 1995.},
   Key = {fds8947}
}

@article{fds9607,
   Author = {Chou, Chung-Lin and Mark A. Knepper and H. E.
             Layton},
   Title = {Urinary concentrating mechanism: role of the inner
             medulla},
   Journal = {Seminars in Nephrology 13(2): 168-181, 1993.},
   Key = {fds9607}
}

@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
             AMS-IMS-SIAM Joint Research Conference, July 1991, Edited by
             Angela Cheer and C. P. van Dam, appearing as Contemporary
             Mathematics (American Mathematical Society) 141: 317-336,
             1993.},
   Key = {fds9606}
}

@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. 144-160, S. Karger, Basel,
             1993.},
   Key = {fds9605}
}

@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. 119-156. (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. 1649-1692.},
   Key = {fds9601}
}

@article{fds9596,
   Author = {Layton, H. E.},
   Title = {Concentrating urine in the inner medulla of the
             kidney},
   Journal = {Comments on Theoretical Biology 1(3): 179-196,
             1989.},
   Key = {fds9596}
}

@article{fds9592,
   Author = {Layton, H. E.},
   Title = {Energy advantage of counter-current oxygen exchange in fish
             gills},
   Journal = {Journal of Theoretical Biology 125: 307-316,
             1987.},
   Key = {fds9592}
}

 

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