Anita T Layton

Duke University, Durham, North Carolina, United States

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Publications (113)234.06 Total impact

  • Anita T Layton · Volker Vallon · Aurélie Edwards
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    ABSTRACT: Diabetes increases the reabsorption of Na+ (TNa}) and glucose via the sodium-glucose cotransporter SGLT2 in the early proximal tubule (S1-S2 segments) of the renal cortex. SGLT2 inhibitors enhance glucose excretion and lower hyperglycemia in diabetes. We aimed to investigate how diabetes and SGLT2 inhibition affect TNa and sodium transport-dependent oxygen consumption (Q O2^{active}) along the whole nephron. To do so, we developed a mathematical model of water and solute transport from Bowman space to the papillary tip of a superficial nephron of the rat kidney. Model simulations indicate that in the non-diabetic kidney, acute and chronic SGLT2 inhibition enhances active TNa in all nephron segments, thereby raising QO2^{active} by ~5-12 % in the cortex and medulla. Diabetes increases overall TNa and QO2^{active} by ~50 and 100 %, mainly because it enhances GFR and transport load. In diabetes, acute and chronic SGLT2 inhibition lowers QO2^{active} in the cortex by ~30 %, due to GFR reduction which lowers proximal tubule active TNa, but raises QO2^{active} in the medulla by ~7 %. In the medulla specifically, chronic SGLT2 inhibition is predicted to increase QO2^{active} by 26 % in late proximal tubules (S3 segments), by 2 \% in medullary thick ascending limbs (mTAL), and by 9 and 21 % in outer and inner medullary collecting ducts (OMCD, IMCD), respectively. Additional blockade of SGLT1 in S3 segments enhances glucose excretion, reduces QO2^{active} by 33 % in S3 segments, and raises QO2^{ active} by < 1 % in mTAL, OMCD, and IMCD. In summary, the model predicts that SGLT2 blockade in diabetes lowers cortical QO2^{active} and raises medullary QO2^{active}, particularly in S3 segments.
    No preview · Article · Jan 2016 · AJP Renal Physiology
  • Gregory Herschlag · Jian-Guo Liu · Anita T. Layton
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    ABSTRACT: In biological transport mechanisms such as insect respiration and renal filtration, fluid travels along a leaky channel allowing exchange with systems exterior the the channel. The channels in these systems may undergo peristaltic pumping which is thought to enhance the material exchange. To date, little analytic work has been done to study the effect of pumping on material extraction across the channel walls. In this paper, we examine a fluid extraction model in which fluid flowing through a leaky channel is exchanged with fluid in a reservoir. The channel walls are allowed to contract and expand uniformly, simulating a pumping mechanism. In order to efficiently determine solutions of the model, we derive a formal power series solution for the Stokes equations in a finite channel with uniformly contracting/expanding permeable walls. This flow has been well studied in the case of weakly permeable channel walls in which the normal velocity at the channel walls is proportional to the wall velocity. In contrast we do not assume weakly driven flow, but flow driven by hydrostatic pressure, and we use Dacry's law to close our system for normal wall velocity. We use our flow solution to examine flux across the channel-reservoir barrier and demonstrate that pumping can either enhance or impede fluid extraction across channel walls. We find that associated with each set of physical flow and pumping parameters, there are optimal reservoir conditions that maximizes the amount of material flowing from the channel into the reservoir.
    No preview · Article · Nov 2015
  • Brendan C. Fry · Aurélie Edwards · Anita T. Layton

    No preview · Article · Oct 2015 · American journal of physiology. Renal physiology
  • H. Nganguia · Y.-N. Young · A.T. Layton · W.-F. Hu · M.-C. Lai
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    ABSTRACT: A numerical scheme based on the immersed interface method (IIM) is developed to simulate the dynamics of an axisymmetric viscous drop under an electric field. In this work, the IIM is used to solve both the fluid velocity field and the electric potential field. Detailed numerical studies on the numerical scheme show a second-order convergence. Moreover, our numerical scheme is validated by the good agreement with previous analytical models, and numerical results from the boundary integral simulations. Our method can be extended to Navier-Stokes fluid flow with nonlinear inertia effects.
    No preview · Article · Jul 2015 · Communications in Computational Physics
  • Anita T Layton · Aurélie Edwards
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    ABSTRACT: We expanded a published mathematical model of an afferent arteriole smooth muscle cell in rat kidney (Edwards and Layton, Am J Physiol Renal Physiol 306: F34-F48, 2014) to understand how nitric oxide (NO) and superoxide (O2 (-)) modulate the arteriolar diameter and its myogenic response. The present model includes the kinetics of NO and O2 (-) formation, diffusion, and reaction. Also included are the effects of NO and its second messenger cGMP on Ca(2+) uptake and efflux into the cell, Ca(2+)-activated K+ currents, and myosin light chain phosphatase activity. In addition, the model accounts for pressure-induced increases in O2 (-) production, O2 (-)-mediated regulation of L-type Ca(2+) channel conductance, and increased O2 (-) production in spontaneous hypertensive rats (SHR). Our results indicate that elevated O$_2^-$ production in SHR is sufficient to account for observed differences between normotensive and hypertensive rats in the response of the afferent arteriole to NO synthase inhibition, Tempol, and angiotensin II at ba seline perfusion pressures. In vitro, whether the myogenic response is stronger in SHR remains uncertain. Our model predicts that if mechano-sensitive cation channels are not modulated by O$_2^-$, then fractional changes in diameter induced by pressure elevations should be smaller in SHR than in normotensive rats. Our results also suggest that most NO diffuses out of the smooth muscle cell without being consumed, whereas most O$_2^-$ is scavenged, by NO and superoxide dismutase. Moreover, the predicted effects of superoxide on arteriolar constriction are not predominantly due to its scavenging of NO. Copyright © 2015, American Journal of Physiology - Renal Physiology.
    No preview · Article · Jul 2015 · AJP Renal Physiology
  • Anita T Layton · Volker Vallon · Aurélie Edwards
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    ABSTRACT: The objective of this study was to investigate how physiological, pharmacological, and pathological conditions that alter sodium reabsorption (TNa) in the proximal tubule affect oxygen consumption (QO2) and Na(+) transport efficiency (TNa/QO2). To do so, we expanded a mathematical model of solute transport in the proximal tubule of the rat kidney. The model represents compliant S1, S2 and S3 segments, and accounts for their specific apical and basolateral transporters. Sodium is reabsorbed transcellularly, via apical Na(+)/H(+) exchangers (NHE) and Na(+)-glucose (SGLT) cotransporters, and paracellularly. Our results suggest that TNa/QO2 is 80 % higher in S3 than in S1-S2 segments, due to the greater contribution of the passive paracellular pathway to TNa in the former segment. Whereas inhibition of NHE or Na,K-ATPase reduced TNa and QO2, as well as Na(+) transport efficiency. SGLT2 inhibition also reduced proximal tubular TNa but increased QO2; these effects were relatively more pronounced in the S3 versus the S1-S2 segments and in diabetic vs non-diabetic conditions. Diabetes increased TNa and QO2 and reduced TNa/QO2, owing mostly to hyperfiltration. Since SGLT2 inhibition lowers diabetic hyperfiltration, the net effect on TNa, QO2 and Na(+) transport efficiency in the proximal tubule will largely depend on the individual extent to which glomerular filtration rate is lowered. Copyright © 2015, American Journal of Physiology - Renal Physiology.
    No preview · Article · Apr 2015 · AJP Renal Physiology
  • Ioannis Sgouralis · Anita T Layton
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    ABSTRACT: The nephron in the kidney regulates its fluid flow by several autoregulatory mechanisms. Two primary mechanisms are the myogenic response and the tubuloglomerular feedback (TGF). The myogenic response is a property of the pre-glomerular vasculature in which a rise in intravascular pressure elicits vasoconstriction that generates a compensatory increase in vascular resistance. TGF is a negative feedback response that balances glomerular filtration with tubular reabsorptive capacity. While each nephron has its own autoregulatory response, the responses of the kidney's many nephrons do not act autonomously but are instead coupled through the pre-glomerular vasculature. To better understand the conduction of these signals along the pre-glomerular arterioles and the impacts of internephron coupling on nephron flow dynamics, we developed a mathematical model of renal haemodynamics of two neighbouring nephrons that are coupled in that their afferent arterioles arise from a common cortical radial artery. Simulations were conducted to estimate internephron coupling strength, determine its dependence on vascular properties and to investigate the effect of coupling on TGF-mediated flow oscillations. Simulation results suggest that reduced gap-junctional conductances may yield stronger internephron TGF coupling and highly irregular TGF-mediated oscillations in nephron dynamics, both of which experimentally have been associated with hypertensive rats. © The Authors 2015. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
    No preview · Article · Mar 2015 · Mathematical Medicine and Biology
  • Ioannis Sgouralis · Anita T Layton
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    ABSTRACT: In addition to the excretion of metabolic waste and toxin, the kidney plays an indispensable role in regulating the balance of water, electrolyte, acid-base, and blood pressure. For the kidney to maintain proper functions, hemodynamic control is crucial. In this review, we describe representative mathematical models that have been developed to better understand the kidney's autoregulatory processes. We consider mathematical models that simulate glomerular filtration, and renal blood flow regulation by means of the myogenic response and tubuloglomerular feedback. We discuss the extent to which these modeling efforts have expanded the understanding of renal functions in health and disease. Copyright © 2015. Published by Elsevier Inc.
    No preview · Article · Mar 2015 · Mathematical Biosciences
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    ABSTRACT: Renal blood flow is maintained within a narrow window by a set of intrinsic autoregulatory mechanisms. Here, a mathematical model of renal hemodynamics control in the rat kidney is used to understand the interactions between two major renal autoregulatory mechanisms: the myogenic response and tubuloglomerular feedback. A bifurcation analysis of the model equations is performed to assess the effects of the delay and sensitivity of the feedback system and the time constants governing the response of vessel diameter and smooth muscle tone. The results of the bifurcation analysis are verified using numerical simulations of the full nonlinear model. Both the analytical and numerical results predict the generation of limit cycle oscillations under certain physiologically relevant conditions, as observed in vivo. Copyright © 2015. Published by Elsevier Inc.
    No preview · Article · Mar 2015 · Mathematical Biosciences
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    Anita T Layton
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    ABSTRACT: It has been long known that the kidney plays an essential role in the control of body fluids and blood pressure and that impairment of renal function may lead to the development of diseases such as hypertension (Guyton AC, Coleman TG, Granger Annu Rev Physiol 34: 13–46, 1972). In this review, we highlight recent advances in our understanding of renal hemodynamics, obtained from experimental and theoretical studies. Some of these studies were published in response to a recent Call for Papers of this journal: Renal Hemodynamics: Integrating with the Nephron and Beyond.
    Preview · Article · Feb 2015 · American journal of physiology. Renal physiology
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    Brendan C Fry · Aurélie Edwards · Anita T Layton
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    ABSTRACT: The goal of this study was to investigate the reciprocal interactions among oxygen (O2), nitric oxide (NO), and superoxide (O2 (-)), and their effects on medullary oxygenation and urinary output. To accomplish that goal, we have developed a detailed mathematical model of solute transport in the renal medulla of the rat kidney. The model represents the radial organization of the renal tubules and vessels, which centers around the vascular bundles in the outer medulla and around clusters of collecting ducts in the inner medulla. Model simulations yield significant radial gradients in interstitial fluid oxygen tension (PO2) and NO and O2 (-) concentration in the outer medulla and upper inner medulla. In the deep inner medulla, interstitial fluid concentrations become much more homogeneous, as the radial organization of tubules and vessels is not distinguishable. The model further predicts that due to the nonlinear interactions among O2, NO, and O2 (-), the effects of NO and O2 (-) on sodium transport, osmolality, and medullary oxygenation cannot be gleaned by considering each solute's effect in isolation. An additional simulation suggests that a sufficiently large reduction in tubular transport efficiency may be the key contributing factor - more so than oxidative stress alone - to hypertension-induced medullary hypoxia. Moreover, model predictions suggest that urine PO2 could serve as a biomarker for medullary hypoxia and a predictor of the risk for hospital-acquired acute kidney injury. Copyright © 2014, American Journal of Physiology - Renal Physiology.
    Preview · Article · Jan 2015 · American journal of physiology. Renal physiology
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    ABSTRACT: Acute kidney injury, a prevalent complication of cardiac surgery performed on cardiopulmonary bypass (CPB), is thought to be driven partly by hypoxic damage in the renal medulla. To determine the causes of medullary hypoxia during CPB, we modeled its impact on renal hemodynamics and function, and thus oxygen delivery and consumption in the renal medulla. The model incorporates autoregulation of renal blood flow and glomerular filtration rate and the utilization of oxygen for tubular transport. The model predicts that renal medullary oxygen delivery and consumption are reduced by a similar magnitude during the hypothermic (down to 28°C) phase of CPB. Thus, the fractional extraction of oxygen in the medulla, an index of hypoxia, is increased only by 58% from baseline. However, during the rewarming phase (up to 37°C), oxygen consumption by the medullary thick ascending limb increases 2.3-fold but medullary oxygen delivery increases only by 33%. Consequently, the fractional extraction of oxygen in the medulla is increased 2.7-fold from baseline. Thus, the renal medulla is particularly susceptible to hypoxia during the rewarming phase of CPB. Furthermore, autoregulation of both renal blood flow and glomerular filtration rate is blunted during CPB by the combined effects of hemodilution and nonpulsatile blood flow. Thus, renal hypoxia can be markedly exacerbated if arterial pressure falls below its target level of 50 mmHg. Our findings suggest that tight control of arterial pressure, and thus renal oxygen delivery, may be critical in the prevention of acute kidney injury associated with cardiac surgery performed on CPB.
    Full-text · Article · Jan 2015
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    Gregory J. Herschlag · Jian-Guo Liu · Anita T. Layton
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    ABSTRACT: We derive an exact solution for Stokes flow in an in a channel with permeable walls. We assume that at the channel walls, the normal component of the fluid velocity is described by Darcy's law and the tangential component of the fluid velocity is described by the no slip condition. The pressure exterior to the channel is assumed to be constant. Although this problem has been well studied, typical studies assume that the permeability of the wall is small relative to other non-dimensional parameters; this work relaxes this assumption and explores a regime in parameter space that has not yet been well studied. A consequence of this relaxation is that transverse velocity is no longer necessarily small when compared with the axial velocity. We use our result to explore how existing asymptotic theories break down in the limit of large permeability.
    Full-text · Article · Nov 2014 · SIAM Journal on Applied Mathematics
  • Y. Li · I. Sgouralis · A.T. Layton
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    ABSTRACT: We have developed a numerical method for simulating viscous flow through a compliant closed tube, driven by a pair of fluid source and sink. As is natural for tubular flow simulations, the problem is formulated in axisymmetric cylindrical coordinates, with fluid flow described by the Navier-Stokes equations. Because the tubular walls are assumed to be elastic, when stretched or compressed they exert forces on the fluid. Since these forces are singularly supported along the boundaries, the fluid velocity and pressure fields become unsmooth. To accurately compute the solution, we use the velocity decomposition approach, according to which pressure and velocity are decomposed into a singular part and a remainder part. The singular part satisfies the Stokes equations with singular boundary forces. Because the Stokes solution is unsmooth, it is computed to second-order accuracy using the immersed interface method, which incorporates known jump discontinuities in the solution and derivatives into the finite difference stencils. The remainder part, which satisfies the Navier-Stokes equations with a continuous body force, is regular. The equations describing the remainder part are discretized in time using the semi-Lagrangian approach, and then solved using a pressure-free projection method. Numerical results indicate that the computed overall solution is secondorder accurate in space, and the velocity is second-order accurate in time.
    No preview · Article · Nov 2014
  • Anita T Layton
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    ABSTRACT: Mathematical modeling techniques have been useful in providing insights into biological systems, including the kidney. This article considers some of the mathematical models that concern urea transport in the kidney. Modeling simulations have been conducted to investigate, in the context of urea cycling and urine concentration, the effects of hypothetical active urea secretion into pars recta. Simulation results suggest that active urea secretion induces a "urea-selective" improvement in urine concentrating ability. Mathematical models have also been built to study the implications of the highly structured organization of tubules and vessels in the renal medulla on urea sequestration and cycling. The goal of this article is to show how physiological problems can be formulated and studied mathematically, and how such models may provide insights into renal functions.
    No preview · Article · Oct 2014 · Sub-cellular biochemistry
  • Brendan C. Fry · Anita T. Layton
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    ABSTRACT: We have developed a highly detailed mathematical model of oxygen transport in a cross section of the upper inner medulla of the rat kidney. The model is used to study the impact of the structured organization of nephrons and vessels revealed in anatomic studies, in which descending vasa recta are found to lie distant from clusters of collecting ducts. Specifically, we formulated a two-dimensional oxygen transport model, in which the positions and physical dimensions of renal tubules and vessels are based on an image obtained by immunochemical techniques (T. Pannabecker and W. Dantzler, Three-dimensional architecture of inner medullary vasa recta, Am. J. Physiol. Renal Physiol. 290 (2006) F1355–F1366). The model represents oxygen diffusion through interstitium and other renal structures, oxygen consumption by the Na+/K+-ATPase activities of the collecting ducts, and basal metabolic consumption. Model simulations yield marked variations in interstitial PO2, which can be attributed, in large part, to the heterogeneities in the position and physical dimensions of the collecting ducts. Further, results of a sensitivity study suggest that medullary oxygenation is highly sensitive to medullary blood flow, and that, at high active consumption rates, localized patches of tissue may be vulnerable to hypoxic injury.
    No preview · Article · Sep 2014 · Mathematical Biosciences
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    Thomas L Pannabecker · Anita T Layton
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    ABSTRACT: Renal medullary function is characterized by corticopapillary concentration gradients of various molecules. One example is the generally decreasing axial gradient in oxygen tension (PO2). Another example, found in animals in the antidiuretic state, is a generally increasing axial solute gradient, consisting mostly of NaCl and urea. This osmolality gradient, which plays a principal role in the urine concentrating mechanism, is generally considered to involve countercurrent multiplication and countercurrent exchange, although the underlying mechanism is not fully understood. Radial oxygen and solute gradients in the transverse dimension of the medullary parenchyma have been hypothesized to occur, although strong experimental evidence in support of these gradients remains lacking. This review considers anatomical features of the renal medulla that may impact the formation and maintenance of oxygen and solute gradients. A better understanding of medullary architecture is essential for more clearly defining the compartment-to-compartment flows taken by fluid and molecules that are important in producing axial and radial gradients. Preferential interactions between nephron and vascular segments provide clues as to how tubular and interstitial oxygen flows contribute to safeguarding active transport pathways in renal function in health and disease.
    Preview · Article · Jul 2014 · American journal of physiology. Renal physiology
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    ABSTRACT: We have developed a highly detailed mathematical model of solute transport in the renal medulla of the rat kidney to study the impact of the structured organization of nephrons and vessels revealed in anatomic studies. The model represents the arrangement of tubules around a vascular bundle in the outer medulla, and around a collecting duct cluster in the upper inner medulla~(IM). Model simulations yield marked gradients in intrabundle and interbundle interstitial fluid oxygen tension (PO2), [NaCl], and osmolality in the outer medulla, owing to the vigorous active reabsorption of NaCl by the thick ascending limbs. In the IM, where the thin ascending limbs do not mediate significant active NaCl transport, interstitial fluid composition becomes much more homogeneous with respect to NaCl, urea, and osmolality. Nonetheless, a substantial PO2 gradient remains, owing to the relatively high oxygen demand of the IM collecting ducts. Perhaps more importantly, the model predicts that in the absence of the 3D medullary architecture, oxygen delivery to the IM would drastically decrease, with the terminal IM nearly completely deprived of oxygen. Thus, model results suggest that the functional role of the 3D medullary architecture may be to preserve oxygen delivery to the papilla. Additionally, a simulation that represents low medullary blood flow suggests that the separation of thick limbs from the vascular bundles substantially increases the segments' risk to hypoxic injury. When nephrons and vessels are more homogeneously distributed, luminal PO2 in the thick ascending limb of superficial nephrons increases by 66% in the inner stripe. Furthermore, simulations predict that owing to the Bohr effect, the presumed greater acidity of blood in the interbundle regions, where thick ascending limbs are located, relative to that in the vascular bundles, facilitates the delivery of O$_2$ to support the high metabolic requirements of the thick limbs and raises NaCl reabsorption.
    Preview · Article · Jun 2014 · American journal of physiology. Renal physiology
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    ABSTRACT: This study aims to understand the extent to which modulation of NKCC2 differential splicing affects NaCl delivery to the macula densa. NaCl absorption by the thick ascending limb and macula densa cells is mediated by the apical Na+-K+-2Cl- cotransporter NKCC2. A recent study has indicated that differential splicing by NKCC2 is modulated by dietary salt (Schiebl et al., Am J Physiol Renal Physiol, 2013). Given the markedly different ion affinities of its splice variants, modulation of NKCC2 differential splicing is believed to impact NaCl reabsorption. To assess the validity of that hypothesis, we have developed a mathematical model of the macula densa cell transport, and incorporated that cell model into a previously-applied model of the thick ascending limb (Weinstein, Am J Physiol Renal Physiol, 2010). The macula densa model predicts a 27.4 and 13.1~mV depolarization of the basolateral membrane (as a surrogate for activation of tubuloglomerular feedback, TGF) when luminal [NaCl] is increased from 25 to 145~mM or luminal [K+] is increased from 1.5 to 3.5~mM, respectively, consistent with experimental measurements. Simulations indicate that with luminal solute concentrations consistent with in vivo conditions near the macula densa, NKCC2 operates near its equilibrium state. Results also suggest that modulation of NKCC2 differential splicing by low salt, which induces a shift from NKCC2-A to NKCC2-B primarily in the cortical thick ascending limb and macula densa cells, significantly enhances salt reabsorption in the thick ascending limb, and reduces Na+ and Cl- delivery to the macula densa by 3.7% and 12.5%, respectively. Simulation results also predict that NKCC2 isoform shift hyperpolarizes the macula densa basolateral cell membrane, which, taken in isolation, may inhibit TGF signal release. However, excessive early distal salt delivery and renal salt loss during a low-salt diet may be prevented by an asymmetric TGF response, which may be more sensitive to flow increases.
    Full-text · Article · May 2014 · American journal of physiology. Renal physiology
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    Ioannis Sgouralis · Anita T Layton
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    ABSTRACT: A mathematical model of renal hemodynamics is used to assess the individual contributions of the tubuloglomerular feedback (TGF) mechanism and the myogenic response to glomerular filtration rate regulation in the rat kidney. The model represents an afferent arteriole segment, glomerular filtration, and a short loop of Henle. The afferent arteriole model exhibits myogenic response, which is activated by hydrostatic pressure variations to induce changes in membrane potential and vascular muscle tone. The tubule model predicts tubular fluid and Cl00; transport. Macula densa Cl00; concentration is sensed as the signal for TGF, which acts to constrict or dilate the afferent arteriole. With this configuration, the model afferent arteriole maintains stable glomerular filtration rate within a physiologic range of perfusion pressure (80-180 mmHg). The contribution of TGF to overall autoregulation is significant only within a narrow band of perfusion pressure values (80-110 mmHg). Model simulations of ramp-like perfusion pressure perturbations agree well with findings by Flemming et al. (J Am Soc Nephrol 12:2253- 2262, 2001), which indicate that changes in vascular conductance is markedly sensitive to pressure velocity. That asymmetric response is attributed to the rate-dependent kinetics of the myogenic mechanism. Moreover, simulations of renal autoregulation in diabetes mellitus predict that, due to the impairment of the voltage-gated Ca2+ channels of the afferent arteriole smooth muscle cells, the perfusion pressure range in which SNGFR remains stable is reduced by ~70%, and that TGF gain is reduced by nearly 40%, consistent with experimental findings.
    Full-text · Article · Mar 2014 · AJP Renal Physiology

Publication Stats

1k Citations
234.06 Total Impact Points

Institutions

  • 2004-2015
    • Duke University
      • Department of Mathematics
      Durham, North Carolina, United States
  • 2009
    • Tufts University
      • Department of Chemical and Biological Engineering
      Medford, MA, United States
  • 2002-2004
    • University of North Carolina at Chapel Hill
      • Department of Mathematics
      North Carolina, United States
    • University of Toronto
      • Department of Computer Science
      Toronto, Ontario, Canada