Anita T Layton

Duke University, Durham, NC, United States

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Publications (82)203.33 Total impact

  • 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.
    AJP Renal Physiology 03/2014; · 4.42 Impact Factor
  • Aurélie Edwards, Anita T Layton
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    ABSTRACT: The renal afferent arteriole reacts to an elevation in blood pressure with an increase in muscle tone and a decrease in luminal diameter. This effect, known as the myogenic response, is believed to stabilize glomerular filtration and to protect the glomerulus from systolic blood pressure increases, especially in hypertension. To study the mechanisms underlying the myogenic response, we developed a mathematical model of intracellular Ca(2+) signaling in an afferent arteriole smooth muscle cell. The model represents detailed transmembrane ionic transport, intracellular Ca(2+) dynamics, the kinetics of myosin light chain phosphorylation, and the mechanical behavior of the cell. It assumes that the myogenic response is initiated by pressure-induced changes in the activity of non-selective cation channels. Our model predicts spontaneous vasomotion at physiological luminal pressures, and KCl- and diltiazem-induced diameter changes comparable to experimental findings. The time-periodic oscillations stem from the dynamic exchange of Ca(2+) between the cytosol and the sarcoplasmic reticulum, coupled to the stimulation of Ca(2+)-activated potassium (KCa) and chloride (ClCa) channels, and the modulation of voltage-activated L-type channels; blocking sarco/endoplasmic reticulum Ca(2+) pumps or ryanodyne receptors (RyR), KCa, ClCa or L-type channels abolishes these oscillations. Our results indicate that the profile of the myogenic response is also strongly dependent upon the conductance of ClCa and L-type channels, as well as the activity of plasmalemmal Ca(2+) pumps. Furthermore, inhibition of Ca(2+)-activated K+ channels is not necessary to induce myogenic contraction. Lastly, our model suggests that the kinetic behavior of L-type channels results in myogenic kinetics that are substantially faster during constriction than during dilation, consistent with in vitro observations (Loutzenhiser et al., Circ. Res. 90:1316--1324, 2002).
    AJP Renal Physiology 10/2013; · 4.42 Impact Factor
  • Ioannis Sgouralis, Anita T Layton
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    ABSTRACT: We have developed a mathematical model of the rat's renal hemodynamics in the nephron level, and used that model to study flow control and signal transduction in the rat kidney. The model represents an afferent arteriole, glomerular filtration, and a segment of a short-loop nephron. The model afferent arteriole is myogenically active and represents smooth muscle membrane potential and electrical coupling. The myogenic mechanism is based on the assumption that the activity of nonselective cation channels is shifted by changes in transmural pressure, such that elevation in pressure induces vasoconstriction, which increases resistance to blood flow. From the afferent arteriole's fluid delivery output, glomerular filtration rate is computed, based on conservation of plasma and plasma protein. Chloride concentration is then computed along the renal tubule based on solute conservation that represents water reabsorption along the proximal tubule and the water-permeable segment of the descending limb, and chloride fluxes driven by passive diffusion and active transport. The model's autoregulatory response is predicted to maintain stable renal blood flow within a physiologic range of blood pressure values. Power spectra associated with time series predicted by the model reveal a prominent fundamental peak at ∼165 mHz arising from the afferent arteriole's spontaneous vasomotion. Periodic external forcings interact with vasomotion to introduce heterodynes into the power spectra, significantly increasing their complexity.
    Bulletin of Mathematical Biology 10/2013; · 2.02 Impact Factor
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    Anita T Layton, Lise Bankir
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    ABSTRACT: It has been observed experimentally that early distal tubular urea flow exceeds urea delivery by the proximal convoluted tubule to the pars recta and loop of Henle. Moreover, the fractional excretion of urea in the urine may exceed values compatible with the reabsorption known to occur in the proximal convoluted tubule in the cortex. A likely explanation for these observations is that urea may be actively secreted into the pars recta, as proposed in a few studies. However, this hypothesis has yet to be demonstrated experimentally. In this study, we used a mathematical model of the renal medulla of the rat kidney to investigate the impacts of active urea secretion in the intrarenal handling of urea and in the urine concentrating ability. The model represents only the outer and inner medullary zones, with the actions taking place in the cortex incorporated via boundary conditions. Blood flow in the model vasculature is divided into plasma and red blood cell compartments. We compared urea flow rates and other related model variables without and with the hypothetical active urea secretion in the pars recta. The simulation suggests that active urea secretion induces a "urea-selective" improvement in urine concentrating ability by enhancing the efficiency of urea excretion without requiring a higher urine flow rate, and with only modest changes in the excretion of other solutes. These results should encourage experimental studies in order to assess the existence of an active urea secretion in the rodent kidney.
    Physiological reports. 09/2013; 1(3).
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    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.
    Clinical Journal of the American Society of Nephrology 08/2013; · 5.07 Impact Factor
  • Anita T Layton
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    ABSTRACT: In addition to metabolic waste and toxin excretion, the kidney also plays an indispensable role in regulating the balance of water, electrolytes, nitrogen, and acid-base. In this review, we describe representative mathematical models that have been developed to better understand kidney physiology and pathophysiology, including the regulation of glomerular filtration, the regulation of renal blood flow by means of the tubuloglomerular feedback mechanisms and of the myogenic mechanism, the urine concentrating mechanism, epithelial transport, and regulation of renal oxygen transport. We discuss the extent to which these modeling efforts have expanded our understanding of renal function in both health and disease. WIREs Syst Biol Med 2013. doi: 10.1002/wsbm.1232 For further resources related to this article, please visit the WIREs website. Conflict of interest: The authors have declared no conflicts of interest for this article.
    Wiley Interdisciplinary Reviews Systems Biology and Medicine 07/2013; · 3.68 Impact Factor
  • Hwayeon Ryu, Anita T Layton
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    ABSTRACT: The glomerular filtration rate in the kidney is controlled, in part, by the tubuloglomerular feedback (TGF) system, which is a negative feedback loop that mediates oscillations in tubular fluid flow and in fluid NaCl concentration of the loop of Henle. In this study, we developed a mathematical model of the TGF system that represents NaCl transport along a short loop of Henle with compliant walls. The proximal tubule and the outer-stripe segment of the descending limb are assumed to be highly water permeable; the thick ascending limb (TAL) is assumed to be water impermeable and have active NaCl transport. A bifurcation analysis of the TGF model equations was performed by computing parameter boundaries, as functions of TGF gain and delay, that separate differing model behaviors. The analysis revealed a complex parameter region that allows a variety of qualitatively different model equations: a regime having one stable, time-independent steady-state solution and regimes having stable oscillatory solutions of different frequencies. A comparison with a previous model, which represents only the TAL explicitly and other segments using phenomenological relations, indicates that explicit representation of the proximal tubule and descending limb of the loop of Henle lowers the stability of the TGF system. Model simulations also suggest that the onset of limit-cycle oscillations results in increases in the time-averaged distal NaCl delivery, whereas distal fluid delivery is not much affected.
    Journal of Mathematical Biology 03/2013; · 2.37 Impact Factor
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    ABSTRACT: We introduce a regularization method that gives a smooth formulation for the fundamental solution to Stokes flow driven by an infinite, triply-periodic array of point forces. With this formulation, the velocity at any spatial location may be calculated, including at and very near the point forces; these locations typically lead to numerical difficulties due to the singularity within the Stokeslet when using other methods. For computational efficiency, we build upon previous methods in which the periodic Stokeslet is split into two rapidly decaying sums, one in physical space and one in reciprocal, or Fourier, space. We present two validation studies of our method. First, we compute the drag coefficient for periodic arrays of spheres with a variety of concentrations of sphere packings; and second, we prescribe a force density onto a periodic array of spheres, compute the resulting nearby velocity field, and compare these velocities to those computed using an immersed boundary method formulation. The drag coefficients computed with our method are within 0.63%0.63% of previously published values. The velocity field comparison shows a relative error of about 0.18%0.18% in the L2L2-norm. We then apply our numerical method to a periodic arrangement of sinusoidal swimmers. By systematically varying their spacing in three directions, we are able to explore how their spacing affects their collective swimming speed.
    Journal of Computational Physics 03/2013; 236:187–202. · 2.14 Impact Factor
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    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 multi-cell 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, which varies TAL tubular fluid inflow rate as a function of outflow fluid [Cl(-)]. 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)CVR in individual cells influences the distribution of net Na(+) transport along the TAL; (2)CVR responses in conjunction with TGF increase the overall efficiency of Na(+) transport; (3)the transepithelial [Na(+)] gradient is a major determinant of transport efficiency; and (4)under the condition that the distribution of Na(+) transport along the TAL is quasi-uniform, the tubular fluid axial [Cl(-)] gradient near the macula densa is sufficiently steep to yield a TGF gain consistent with experimental data.
    AJP Renal Physiology 10/2012; · 4.42 Impact Factor
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    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], [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.
    AJP Renal Physiology 10/2012; · 4.42 Impact Factor
  • Anita T Layton
    [show abstract] [hide abstract]
    ABSTRACT: The kidney plays an indispensable role in the regulation of whole-organism water balance, electrolyte balance, and acid-base balance, and in the excretion of metabolic wastes and toxins. In this paper, we review representative mathematical models that have been developed to better understand kidney physiology and pathophysiology, including the regulation of glomerular filtration, the regulation of renal blood flow by means of the tubuloglomerular feedback mechanisms and of the myogenic mechanism, the urine concentrating mechanism, and regulation of renal oxygen transport. We discuss how such modeling efforts have significantly expanded our understanding of renal function in both health and disease.
    ISRN Biomathematics 07/2012; 2012(2012).
  • Aurélie Edwards, Anita T Layton
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    ABSTRACT: The present study aimed to elucidate the reciprocal interactions between oxygen (O(2)), nitric oxide (NO), and superoxide (O(2)(-)) and their effects on vascular and tubular function in the outer medulla. We expanded our region-based model of transport in the rat outer medulla (Edwards A, Layton AT. Am J Physiol Renal Physiol 301: F979-F996, 2011) to incorporate the effects of NO on descending vasa recta (DVR) diameter and blood flow. Our model predicts that the segregation of long DVR in the center of vascular bundles, away from tubular segments, gives rise to large radial NO concentration gradients that in turn result in differential regulation of vasoactivity in short and long DVR. The relative isolation of long DVR shields them from changes in the rate of NaCl reabsorption, and hence from changes in O(2) requirements, by medullary thick ascending limbs (mTALs), thereby preserving O(2) delivery to the inner medulla. The model also predicts that O(2)(-) can sufficiently decrease the bioavailability of NO in the interbundle region to affect the diameter of short DVR, suggesting that the experimentally observed effects of O(2)(-) on medullary blood flow may be at least partly mediated by NO. In addition, our results indicate that the tubulovascular cross talk of NO, that is, the diffusion of NO produced by mTAL epithelia toward adjacent DVR, helps to maintain blood flow and O(2) supply to the interbundle region even under basal conditions. NO also acts to preserve local O(2) availability by inhibiting the rate of active Na(+) transport, thereby reducing the O(2) requirements of mTALs. The dual regulation by NO of oxygen supply and demand is predicted to significantly attenuate the hypoxic effects of angiotensin II.
    AJP Renal Physiology 07/2012; 303(7):F907-17. · 4.42 Impact Factor
  • Yi Li, Anita T. Layton
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    ABSTRACT: We present numerical methods for computing two-dimensional Stokes flow driven by forces singularly supported along an open, immersed interface. Two second-order accurate methods are developed: one for accurately evaluating boundary integral solutions at a point, and another for computing Stokes solution values on a rectangular mesh. We first describe a method for computing singular or nearly singular integrals, such as a double layer potential due to sources on a curve in the plane, evaluated at a point on or near the curve. To improve accuracy of the numerical quadrature, we add corrections for the errors arising from discretization, which are found by asymptotic analysis. When used to solve the Stokes equations with sources on an open, immersed interface, the method generates second-order approximations, for both the pressure and the velocity, and preserves the jumps in the solutions and their derivatives across the boundary. We then combine the method with a mesh-based solver to yield a hybrid method for computing Stokes solutions at N2 grid points on a rectangular grid. Numerical results are presented which exhibit second-order accuracy. To demonstrate the applicability of the method, we use the method to simulate fluid dynamics induced by the beating motion of a cilium. The method preserves the sharp jumps in the Stokes solution and their derivatives across the immersed boundary. Model results illustrate the distinct hydrodynamic effects generated by the effective stroke and by the recovery stroke of the ciliary beat cycle.
    Journal of Computational Physics 06/2012; 231(15):5195–5215. · 2.14 Impact Factor
  • Hwayeon Ryu, Anita T Layton
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    ABSTRACT: One of the key mechanisms that mediate renal autoregulation is the tubuloglomerular feedback (TGF) system, which is a negative feedback loop in the kidney that balances glomerular filtration with tubular reabsorptive capacity. Tubular fluid flow, NaCl concentration and other related variables are known to exhibit TGF-mediated oscillations. In this study, we used a mathematical model of the thick ascending limb (TAL) of a short loop of Henle of the rat kidney to study the effects of (i) spatially inhomogeneous TAL NaCl active transport rate, (ii) spatially inhomogeneous tubular radius and (iii) compliance of the tubular walls on TGF-mediated dynamics. A bifurcation analysis of the TGF model equations was performed by deriving a characteristic equation and finding its roots. Results of the bifurcation analysis were validated via numerical simulations of the full model equations. Model results suggest that a higher TAL NaCl active transport rate or a smaller TAL radius near the loop bend gives rise to stable oscillatory solutions at sufficiently high TGF gain values, even with zero TGF delay. In addition, when the TAL walls are assumed to be compliant, the TGF system exhibits a heightened tendency to oscillate, a result that is consistent with predictions of a previous modelling study.
    Mathematical Medicine and Biology 04/2012; · 2.41 Impact Factor
  • Ioannis Sgouralis, Anita T Layton
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    ABSTRACT: We have formulated a mathematical model for the rat afferent arteriole (AA). Our model consists of a series of arteriolar smooth muscle cells and endothelial cells, each of which represents ion transport, cell membrane potential, and gap junction coupling. Cellular contraction and wall mechanics are also represented for the smooth muscle cells. Blood flow through the AA lumen is described by Poiseuille flow. The AA model's representation of the myogenic response is based on the hypothesis that changes in hydrostatic pressure induce changes in the activity of nonselective cation channels. The resulting changes in membrane potential then affect calcium influx through changes in the activity of the voltage-gated calcium channels, so that vessel diameter decreases with increasing pressure values. With this configuration, the model AA maintains roughly stable renal blood flow within a physiologic range of blood flow pressure. Model simulation of vasoconstriction initiated from local stimulation also agrees well with findings in the experimental literature, notably those of Steinhausen et al. (Steinhausen M, Endlich K, Nobiling R, Rarekh N, Schütt F. J Physiol 505: 493-501, 1997), which indicated that conduction of vasoconstrictive response decays more rapidly in the upstream flow direction than downstream. The model can be incorporated into models of integrated renal hemodynamic regulation.
    AJP Renal Physiology 04/2012; 303(2):F229-39. · 4.42 Impact Factor
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    Natasha S Savage, Anita T Layton, Daniel J Lew
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    ABSTRACT: The establishment of cell polarity involves positive-feedback mechanisms that concentrate polarity regulators, including the conserved GTPase Cdc42p, at the "front" of the polarized cell. Previous studies in yeast suggested the presence of two parallel positive-feedback loops, one operating as a diffusion-based system, and the other involving actin-directed trafficking of Cdc42p on vesicles. F-actin (and hence directed vesicle traffic) speeds fluorescence recovery of Cdc42p after photobleaching, suggesting that vesicle traffic of Cdc42p contributes to polarization. We present a mathematical modeling framework that combines previously developed mechanistic reaction-diffusion and vesicle-trafficking models. Surprisingly, the combined model recapitulated the observed effect of vesicle traffic on Cdc42p dynamics even when the vesicles did not carry significant amounts of Cdc42p. Vesicle traffic reduced the concentration of Cdc42p at the front, so that fluorescence recovery mediated by Cdc42p flux from the cytoplasm took less time to replenish the bleached pool. Simulations in which Cdc42p was concentrated into vesicles or depleted from vesicles yielded almost identical predictions, because Cdc42p flux from the cytoplasm was dominant. These findings indicate that vesicle-mediated delivery of Cdc42p is not required to explain the observed Cdc42p dynamics, and raise the question of whether such Cdc42p traffic actually contributes to polarity establishment.
    Molecular biology of the cell 03/2012; 23(10):1998-2013. · 5.98 Impact Factor
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    Anita T Layton, Philip Pham, Hwa-Yeon Ryu
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    ABSTRACT: To study the transformation of fluctuations in filtration rate into tubular fluid chloride concentration oscillations alongside the macula densa, we have developed a mathematical model for tubuloglomerular feedback (TGF) signal transduction along the pars recta, the descending limb, and the thick ascending limb of a short-looped nephron. The model tubules are assumed to have compliant walls and thus a tubular radius that depends on the transmural pressure difference. Previously it has been predicted that TGF transduction by the thick ascending limb (TAL) is a generator of nonlinearities: if a sinusoidal oscillation is added to a constant TAL flow rate, then the time required for a fluid element to traverse the TAL is oscillatory in time but nonsinusoidal. The results from the new model simulations presented here predict that TGF transduction by the loop of Henle is also, in the same sense, a generator of nonlinearities. Thus this model predicts that oscillations in tubular fluid alongside the macula densa will be nonsinusoidal and will exhibit harmonics of sinusoidal perturbations of pars recta flow. Model results also indicate that the loop acts as a low-pass filter in the transduction of the TGF signal.
    International journal for numerical methods in biomedical engineering. 03/2012; 28(3):369-383.
  • Anita T Layton, Leon C Moore, Harold E Layton
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    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.
    AJP Renal Physiology 01/2012; 302(9):F1188-202. · 4.42 Impact Factor
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    ABSTRACT: Recent anatomic findings indicate that in the upper inner medulla of the rodent kidney, tubules, and vessels are organized around clusters of collecting ducts (CDs). Within CD clusters, CDs and some of the ascending vasa recta (AVR) and ascending thin limbs (ATLs), when viewed in transverse sections, form interstitial nodal spaces, which are arrayed at structured intervals throughout the inner medulla. These spaces, or microdomains, are bordered on one side by a single CD, on the opposite side by one or more ATLs, and on the other two sides by AVR. To study the interactions among these CDs, ATLs, and AVR, we have developed a mathematical compartment model, which simulates steady-state solute exchange through the microdomain at a given inner medullary level. Fluid in all compartments contains Na(+), Cl(-), urea and, in the microdomain, negative fixed charges that represent macromolecules (e.g., hyaluronan) balanced by Na(+). Fluid entry into AVR is assumed to be driven by hydraulic and oncotic pressures. Model results suggest that the isolated microdomains facilitate solute and fluid mixing among the CDs, ATLs, and AVR, promote water withdrawal from CDs, and consequently may play an important role in generating the inner medullary osmotic gradient.
    AJP Renal Physiology 12/2011; 302(7):F830-9. · 4.42 Impact Factor
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    ABSTRACT: We extended a region-based mathematical model of the renal medulla of the rat kidney, previously developed by us, to represent new anatomic findings on the vascular architecture in the rat inner medulla (IM). In the outer medulla (OM), tubules and vessels are organized around tightly packed vascular bundles; in the IM, the organization is centered around collecting duct clusters. In particular, the model represents the separation of descending vasa recta from the descending limbs of loops of Henle, and the model represents a papillary segment of the descending thin limb that is water impermeable and highly urea permeable. Model results suggest that, despite the compartmentalization of IM blood flow, IM interstitial fluid composition is substantially more homogeneous compared with OM. We used the model to study medullary blood flow in antidiuresis and the effects of vascular countercurrent exchange. We also hypothesize that the terminal aquaporin-1 null segment of the long descending thin limbs may express a urea-Na(+) or urea-Cl(-) cotransporter. As urea diffuses from the urea-rich papillary interstitium into the descending thin limb luminal fluid, NaCl is secreted via the cotransporter against its concentration gradient. That NaCl is then reabsorbed near the loop bend, raising the interstitial fluid osmolality and promoting water reabsorption from the IM collecting ducts. Indeed, the model predicts that the presence of the urea-Na(+) or urea- Cl(-) cotransporter facilitates the cycling of NaCl within the IM and yields a loop-bend fluid composition consistent with experimental data.
    AJP Renal Physiology 11/2011; 302(5):F591-605. · 4.42 Impact Factor

Publication Stats

660 Citations
203.33 Total Impact Points

Institutions

  • 2005–2013
    • Duke University
      • Department of Mathematics
      Durham, NC, United States
  • 2012
    • Centre de Recherche des Cordeliers de Jussieu (CRC)
      Lutetia Parisorum, Île-de-France, France
  • 2009–2011
    • Tufts University
      • Department of Chemical and Biological Engineering
      Medford, MA, United States
    • Old Dominion University
      • Department of Mathematics and Statistics
      Norfolk, VA, United States
  • 2006–2009
    • University of Puerto Rico at Rio Piedras
      • • Department of Computer Science
      • • Department of Mathematics
      San Juan, San Juan, Puerto Rico
  • 2008
    • The University of Arizona
      • Department of Physiology
      Tucson, AZ, United States
  • 2003–2004
    • University of North Carolina at Chapel Hill
      • Department of Mathematics
      Chapel Hill, NC, United States