Donald J. Marsh

Redistribution of Na+/H+ exchanger isoform NHE3 in proximal tubules induced by acute and chronic hypertension

Redistribution of apical Na+/H+exchangers (NHE) in the proximal tubules as a plausible mechanism of pressure natriuresis was investigated with confocal immunofluorescence microscopy in Sprague-Dawley rats (SD), spontaneously hypertensive rats (SHR), and two-kidney, one-clip Goldblatt hypertensive rats (GH). NHE isoform NHE3 was localized in the brush border of proximal tubules in SD. Twenty minutes of induced acute hypertension (20-40 mmHg) resulted in a pronounced redistribution of isoform NHE3 from the brush border into the base of microvilli, where clathrin-coated pits were localized. Prehypertensive young SHR (5 wk old, mean blood pressure 105u2009±u20093 mmHg, nu2009=u200911) produced similar findings. However, NHE3 was found to concentrate in the base of microvilli in adult SHR (12 wk old, mean blood pressure 134u2009±u20096 mmHg, nu2009=u200912) and nonclipped kidneys of GH (mean blood pressure 131u2009±u20096 mmHg, nu2009=u20096). In clipped kidneys of GH, which were not exposed to the hypertension because of the arterial clips, NHE3 was localized on the brush border as in normal SD. No further redistribution of NHE3 was detected in adult SHR or GH when acute hypertension was induced. Since both acute and chronic increase of arterial pressure can provoke the redistribution of apical NHE in proximal tubules, the pressure-induced NHE redistribution could be a physiological response and an integral part of pressure natriuresis.

Vascular coupling induces synchronization, quasiperiodicity, and chaos in a nephron tree

The paper presents a study of synchronization phenomena in a system of 22 nephrons supplied with blood from a common cortical radial artery. The nephrons are assumed to interact via hemodynamic and vascularly propagated coupling, both mediated by vascular connections. Using anatomic and physiological criteria, the nephrons are divided into groups: cortical nephrons and medullary nephrons with short, intermediate and long Henle loops. Within each of these groups the delay parameters of the internal feedback regulation are given a random component to represent the internephron variability. For parameters that generate simple limit cycle dynamics in the pressure and flow regulation of single nephrons, the ensemble of coupled nephrons showed steady state, quasiperiodic or chaotic dynamics, depending on the interaction strengths and the arterial blood pressure. When the solutions were either quasiperiodic or chaotic, cortical nephrons synchronized to a single frequency, but the longer medullary nephrons formed two clusters with different frequencies. Under no physiologically realistic combination of parameters did all nephrons assume a common frequency. Our results suggest a greater variability in the nephron dynamics than is apparent from measurements performed on cortical nephrons only. This variability may explain the development of chaotic dynamics in tubular pressure records from hypertensive rats.

Double-wavelet approach to studying the modulation properties of nonstationary multimode dynamics

On the basis of double-wavelet analysis, the paper proposes a method to study interactions in the form of frequency and amplitude modulation in nonstationary multimode data series. Special emphasis is given to the problem of quantifying the strength of modulation for a fast signal by a coexisting slower dynamics and to its physiological interpretation. Application of the approach is demonstrated for a number of model systems, including a model that generates chaotic dynamics. The approach is then applied to proximal tubular pressure data from rat nephrons in order to estimate the degree to which the myogenic dynamics of the afferent arteriole is modulated by the slower tubulo-glomerular dynamics. Our analysis reveals a significantly stronger interaction between the two mechanisms in spontaneously hypertensive rats than in normotensive rats.

The effect of solution non-ideality on membrane transport in three-dimensional models of the renal concentrating mechanism

Previous models of the renal concentrating mechanism employ ideal approximations of solution thermodynamics for membrane transport calculation. In three-dimensional models of the renal medulla, predicted urine concentrations reach levels where these idealized approximations begin to break down. In this paper we derive equations that govern membrane transport for non-dilute solutions and use these equations in a three-dimensional model of the concentrating mechanism. New numerical methods were employed that are more stable than those employed previously. Compared to ideal solution models, the urea non-ideality tends to increase predicted osmolarities, whereas NaCl non-ideality decreases predictions.

Robust nonlinear autoregressive moving average model parameter estimation using stochastic recurrent artificial neural networks.

AbstractIn this study, we introduce a new approach for estimating linear and nonlinear stochastic autoregressive moving average (ARMA) model parameters, given a corrupt signal, using artificial recurrent neural networks. This new approach is a two-step approach in which the parameters of the deterministic part of the stochastic ARMA model are first estimated via a three-layer artificial neural network (deterministic estimation step) and then reestimated using the prediction error as one of the inputs to the artificial neural networks in an iterative algorithm (stochastic estimation step). The prediction error is obtained by subtracting the corrupt signal of the estimated ARMA model obtained via the deterministic estimation step from the system output response. We present computer simulation examples to show the efficacy of the proposed stochastic recurrent neural network approach in obtaining accurate model predictions. Furthermore, we compare the performance of the new approach to that of the deterministic recurrent neural network approach. Using this simple two-step procedure, we obtain more robust model predictions than with the deterministic recurrent neural network approach despite the presence of significant amounts of either dynamic or measurement noise in the output signal. The comparison between the deterministic and stochastic recurrent neural network approaches is furthered by applying both approaches to experimentally obtained renal blood pressure and flow signals.

Multinephron dynamics on the renal vascular network

Tubuloglomerular feedback (TGF) and the myogenic mechanism combine in each nephron to regulate blood flow and glomerular filtration rate. Both mechanisms are nonlinear, generate self-sustained oscillations, and interact as their signals converge on arteriolar smooth muscle, forming a regulatory ensemble. Ensembles may synchronize. Smooth muscle cells in the ensemble depolarize periodically, generating electrical signals that propagate along the vascular network. We developed a mathematical model of a nephron-vascular network, with 16 versions of a single nephron model containing representations of both mechanisms in the regulatory ensemble, to examine the effects of network structure on nephron synchronization. Symmetry, as a property of a network, facilitates synchronization. Nephrons received blood from a symmetric electrically conductive vascular tree. Symmetry was created by using identical nephron models at each of the 16 sites and symmetry breaking by varying nephron length. The symmetric model achieved synchronization of all elements in the network. As little as 1% variation in nephron length caused extensive desynchronization, although synchronization was maintained in small nephron clusters. In-phase synchronization predominated among nephrons separated by one or three vascular nodes and antiphase synchronization for five or seven nodes of separation. Nephron dynamics were irregular and contained low-frequency fluctuations. Results are consistent with simultaneous blood flow measurements in multiple nephrons. An interaction between electrical signals propagated through the network to cause synchronization; variation in vascular pressure at vessel bifurcations was a principal cause of desynchronization. The results suggest that the vasculature supplies blood to nephrons but also engages in robust information transfer.

Nonlinear analysis of renal autoregulation in rats using principal dynamic modes

AbstractThis article presents results of the use of a novel methodology employing principal dynamic modes (PDM) for modeling the nonlinear dynamics of renal autoregulation in rats. The analyzed experimental data are broadband (0–0.5 Hz) blood pressure-flow data generated by pseudorandom forcing and collected in normotensive and hypertensive rats for two levels of pressure forcing (as measured by the standard deviation of the pressure fluctuation). The PDMs are computed from first-order and second-order kernel estimates obtained from the data via the Laguerre expansion technique. The results demonstrate that two PDMs suffice for obtaining a satisfactory nonlinear dynamic model of renal autoregulation under these conditions, for both normotensive and hypertensive rats. Furthermore, the two PDMs appear to correspond to the two main autoregulatory mechanisms: the first to the myogenic and the second to the tubuloglomerular feedback (TGF) mechanism. This allows the study of the separate contributions of the two mechanisms to the autoregulatory response dynamics, as well as the effects of the level of pressure forcing and hypertension on the two distinct autoregulatory mechanisms. It is shown that the myogenic mechanism has a larger contribution and is affected only slightly, while the TGF mechanism is affected considerably by increasing pressure forcing or hypertension (the emergence of a second resonant peak and the decreased relative contribution to the response flow signal).

Evidence of low dimensional chaos in renal blood flow control in genetic and experimental hypertension

Abstract We applied a surrogate data technique to test for nonlinear structure in spontaneous fluctuations of hydrostatic pressure in renal tubules of hypertensive rats. Tubular pressure oscillates at 0.03–0.05 Hz in animals with normal blood pressure, but the fluctuations become irregular with chronic hypertension. Using time series from rats with hypertension we produced surrogate data sets to test whether they represent linearly correlated noise or ‘static’ nonlinear transforms of a linear stochastic process. The correlation dimension and the forecasting error were used as discriminating statistics to compare surrogate with experimental data. The results show that the original experimental time series can be distinguished from both linearly and static nonlinearly correlated noise, indicating that the nonlinear behavior is due to the intrinsic dynamics of the system. Together with other evidence this strongly suggests that a low dimensional chaotic attractor governs renal hemodynamics in hypertension. This appears to be the first demonstration of a transition to chaotic dynamics in an integrated physiological control system occurring in association with a pathological condition.

Dynamics of Nephron-Vascular Network

The paper presents a modeling study of the spatial dynamics of a nephro-vascular network consisting of individual nephrons connected via a tree-like vascular branching structure. We focus on the effects of nonlinear mechanisms that arexa0responsible for the formation of synchronous patterns in order to learn about processes not directly amenable to experimentation. We demonstrate that: (i) the nearest nephrons are synchronized in-phase due to a vascular propagated electrical coupling, (ii) the next few branching levels display a formation of phase-shifted patterns due to hemodynamic coupling and mode elimination, and (iii) distantly located areas show asynchronous behavior or, if all nephrons and branches are perfectly identical, an infinitely long transient behavior. These results contribute to the understanding of mechanisms responsible for the highly dynamic and limited synchronization observed among groups of nephrons despite of the fairly strong interaction between the individual units.

A Robust Method for Detection of Linear and Nonlinear Interactions: Application to Renal Blood Flow Dynamics

We have developed a method that can identify switching dynamics in time series, termed the improved annealed competition of experts (IACE) algorithm.6 In this paper, we extend the approach and use it for detection of linear and nonlinear interactions, by employing histograms showing the frequency of switching modes obtained from the IACE, then examining time-frequency spectra. This extended approach is termed Histogram of improved annealed competition of experts—time frequency (HIACE-TF). The hypothesis is that frequent switching dynamics in HIACE-TF results are due to interactions between different dynamic components. To validate this assertion, we used both simulation examples as well as application to renal blood flow data. We compared simulation results to a time-phase bispectrum (TPB) approach,16 which can also be used to detect time-varying quadratic phase coupling between various components. We found that the HIACE-TF approach is more accurate than the TPB in detecting interactions, and remains accurate for signal-to-noise ratios as low as 15xa0dB. With all 10 data sets, comprised of volumetric renal blood flow data, we also validated the feasibility of the HIACE-TF approach in detecting nonlinear interactions between the two mechanisms responsible for renal autoregulation. Further validation of the HIACE-TF approach was achieved by comparing it to a realistic mathematical model that has the capability to generate either the presence or the absence of nonlinear interactions between two renal autoregulatory mechanisms.