Nonlinear system analysis of renal autoregulation in normotensive and hypertensive rats

In vivo mapping of hemodynamic responses mediated by tubuloglomerular feedback in hypertensive kidneys

The kidney has a sophisticated vascular structure that performs the unique function of filtering blood and managing blood pressure. Tubuloglomerular feedback is an intra-nephron negative feedback mechanism stabilizing single-nephron blood flow, glomerular filtration rate, and tubular flow rate, which is exhibited as self-sustained oscillations in single-nephron blood flow. We report the application of multi-scale laser speckle imaging to monitor global blood flow changes across the kidney surface (low zoom) and local changes in individual microvessels (high zoom) in normotensive and spontaneously hypertensive rats in vivo. We reveal significant differences in the parameters of TGF-mediated hemodynamics and patterns of synchronization. Furthermore, systemic infusion of a glucagon-like-peptide-1 receptor agonist, a potential renoprotective agent, induces vasodilation in both groups but only alters the magnitude of the TGF in Sprague Dawleys, although the underlying mechanisms remain unclear.

Efficacy of Dynamics-based Features for Machine Learning Classification of Renal Hemodynamics

Different machine learning approaches for analyzing renal hemodynamics using time series of arterial blood pressure and renal blood flow rate measurements in conscious rats are developed and compared. Particular emphasis is placed on features used for machine learning. The test scenario involves binary classification of Sprague-Dawley rats obtained from two different suppliers, with the suppliers' rat colonies having drifted slightly apart in hemodynamic characteristics. Models used for the classification include deep neural network (DNN), random forest, support vector machine, multilayer perceptron. While the DNN uses raw pressure/flow measurements as features, the latter three use a feature vector of parameters of a nonlinear dynamic system fitted to the pressure/flow data, thereby restricting the classification basis to the hemodynamics. Although the performance in these cases is slightly reduced in comparison to that of the DNN, they still show promise for machine learning (ML) application. The pioneering contribution of this work is the establishment that even with features limited to hemodynamics-based information, the ML models can successfully achieve classification with reasonably high accuracy.

The nephron-arterial network and its interactions

Tubuloglomerular feedback and the myogenic mechanism form an ensemble in renal afferent arterioles that regulate single-nephron blood flow and glomerular filtration. Each mechanism generates a self-sustained oscillation, the mechanisms interact, and the oscillations synchronize. The synchronization generates a bimodal electrical signal in the arteriolar wall that propagates retrograde to a vascular node, where it meets similar electrical signals from other nephrons. Each signal carries information about the time-dependent behavior of the regulatory ensemble. The converging signals support synchronization of the nephrons participating in the information exchange, and the synchronization can lead to formation of nephron clusters. We review the experimental evidence and the theoretical implications of these interactions and consider additional interactions that can limit the size of nephron clusters. The architecture of the arterial tree figures prominently in these interactions.

Effect of Shallow and Deep SCUBA Dives on Heart Rate Variability

Prolonged and high pressure diving may lead to various physiological changes including significant alterations of autonomic nervous system (ANS) activity that may be associated with altered physical performance, decompression sickness, or central nervous system oxygen toxicity. Ideally, researchers could elucidate ANS function before, during, and after dives that are most associated with altered function and adverse outcomes. However, we have a limited understanding of the activities of the ANS especially during deeper prolonged SCUBA diving because there has never been a convenient way to collect physiological data during deep dives. This work is one of the first studies which was able to collect electrocardiogram (ECG) data from SCUBA divers at various depths (33, 66, 99, 150, and 200 ftsw; equivalent to 10.05, 20.10, 30.17, 45.72, and 60.96 m of salt water, respectively) breathing different gas mixtures (air, nitrox and trimix). The aim of this study was to shed light on cardiac ANS behavior during dives, including deep dives. With the aid of dry suits, a Holter monitor that could handle the pressure of a 200 ft. dive, and a novel algorithm that can provide a useful assessment of the ANS from the ECG signal, we investigated the effects of SCUBA dives with different time durations, depths and gas mixtures on the ANS. Principal dynamic mode (PDM) analysis of the ECG, which has been shown to provide accurate separation of the sympathetic and parasympathetic dynamics, was employed to assess the difference of ANS behavior between baseline and diving conditions of varying depths and gas mixtures consisting of air, nitrox and trimix. For all depths and gas mixtures, we found consistent dominance in the parasympathetic activity and a concomitant increase of the parasympathetic dynamics with increasing diving duration and depth. For 33 and 66 ft. dives, we consistently found significant decreases in heart rates (HR) and concomitant increases in parasympathetic activities as estimated via the PDM and root mean square of successive differences (RMSSD) for all time intervals (from the first 5 min to the last 30 min) at the bottom depth when compared to the baseline depth at sea level. The sympathetic dynamics did not change with dive duration or gas mixtures, but at the 150 and 200 ft. dives, we found a significant increase in the sympathetic dynamics in addition to the elevated parasympathetic dynamics when compared to baseline The power spectral density (PSD) measures such as the low frequency (LF), high frequency (HF) and its ratio, and approximate entropy (ApEn) indices were not as consistent when compared to PDM-derived parasympathetic dynamics and RMSSD index.

Renal autoregulation in health and disease

Intrarenal autoregulatory mechanisms maintain renal blood flow (RBF) and glomerular filtration rate (GFR) independent of renal perfusion pressure (RPP) over a defined range (80-180 mmHg). Such autoregulation is mediated largely by the myogenic and the macula densa-tubuloglomerular feedback (MD-TGF) responses that regulate preglomerular vasomotor tone primarily of the afferent arteriole. Differences in response times allow separation of these mechanisms in the time and frequency domains. Mechanotransduction initiating the myogenic response requires a sensing mechanism activated by stretch of vascular smooth muscle cells (VSMCs) and coupled to intracellular signaling pathways eliciting plasma membrane depolarization and a rise in cytosolic free calcium concentration ([Ca(2+)]i). Proposed mechanosensors include epithelial sodium channels (ENaC), integrins, and/or transient receptor potential (TRP) channels. Increased [Ca(2+)]i occurs predominantly by Ca(2+) influx through L-type voltage-operated Ca(2+) channels (VOCC). Increased [Ca(2+)]i activates inositol trisphosphate receptors (IP3R) and ryanodine receptors (RyR) to mobilize Ca(2+) from sarcoplasmic reticular stores. Myogenic vasoconstriction is sustained by increased Ca(2+) sensitivity, mediated by protein kinase C and Rho/Rho-kinase that favors a positive balance between myosin light-chain kinase and phosphatase. Increased RPP activates MD-TGF by transducing a signal of epithelial MD salt reabsorption to adjust afferent arteriolar vasoconstriction. A combination of vascular and tubular mechanisms, novel to the kidney, provides for high autoregulatory efficiency that maintains RBF and GFR, stabilizes sodium excretion, and buffers transmission of RPP to sensitive glomerular capillaries, thereby protecting against hypertensive barotrauma. A unique aspect of the myogenic response in the renal vasculature is modulation of its strength and speed by the MD-TGF and by a connecting tubule glomerular feedback (CT-GF) mechanism. Reactive oxygen species and nitric oxide are modulators of myogenic and MD-TGF mechanisms. Attenuated renal autoregulation contributes to renal damage in many, but not all, models of renal, diabetic, and hypertensive diseases. This review provides a summary of our current knowledge regarding underlying mechanisms enabling renal autoregulation in health and disease and methods used for its study.

Closed-loop control of renal perfusion pressure in physiological experiments

This paper presents the design, experimental modeling, and control of a pump-driven renal perfusion pressure (RPP)-regulatory system to implement precise and relatively fast RPP regulation in rats. The mechatronic system is a simple, low-cost, and reliable device to automate the RPP regulation process based on flow-mediated occlusion. Hence, the regulated signal is the RPP measured in the left femoral artery of the rat, and the manipulated variable is the voltage applied to a dc motor that controls the occlusion of the aorta. The control system is implemented in a PC through the LabView software, and a data acquisition board NI USB-6210. A simple first-order linear system is proposed to approximate the dynamics in the experiment. The parameters of the model are chosen to minimize the error between the predicted and experimental output averaged from eight input/output datasets at different RPP operating conditions. A closed-loop servocontrol system based on a pole-placement PD controller plus dead-zone compensation was proposed for this purpose. First, the feedback structure was validated in simulation by considering parameter uncertainty, and constant and time-varying references. Several experimental tests were also conducted to validate in real time the closed-loop performance for stepwise and fast switching references, and the results show the effectiveness of the proposed automatic system to regulate the RPP in the rat, in a precise, accurate (mean error less than 2 mmHg) and relatively fast mode (10-15 s of response time).

Understanding neuronal systems in movement control using Wiener/Volterra kernels: a dominant feature analysis

Although Volterra kernels have been extensively applied in modelling and analysis of biological systems, the relationship between the kernel characteristics and physiologically important features under study is still not revealed clearly. In this study, the link between Volterra kernels and dynamic response of neural systems which control animal movements was investigated and demonstrated using a dominant feature analysis. The new results show an effective but simplified method to use Volterra or Wiener kernels to understand and classify the neural systems which are responsible for the fundamental movements such as flexion and extension of animal limbs, and importantly demonstrate how the neuron pathways in locusts control joint activities of low and high frequency and perform fundamental joint movements such as position, velocity and acceleration. These results provide a useful insight into the nonlinear characteristics of neural systems in movement control and show a useful approach to the analysis of physiological systems using Volterra/Wiener kernels.

Analysis of nonstationarity in renal autoregulation mechanisms using time-varying transfer and coherence functions

The extent to which renal blood flow dynamics vary in time and whether such variation contributes substantively to dynamic complexity have emerged as important questions. Data from Sprague-Dawley rats (SDR) and spontaneously hypertensive rats (SHR) were analyzed by time-varying transfer functions (TVTF) and time-varying coherence functions (TVCF). Both TVTF and TVCF allow quantification of nonstationarity in the frequency ranges associated with the autoregulatory mechanisms. TVTF analysis shows that autoregulatory gain in SDR and SHR varies in time and that SHR exhibit significantly more nonstationarity than SDR. TVTF gain in the frequency range associated with the myogenic mechanism was significantly higher in SDR than in SHR, but no statistical difference was found with tubuloglomerular (TGF) gain. Furthermore, TVCF analysis revealed that the coherence in both strains is significantly nonstationary and that low-frequency coherence was negatively correlated with autoregulatory gain. TVCF in the frequency range from 0.1 to 0.3 Hz was significantly higher in SDR (7 out of 7, >0.5) than in SHR (5 out of 6, <0.5), and consistent for all time points. For TGF frequency range (0.03-0.05 Hz), coherence exhibited substantial nonstationarity in both strains. Five of six SHR had mean coherence (<0.5), while four of seven SDR exhibited coherence (<0.5). Together, these results demonstrate substantial nonstationarity in autoregulatory dynamics in both SHR and SDR. Furthermore, they indicate that the nonstationarity accounts for most of the dynamic complexity in SDR, but that it accounts for only a part of the dynamic complexity in SHR.

Multimodal Pressure Flow Analysis: Application of Hilbert Huang Transform in Cerebral Blood Flow Regulation

Quantification of nonlinear interactions between two nonstationary signals presents a computational challenge in different research fields, especially for assessments of physiological systems. Traditional approaches that are based on theories of stationary signals cannot resolve nonstationarity-related issues and, thus, cannot reliably assess nonlinear interactions in physiological systems. In this review we discuss a new technique "Multi-Modal Pressure Flow method (MMPF)" that utilizes Hilbert-Huang transformation to quantify dynamic cerebral autoregulation (CA) by studying interaction between nonstationary cerebral blood flow velocity (BFV) and blood pressure (BP). CA is an important mechanism responsible for controlling cerebral blood flow in responses to fluctuations in systemic BP within a few heart-beats. The influence of CA is traditionally assessed from the relationship between the well-pronounced systemic BP and BFV oscillations induced by clinical tests. Reliable noninvasive assessment of dynamic CA, however, remains a challenge in clinical and diagnostic medicine.In this brief review we: 1) present an overview of transfer function analysis (TFA) that is traditionally used to quantify CA; 2) describe the a MMPF method and its modifications; 3) introduce a newly developed automatic algorithm and engineering aspects of the improved MMPF method; and 4) review clinical applications of MMPF and its sensitivity for detection of CA abnormalities in clinical studies. The MMPF analysis decomposes complex nonstationary BP and BFV signals into multiple empirical modes adaptively so that the fluctuations caused by a specific physiologic process can be represented in a corresponding empirical mode. Using this technique, we recently showed that dynamic CA can be characterized by specific phase delays between the decomposed BP and BFV oscillations, and that the phase shifts are significantly reduced in hypertensive, diabetics and stroke subjects with impaired CA. In addition, the new technique enables reliable assessment of CA using both data collected during clinical test and spontaneous BP/BFV fluctuations during baseline resting conditions.

Assessment of renal autoregulation

The kidney displays highly efficient autoregulation so that under steady-state conditions renal blood flow (RBF) is independent of blood pressure over a wide range of pressure. Autoregulation occurs in the preglomerular microcirculation and is mediated by two, perhaps three, mechanisms. The faster myogenic mechanism and the slower tubuloglomerular feedback contribute both directly and interactively to autoregulation of RBF and of glomerular capillary pressure. Multiple experiments have been used to study autoregulation and can be considered as variants of two basic designs. The first measures RBF after multiple stepwise changes in renal perfusion pressure to assess how a biological condition or experimental maneuver affects the overall pressure-flow relationship. The second uses time-series analysis to better understand the operation of multiple controllers operating in parallel on the same vascular smooth muscle. There are conceptual and experimental limitations to all current experimental designs so that no one design adequately describes autoregulation. In particular, it is clear that the efficiency of autoregulation varies with time and that most current techniques do not adequately address this issue. Also, the time-varying and nonadditive interaction between the myogenic mechanism and tubuloglomerular feedback underscores the difficulty of dissecting their contributions to autoregulation. We consider the modulation of autoregulation by nitric oxide and use it to illustrate the necessity for multiple experimental designs, often applied iteratively.

Characterization of Dynamics in Renal Autoregulation Using Volterra Models

The dynamics of renal autoregulation are modeled using a modified Volterra representation called the fixed pole expansion technique (FPET). A data dependent procedure is proposed for selecting the pole locations in this expansion that enables a reduction in model complexity compared to standard Volterra models. Furthermore, a quantitative characterization of frequency dependent features of the renal autoregulatory response is enabled via the model's pole locations. The utility of this approach is demonstrated by applying the modeling technique to renal blood pressure and renal blood flow measurements in conscious rats. The model is used to characterize the myogenic autoregulatory response in control rats and rats whose renal autoregulation has been impaired by calcium channel blockers.

Cerebral hemodynamics during orthostatic stress assessed by nonlinear modeling

The effects of orthostatic stress, induced by lower body negative pressure (LBNP), on cerebral hemodynamics were examined in a nonlinear context. Spontaneous fluctuations of beat-to-beat mean arterial blood pressure (MABP) in the finger, mean cerebral blood flow velocity (MCBFV) in the middle cerebral artery, as well as breath-by-breath end-tidal CO2 concentration (PetCO2) were measured continuously in 10 healthy subjects under resting conditions and during graded LBNP to presyncope. A two-input nonlinear Laguerre-Volterra network model was employed to study the dynamic effects of MABP and PetCO2 changes, as well as their nonlinear interactions, on MCBFV variations in the very low (VLF; below 0.04 Hz), low (LF; 0.04–0.15 Hz), and high frequency (HF; 0.15–0.30 Hz) ranges. Dynamic cerebral autoregulation was described by the model terms corresponding to MABP, whereas cerebral vasomotor reactivity was described by the model PetCO2 terms. The nonlinear model terms reduced the output prediction normalized mean square error substantially (by 15–20%) and had a prominent effect in the VLF range, both under resting conditions and during LBNP. Whereas MABP fluctuations dominated in the HF range and played a significant role in the VLF and LF ranges, changes in PetCO2 accounted for a considerable fraction of the VLF and LF MCBFV variations, especially at high LBNP levels. The magnitude of the linear and nonlinear MABP-MCBFV Volterra kernels increased substantially above −30 mmHg LBNP in the VLF range, implying impaired dynamic autoregulation. In contrast, the magnitude of the PetCO2-MCBFV kernels reduced during LBNP at all frequencies, suggesting attenuated cerebral vasomotor reactivity under dynamic conditions. We speculate that these changes may reflect a progressively reduced cerebrovascular reserve to compensate for the increasingly unstable systemic circulation during orthostatic stress that could ultimately lead to cerebral hypoperfusion and syncope.

Combined transfer function analysis and modelling of cerebral autoregulation

The clinical importance of cerebral autoregulation has resulted in a significant body of literature that attempts both to model the underlying physiological processes and to estimate the mathematical relationships between clinically measurable variables, the most common of which are Arterial Blood Pressure and Cerebral Blood Flow Velocity. These approaches have, however, rarely been used together to interpret clinical data. A simple model of cerebral autoregulation is thus proposed here, based on a flow dependent feedback mechanism with gain and time constant that adjusts arterial compliance. Analysis of this model shows that it closely approximates a second order system for typical values of physiological parameters. The model parameters can be optimally estimated from available experimental data for the Impulse Response (IR), yielding physiologically reasonable values, although there is one free parameter that must be fixed. The effects of changes in feedback gain and time constant are found to be significant on the predicted IR and can thus be estimated robustly from experimental data. The effects of elevated baseline Intracranial Pressure (ICP) are found to be exactly equivalent to a reduced feedback gain, although the solution is much less sensitive to the former effect. A transfer function approach can be used to estimate autoregulation status clinically using a physiologically-based model, thus providing greater insight into the processes that govern cerebral autoregulation.

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. 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, 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 15 dB. 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.

Estimation of Time-Varying Coherence Function Using Time-Varying Transfer Functions

We introduce a new method to estimate reliable time-varying coherence functions (TVCF) for causal systems. The technique is based on our previously developed method to estimate time-varying transfer functions (TVTF), known as the time-varying optimal parameter search algorithm [Zou, R., H. Wang, and K. H. Chon. A robust time-varying identification algorithm using basis functions. Ann. Biomed. Eng. 31: 840-853, 2003]. The TVCF is estimated by the multiplication of two TVTFs. The two TVTFs are obtained using signal x as the input and signal y as the output to produce the first TVTF, and signal y as the input and signal x as the output to produce the second TVTF. Demonstration of the feasibility and efficacy of the proposed approach is provided with both simulation examples and application to renal blood flow and pressure data. The proposed approach provides higher time-frequency resolution TVCF than afforded by the short time Fourier transform based TVCF.

Robust Algorithm for Estimation of Time-Varying Transfer Functions

We introduce a new method to estimate reliable time-varying (TV) transfer functions (TFs) and TV impulse response functions. The method is based on TV autoregressive moving average models in which the TV parameters are accurately obtained using the optimal parameter search method which we have previously developed. The new method is more accurate than the recursive least-squares (RLS), and remains robust even in the case of significant noise contamination. Furthermore, the new method is able to track dynamics that change abruptly, which is certainly a deficiency of the RLS. Application of the new method to renal blood pressure and flow revealed that hypertensive rats undergo more complex and TV autoregulation in maintaining stable blood flow than do normotensive rats. This observation has not been previously revealed using time-invariant TF analyses. The newly developed approach may promote the broader use of TV system identification in studies of physiological systems and makes linear and nonlinear TV modeling possible in certain cases previously thought intractable.

Linear and nonlinear analysis of human dynamic cerebral autoregulation

The linear dynamic relationship between systemic arterial blood pressure (ABP) and cerebral blood flow velocity (CBFV) was studied by time- and frequency-domain analysis methods. A nonlinear moving-average approach was also implemented using Volterra-Wiener kernels. In 47 normal subjects, ABP was measured with Finapres and CBFV was recorded with Doppler ultrasound in both middle cerebral arteries at rest in the supine position and also during ABP drops induced by the sudden deflation of thigh cuffs. Impulse response functions estimated by Fourier transfer function analysis, a second-order mathematical model proposed by Tiecks, and the linear kernel of the Volterra-Wiener moving-average representation provided reconstructed velocity model responses, for the same segment of data, with significant correlations to CBFV recordings corresponding to r = 0.52 +/- 0.19, 0.53 +/- 0.16, and 0.67 +/- 0.12 (mean +/- SD), respectively. The correlation coefficient for the linear plus quadratic kernels was 0.82 +/- 0.08, significantly superior to that for the linear models (P < 10(-6)). The supine linear impulse responses were also used to predict the velocity transient of a different baseline segment of data and of the thigh cuff velocity response with significant correlations. In both cases, the three linear methods provided equivalent model performances, but the correlation coefficient for the nonlinear model dropped to 0.26 +/- 0.25 for the baseline test set of data and to 0.21 +/- 0.42 for the thigh cuff data. Whereas it is possible to model dynamic cerebral autoregulation in humans with different linear methods, in the supine position a second-order nonlinear component contributes significantly to improve model accuracy for the same segment of data used to estimate model parameters, but it cannot be automatically extended to represent the nonlinear component of velocity responses of different segments of data or transient changes induced by the thigh cuff test.