On the efficacy of linear system analysis of renal autoregulation in rats

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.

Synchronization in renal microcirculation unveiled with high-resolution blood flow imaging

Internephron interaction is fundamental for kidney function. Earlier studies have shown that nephrons signal to each other, synchronise over short distances, and potentially form large synchronised clusters. Such clusters would play an important role in renal autoregulation, but due to the technological limitations, their presence is yet to be confirmed. In the present study, we introduce an approach for high-resolution laser speckle imaging of renal blood flow and apply it to estimate frequency and phase differences in rat kidney microcirculation under different conditions. The analysis unveiled spatial and temporal evolution of synchronised blood flow clusters of various sizes, including the formation of large (>90 vessels) long-lived clusters (>10 periods) locked at the frequency of the tubular glomerular feedback mechanism. Administration of vasoactive agents caused significant changes in the synchronisation patterns and, thus, in nephrons' co-operative dynamics. Specifically, infusion of vasoconstrictor angiotensin II promoted stronger synchronisation, while acetylcholine caused complete desynchronisation. The results confirm the presence of the local synchronisation in the renal microcirculatory blood flow and that it changes depending on the condition of the vascular network and the blood pressure, which will have further implications for the role of such synchronisation in pathologies development.

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.

Molecular mechanisms of renal blood flow autoregulation

Diabetes and hypertension are the leading causes of chronic kidney disease and their incidence is increasing at an alarming rate. Both are associated with impairments in the autoregulation of renal blood flow (RBF) and greater transmission of fluctuations in arterial pressure to the glomerular capillaries. The ability of the kidney to maintain relatively constant blood flow, glomerular filtration rate (GFR) and glomerular capillary pressure is mediated by the myogenic response of afferent arterioles working in concert with tubuloglomerular feedback that adjusts the tone of the afferent arteriole in response to changes in the delivery of sodium chloride to the macula densa. Despite intensive investigation, the factors initiating the myogenic response and the signaling pathways involved in the myogenic response and tubuloglomerular feedback remain uncertain. This review focuses on current thought regarding the molecular mechanisms underlying myogenic control of renal vascular tone, the interrelationships between the myogenic response and tubuloglomerular feedback, the evidence that alterations in autoregulation of RBF contributes to hypertension and diabetes-induced nephropathy and the identification of vascular therapeutic targets for improved renoprotection in hypertensive and diabetic patients.

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).

Detection of low-frequency oscillations in renal blood flow

Detection of the low-frequency (LF; ∼0.01 Hz) component of renal blood flow, which is theorized to reflect the action of a third renal autoregulatory mechanism, has been difficult due to its slow dynamics. In this work, we used three different experimental approaches to detect the presence of the LF component of renal autoregulation using normotensive and spontaneously hypertensive rats (SHR), both anesthetized and unanesthetized. The first experimental approach utilized a blood pressure forcing in the form of a chirp, an oscillating perturbation with linearly increasing frequency, to elicit responses from the LF autoregulatory component in anesthetized normotensive rats. The second experimental approach involved collection and analysis of spontaneous blood flow fluctuation data from anesthetized normotensive rats and SHR to search for evidence of the LF component in the form of either amplitude or frequency modulation of the myogenic and tubuloglomerular feedback mechanisms. The third experiment used telemetric recordings of arterial pressure and renal blood flow from normotensive rats and SHR for the same purpose. Our transfer function analysis of chirp signal data yielded a resonant peak centered at 0.01 Hz that is greater than 0 dB, with the transfer function gain attenuated to lower than 0 dB at lower frequencies, which is a hallmark of autoregulation. Analysis of the data from the second experiments detected the presence of ∼0.01-Hz oscillations only with isoflurane, albeit at a weaker strength compared with telemetric recordings. With the third experimental approach, the strength of the LF component was significantly weaker in the SHR than in the normotensive rats. In summary, our detection via the amplitude modulation approach of interactions between the LF component and both tubuloglomerular feedback and the myogenic mechanism, with the LF component having an identical frequency to that of the resonant gain peak, provides evidence that 0.01-Hz oscillations may represent the third autoregulatory mechanism.

Electrohydraulic pump-driven closed-loop blood pressure-regulatory system

In this paper, we describe our design for a new electrohydraulic (EH) pump-driven renal perfusion pressure (RPP)-regulatory system capable of implementing precise and rapid RPP regulation in experimental animals. Without this automated system, RPP is manually controlled via a blood pressure clamp, and the imprecision in this method leads to compromised RPP data. This motivated us to develop an EH pump-driven closed-loop blood pressure regulatory system based on flow-mediated occlusion using the vascular occlusive cuff technique. A closed-loop servo-controller system based on a proportional plus integral (PI) controller was designed using the dynamic feedback RPP signal from animals. In vivo performance was evaluated via flow-mediated RPP occlusion, maintenance, and release responses during baseline and ANG II-infused conditions. A step change of -30 mmHg, referenced to normal RPP, was applied to Sprague-Dawley rats with the proposed system to assess the performance of the PI controller. The PI's performance was compared against manual control of blood pressure clamp to regulate RPP. Rapid RPP occlusion (within 3 s) and a release time of approximately 0.3 s were obtained for the PI controller for both baseline and ANG II infusion conditions, in which the former condition was significantly better than manual control. We concluded that the proposed EH RPP-regulatory system could fulfill in vivo needs to study various pressure-flow relationships in diverse fields of physiology, in particular, studying the dynamics of the renal autoregulatory mechanisms.

Renal blood flow and dynamic autoregulation in conscious mice

Autoregulation of renal blood flow (RBF) occurs via myogenic and tubuloglomerular feedback (TGF) mechanisms that are engaged by pressure changes within preglomerular arteries and by tubular flow and content, respectively. Our understanding of autoregulatory function in the kidney largely stems from experiments in anesthetized animals where renal perfusion pressure is precisely controlled. However, normally occurring variations in blood pressure are sufficient to engage both myogenic and TGF mechanisms, making the assessment of autoregulatory function in conscious animals of significant value. To our knowledge, no studies have evaluated the dynamics of RBF in conscious mice. Therefore, we used spectral analysis of blood pressure and RBF and identified dynamic operational characteristics of the myogenic and TGF mechanisms in conscious, freely moving mice instrumented with ultrasound flow probes and arterial catheters. The myogenic response generates a distinct resonance peak in transfer gain at 0.31 +/- 0.01 Hz. Myogenic-dependent attenuation of RBF oscillations, indicative of active autoregulation, is apparent as a trough in gain below 0.3 Hz (-6.5 +/- 1.3 dB) and a strong positive phase peak (93 +/- 9 deg), which are abolished by amlodipine infusion. Operation of TGF produces a local maximum in gain at 0.05 +/- 0.01 Hz and a positive phase peak (62.3 +/- 12.3 deg), both of which are eliminated by infusion of furosemide. Administration of amlodipine eliminated both myogenic and TGF signature peaks, whereas furosemide shifted the myogenic phase peak to a slower operational frequency. These data indicate that myogenic and TGF dynamics may be used to investigate the effectiveness of renal autoregulatory mechanisms in conscious mice.

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.

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.

Renal autoregulation: new perspectives regarding the protective and regulatory roles of the underlying mechanisms

When the kidney is subjected to acute increases in blood pressure (BP), renal blood flow (RBF) and glomerular filtration rate (GFR) are observed to remain relatively constant. Two mechanisms, tubuloglomerular feedback (TGF) and the myogenic response, are thought to act in concert to achieve a precise moment-by-moment regulation of GFR and distal salt delivery. The current view is that this mechanism insulates renal excretory function from fluctuations in BP. Indeed, the concept that renal autoregulation is necessary for normal renal function and volume homeostasis has long been a cornerstone of renal physiology. This article presents a very different view, at least regarding the myogenic component of this response. We suggest that its primary purpose is to protect the kidney against the damaging effects of hypertension. The arguments advanced take into consideration the unique properties of the afferent arteriolar myogenic response that allow it to protect against the oscillating systolic pressure and the accruing evidence that when this response is impaired, the primary consequence is not a disturbed volume homeostasis but rather an increased susceptibility to hypertensive injury. It is suggested that redundant and compensatory mechanisms achieve volume regulation, despite considerable fluctuations in distal delivery, and the assumed moment-by-moment regulation of renal hemodynamics is questioned. Evidence is presented suggesting that additional mechanisms exist to maintain ambient levels of RBF and GFR within normal range, despite chronic alterations in BP and severely impaired acute responses to pressure. Finally, the implications of this new perspective on the divergent roles of the myogenic response to pressure vs. the TGF response to changes in distal delivery are considered, and it is proposed that in addition to TGF-induced vasoconstriction, vasodepressor responses to reduced distal delivery may play a critical role in modulating afferent arteriolar reactivity to integrate the regulatory and protective functions of the renal microvasculature.

Systolic blood pressure as the trigger for the renal myogenic response: protective or autoregulatory?

PURPOSE OF REVIEW

The ability of the kidney to autoregulate renal blood flow and glomerular filtration rate has long been viewed as existing to prevent fluctuations in blood pressure from causing parallel fluctuations in renal function and distal delivery of filtrate. This review, however, points out that the primary consequence of the loss of this autoregulatory capacity is not a disturbance in volume regulation, but rather an increased susceptibility to hypertensive injury. Moreover, the kinetic requirements for renal protection indicate that current views of dynamic autoregulation cannot explain how the kidney is normally protected against acute elevations in systolic blood pressure.

RECENT FINDINGS

Recent findings suggest that the kinetics of the myogenic mechanism of the afferent arteriole are uniquely suited to protect against acute elevations in the systolic blood pressure, in that this vessel not only senses this rapidly oscillating blood pressure component, but that its response is exclusively dependent on this signal.

SUMMARY

These new findings are consistent with recent data indicating that it is the systolic blood pressure elevations that most closely correlate with target organ damage. The fact that the myogenic mechanism is also a necessary component of renal autoregulation may explain the strong linkage between autoregulatory impairment and increased susceptibility to hypertensive injury.

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.

Identification of Transient Renal Autoregulatory Mechanisms Using Time-Frequency Spectral Techniques

Identification of the two principal mediators of renal autoregulation from time-series data is difficult, as both the tubuloglomerular feedback (TGF) and myogenic (MYO) mechanisms interact and share a common effector, the afferent arteriole. Moreover, although both mechanisms can exhibit oscillations in well-characterized frequency bands, these systems often operate in nonoscillatory states not detectable by frequency-domain analysis. To overcome these difficulties, we have developed a new approach to the characterization of the TGF and MYO systems. A laser Doppler probe is used to measure fluctuations in local cortical blood flow (CBF) in response to spontaneous changes in blood pressure (BP) and to large imposed perturbations in BP, which elicit strong, simultaneous, transient, oscillatory blood flow responses. These transient responses are identified by high-resolution time-frequency spectral analysis of the time-series data. In this report, we compare four different time-frequency spectral techniques (the short-time Fourier transform (STFT), smoothed pseudo Wigner-Ville, and two recently developed methods: the Hilbert-Huang transform and time varying optimal parameter search (TVOPS)) to determine which of these four methods is best suited for the identification of transient oscillations in renal autoregulatory mechanisms. We found that TVOPS consistently provided the best performance in both simulation examples and identification of the two autoregulatory mechanisms in actual data. While the STFT suffers in time and frequency resolution as compared to the other three methods, it was able to identify the two autoregulatory mechanisms. Taken together, our experience suggests a two level approach to the analysis of renal blood flow (RBF) data: STFT to obtain a low-resolution time-frequency spectrogram, followed by the use of a higher resolution technique, such as the TVOPS, if even higher time-frequency resolution of the transient responses is required.

Dynamic Modeling of Renal Blood Flow in Dahl Hypertensive and Normotensive Rats

A method is proposed in this paper which allows characterization of renal autoregulatory dynamics and efficiency using quantitative mathematical methods. Based on data from rat experiments, where arterial blood pressure and renal blood flow are measured, a quantitative model for renal blood flow dynamics is constructed. The mathematical structure for the dynamics is chosen as a "grey-box model," i.e. the model structure is inspired from physiology, but the actual parameters is found by numerical methods. Based on a number of experiments, features are extracted from the estimated parameters, which describe myogenic responses and tubuloglomerular feedback responses separately. The method is applied to data from normo- and hypertensive Dahl rats, and a discriminator that separates data from normotensive Dahl R rats and hypertensive Dahl S rats is constructed.

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.

Time-varying properties of renal autoregulatory mechanisms

In order to assess the possible time-varying properties of renal autoregulation, time-frequency and time-scaling methods were applied to renal blood flow under broad-band forced arterial blood pressure fluctuations and single-nephron renal blood flow with spontaneous oscillations obtained from normotensive (Sprague-Dawley, Wistar, and Long-Evans) rats, and spontaneously hypertensive rats. Time-frequency analyses of normotensive and hypertensive blood flow data obtained from either the whole kidney or the single-nephron show that indeed both the myogenic and tubuloglomerular feedback (TGF) mechanisms have time-varying characteristics. Furthermore, we utilized the Renyi entropy to measure the complexity of blood-flow dynamics in the time-frequency plane in an effort to discern differences between normotensive and hypertensive recordings. We found a clear difference in Renyi entropy between normotensive and hypertensive blood flow recordings at the whole kidney level for both forced (p < 0.037) and spontaneous arterial pressure fluctuations (p < 0.033), and at the single-nephron level (p < 0.008). Especially at the single-nephron level, the mean Renyi entropy is significantly larger for hypertensive than normotensive rats, suggesting more complex dynamics in the hypertensive condition. To further evaluate whether or not the separation of dynamics between normotensive and hypertensive rats is found in the prescribed frequency ranges of the myogenic and TGF mechanisms, we employed multiresolution wavelet transform. Our analysis revealed that exclusively over scale ranges corresponding to the frequency intervals of the myogenic and TGF mechanisms, the widths of the blood flow wavelet coefficients fall into disjoint sets for normotensive and hypertensive rats. The separation of the scales at the myogenic and TGF frequency ranges is distinct and obtained with 100% accuracy. However, this observation remains valid only for the whole kidney blood pressure/flow data. The results suggest that understanding of the time-varying properties of the two mechanisms is required for a complete description of renal autoregulation.

A new algorithm for linear and nonlinear ARMA model parameter estimation using affine geometry

A linear and nonlinear autoregressive (AR) moving average (MA) (ARMA) identification algorithm is developed for modeling time series data. The new algorithm is based on the concepts of affine geometry in which the salient feature of the algorithm is to remove the linearly dependent ARMA vectors from the pool of candidate ARMA vectors. For noiseless time series data with a priori incorrect model-order selection, computer simulations show that accurate linear and nonlinear ARMA model parameters can be obtained with the new algorithm. Many algorithms, including the fast orthogonal search (FOS) algorithm, are not able to obtain correct parameter estimates in every case, even with noiseless time series data, because their model-order search criteria are suboptimal. For data contaminated with noise, computer simulations show that the new algorithm performs better than the FOS algorithm for MA processes, and similarly to the FOS algorithm for ARMA processes. However, the computational time to obtain the parameter estimates with the new algorithm is faster than with FOS. Application of the new algorithm to experimentally obtained renal blood flow and pressure data show that the new algorithm is reliable in obtaining physiologically understandable transfer function relations between blood pressure and flow signals.

Impaired myogenic autoregulation in kidneys of Brown Norway rats

The Brown Norway (BN) rat is normotensive and has an extended lifespan but is extremely sensitive to hypertension-induced renal injury. Relative impairment of autoregulation has been implicated in the progression of renal failure whereas absence of myogenic autoregulation is associated with early renal failure. Therefore, we tested the hypothesis that there is conditional failure of renal autoregulation in BN rats. In isoflurane-anesthetized BN rats, the pressure-flow transfer function was normal when pressure fluctuated spontaneously. External forcing increased pressure fluctuation and exposed weakness of the myogenic component of autoregulation; the component mediated by tubuloglomerular feedback was less affected. In the presence of vasopressin to raise renal perfusion pressure, myogenic autoregulation was further impaired during forcing in BN rats but not in Wistar rats. Compensation by the myogenic system was rapidly restored on cessation of forcing, suggesting a functional limitation rather than a structural failure. Graded forcing in Wistar rats and in spontaneously hypertensive rats revealed that compensation due to the myogenic system was strong and independent of forcing amplitude. In contrast, graded forcing in BN rats showed that compensation was reduced when fluctuation of blood pressure was increased but that the reduction was independent of forcing amplitude. The results demonstrate conditional failure of myogenic autoregulation in BN rats. These acute studies provide a possible explanation for the observed sensitivity to hypertension-induced renal injury in BN rats.

Evaluation of linear diaphragm-chest expansion models for magnetic resonance imaging motion artifact correction

The efficacy of Fourier analysis, autoregressive with exogenous input (ARX) and adaptive models to estimate diaphragm position from respiratory belt signal (a measure of chest expansion) was evaluated for the purpose of correcting respiratory motion artifacts in magnetic resonance imaging (MRI). Respiratory belt signal and diaphragm position data were obtained simultaneously during one-dimensional MRI scans with sampling intervals of 100 ms for 128 s (1280 samples). The models were trained using the first 512 data samples for the Fourier method and the first 640 samples for the ARX and adaptive methods. The remaining samples were used as a test set for evaluating the models. Both ARX and adaptive methods produced more accurate results than the Fourier method as reflected by the normalized mean square error (NMSE) and correlation coefficient (R) between the estimated and actual diaphragm position during normal breathing (P < 0.05). However, all three models had difficulty modeling diaphragm positions during breathing plateaus.

Nonlinear system analysis of renal autoregulation in normotensive and hypertensive rats

We compared the dynamic characteristics in renal autoregulation of blood flow of normotensive Sprague-Dawley rats (SDR) and spontaneously hypertensive rats (SHR), using both linear and nonlinear systems analysis. Linear analysis yielded only limited information about the differences in dynamics between SDR and SHR. The predictive ability, as determined by normalized mean-square errors (NMSE), of a third-order Volterra model is better than for a linear model. This decrease in NMSE with a third-order model from that of a linear model is especially evident at frequencies below 0.2 Hz. Furthermore, NMSE are significantly higher in SHR than SDR, suggesting a more complex nonlinear system in SHR. The contribution of the third-order kernel in describing the dynamics of renal autoregulation in arterial blood pressure and blood flow was found to be important. Moreover, we have identified the presence of nonlinear interactions between the oscillatory components of the myogenic mechanism and tubuloglomerular feedback (TGF) at the level of whole kidney blood flow in SDR. An interaction between these two mechanisms had previously been revealed for SDR only at the single nephron level. However, nonlinear interactions between the myogenic and TGF mechanisms are not detected for SHR.

Spectrum analysis of cardiovascular time series

The demand for noninvasive assessment of cardiovascular control parameters has promoted the use of spectrum analysis. These techniques have been applied on a broad basis; however, because of the abstract mathematical approach, spectrum analysis in physiology is still not fully accepted by some circles in the scientific community. Thus it is the goal of the following review to focus on the rationale for applying spectrum analysis in different fields of circulation research, which range from determining arterial baroreceptor reflex sensitivity to the early detection of heart allograft rejection. Within this scope, major findings regarding the physiological and pathophysiological regulation of the cardiovascular system are discussed. In addition, inherent limitations of these methods are made clear. Toward the end of this survey, a perspective is provided for the general readership.

Application of fast orthogonal search to linear and nonlinear stochastic systems

Standard deterministic autoregressive moving average (ARMA) models consider prediction errors to be unexplainable noise sources. The accuracy of the estimated ARMA model parameters depends on producing minimum prediction errors. In this study, an accurate algorithm is developed for estimating linear and nonlinear stochastic ARMA model parameters by using a method known as fast orthogonal search, with an extended model containing prediction errors as part of the model estimation process. The extended algorithm uses fast orthogonal search in a two-step procedure in which deterministic terms in the nonlinear difference equation model are first identified and then reestimated, this time in a model containing the prediction errors. Since the extended algorithm uses an orthogonal procedure, together with automatic model order selection criteria, the significant model terms are estimated efficiently and accurately. The model order selection criteria developed for the extended algorithm are also crucial in obtaining accurate parameter estimates. Several simulated examples are presented to demonstrate the efficacy of the algorithm.

Nonlinear analysis of renal autoregulation under broadband forcing conditions

Linear analysis of renal blood flow fluctuations, induced experimentally in rats by broad-band (pseudorandom) arterial blood pressure forcing at various power levels, has been unable to explain fully the dynamics of renal autoregulation at low frequencies. This observation has suggested the possibility of nonlinear mechanisms subserving renal autoregulation at frequencies below 0.2 Hz. This paper presents results of 3rd-order Volterra-Wiener analysis that appear to explain adequately the nonlinearities in the pressure-flow relation below 0.2 Hz in rats. The contribution of the 3rd-order kernel in describing the dynamic pressure-flow relation is found to be important. Furthermore, the dependence of 1st-order kernel waveforms on the power level of broadband pressure forcing indicates the presence of nonlinear feedback (of sigmoid type) based on previously reported analysis of a class of nonlinear feedback systems.