Chaos in blood flow control in genetic and renovascular hypertensive rats

1991 ◽  
Vol 261 (3) ◽  
pp. F400-F408 ◽  
Author(s):  
K. P. Yip ◽  
N. H. Holstein-Rathlou ◽  
D. J. Marsh
Keyword(s):  
Time Series ◽  
Blood Flow ◽  
Phase Space ◽  
Renal Artery ◽  
Initial Conditions ◽  
Pressure Fluctuations ◽  
Deterministic Chaos ◽  
Tubuloglomerular Feedback ◽  
Hypertensive Rats ◽  
Statistical Measures

Hydrostatic pressure and flow in renal proximal tubules oscillate at 30–40 mHz in normotensive rats anesthetized with halothane. The oscillations originate in tubuloglomerular feedback, a mechanism that provides local blood flow regulation. Instead of oscillations, spontaneously hypertensive rats (SHR) have aperiodic tubular pressure fluctuations; the pattern is suggestive of deterministic chaos. Normal rats made hypertensive by clipping one renal artery had similar aperiodic tubular pressure fluctuations in the unclipped kidney, and the fraction of rats with irregular fluctuations increased with time after the application of the renal artery clip. Statistical measures of deterministic chaos were applied to tubular pressure data. The correlation dimension, a measure of the dimension of the phase space attractor generating the time series, indicated the presence of a low-dimension strange attractor, and the largest Lyapunov exponent, a measure of the rate of divergence in phase space, was positive, indicating sensitivity to initial conditions. These time series therefore satisfy two criteria of deterministic chaos. The measures were the same in SHR as in rats with renovascular hypertension. Since two different models of hypertension displayed similar dynamics, we suggest that chaotic behavior is a common feature of renal vascular control in the natural history of the disease.

MODELING NONLINEAR DETERMINISM IN SHORT TIME SERIES FROM NOISE DRIVEN DISCRETE AND CONTINUOUS SYSTEMS

2000 ◽  
Vol 10 (12) ◽  
pp. 2745-2766 ◽  
Author(s):  
K. H. CHON ◽  
K. P. YIP ◽  
B. M. CAMINO ◽  
D. J. MARSH ◽  
N.-H. HOLSTEIN-RATHLOU
Keyword(s):  
Time Series ◽  
Lyapunov Exponents ◽  
Initial Conditions ◽  
Deterministic Chaos ◽  
Continuous Systems ◽  
Hypertensive Rats ◽  
Free Data ◽  
Renal Tubular ◽  
Short Time ◽  
Sensitivity To Initial Conditions

Current methods for detecting deterministic chaos in a time series require long, stationary, and relatively noise-free data records. This limits the utility of these methods in most experimental and clinical settings. Recently we presented a new method for detecting determinism in a time series, and for assessing whether this determinism has chaotic attributes, i.e. sensitivity to initial conditions. The method is based on fitting a deterministic nonlinear autoregressive (NAR) model to the data [Chon et al., 1997]. This approach assumes that the noise in the model can be represented as a series of independent, identically distributed random variables. If this is not the case the accuracy of the algorithm may be compromised. To explicitly deal with the possibility of more complex noise structures, we present a method based on a stochastic NAR model. The method iteratively estimates NAR models for both the deterministic and the stochastic parts of the signal. An additional feature of the algorithm is that it includes only the significant autoregressive terms among the pool of candidate terms searched. As a result the algorithm results in a model with significantly fewer terms than a model obtained by traditional model order search criterions. Subsequently, Lyapunov exponents are calculated for the estimated models to examine if chaotic determinism (i.e. sensitivity to initial conditions) is present in the time series. The major advantages of this algorithm are: (1) it provides accurate parameter estimation with a small number of data points, (2) it is accurate for signal-to-noise ratios as low as -9 dB for discrete and -6 dB for continuous chaotic systems, and (3) it allows characterization of the dynamics of the system, and thus prediction of future states of the system, over short time scales. The stochastic NAR model is applied to renal tubular pressure data from normotensive and hypertensive rats. One form of hypertension was genetic, and the other was induced on normotensive rats by placing a restricting clip on one of their renal arteries. In both types of hypertensive rats, positive Lyapunov exponents were present, indicating that the fluctuations observed in the proximal tubular pressure were due to the operation of a system with chaotic determinism. In contrast, only negative exponents were found in the time series from normotensive rats.

scholarly journals Oscillations and chaos in renal blood flow control.

1993 ◽  
Vol 4 (6) ◽  
pp. 1275-1287
Author(s):  
N H Holstein-Rathlou
Keyword(s):  
Blood Flow ◽  
Signal Transmission ◽  
Deterministic Chaos ◽  
Open Loop ◽  
Tubuloglomerular Feedback ◽  
Hypertensive Rats ◽  
Spontaneously Hypertensive ◽  
Model Studies ◽  
Mechanism Model ◽  
The Difference

In normotensive, halothane-anesthetized rats, oscillations can be found both in the single-nephron blood flow and in the tubular pressure. Experimental data and computer simulations support the hypothesis that the oscillations are caused by the tubuloglomerular feedback (TGF) mechanism. Model studies show that the key parameters determining the stability of the TGF system are the open loop gain of the system and the time delays in the signal transmission through the various components of the feedback loop. Within a broad range of parameters, the system is unstable and has self-sustained stable oscillations. The parameter range where model studies show instability overlaps with the physiologic range for the values of the same parameters. The system appears to be poised on the border between stability and oscillation, and a small parameter change may cause the system to move from one state to the other. In renovascular and spontaneously hypertensive rats, regular oscillations give way to highly irregular, chaotic fluctuations. The chaotic fluctuations appear to have the same mechanism as the regular TGF-mediated oscillations. The irregular fluctuations most likely represent a parameter-dependent transition from a limit cycle (regular oscillation) to deterministic chaos. The key parameters causing the transition have not been identified. Associated with the difference in the dynamics of TGF between normotensive and hypertensive rats is a change in the dynamic autoregulation of total RBF. This is especially prominent in the frequency range in which TGF operates, and it is suggested that a causal relationship may exist between the two phenomena. This difference may play a role in the pathogenesis of hypertension by altering the renal response to the normal fluctuations in arterial pressure.

Synchronization among mechanisms of renal autoregulation is reduced in hypertensive rats

2007 ◽  
Vol 293 (5) ◽  
pp. F1545-F1555 ◽  
Author(s):  
Olga V. Sosnovtseva ◽  
Alexey N. Pavlov ◽  
Erik Mosekilde ◽  
Kay-Pong Yip ◽  
Niels-Henrik Holstein-Rathlou ◽  
...  
Keyword(s):  
Wavelet Transforms ◽  
Pressure Fluctuations ◽  
Deterministic Chaos ◽  
Tubuloglomerular Feedback ◽  
Hypertensive Rats ◽  
Spontaneously Hypertensive ◽  
Renal Autoregulation ◽  
Probable State ◽  
Frequency Ratios ◽  
Full Synchronization

We searched for synchronization among autoregulation mechanisms using wavelet transforms applied to tubular pressure recordings in nephron pairs from the surface of rat kidneys. Nephrons have two oscillatory modes in the regulation of their pressures and flows: a faster (100–200 mHz) myogenic mode, and a slower (20–40 mHz) oscillation in tubuloglomerular feedback (TGF). These mechanisms interact; the TGF mode modulates both the amplitude and the frequency of the myogenic mode. Nephrons also communicate with each other using vascular signals triggered by membrane events in arteriolar smooth muscle cells. In addition, the TGF oscillation changes in hypertension to an irregular fluctuation with characteristics of deterministic chaos. The analysis shows that, within single nephrons of normotensive rats, the myogenic mode and TGF are synchronized at discrete frequency ratios, with 5:1 most common. There is no distinct synchronization ratio in spontaneously hypertensive rats (SHR). In normotensive rats, full synchronization of both TGF and myogenic modes is the most probable state for pairs of nephrons originating in a common cortical radial artery. For SHR, full synchronization is less probable; most common in SHR is a state of partial synchronization with entrainment between neighboring nephrons for only one of the modes. Modulation of the myogenic mode by the TGF mode is much stronger in hypertensive than in normotensive rats. Synchronization among nephrons forms the basis for an integrated reaction to blood pressure fluctuations. Reduced synchronization in SHR suggests that the effectiveness of the coordinated response is impaired in hypertension.

Abstract 104: Dynamic Autoregulation of Glomerular Capillary Pressure

Hypertension ◽  
2016 ◽  
Vol 68 (suppl_1) ◽  
Author(s):  
Scott C Thomson
Keyword(s):  
Blood Pressure ◽  
Time Series ◽  
Blood Flow ◽  
Capillary Pressure ◽  
Tubuloglomerular Feedback ◽  
Step Response ◽  
Glomerular Capillary ◽  
Arterial Blood ◽  
Glomerular Capillary Pressure ◽  
Step Responses

It is generally accepted that renal blood flow (RBF) autoregulation is mediated by myogenic and tubuloglomerular feedback responses acting on the pre-glomerular resistance. If this is so, then autoregulation of RBF and glomerular capillary pressure (PGC) should change in the same direction throughout an autoregulatory step response. We computed autoregulatory step responses from time series recordings of arterial blood pressure (BP) and RBF (Transonics) blood flow or tubular stop-flow pressure (micropuncture), which is a surrogate for PGC in Wistar-Froemter rats fed for one week on low or high salt diets (n=6-10 ). Autoregulatory step responses were generated from time series by an algorithm that treats BP as a leading indicator of RBF or PGC and uses the projection theorem to solve for the impulse response which is integrated to obtain the step response. Step responses shown in the figure represent the uncompensated changes in RBF and PGC (mean + SEM) following a 1 mmHg BP step. The data clearly reveal that the time courses of RBF and PGC differ such that changes in RBF cannot predict changes in PGC. This implies that the renal hemodynamic response to a blood pressure disturbance is not confined to the pre-glomerular resistance. Furthermore, the participation of post-glomerular resistance in the autoregulatory response is sensitive to dietary salt such that PGC is more sensitive to BP on low salt diet.

TIME SERIES ANALYSIS OF COMPLEX DYNAMICAL BEHAVIOR CONTAMINATED WITH OBSERVATIONAL NOISE

1996 ◽  
Vol 06 (11) ◽  
pp. 2031-2045 ◽  
Author(s):  
TAKAYA MIYANO
Keyword(s):  
Time Series ◽  
Phase Space ◽  
Random Noise ◽  
Dynamical Behavior ◽  
Deterministic Chaos ◽  
Diagnostic Algorithm ◽  
Diagnostic Methods ◽  
Observational Noise ◽  
Nonlinear Forecasting ◽  
Complex Dynamical Behavior

Diagnostic methods for discovering deterministic chaos based on the instability and the parallelness of nearby trajectories generated from a time series in phase space are applied to numerical time series contaminated with additive random noise. The diagnostic algorithm based on nonlinear forecasting is prone to be fooled when handling chaotic data including observational noise. Such a misdiagnosis can be circumvented by estimating the degrees of parallelness of neighboring trajectories in the phase space. Dynamical properties of global temperature variations and voice signals of Japanese vowel /a/ are examined by the combinational use of the diagnostic algorithms.

Chronic hydralazine treatment alters the acute pressure–natriuresis curve in young spontaneously hypertensive rats

1991 ◽  
Vol 69 (2) ◽  
pp. 164-169 ◽  
Author(s):  
Robert L. Kline ◽  
Graham P. McLennan
Keyword(s):  
Blood Flow ◽  
Renal Function ◽  
Renal Artery ◽  
Sodium Excretion ◽  
Spontaneously Hypertensive Rats ◽  
Hypertensive Rats ◽  
Spontaneously Hypertensive ◽  
Artery Pressure ◽  
Fractional Sodium Excretion ◽  
Pressure Natriuresis

The pressure–natriuresis relationship was studied in anesthetized, 7- to 9-week-old control spontaneously hypertensive rats (SHR) and in SHR that had been treated with hydralazine (20 mg∙kg−1∙day−1 in drinking water) starting at 4–5 weeks of age. To minimize reflex changes in kidney function during changes in renal artery pressure, neural and hormonal influences on the kidney were fixed by surgical renal denervation, adrenalectomy, and infusion of a hormone cocktail (330 μL∙kg−1∙min−1) containing high levels of aldosterone, arginine vasopressin, hydrocortisone, and norepinephrine dissolved in 0.9% NaCl containing 1% albumin. Changes in renal function were measured using standard clearance techniques, while renal artery pressure was varied between 136 ± 1 and 186 ± 2 mmHg (1 mmHg = 133.32 Pa) in control SHR (n = 10) and between 113 ± 1 and 162 ± 2 mmHg in treated SHR (n = 11). Mean arterial pressure (+SE) under Inactin anesthesia was 172 ± 3 mmHg in control SHR and 146 ± 3 mmHg in treated SHR (p < 0.05). Where renal artery pressure overlapped between groups, there were no significant differences in glomerular filtration rate. Renal blood flow was also similar in both groups, although at 160 mmHg blood flow was slightly but significantly reduced in treated SHR. Urine flow and total and fractional sodium excretion increased similarly with increases in renal artery pressure in both groups, but the pressure–natriuresis curve in hydralazine-treated SHR was displaced to the left along the pressure axis. The data indicate that chronic administration of hydralazine in young SHR enhances fractional sodium excretion, suggesting that tubular reabsorption of sodium is decreased by hydralazine.Key words: renal function, volume loading, sodium excretion.

Dynamics of TGF-initiated nephron-nephron interactions in normotensive rats and SHR

1992 ◽  
Vol 262 (6) ◽  
pp. F980-F988 ◽  
Author(s):  
K. P. Yip ◽  
N. H. Holstein-Rathlou ◽  
D. J. Marsh
Keyword(s):  
Correlation Coefficient ◽  
Filtration Rate ◽  
Spectral Power ◽  
Pressure Fluctuations ◽  
Distal Tubule ◽  
Tubuloglomerular Feedback ◽  
Similar Amount ◽  
Hypertensive Rats ◽  
Spontaneously Hypertensive ◽  
Proximal Tubular

Proximal tubular pressure, glomerular filtration rate, and early distal tubule Cl- oscillate at 35 mHz in normotensive rats because of tubuloglomerular feedback (TGF); the oscillation bifurcates to chaos in spontaneously hypertensive rats (SHR). To examine the importance of TGF-initiated vascular interactions between nephrons in these dynamics, we measured tubular pressure simultaneously in two or more nephrons. The oscillations were synchronized in nephrons supplied by a common cortical radial artery. The correlation coefficient of pressure records from coupled nephrons was 0.86 +/- 0.02. Intratubular furosemide perfusion diminished the oscillation in both the perfused and the coupled nephron; total autospectral power in each of the nephrons and cross-spectral power were reduced to 45% of control. The correlation between noncoupled nephrons was not significant, and intratubular furosemide perfused in one nephron had no effect on adjacent but noncoupled nephrons. In SHR, the correlation coefficient of tubular pressure records was high from coupled nephrons only; furosemide diminished the autospectral power of pressure fluctuations to approximately 60-75% of control in both perfused and coupled nephrons, and cross-spectral power was affected by a similar amount. Nephron-nephron interactions, specific to vascular connectivity, persist in SHR and appear to be stronger than in normotensive rats.

scholarly journals Deterministic Chaos Detection and Simplicial Local Predictions Applied to Strawberry Production Time Series

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3034
Author(s):  
Juan D. Borrero ◽  
Jesus Mariscal
Keyword(s):  
Time Series ◽  
Initial Conditions ◽  
Moving Average ◽  
Deterministic Chaos ◽  
Autoregressive Moving Average ◽  
Chaos Detection ◽  
Moving Average Models ◽  
Non Linear ◽  
Long Time ◽  
Novel Method

In this work, we attempted to find a non-linear dependency in the time series of strawberry production in Huelva (Spain) using a procedure based on metric tests measuring chaos. This study aims to develop a novel method for yield prediction. To do this, we study the system’s sensitivity to initial conditions (exponential growth of the errors) using the maximal Lyapunov exponent. To check the soundness of its computation on non-stationary and not excessively long time series, we employed the method of over-embedding, apart from repeating the computation with parts of the transformed time series. We determine the existence of deterministic chaos, and we conclude that non-linear techniques from chaos theory are better suited to describe the data than linear techniques such as the ARIMA (autoregressive integrated moving average) or SARIMA (seasonal autoregressive moving average) models. We proceed to predict short-term strawberry production using Lorenz’s Analog Method.

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