Chaos in blood flow control in genetic and renovascular hypertensive rats KAY-PONG YIP, N.-H. HOLSTEIN-RATHLOU, AND DONALD J. MARSH Department of Physiology and Biophysics, University of Southern California School of Medicine, Los Angeles, California 90033
YIP, KAY-P• NG, N.-H. HOLSTEIN-RATHLOU, AND DONALD J. MARSH. Chaos in blood flow control in genetic and renovascular hypertensive rats. Am. J. Physiol. 261 (Renal Fluid Electrolyte Physiol. 30): F400-F408, 1991.-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 lowdimension 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. glomerular filtration rate; oscillations; nonlinear renal blood flow; tubuloglomerular feedback
dynamics;
IT HAS BEEN APPRECIATED for decades that disordered renal function is important for the development and maintenance of many forms of hypertension, the causal role of the kidney remains incompletely understood. Analysis of several forms of experimental hypertension have provided detail, but no convincing explanation, of the kidney’s role. Regulation of renal blood flow is probably an important part of the blood pressurekidney interaction. Most attempts to explain this interaction have been formulated in terms of simple dynamic processes, but tubuloglomerular feedback (TGF), a system that acts at the level of individual nephrons to regulate blood flow, oscillates autonomously at 30-40 mHz (10, 11, 13, 18). Oscillations in control systems permit a variety of interactions that could be important in blood pressure regulation. The oscillations are found in normotensive rats anesthetized with halothane, but the fluctuations in tubular pressure are aperiodic in a ALTHOUGH
F400
0363-6127/91
$1.50
genetic form of experimental hypertension (11). We wish to determine whether this change in dynamics is an example of deterministic chaos (9, 17) and whether it is found in other types of experimental hypertension. The oscillation in normotensive animals is found in proximal and distal tubular pressure, end-proximal flow rate, and early distal chloride concentration (13). Each tubule has a single frequency at which all measured variables oscillate, and the variables maintain definite phase relations. Thus the NaCl signal to the macula densa, the sensor for TGF, and glomerular filtration rate (GFR), a variable affected by TGF, are entrained in a common oscillation. The frequency is independent of respiratory and cardiac rhythms, and the oscillation can be interrupted by intratubular perfusion with furosemide, which acts on the macula densa and is known to inhibit TGF (18). Simulations (12, 14, 27) suggest that the oscillation arises in the operation of TGF without an external pacemaker, because nonlinearities of the system give rise to several delays around the feedback loop, including a delay due to the effect of tubular compliance on pulse-wave propagation, a delay as epithelial transport changes loop of Henle NaCl concentration when tubula r flow rate cha.nges, and a delay as the NaCl slignal at the macu la densa leads to an effec to n afferent arteriolar diameter (13, 14). The change of tubular pressure dynamics from an oscillation in normotensive animals to an aperiodic fluctuation in spontaneously hypertensive rats (SHR) could be due to an effect of hypertension on TGF dynamics or to the genetic lesion specific to this model of hypertension. We have tested this question by using a renovascular hypertension model. In the unclipped kidney of rats with two-kidney (2K,lC) Goldblatt hypertension caused by placing a clip around one renal artery, tubular pressure had the same irregular fluctuation as seen in SHR. To analyze the dynamics of tubular pressure in the two models of hypertension, we applied statistical measures that have been useful in the study of deterministic chaos (1, 7, 32). Deterministic chaos arises in nonlinear dynamic systems and can generate apparently random time series, which closer analysis reveals to be highly ordered. Chaos can arise in fairly simple systems if key parameters take on values that are critical for the system. TGF is a feedback system with several well-characterized nonli nearities, and we were therefore interes ted to determine whether the change in its dynamics is an example
Copyright 0 1991 the American Physiological Society
Downloaded from www.physiology.org/journal/ajprenal by ${individualUser.givenNames} ${individualUser.surname} (130.070.008.131) on January 13, 2019.
CHAOS
IN
TGF
of a bifurcation to chaos. The results of the analysis support this conclusion.
IN
F401
HYPERTENSION
Data Collection
and Analysis
Spectral analysis. The arterial and proximal tubular pressures were replayed from the tape recorder to a l2METHODS bit analog-to-digital converter (Data Translation) connected to a microcomputer with an Intel 80286 microAnimal Preparation processor and 80287 floating point processor. To prevent Four groups of male rats were used: normotensive aliasing each signal was passed through an analog twoSprague-Dawley controls; lo- to 12-wk-old spontapole Butterworth low-pass filter with a cutoff frequency neously hypertensive rats (SHR); Sprague-Dawley rats of 1.5 Hz. The blood pressure and tubular pressure sigin which hypertension was induced by placing a con- nals were sampled simultaneously. The sampling rate stricting clip (0.25 mm diam) around the right renal varied between 3.3 and 4.8 Hz and generated two 4,096artery, leaving the other kidney untouched (2K,lC); and point data sets from each experiment. Each time series sham-operated Sprague-Dawley controls. All rats were was subjected to linear trend removal, operated on by a purchased from Harlan Farms. The rats had free access cosine window function to minimize leakage, and transto food and tap water before the experiments. Anesthesia formed to the frequency domain with a fast Fourier was induced by placing each rat in a chamber containing transform. The power spectral density was then com5% halothane administered in 25% oxygen and 75% puted (3). nitrogen through a Fluotec Mark-3 vaporizer. Halothane Correlation dimension and Lyapunov exponent. Correwas selected as an anesthetic, because oscillations in lation dimension and the largest Lyapunov exponent proximal tubule pressure of normotensive rats are more were estimated from the time series of proximal tubular readily discernible than with barbiturate anesthetics. A pressure. Tape-recorded data were passed through the tracheostomy was performed, and the rats were placed Butterworth low-pass filter with 1.5-Hz cutoff frequency. on a servo-controlled heated operating table which mainThe sampling rate was 12.5 Hz; 15,000 data points were tained body temperature at 37OC. recorded from each experiment. Each time series was The trachostomy tube was connected to a small animal treated with a Kaiser-Bessel low-pass filter with variable respirator (Harvard model 683) adjusted to maintain cutoff frequency, as described below, and attenuation of arterial blood pH between 7.35 and 7.45 with a mixture 50 dB. The time series was normalized to provide a mean of 25% oxygen-75% nitrogen. Tidal volume ranged from of 0 and unit variance. The low-pass filter was used to 1.9 to 2.5 ml, depending on body weight, with a frequency remove the large l-Hz signal caused by the respirator; of 57-60 breaths per min. The final concentration of the power spectrum located most of the signal power at halothane needed to maintain sufficient anesthesia was frequencies
YIP, KAY-P• NG, N.-H. HOLSTEIN-RATHLOU, AND DONALD J. MARSH. Chaos in blood flow control in genetic and renovascular hypertensive rats. Am. J. Physiol. 261 (Renal Fluid Electrolyte Physiol. 30): F400-F408, 1991.-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 lowdimension 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. glomerular filtration rate; oscillations; nonlinear renal blood flow; tubuloglomerular feedback
dynamics;
IT HAS BEEN APPRECIATED for decades that disordered renal function is important for the development and maintenance of many forms of hypertension, the causal role of the kidney remains incompletely understood. Analysis of several forms of experimental hypertension have provided detail, but no convincing explanation, of the kidney’s role. Regulation of renal blood flow is probably an important part of the blood pressurekidney interaction. Most attempts to explain this interaction have been formulated in terms of simple dynamic processes, but tubuloglomerular feedback (TGF), a system that acts at the level of individual nephrons to regulate blood flow, oscillates autonomously at 30-40 mHz (10, 11, 13, 18). Oscillations in control systems permit a variety of interactions that could be important in blood pressure regulation. The oscillations are found in normotensive rats anesthetized with halothane, but the fluctuations in tubular pressure are aperiodic in a ALTHOUGH
F400
0363-6127/91
$1.50
genetic form of experimental hypertension (11). We wish to determine whether this change in dynamics is an example of deterministic chaos (9, 17) and whether it is found in other types of experimental hypertension. The oscillation in normotensive animals is found in proximal and distal tubular pressure, end-proximal flow rate, and early distal chloride concentration (13). Each tubule has a single frequency at which all measured variables oscillate, and the variables maintain definite phase relations. Thus the NaCl signal to the macula densa, the sensor for TGF, and glomerular filtration rate (GFR), a variable affected by TGF, are entrained in a common oscillation. The frequency is independent of respiratory and cardiac rhythms, and the oscillation can be interrupted by intratubular perfusion with furosemide, which acts on the macula densa and is known to inhibit TGF (18). Simulations (12, 14, 27) suggest that the oscillation arises in the operation of TGF without an external pacemaker, because nonlinearities of the system give rise to several delays around the feedback loop, including a delay due to the effect of tubular compliance on pulse-wave propagation, a delay as epithelial transport changes loop of Henle NaCl concentration when tubula r flow rate cha.nges, and a delay as the NaCl slignal at the macu la densa leads to an effec to n afferent arteriolar diameter (13, 14). The change of tubular pressure dynamics from an oscillation in normotensive animals to an aperiodic fluctuation in spontaneously hypertensive rats (SHR) could be due to an effect of hypertension on TGF dynamics or to the genetic lesion specific to this model of hypertension. We have tested this question by using a renovascular hypertension model. In the unclipped kidney of rats with two-kidney (2K,lC) Goldblatt hypertension caused by placing a clip around one renal artery, tubular pressure had the same irregular fluctuation as seen in SHR. To analyze the dynamics of tubular pressure in the two models of hypertension, we applied statistical measures that have been useful in the study of deterministic chaos (1, 7, 32). Deterministic chaos arises in nonlinear dynamic systems and can generate apparently random time series, which closer analysis reveals to be highly ordered. Chaos can arise in fairly simple systems if key parameters take on values that are critical for the system. TGF is a feedback system with several well-characterized nonli nearities, and we were therefore interes ted to determine whether the change in its dynamics is an example
Copyright 0 1991 the American Physiological Society
Downloaded from www.physiology.org/journal/ajprenal by ${individualUser.givenNames} ${individualUser.surname} (130.070.008.131) on January 13, 2019.
CHAOS
IN
TGF
of a bifurcation to chaos. The results of the analysis support this conclusion.
IN
F401
HYPERTENSION
Data Collection
and Analysis
Spectral analysis. The arterial and proximal tubular pressures were replayed from the tape recorder to a l2METHODS bit analog-to-digital converter (Data Translation) connected to a microcomputer with an Intel 80286 microAnimal Preparation processor and 80287 floating point processor. To prevent Four groups of male rats were used: normotensive aliasing each signal was passed through an analog twoSprague-Dawley controls; lo- to 12-wk-old spontapole Butterworth low-pass filter with a cutoff frequency neously hypertensive rats (SHR); Sprague-Dawley rats of 1.5 Hz. The blood pressure and tubular pressure sigin which hypertension was induced by placing a con- nals were sampled simultaneously. The sampling rate stricting clip (0.25 mm diam) around the right renal varied between 3.3 and 4.8 Hz and generated two 4,096artery, leaving the other kidney untouched (2K,lC); and point data sets from each experiment. Each time series sham-operated Sprague-Dawley controls. All rats were was subjected to linear trend removal, operated on by a purchased from Harlan Farms. The rats had free access cosine window function to minimize leakage, and transto food and tap water before the experiments. Anesthesia formed to the frequency domain with a fast Fourier was induced by placing each rat in a chamber containing transform. The power spectral density was then com5% halothane administered in 25% oxygen and 75% puted (3). nitrogen through a Fluotec Mark-3 vaporizer. Halothane Correlation dimension and Lyapunov exponent. Correwas selected as an anesthetic, because oscillations in lation dimension and the largest Lyapunov exponent proximal tubule pressure of normotensive rats are more were estimated from the time series of proximal tubular readily discernible than with barbiturate anesthetics. A pressure. Tape-recorded data were passed through the tracheostomy was performed, and the rats were placed Butterworth low-pass filter with 1.5-Hz cutoff frequency. on a servo-controlled heated operating table which mainThe sampling rate was 12.5 Hz; 15,000 data points were tained body temperature at 37OC. recorded from each experiment. Each time series was The trachostomy tube was connected to a small animal treated with a Kaiser-Bessel low-pass filter with variable respirator (Harvard model 683) adjusted to maintain cutoff frequency, as described below, and attenuation of arterial blood pH between 7.35 and 7.45 with a mixture 50 dB. The time series was normalized to provide a mean of 25% oxygen-75% nitrogen. Tidal volume ranged from of 0 and unit variance. The low-pass filter was used to 1.9 to 2.5 ml, depending on body weight, with a frequency remove the large l-Hz signal caused by the respirator; of 57-60 breaths per min. The final concentration of the power spectrum located most of the signal power at halothane needed to maintain sufficient anesthesia was frequencies
