NONLINEAR CHAOTIC DYNAMICS OF ARTERIAL BLOOD-PRESSURE AND RENAL BLOOD-FLOW

To determine whether arterial pressure (AP) and renal blood flow (RBF) are nonlinear dynamic processes (chaotic), we measured resting AP and RBF over 4 h in six conscious dogs. A catheter was placed in the aort a, and transit-time flowmeters were positioned around the renal artery . The average AP was 102 +/- 3 mmHg, and the mean RBF was 318 +/- 42 m l/min. We applied four analytic procedures to test the nature of AP an d RBF time series, i.e., to determine if these variables are controlle d randomly, if they consist of periodic oscillations, or whether they are best characterized as nonlinear dynamic processes. To this end, a fast Fourier transform was performed to quantify the amount of distinc t periodic oscillations and nonperiodic variability in the very low fr equency domain (<0.01 Hz). The power spectrum of AP and RBF revealed b road band noise with no distinct peaks, which is commonly referred to as ''1/f noise.'' As a second procedure, time-delayed phase return map s were constructed, and as a third approach the correlation dimensions were estimated via the Grassberger-Procaccia algorithm. The correlati on dimensions of RBF and AP were similar (RBF 3.3 +/- 0.37 vs. AP 3.6 +/- 0.23; P = 0.2). The fourth method determined sensitive dependence on initial conditions, a hallmark of nonlinear ''chaotic'' dynamics. W e determined the maximal Lyapunov exponents and found them to be posit ive for AP (0.1 +/- 0.01) and for RBF (0.04 +/- 0.01), indicating that they both are nonlinear dynamic processes. The Lyapunov exponent was significantly lower for RBF (P < 0.01). In conclusion, AP and RBF are not homeostatic in the classical sense. These parameters are sensitive to initial conditions, and there is a large amount of nonperiodic var iability resulting from the nonlinear chaotic nature of AP and RBF.