Empirical and theoretical analysis of the extremely low frequency arterial blood pressure power spectrum in unanesthetized rat.

The slope of the log of power versus the log of frequency in the arterial blood pressure (BP) power spectrum is classically considered constant over the low-frequency range (i.e., "fractal" behavior), and is quantified by beta in the relationship "1/f(beta)." In practice, the fractal range cannot extend to indefinitely low frequencies, but factor(s) that terminate this behavior, and determine beta, are unclear. We present 1) data in rats (n = 8) that reveal an extremely low frequency spectral region (0.083-1 cycle/h), where beta approaches 0 (i.e., the "shoulder"); and 2) a model that 1) predicts realistic values of beta within that range of the spectrum that conforms to fractal dynamics (approximately 1-60 cycles/h), 2) offers an explanation for the shoulder, and 3) predicts that the "successive difference" in mean BP (mBP) is an important parameter of circulatory function. We recorded BP for up to 16 days. The absolute difference between successive mBP samples at 0.1 Hz (the successive difference, or Delta) was 1.87 +/- 0.21 mmHg (means +/- SD). We calculated beta for three frequency ranges: 1) 0.083-1; 2) 1-6; and 3) 6-60 cycles/h. The beta for all three regions differed (P < 0.01). For the two higher frequency ranges, beta indicated a fractal relationship (beta(6-60/h) = 1.27 +/- 0.01; beta(1-6/h) = 1.80 +/- 0.16). Conversely, the slope of the lowest frequency region (i.e., the shoulder) was nearly flat (beta(0.083-1 /h) = 0.32 +/- 0.28). We simulated the BP time series as a random walk about 100 mmHg with ranges above and below of 10, 30, and 50 mmHg and with Delta from 0.5 to 2.5. The spectrum for the conditions mimicking actual BP time series (i.e., range, 85-115 mmHg; Delta, 2.00) resembled the observed spectra, with beta in the lowest frequency range = 0.207 and fractal-like behavior in the two higher frequency ranges (beta = 1.707 and 2.057). We suggest that the combined actions of mechanisms limiting the excursion of arterial BP produce the shoulder in the spectrum and that Delta contributes to determining beta.