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

Authors:
Open Access
Publisher website
Google Scholar
Abstract
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 β in the relationship “1/ fβ.” In practice, the fractal range cannot extend to indefinitely low frequencies, but factor(s) that terminate this behavior, and determine β, are unclear. We present 1) data in rats ( n = 8) that reveal an extremely low frequency spectral region (0.083–1 cycle/h), where β approaches 0 (i.e., the “shoulder”); and 2) a model that 1) predicts realistic values of β within that range of the spectrum that conforms to fractal dynamics (∼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 Δ) was 1.87 ± 0.21 mmHg (means ± SD). We calculated β for three frequency ranges: 1) 0.083–1; 2) 1–6; and 3) 6–60 cycles/h. The β for all three regions differed ( P < 0.01). For the two higher frequency ranges, β indicated a fractal relationship (β6–60/h = 1.27 ± 0.01; β1–6/h = 1.80 ± 0.16). Conversely, the slope of the lowest frequency region (i.e., the shoulder) was nearly flat (β0.083–1 /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 Δ from 0.5 to 2.5. The spectrum for the conditions mimicking actual BP time series (i.e., range, 85–115 mmHg; Δ, 2.00) resembled the observed spectra, with β in the lowest frequency range = 0.207 and fractal-like behavior in the two higher frequency ranges (β = 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 Δ contributes to determining β.

This publication has 27 references indexed in Scilit: