Fractal organization of the pointwise correlation dimension of the heart rate

Abstract 

Objective: To depict and quantify the degree of organization of the heart rate variability (HRV) in normal subjects. Methods: A modified algorithm was created to estimate series of ‘point-dimensions’ (PD2) from interbeat (R-R) interval series of 10 healthy subjects (21–56 years). Our innovation is twofold: (i) we quantified instances of low-dimensional chaos, random fluctuations, and those for which our method failed to provide either (due to poor statistics); (ii) consecutive subepochs of PD2s underwent a relative dispersion (RD) analysis, yielding an index (D) which quantifies the dynamical organization of the heart rate generator.

Results: The mean values of PD2 series varied between 4.58 and 5.88 (mean ± SD= 5.21 ± 0.41, n = 10). For group 1 (21–30 years, n = 6) we found an averaged PD2 of 5.49 ± 0.27, while for group 2 (47–56 years, n = 4) PD2 averaged 4.79 ± 0.17. The RD analysis performed for subepochs of PD2s yielded both instances obeying fractal scaling (D < 1.5) and stochasticity (D > 1.5). The average D for group 1 was 1.39 ± 0.04 (14 subepochs) and for group 2, 1.20 ± 0.008 (8 subepochs). Paired t-test and Hartley F-max test for comparison between D values and homogeneity of variance between the two groups were performed, yielding P-values 0.004 and 0.02, respectively.

Conclusions: The complexity of the HRV seems to be modulated by a non-random fractal mechanism of a ‘hyperchaotic’ system, i.e. it can be hypothesized to contain more than one attractor. Also, our results support the ‘chaos hypothesis’ put forth recently, namely, the complexity of the cardiovascular dynamics is reduced with aging. The index of relative dispersion of the dimensional complexity has to be tested in various clinico-pathological settings, in order to corroborate its value as a potential new physiological measure.

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