FRACTAL ORGANIZATION OF THE POINTWISE CORRELATION DIMENSION OF THE HEART-RATE

Objective: To depict and quantify the degree of organization of the he art rate variability (HRV) in normal subjects. Methods: A modified alg orithm 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-dimensi onal chaos, random fluctuations, and those for which our method failed to provide either (due to poor statistics); (ii) consecutive subepoch s of PD2s underwent a relative dispersion (RD) analysis, yielding an i ndex (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 ye ars, 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 pe rformed for subepochs of PD2s yielded both instances obeying fractal s caling (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 betwee n D values and homogeneity of variance between the two groups were per formed, yielding P-values 0.004 and 0.02, respectively. Conclusions: T he 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 cardiova scular dynamics is reduced with aging. The index of relative dispersio n of the dimensional complexity has to be tested in various clinico-pa thological settings, in order to corroborate its value as a potential new physiological measure.