Session S33.2

Characterizing Histograms of Heartbeat Interval Differences with Gaussian Mixture Densities

R Sassi*

Università degli Studi di Milano
Milano, Italy

When analyzing HRV in long recordings, RR series typically show non stationary evidences. For this reason it is common choice to study the difference signal I(i)=RR(i+1)-RR(i), which is, by construction, nearly stationary. Peng and coworkers (1993) showed that such difference signal displays a normalized histogram with very long tails which can be properly modeled as a Lévy stable distribution. Lévy stable distributions are inherently statistical type of fractals and have generally second moments which are not finite. Also, they depend on the parameter a which defines the spread of probability towards the tails of the density function. For a=2, Lévy stable distributions turn into Gaussian distributions.
In this work we first studied the histograms of the difference signals obtained from four different databases of long term HRV recordings, available on Physionet. Such databases were selected to contain normal subjects (N, 72 cases) but also individuals suffering from congestive heart failure (CHF, 29 cases) and ischemic ST episodes (ST, 86 cases). The fit of a discrete Lévy stable distribution to each sample was performed using maximum likelihood employing a very robust code (STABLE). The computations showed that the mean value of a across each population was smaller than 2 and the fit appropriate on the series (N: 1.70±0.19; CHF: 1.74±0.18; ST: 1.66±0.22). The differences between the populations were not significant (p>5%, t test for multiple comparisons) thus confirming the early findings of Peng.
Several reasons might induce the presence of a density similar to a Lévy stable distribution. To understand this further we repeated the fitting procedure on shorter non-overlapping segments of 500 points, about 5 minutes long, a time span under which we might assume a larger degree of stationarity. While the histograms were still well described by a stable distribution, the mean value of a across the populations was markedly larger (N: 1.88±0.10; CHF: 1.88±0.11; ST: 1.84±0.13) and closer to a normal distribution (i.e. a=2). Similar results were obtained considering longer segments (1000 points). To cast away the possibility that such discrepancies were due to numerical problems of convergence (shorter series implies a smaller number of extreme events, on average) we then fitted a gaussian mixture density on each histogram. At each position, the sample was drawn from a Gaussian distribution of zero mean and variable standard deviation (RMSSD on local short intervals). Such mixture density were able to properly describe the histograms in the databases under analysis. We conclude that the long tails seen in the difference series can be also generated by Gaussian non-stationary stochastic processes which adapt continuously the local power. Occam’s razor would prefer this simple explanation which also avoids the necessity of invariant densities with not-finite second moments (unlikely in a physiological system).

(Abstract Control Number: 174)