FRACTAL CHARACTER OF THE ELECTROCARDIOGRAM - DISTINGUISHING HEART-FAILURE AND NORMAL-PATIENTS

Statistical analysis of the sequence of heartbeats can provide informa tion about the state of health of the heart. We used a variety of stat istical measures to identify the form of the point process that descri bes the human heartbeat. These measures are based on both interevent i ntervals and counts, and include the interevent-interval histogram, in terval-based periodogram, rescaled range analysis, the event-number hi stogram, Fano-factor, Allan Factor, and generalized-rate-based periodo gram. All of these measures have been applied to data from both normal and heart-failure patients, and various surrogate versions thereof. T he results show that almost all of the interevent-interval and the lon g-term counting statistics differ in statistically significant ways fo r the two classes of data. Several measures reveal 1/f-type fluctuatio ns (long-duration power-law correlation). The analysis that we have co nducted suggests the use of a conveniently calculated, quantitative in dex, based on the Allan factor, that indicates whether a particular pa tient does or does not suffer from heart failure. The Allan factor tur ns out to be particularly useful because it is easily calculated and i s jointly responsive to both short-term and long-term characteristics of the heartbeat time series. A phase-space reconstruction based on th e generalized heart rate is used to obtain a putative attractor's capa city dimension. Though the dependence of this dimension on the embeddi ng dimension is consistent with that of a low-dimensional dynamical sy stem (with a larger apparent dimension for normal subjects), surrogate -data analysis shows that identical behavior emerges from temporal cor relation in a stochastic process. We present simulated results for a p urely stochastic integrate-and-fire model, comprising a fractal-Gaussi an-noise kernel, in which the sequence of heartbeats is determined by level crossings of fractional Brownian motion. This model characterize s the statistical behavior of the human electrocardiogram remarkably w ell, properly accounting for the behavior of all of the measures studi ed, over all time scales.