Zipf's law in human heartbeat dynamics

It is shown that the distribution of low variability periods in the activity of human heart rate typically follows a multi-scaling Zipf's law. The presence or failure of a power law, as well as the values of the scaling exponents, are personal characteristics depending on the daily habits of the subjects. Meanwhile, the distribution function of the low-variability periods as a whole discriminates efficiently between various heart pathologies. This new technique is also applicable to other non-linear time-series and reflects these aspects of the underlying intermittent dynamics, which are not covered by other methods of linear-and nonlinear analysis. The nonlinear and scale-invariant aspects of the heart rate variability (HRV) have been studied intensively during the last decades. This continuous interest to the HRV can be attributed to the controversial state of affairs: on the one hand, the nonlinear and scale-invariant analysis of HRV has resulted in many methods of very high prog-nostic performance (at least on test groups) [1, 2, 3, 4]; on the other hand, practical medicine is still confident to the traditional " linear " methods. The situation is quite different from what has been observed three decades ago, when the " linear " measures of HRV became widely used as important noninvasive diagnostic and prognostic tools, soon after the pioneering paper [5]. Apparently, there is a need for further evidences for the superiority of new methods and for the resolution of the existing ambiguities. During recent years the main attention of studies has been focused on the analysis of the scale-invariant methods. It has been argued that measures related to a certain timescale (e.g. 5 min) are less reliable, because the characteristic timescales of physiological processes are patient-specific. The scale-invariant measures are often believed to be more universal and sensitive to life-threatening pathologies [1, 2]. However, carefully designed timescale related measures can be also highly successful, because certain physiological processes are related to a specific time scale [3]. The scale invariance has been exclusively seen in the heart rhythm following the (multi)fractional Brownian motion (fBm) [6]. It has been understood that the heart rhythm fluctuates in a very complex manner and reflects the activities of the subject (sleeping, watching TV, walking etc.) [7, 9] and cannot be adequately described by a single Hurst exponent of a simple fBm. In order to reflect the complex behavior of the heart rhythm, the multi-affine generalization of the fBm has been …