Hierarchical Structure in Healthy and Diseased Heart Rate Variability in Humans

It is shown that the heart rate variability (HRV) in healthy and diseased humans possesses a hierarchical structure of the She-Leveque (SL) form. This structure, first found in measurements in turbulent fluid flows, implies further details in the HRV multifractal scaling. The potential of diagnosis is also discussed based on the characteristics derived from the SL hierarchy. The heart beat interval in humans is known to exhibit fluctuation which is referred to as heart rate variability (HRV). Power spectrum analysis of the fluctuation revealed a 1/f-like scaling [1]. Recent studies indicated that healthy human HRV exhibits even higher complexity which can be characterized by multifractal scaling [2, 3]. In contrast, HRV in the pathological state such as congestive heart failure exhibits more monofractal-like scaling [2]. The change of the HRV 1/f law in congestive heart failure is consistent with this result [4]. Such a multifractal-monofractal transition was also reported in parasympathetic nervous system (PNS) blockade experiment [3]. Hence the manifestation of multifractal HRV is indicative of the proper autonomic regulation of the heart rate. Further studies revealed that the multifractal HRV have properties analogous to those found in fluid turbulence [5]. However, there is little understanding beyond the phenomenological description of multifractal HRV. In this paper, we exploit further the analogy of HRV to fluid turbulence and show the existence of a hierarchical structure in healthy and diseased HRV. This structure allows us to model the multifractality of HRV and make conjecture to the heart beat dynamics responsible for the multifractal scaling. The hierarchy, first proposed by She and Leveque (SL) to understand the statistical properties of turbulent flows, provides a successful framework to discuss and characterize the deviation from Kolmogorov monofractal scaling in fluid turbulence [6]. When applied to study HRV, the SL hierarchy provides a model structure which possesses two advantages: (a) it simplifies the functional description of the multiscaling by using a maximum of only three parameters, and (b) it contains predictive power for HRV scaling in physiological states related to PNS withdrawal. One immediate implication is the potential use of this notion in applications such as diagnosis. Let the beat-to-beat RR interval (RRi) be r(t), where t is the beat number, and its increment be ∆r(τ) = r(t + τ) − r(t). The SL hierarchy implies, for a range of τ , S p+2 (τ) S p+1 (τ) = A p S p+1 (τ) S p …