A cardiodynamic model for power laws of heartbeats in aging and congestive heart failure

The output of a healthy physiological system exhibits complex fluctuation. Nonlinear analysis, such as power-law characteristics, shows the potential for detecting changes in the biological complexity of disease and aging. This paper characterized the heart rate variability (HRV) of aging and patients with congestive heart failure (CHF) by three types of distribution: Zipf's law, Heaps' law, and frequency distribution. All data analysis and modeling are based on a constructed sequence, that is, the monotonous increase to monotonous decrease amplitude ratios as derived from heartbeat interval data. The experimental result shows a significant decrease of HRV from healthy young people to healthy elderly to CHF patients. We proposed a model by taking account of the “rich-get-richer” theory in experimental observations, which successfully reproduced three types of distribution characterizing the constructed ratio sequences as obtained from the analysis of measured cardiac data. This work provides insight into the dynamic mechanism of cardiac data underlying the regulation of autonomic nerve.