Power Laws and Self-Organized Criticality in Cardiovascular Avalanches

Self-organized criticality (SOC) describes natural systems spontaneously tuned at equilibrium yet capable of catastrophic events or avalanches. The cardiovascular system, characterized by homeostasis and vasovagal syncope, is a prime candidate for SOC. Power laws are the cornerstone for demonstrating the presence of SOC. This study aimed to provide evidence of power-law behavior in cardiovascular dynamics. We analyzed beat-by-beat blood pressure and heart rate data from seven healthy subjects in the head-up position over 40 min. Cardiovascular avalanches were quantified by their duration (in beats), and symbolic sequences were identified. Five types of distributions were assessed for power-law behavior: Gutenberg–Richter, classical Zipf, modified Zipf, Zipf of time intervals between avalanches, and Zipf of symbolic sequences. A three-stage approach was used to show power laws: (1) regression coefficient r > 0.95, (2) comparison with randomized data, and (3) Clauset’s statistical test for power law. Numerous avalanches were identified (13.9 ± 0.8 per minute). The classical and modified Zipf distributions met all the criteria (r = 0.99 ± 0.00 and 0.98 ± 0.01, respectively), while the others showed partial agreement, likely due to the limited data duration. These findings reveal that Zipf’s distributions of cardiovascular avalanches strongly support SOC, shedding light on the organization of this complex system.