A Mathematical Theory of Heartbeat

Abstract

This article develops a novel mathematical theory of pacemaker operation using complexity theory and network science ideas. Specifically, the author claims that pacing is a byproduct of emergence of a self-synchronizing electrical network in humans (and animals) based on a fundamental property of feedback networks – aperiodicity. The exceptional resilience and reliability of the ordinary heartbeat may be due to the emergence of a self-organized network in the sinoatrial node and the particular property of aperiodic networks. Clinical studies should be performed to verify the model. Using simulation, we show that aperiodic synchronization arises almost naturally in random network structures due to the presence of many feedback loops with lengths that are relatively prime to each other. Furthermore, we show that nearly any random network of sufficient density “naturally” forms an aperiodic subset of nodes that synchronize to provide a reliable and resilient “clock” for regulating biological rhythms such as heartbeat.