Universal Inverse Square Relationship between Heart Rate Variability and Heart Rate

In our previous study, we analyzed heart rate variability and heart rate from a large variety of cardiac preparations (including humans, living animals, Langendorff-perfused isolated hearts, and single sinoatrial nodal cells) in diverse species, combining our data with those of previously published articles. The analysis revealed that regardless of conditions, heart rate variability (for the purposes of the study assessed as standard deviation) of beat-to-beat intervals heart rate follows a universal exponential decay-like relationship. Numerical simulations of DI variability by adding a randomly fluctuating term to net current revealed a similar relationship. In the present study, using a Taylor series, we found that this relationship is, in fact, inverse square, and we derive an explicit formula for sd(CL) vs. heart rate with biophysically meaningful parameters.