A Universal Scaling Relation for Defining Power Spectral Bands in Mammalian Heart Rate Variability Analysis

Joachim A. Behar, Aviv A. Rosenberg, Ori Shemla, Kevin R. Murphy, Gideon Koren, George E. Billman, Yael Yaniv

Background: Power spectral density (PSD) analysis of the heartbeat intervals in the three main frequency bands [very low frequency (VLF), low frequency (LF), and high frequency (HF)] provides a quantitative non-invasive tool for assessing the function of the cardiovascular control system. In humans, these frequency bands were standardized following years of empirical evidence. However, no quantitative approach has justified the frequency cutoffs of these bands and how they might be adapted to other mammals. Defining mammal-specific frequency bands is necessary if the PSD analysis of the HR is to be used as a proxy for measuring the autonomic nervous system activity in animal models. Methods: We first describe the distribution of prominent frequency peaks found in the normalized PSD of mammalian data using a Gaussian mixture model while assuming three components corresponding to the traditional VLF, LF and HF bands. We trained the algorithm on a database of human electrocardiogram recordings (n = 18) and validated it on databases of dogs (n = 17) and mice (n = 8). Finally, we tested it to predict the bands for rabbits (n = 4) for the first time. Results: Double-logarithmic analysis demonstrates a scaling law between the GMM-identified cutoff frequencies and the typical heart rate (HRm): fVLF-LF = 0.0037⋅ HR m 0.58 , fLF-HF = 0.0017⋅ HR m 1.01 and fHFup = 0.0128⋅ HR m 0.86 . We found that the band cutoff frequencies and Gaussian mean scale with a power law of 1/4 or 1/8 of the typical body mass (BMm), thus revealing allometric power laws. Conclusion: Our automated data-driven approach allowed us to define the frequency bands in PSD analysis of beat-to-beat time series from different mammals. The scaling law between the band frequency cutoffs and the HRm can be used to approximate the PSD bands in other mammals.