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. 2018 Aug 2:9:1001.
doi: 10.3389/fphys.2018.01001. eCollection 2018.

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

Joachim A Behar  1 , Aviv A Rosenberg  1 , Ori Shemla  1 , Kevin R Murphy  2 , Gideon Koren  2 , George E Billman  3 , Yael Yaniv  1
Affiliations

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

Joachim A Behar et al. Front Physiol. .

Abstract

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⋅ HRm0.58 , fLF-HF = 0.0017⋅ HRm1.01 and fHFup = 0.0128⋅ HRm0.86 . 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.

Keywords: animal models; heart rate variability; mammals; power allometric law; power spectral analysis.

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Figures

FIGURE 1
FIGURE 1
Block diagram of the algorithm for identifying the frequency bands from a database of mammalian NN intervals. PSD, power spectral density; GMM, Gaussian mixture model; VLF, very low frequency; LF, low frequency; HF, high frequency.
FIGURE 2
FIGURE 2
Gaussian Mixture Model and frequency band clustering. Cutoff frequency identification for the VLF, LF, and HF regimes for (A) humans, (B) dogs, (C) mice, and (D) rabbits. The vertical dotted line corresponds to values used in the literature: human (Malik et al., 1996), dog (Billman, 2013a; Billman et al., 2015b), and mouse (Thireau et al., 2008). For dogs, no VLF-LF cutoff could be found in the literature, so only the LF-HF and fHFup vertical lines from the literature are shown. The intersection between two consecutive Gaussians defines the band cutoffs.
FIGURE 3
FIGURE 3
Double-logarithmic plot of PSD band cutoff frequency and Gaussian means versus median HRm for (A) fVLF-LF the cutoff frequency between the VLF and LF bands versus the HRm; (B) fLF-HF, the cutoff frequency between the LF and HF bands versus the HRm; (C) fHFup, the upper bound of the HF band versus the HRm; (D) GV LF, the mean of the Gaussian describing the VLF band; (E) GLF, the mean of the Gaussian describing the LF band, and (F) GHF, the mean of the Gaussian describing the HF band.
FIGURE 4
FIGURE 4
Double-logarithmic plot of PSD band cutoff frequencies and Gaussian means versus BMm for (A) VLF to LF cutoff versus BMm, (B) LF to HF cutoff versus BMm, (C) upper bound of HF versus BMm. Center of the Gaussian describing (D) the VLF band versus BMm, (E) the LF band versus BMm and (F) the HF band versus BMm.
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References

    1. Adachi Y., Nakajima Y., Satomoto M., Morita K., Doi M., Sato S. (2006). The heart rate variability in mice: telemetric evaluation of endotoxin shock. Masui 55 436–440. - PubMed
    1. Ahmed A. K., Harness J. B., Mearns A. J. (1982). Respiratory control of heart rate. Eur. J. Appl. Physiol. Occup. Physiol. 50 95–104. 10.1007/BF00952248 - DOI
    1. Akselrod S., Gordon D., Ubel F. A., Shannon D. C., Berger A. C., Cohen R. J. (1981). Power spectrum analysis of heart rate fluctuation: a quantitative probe of beat-to-beat cardiovascular control. Science 213 220–222. 10.1126/science.6166045 - DOI - PubMed
    1. Aubert A. E., Ramaekers D., Beckers F., Breem R., Denef C., Van de Werf F., et al. (1999). The analysis of heart rate variability in unrestrained rats. Validation of method and results. Comput. Methods Programs Biomed. 60 197–213. 10.1016/S0169-2607(99)00017-6 - DOI - PubMed
    1. Baudrie V., Laude D., Elghozi J.-L. (2007). Optimal frequency ranges for extracting information on cardiovascular autonomic control from the blood pressure and pulse interval spectrograms in mice. Am. J. Physiol. Regul. Integr. Comp. Physiol. 292 R904–R912. 10.1152/ajpregu.00488.2006 - DOI - PubMed