Biophysical characterization of the underappreciated and important relationship between heart rate variability and heart rate

Abstract

Heart rate (HR) variability (HRV; beat-to-beat changes in the R-wave to R-wave interval) has attracted considerable attention during the past 30+ years (PubMed currently lists >17 000 publications). Clinically, a decrease in HRV is correlated to higher morbidity and mortality in diverse conditions, from heart disease to fetal distress. It is usually attributed to fluctuation in cardiac autonomic nerve activity. We calculated HRV parameters from a variety of cardiac preparations (including humans, living animals, Langendorff-perfused heart, and single sinoatrial nodal cell) in diverse species, combining this with data from previously published articles. We show that regardless of conditions, there is a universal exponential decay-like relationship between HRV and HR. Using 2 biophysical models, we develop a theory for this and confirm that HRV is primarily dependent on HR and cannot be used in any simple way to assess autonomic nerve activity to the heart. We suggest that the correlation between a change in HRV and altered morbidity and mortality is substantially attributable to the concurrent change in HR. This calls for re-evaluation of the findings from many articles that have not adjusted properly or at all for HR differences when comparing HRV in multiple circumstances.

Keywords: autonomic nervous system; ion channels; physiology; sinoatrial node.

Fig. 1. Differences in HRV among different cardiac preparations (baseline conditions)

A-E, tachograms (150 s stationary epochs) from: A, conscious human (n = 11); B, Langendorffperfused rabbit heart (n = 58); C, rabbit SANC (n = 67); D, Langendorff-perfused rat heart (n = 8); E, conscious rat (n = 11). Individual experiments are plotted in unique colours. F-H, summary of baseline differences in CL and HRV among cardiac preparations. Mean (+SEM) CL (F), SDNN (G) and RMSSD (H) for different preparations. Asterisk and letters atop bars demonstrate statistically significant differences from other lettered bars (P<0·05; 1-way ANOVA).

Fig. 2. Effect of β-agonists on HRV in different cardiac preparations

A-D, tachograms demonstrating the effect of β-agonists on HRV. A, before and after dobutamine in conscious humans. B, data before and after 100 nM isoprenaline in rabbit SANC. C, data before and after 100 nM isoprenaline in Langendorff-perfused rabbit hearts. D, data before and after 100 nM isoprenaline in Langendorff-perfused rat hearts. Baseline data = red, data in presence of β-adrenergic agonist = green. E-G, summary of the effect of β-adrenergic agonists on HRV. Mean (+SEM) CL (E), SDNN (F), and RMSSD (G) under baseline conditions (= ‘B’; red bars) and with β-adrenergic agonist (= ‘C’; green bars) for the different preparations. Asterisk and bar = statistically different (P<0·05; 1-way ANOVA). Sword and bar = P=0·1>P>0·05.

Fig. 3. Relationship between HRV (SDNN) and heart rate – comparison of theory and experiment

A, relationship between SDNN and heart rate. Data from experiments undertaken in this paper and elsewhere, and our mathematical models are plotted. Basic key under panel A; for detailed key see ODS. B, relationship between SDNN and heart rate (heart rate range 40-240 beats/min only). C, relationship between log_n(SDNN) and heart rate (same data as A). Black line shows that for every 10 beats/min increase in heart rate, log_n(SDNN) decreases by 0·17 ms.

Fig. 4. Relationship between HRV and heart rate predicted by a biophysically detailed model

Computed action potentials from a SANC model with (green) and without (red) a maximum 20 pA perturbing current (I_per) at fast (top, e.g. Ai) to slow (bottom, e.g. Ci) rates, and corresponding tachograms (Aii – Cii). Rate was varied by altering I_K,ACh. D, relationship between SDNN and heart rate in this model.

Fig. 4. Relationship between HRV and heart rate predicted by a biophysically detailed model

Computed action potentials from a SANC model with (green) and without (red) a maximum 20 pA perturbing current (I_per) at fast (top, e.g. Ai) to slow (bottom, e.g. Ci) rates, and corresponding tachograms (Aii – Cii). Rate was varied by altering I_K,ACh. D, relationship between SDNN and heart rate in this model.

Fig. 5. Application of a correcting factor facilitates clarification of whether changes in HRV are attributable to heart rate differences alone

Analysis of baseline differences in HRV among different preparations (A); analysis of changes in HRV following administration of β-agonists to different preparations (B-E). SDNN is plotted against heart rate. Predicted effect of heart rate on SDNN is plotted (green lines) using calculated correcting factor from Fig. 3C. Conscious human data (A) or baseline data (B-E) are arbitrarily used as starting point from which to calculate the effect of heart rate on SDNN.

Fig. 5. Application of a correcting factor facilitates clarification of whether changes in HRV are attributable to heart rate differences alone

Analysis of baseline differences in HRV among different preparations (A); analysis of changes in HRV following administration of β-agonists to different preparations (B-E). SDNN is plotted against heart rate. Predicted effect of heart rate on SDNN is plotted (green lines) using calculated correcting factor from Fig. 3C. Conscious human data (A) or baseline data (B-E) are arbitrarily used as starting point from which to calculate the effect of heart rate on SDNN.