Central regulation of heart rate and the appearance of respiratory sinus arrhythmia: New insights from mathematical modeling

Abstract

A minimal model for the neural control of heart rate (HR) has been developed with the aim of better understanding respiratory sinus arrhythmia (RSA) – a modulation of HR at the frequency of breathing. This model consists of two differential equations and is integrated into a previously-published model of gas exchange. The heart period is assumed to be affected primarily by the parasympathetic signal, with the sympathetic signal taken as a parameter in the model. We include the baroreflex, mechanical stretch-receptor feedback from the lungs, and central modulation of the cardiac vagal tone by the respiratory drive. Our model mimics a range of experimental observations and provides several new insights. Most notably, the model mimics the growth in the amplitude of RSA with decreasing respiratory frequency up to 7 breaths per minute (for humans). Our model then mimics the decrease in the amplitude of RSA at frequencies below 7 breaths per minute and predicts that this decrease is due to the baroreflex (we show this both numerically and analytically with a linear baroreflex). Another new prediction of the model is that the gating of the baroreflex leads to the dependency of RSA on mean vagal tone. The new model was also used to test two previously-suggested hypotheses regarding the physiological function of RSA and supports the hypothesis that RSA minimizes the work done by the heart while maintaining physiological levels of arterial CO2. These and other new insights the model provides extend our understanding of the integrative nature of vagal control of the heart.

Enhancing respiratory sinus arrhythmia increases cardiac output in rats with left ventricular dysfunction

“…However, the function of this physiological phenomenon is yet to be fully established. The proposed benefits of RSA include stabilisation of blood pressure, optimisation of cardiopulmonary gas exchange and increased cardiac energy efficiency (Hayano et al 1996;Giardino et al 2003;Elstad, 2012;Ben-Tal et al 2014). Any one of these would assist patients with heart failure where myocardial function and energy are suboptimal.…”

“…However, this theory is contentious (Sin et al 2010) and a recent mathematical modelling study could not validate this finding (Ben-Tal et al 2012). Instead, Ben-Tal and colleagues proposed that RSA reduced cardiac work while maintaining physiological levels of arterial carbon dioxide (Ben-Tal et al 2014). We suggest that through these mechanisms RSA serves to optimize oxygen delivery to the heart with increasing workload (Elstad et al 2018).…”

“…From an evolutionary standpoint it is highly conserved, being found throughout the animal kingdom from primitive cartilaginous fish (Taylor, 1994). However, despite decades of studies on RSA its functional significance remains highly controversial Ben-Tal et al 2014).…”

Information Domain Analysis of Respiratory Sinus Arrhythmia Mechanisms

“…RSA -being mediated predominantly by the parasympathetic nervous system -is widely accepted as an indicator of the healthy cardiovascular control at rest (Grossman and Taylor 2007, Larsen et al 2010, Ben-Tal et al 2014. A decrease of RSA magnitude is associated with many pathological states, including myocardial infarction (Fei et al 1996a), and chronic heart failure (Fei et al 1996b) but it decreases also during challenges leading to a decreased parasympathetic and/or increased sympathetic activity (Allen and Crowell 1989, Herbert et al 2010, Mortola et al 2016.…”

Silicon central pattern generators for cardiac diseases

“…Recently, we built a mathematical model to understand the functional role of RSA and to address the inconsistencies of previous reports (Ben‐Tal et al . , ). We demonstrated that although gas exchange efficiency can improve with both slow and deep breathing, and increased mean heart rate, this was all unrelated to RSA.…”