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Key points• Respiratory sinus arrhythmia (RSA) is the variation of heart rate with breathing: heart rate increases during inspiration and decreases during expiration.• RSA is seen in many species including humans where it is strongest in the young and fit. The loss of RSA has been linked with cardiac mortality; however, the function of RSA is presently unknown.• One hypothesis proposed previously is that RSA allows for more efficient gas exchange between the lungs and the blood.• Our theoretical study does not support this hypothesis. Instead, a new hypothesis is proposed and tested using computational tools -that RSA helps the heart do less work while maintaining healthy levels of blood gases.• Of course, this new hypothesis needs to be further tested both experimentally and by using more sophisticated mathematical models, but if correct, it could explain why inducing RSA artificially in patients with cardiovascular disease improves their health.Abstract We conducted a theoretical study of the physiological significance of respiratory sinus arrhythmia (RSA), a phenomenon used as an index of cardiac vagal tone and wellbeing, whereby the heart rate (HR) increases during inspiration and decreases during expiration. We first tested the hypothesis that RSA improves gas exchange efficiency but found that although gas exchange efficiency improved with slow and deep breathing and with increased mean heart rate, this was unrelated to RSA. We then formulated and tested a new hypothesis: that RSA minimizes the work done by the heart while maintaining physiological levels of arterial carbon dioxide. We tested the new hypothesis using two methods. First, the HR for which the work is minimized was calculated using techniques from optimal control theory. This calculation was done on simplified models that we derived from a previously published model of gas exchange in mammals. We found that the calculated HR was remarkably similar to RSA and that this became more profound under slow and deep breathing. Second, the HR was prescribed and the work done by the heart was calculated by conducting a series of numerical experiments on the previously published gas exchange model. We found that cardiac work was minimized for RSA-like HR functions, most profoundly under slow and deep breathing. These findings provide novel insights into potential reasons for and benefits of RSA under physiological conditions.

The cardiorespiratory system exhibits oscillations from a range of sources. One of the most studied oscillations is heart rate variability, which is thought to be beneficial and can serve as an index of a healthy cardiovascular system. Heart rate variability is dampened in many diseases including depression, autoimmune diseases, hypertension, and heart failure. Thus, understanding the interactions that lead to heart rate variability, and its physiological role, could help with prevention, diagnosis, and treatment of cardiovascular diseases. In this review, we consider three types of cardiorespiratory interactions: respiratory sinus arrhythmia (variability in heart rate at the frequency of breathing), cardioventilatory coupling (synchronization between the heart beat and the onset of inspiration), and respiratory stroke volume synchronization (the constant phase difference between the right and the left stroke volumes over one respiratory cycle). While the exact physiological role of these oscillations continues to be debated, the redundancies in the mechanisms responsible for its generation and its strong evolutionary conservation point to the importance of cardiorespiratory interactions. The putative mechanisms driving cardiorespiratory oscillations as well as the physiological significance of these oscillations will be reviewed. We suggest that cardiorespiratory interactions have the capacity to both dampen the variability in systemic blood flow as well as improve the efficiency of work done by the heart while maintaining physiological levels of arterial CO. Given that reduction in variability is a prognostic indicator of disease, we argue that restoration of this variability via pharmaceutical or device-based approaches may be beneficial in prolonging life.

Breathing is a vital process providing the exchange of gases between the lungs and atmosphere. During quiet breathing, pumping air from the lungs is mostly performed by contraction of the diaphragm during inspiration, and muscle contraction during expiration does not play a significant role in ventilation. In contrast, during intense exercise or severe hypercapnia forced or active expiration occurs in which the abdominal “expiratory” muscles become actively involved in breathing. The mechanisms of this transition remain unknown. To study these mechanisms, we developed a computational model of the closed-loop respiratory system that describes the brainstem respiratory network controlling the pulmonary subsystem representing lung biomechanics and gas (O2 and CO2) exchange and transport. The lung subsystem provides two types of feedback to the neural subsystem: a mechanical one from pulmonary stretch receptors and a chemical one from central chemoreceptors. The neural component of the model simulates the respiratory network that includes several interacting respiratory neuron types within the Bötzinger and pre-Bötzinger complexes, as well as the retrotrapezoid nucleus/parafacial respiratory group (RTN/pFRG) representing the central chemoreception module targeted by chemical feedback. The RTN/pFRG compartment contains an independent neural generator that is activated at an increased CO2 level and controls the abdominal motor output. The lung volume is controlled by two pumps, a major one driven by the diaphragm and an additional one activated by abdominal muscles and involved in active expiration. The model represents the first attempt to model the transition from quiet breathing to breathing with active expiration. The model suggests that the closed-loop respiratory control system switches to active expiration via a quantal acceleration of expiratory activity, when increases in breathing rate and phrenic amplitude no longer provide sufficient ventilation. The model can be used for simulation of closed-loop control of breathing under different conditions including respiratory disorders.

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.