Synchronization-dissipation dynamics in the cardiorespiratory system

Abstract

Dissipative coupling is known to induce synchronization. Conversely it may be hypothesized that oscillators driven to synchronize may reduce power dissipation in their coupling. The latter scenario is realized in the human cardiorespiratory system where cardiac and respiratory rhythms are controlled by the central nervous system while interacting viscoelastically through the pulmonary vasculature. Here we examine the functional significance of this coupling which is observed in respiratory sinus arrhythmia (RSA). By modelling electrical and viscoelastic interactions within the cardiorespiratory system, we identify the conditions leading to synchronization. We demonstrate that, when present, synchronization reduces cardiac power losses by 10% in humans and up to 55% in other species. The predicted gain in cardiac output is compared to the gain observed in-vivo by pacing the heart with a device restoring RSA. It is therefore surmised that RSA may improve cardiac pumping efficiency by reducing dynamic stress and power dissipation in the pulmonary vasculature.

Figures (5)

• Figure 1: Cardiorespiratory coupling through the central nervous system and the pulmonary vascular impedance (a) Central nervous system coupling. Lung stretch receptors synchronize the respiratory rhythm, generated by the post-I, aug-E, early-E neuron populations, to the onset of inspiration. The post-I neuron activation increases vagal tone (cVN) and slows down heart rate during the expiratory phase. This produces the cardiac modulation (RSA) seen in a dog electrocardiogram. (b) RSA restored by our neuronal pacemaker. The pacemaker modulates heart rate within the respiratory cycle while synchronizing cardiac oscillations using the same nonlinear properties as central nervous circuits. Electrocardiograms show the heart rate of an anaesthetized pig and with RSA artificially restored through neuronal pacing. (c) Viscoelastic coupling between cardiac and respiratory oscillators at the site of lung alveoli. Pulmonary vascular impedance oscillates driven by the stretching and contraction of lung alveoli at frequency $\Omega$ and the systole/diastole cycling of blood pressure at cardiac frequency $\omega$. (d) Viscoelastic power density $p_v$ dissipated by the capillary under axial strain $\epsilon$. aVN$\equiv$ vagus nerve $a$ fibre, cVN$\equiv$$c$ fibre, VRG$\equiv$ ventral respiratory group, e.m.g. $\equiv$ electromyography
• Figure 2: Cardiac entrainment by respiration: modulation with synchronization (a) Cardiac rhythm entrained by the lung inflation signal. The pacemaker drives the heart at a faster rate during a breadth intake than during the expiratory phase producing RSA. The cardiac rhythm may also synchronize to respiration in which case the phase of cardiac oscillations $\psi_1$, $\psi_2$, $\psi_3$ locks to the respiratory cycle. (b) Synchronization plateaux in the dependence of $\omega/\Omega$ on breathing frequency $\Omega$. Each synchronization region $m:n$ has $m$ cardiac oscillations matching $n$ respiratory cycles. (c) Synchronization domains $3:1$, $4:1$ and $5:1$ and their dependence on the inspiratory duty cycle $\beta$. The troughs corresponds to one cardiac peak moving from the expiratory interval to the inspiratory interval.
• Figure 3: Viscoelastic energy gains mapped onto regions of cardiorespiratory synchronization The colour map plots the difference in viscoelastic power dissipated by the heart paced with RSA relative to no RSA normalised by the latter. The boundaries of synchronization regions (black lines) are superimposed to show the dependence of $m:n$ synchronization on the breathing frequency $\Omega$ and on the inspiratory duty cycle $\beta$. $\omega_0$ is the cardiac frequency with no RSA modulation applied ($\beta=0$). Parameters: $rsa=100\%$, $\epsilon_H^0=0.25$, $\epsilon_R^0=0.25$, $\Gamma=0.15$s, $\delta=\pi/(3\Omega)$.
• Figure 4: Spectral distribution of power gains and its dependence on RSA dose (rsa) The bandwidth of $m:n$ synchronization regions increases with the RSA dose. The energy gains within these regions (red domains) increase and saturate when RSA dose approaches 50%. In the blue domain, outside $m:n$ synchronization regions, the power dissipated under RSA pacing is marginally greater than under monotonic pacing. $\beta=0.4$.
• Figure 5: Dependence of power gains at the centre of a synchronization domain on RSA dose Dependence of power gains produced by RSA inside the $1:1$ (blue trace) and $3:1$ Arnold tongues (purple trace).