Bonhoeffer-van der Pol Oscillator Model of the Sino-Atrial Node: A Possible Mechanism of Heart Rate Regulation

Formation of second-degree atrioventricular blocks in the cardiac heterogeneous oscillator model

We study formation of second-degree atrioventricular blocks (Wenckebach and Mobitz types) with reduction of coupling between nodes in the heterogeneous oscillator model of cardiac conduction system. We demonstrate that maximal possible number of physiological mode lock patterns in both cases appears at a particular value of coupling coefficient. For the type II atrioventricular block total conduction ratio at high sinus rates might be represented by a product of conduction ratios of atrioventricular nodal and infrahisian blocks.

A heterogeneous coupled oscillator model for simulation of ECG signals

We present a novel model of cardiac conduction system including main pacemakers and heart muscles. Sinoatrial node, atrioventricular node and His-Purkinje system are represented by modified van der Pol-type oscillators connected with time-delay velocity coupling. For description of atrial and ventricular muscles, where depolarization and repolarization processes are considered as separate waves, we use modified FitzHugh-Nagumo model. In this work, we obtained synthetic ECG as a combined signal of atrial and ventricular muscles and reproduced several normal and pathological rhythms. Inclusion of cardiac muscle response allows to investigate interactions between pacemakers and resulting global heartbeat dynamics by means of clinically comparable realistic ECG signals. This feature distinguishes our model from existing cardiac oscillator models. To solve the system of differential equations describing the proposed heterogeneous coupled oscillator model we developed a software in MATLAB environment utilizing special DDE23 function.

Spectral distortion properties of the integral pulse frequency modulation model

The integral pulse frequency modulation (IPFM) model has been used for the following two purposes. First, it has been utilized to verify the correspondence between the spectral structure of autonomic input and the estimated spectrum of heart rate variability (HRV), relying mainly on the theoretical work of Bayly (1968). Second, the IPFM model provides a framework for evaluating how precisely the proposed method of HRV analysis could estimate the input spectral structure. However, the appropriateness of the IPFM model for both purposes has not been examined sufficiently in realistic situations. In this paper, the spectral structure of the pulse train generated by the IPFM model is theoretically derived for an input signal containing multiple frequency components. This is a more general condition than the single sinusoidal input signal used earlier. In accordance with the theoretical results, the magnitude of the spectral distortion is computed for a pair of varied frequencies, considering the corresponding coefficient of variation of interpulse intervals. Results show that the distortion could be nonnegligible under practical values of the coefficient of variation. Such distortion may well affect the spectral structure in the wide frequency range. This study suggests that the spectral structure of HRV should be interpreted carefully, taking the above distortion properties into account, even though the IPFM model appears to be established as a mechanism mediating between autonomic input and heart rate variability.