Applications of Control Theory to the Dynamics and Propagation of Cardiac Action Potentials

Abstract

Sudden cardiac arrest is a widespread cause of death in the industrialized world. Most cases of sudden cardiac arrest are due to ventricular fibrillation (VF), a lethal cardiac arrhythmia. Electrophysiological abnormalities such as alternans (a beat-to-beat alternation in action potential duration) and conduction block have been suspected to contribute to the onset of VF. This study focuses on the use of control-systems techniques to analyze and design methods for suppressing these precursor factors. Control-systems tools, specifically controllability analysis and Lyapunov stability methods, were applied to a two-variable Karma model of the action-potential (AP) dynamics of a single cell, to analyze the effectiveness of strategies for suppressing AP abnormalities. State-feedback-integral (SFI) control was then applied to a Purkinje fiber simulated with the Karma model, where only one stimulating electrode was used to affect the system. SFI control converted both discordant alternans and 2:1 conduction block back toward more normal patterns, over a wider range of fiber lengths and pacing intervals compared with a Pyragas-type chaos controller. The advantages conferred by using feedback from multiple locations in the fiber, and using integral (i.e., memory) terms in the controller, are discussed.

Model-based control of cardiac alternans in Purkinje fibers

“…It can be argued, especially given the importance of calcium cycling in the emergence of alternans, that control may be more effective when feedback is applied to one of the gating variables (i.e., a, b, or c here) [28]. This can significantly alter both the controllability and the observability properties of the dynamics, potentially increasing the size of the tissue which can be controlled using spatially localized feedback.…”

Theory of the development of alternans in the heart during controlled diastolic interval pacing

“…[3][4][5][6][7] Several control methods for suppressing the development of alternans, based on these alternans theories, have also been proposed. [8][9][10][11][12][13][14] An interesting idea for suppressing alternans focuses on regulating the diastolic interval (DI), the time between action potentials. The DI is an attractive target for control, because it is the key dynamical variable that interacts with the APD in order to produce alternans, according to the standard electrical restitution theory.…”

“…8 However, the theory itself involves some approximations and is limited in how control is applied, so attempts have been made to see if the controllable region can be expanded. [12][13][14] In this paper, we focus on methods that attempt to eliminate APD alternans by forcing the DI to assume a constant value at the pacing site. To test our ideas, we compare the results of our theory and simulations to results obtained by Wu and Patwardhan in their controlled-DI experiments.…”

Design of external forces for eliminating traveling wave in a piecewise linear FitzHugh–Nagumo model

“…The main purpose of the present paper is to propose a systematic procedure to design globally weak forces e(t) for eliminating traveling waves. 8,36 However, to the best of our knowledge, no published research has experimentally confirmed the elimination of traveling waves with external forces applied to slow dynamics. As a result, it is difficult to eliminate the traveling wave by applying weak forces to fast dynamics.…”