New approach of controlling cardiac alternans

Mounira Kesmia,Soraya Boughaba,Sabir Jacquir

doi:10.3934/dcdsb.2018051

Abstract

The alternans of the cardiac action potential duration is a pathological rhythm. It is considered to be relating to the onset of ventricular fibrillation and sudden cardiac death. It is well known that, the predictive control is among the control methods that use the chaos to stabilize the unstable fixed point. Firstly, we show that alternans (or period-2 orbit) can be suppressed temporally by the predictive control of the periodic state of the system. Secondly, we determine an estimation of the size of a restricted attraction's basin of the unstable equilibrium point representing the unstable regular rhythm stabilized by the control. This result allows the application of predictive control after one beat of alternans. In particular, using predictive control of periodic dynamics, we can delay the onset of bifurcations and direct a trajectory to a desired target stationary state. Examples of the numerical results showing the stabilization of the unstable normal rhythm are given.

Highlights

Nonlinear dynamics and tools from chaos theory are used to understand, to characterize and to control some cardiac pathologies [2,13,21,29,37,47]
We investigate the control of the periodic rhythms of the one-dimensional map of (APD)
This one gives the duration of the cardiac action potential (APD) current as a function of the previous one

Summary

Introduction

Nonlinear dynamics and tools from chaos theory are used to understand, to characterize and to control some cardiac pathologies [2,13,21,29,37,47]. From dynamic point of view, different states of the cardiac rhythm are qualified by the steady state, the periodicity and the chaos [4]. Spatiotemporal chaos exists in two and three dimensions of excitable media and it has been seen in the breakup of spiral and scroll waves and it is considered as one of the principal mechanisms of cardiac fibrillation (ventricular or atrial) [1,10,14,30,34,48,49]. Many studies deal the understanding the nonlinear dynamics of ventricular fibrillation. This particular arrhythmia is generated by the loss of stability of the periodic rhythm, namely alternans, due to a rapid pacing of the cardiac tissue [2,21,24,27,29,31,43]. The spatiotemporal chaotic behaviors have been studied for cardiac alternans in one dimension [16]

Objectives

Conclusion