New Approach of Controlling Cardiac Alternans

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Control of continuous dynamical systems modeling physiological states

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Control of irregular cardiac rhythm

International audienceThe aim of this work is to investigate the chaos control of the one di- mensional map which modelizes the duration of the current cardiac action potential (APD) as a function of the previous one. Using OGY control method, we obtain very satisfactory numerical results to stabilize the irregular heart rhythm into the normal rhythm

Analyse de la dynamique de la durée du potentiel d'action cardiaque à travers un modèle itératif

International audienceLe présent travail a pour but de caractériser, par une étude mathématique rigoureuse la dynamique du modèle itératif de la durée du potentiel d'action. L'étude de ce modèle, qui découle de celui de Beeler Reuter (BR), se caractérise par une dynamique matérialisée par une courbe de restitution et qui peut servir d'outil pertinent dans l'analyse et le diagnostic d'arythmie. Par ailleurs l'analyse de la stabilité du modèle permet de définir les zones d'existence de différents rythmes cardiaques

Predictive Chaos Control for the 1D-map of Action Potential Duration

International audienceIn the present work, a nonlinear control method namely predictive controlis investigated. The proposed method allows stabilizing unstable period-1 rhythm.Using mathematical analysis and computer simulations, we show that this methodcan be used to control chaotic behavior or pathological rhythms. As example, theresults are illustrated in the case of the 1D-map action potential duration (APDi+1)which modelizes the cardiac action potential duration as the function of the previousone (APDi)

Control of the One Dimensional Map Dynamics of the Cardiac Action Potential Duration

International audienceThe aim of this work is to investigate the control of the chaos in the one dimensional map which modelizes the duration of the current cardiac action potential (APD) as a function of the previous one. Using OGY control method, we obtain very satisfactory numerical results to stabilize the irregular heart rhythm into the normal rhythm

Control of periodic dynamics of nonlinear and chaotic discrete dynamical systems

International audienceThe present work consists of a generalization to dimensions greater than 1 of the results obtained on control and more precisely on the suppression of periodic rhythms in unidimensional nonlinear discrete dynamic systems. This method is based on predictive control which is known for the control of chaos. The suppression of the stable periodic orbit by predictive control requires a rigorous estimation of the control distance. Therefore, predictive control must be corroborated by an estimate of the size of the restricted attraction basin of the unstable fixed point. This clearly improves the work of T. Ushio and S. Yamamoto in which the control distance is arbitrary. The advantage of this mathematical approach is that it can be rigorously applied and the results validated not only to discrete multi-dimensional nonlinear chaotic systems (logistics map, Hénon map) but also in the case of the prevention of some cardiac pathologies using the action potential duration map (APD), a nonlinear chaotic discrete dynamical system. The properties of restitution of the duration of the action potential and the alternation of repolarization are important arrhythmogenic factors. Thus, although the alternating duration of the cardiac action potential has a periodic dynamic, they are considered to be pathological rhythms related to the appearance of ventricular fibrillation. Therefore, the study of the dynamic of the APD is aimed to prevent some serious cardiac pathologies such as fibrillation or sudden cardiac death following ventricular arrhythmias