Instabilities in an asymptotic model of cardiac excitation
Ameneh Asgari Targhi (University of Glasgow)
Friday 5th December, 2014 16:00-17:00 Maths 416
Atrial fibrillation (AF) is a complex arrhythmia in the heart and one of the most difficult abnormal rhythms to treat. AF is characterised by rapid (e.g., 400-600 beats/minute), irregular electrical and mechanical activation of the atrial muscle. It is the most common arrhythmia encountered in clinical practice, and patients with AF have an increased risk of death. This high risk necessi- tates a drive towards an improved understanding of the various and complex electrophysiological mechanisms of AF initiation and maintenance. There are evidence that inducing and maintaining the arrhythmia in AF is due to ectopic atrial beats and spatial heterogeneity of repolarization, respectively. Therefore, repolarization alternans could have a crucial role in initiating AF. Cardiac alternans is alternation in Action Potential Duration (APD), as a consequence an understanding of the alternans behaviour can lead us to an understanding of the AF. To this end we consider a ver- sion of the classical model of Purkinje fibers (Noble, J. Physiol. Lond. 160:317352, 1962) that has been simplified by a well-justified asymptotic embedding approach to a “caricature model”. The caricature is amenable to analytical study but at the same time preserves the essential features of contemporary ionic models of cardiac excitation, unlike models of FitzhHugh-Nagumo type. The Fitzhugh-Nagumo models only reflect features of nerve tissue and they are unlike typical ad-hoc simplifications of cardiac models. We outline the regions in the parameter space of a model of car- diac excitation where normal 1:1 response, alternans 2:2 response and further instabilities occur during repeated stimulation with a dynamic restitution protocol. Then we derive theoretically an explicit discrete “restitution” map, which specifies the action potential duration as a function of the preceding diastolic interval. We then study the stability and bifurcations of this map to deter- mine the region’s parameter space where normal response and alternans occur. Direct numerical simulations confirm the theoretical results.