Mathematical models of Abnormal automaticiy in cardiac tissue

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Ventricular arrhythmia during the acute phase of ischemia and atrial fibrillation (AF) are widespread arrhythmias. Their most common mechanism is reentry, whereby one or multiple self sustained electrical activation fronts travel in the tissue. The resulting high frequency activation supersedes the normal pacemaker of the heart and may lead to life threatening complications. In both cases, the trigger may come from abnormal automaticity of some part of the tissue. Our goal is to study the mechanisms leading to abnormal automaticity in mathematical models of cells and tissues.In previous work, we have established the conditions to get sustained automaticity in a realistic ionic model of the human ventricular myocyte considering parameters that are known to change during ischemia. Similar analyses were performed on a model of atrial myocyte with respect to parameters modified by adrenergic neuronal activation, which is known to favor abnormal automaticity and AF. However, these analyses were incomplete and model dependent. Our first objective is to complete these analyses and reach an understanding of the general conditions by which sustained automaticity may occur that would be applicable to a wide class of cardiac ionic models. We want to identify the subsystem involved and their basic generic properties to reach simplified formulations that would still reproduce the main characteristics of the dynamics. Analysis will be extended to transient automaticity, whereby the system may produce isolated burst of activation. However the real and most significant challenge is to find the conditions needed for automaticity in tissue, in which the cells are interconnected by gap junctions acting as intracellular resistance. We propose a new approach to this problem by which the results of the cell analyses are used to get conditions of automaticity in the tissue. Upon spatial distribution of the parameters associated to either ischemia or adrenergic stimulation, cells have different resting potentials, ending in spatially inhomogeneous stationary voltage profile modulated by the coupling. Automaticity occurs when this stationary solution loses its stability. The problem is to find spatial distributions of parameters that can produce this loss of stability. Our second aim is to develop a method to build these distributions using the stationary solutions of the cells as function of the parameters obtained in the first part of the project.The final and third problem is to examine whether the distribution of parameters producing automaticity obtained in the second part of the project can be physiologically realistic. Consider as an example the extracellular distribution of potassium Ko which is known to vary during ischemia and was shown in our preliminary analysis to be able to induce automaticity. Ko is treated as a parameter in the first two part of the proposal. We propose to develop a model of the spatial dynamics of Ko in the extracellular medium that will be used to assess whether such a profile could indeed occur. The same type of approach will be used for other parameters, such as the spatial distribution of noradrenalin during adrenergic stimulations. In summary, we propose to use mathematical model to reach robust and generic less model dependent conclusion over the distribution of parameters needed to reach abnormal automaticity in condition ischemia and adrenergic stimulation.