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This work deals with the numerical solution of the monodomain and bidomainmodels of electrical activity of myocardial tissue. The bidomain model is asystem consisting of a possibly degenerate parabolic PDE coupled with anelliptic PDE for the transmembrane and extracellular potentials, respectively.This system of two scalar PDEs is supplemented by a time-dependent ODE modelingthe evolution of the so-called gating variable. In the simpler sub-case of themonodomain model, the elliptic PDE reduces to an algebraic equation. Two simplemodels for the membrane and ionic currents are considered, theMitchell-Schaeffer model and the simpler FitzHugh-Nagumo model. Since typicalsolutions of the bidomain and monodomain models exhibit wavefronts with steepgradients, we propose a finite volume scheme enriched by a fully adaptivemultiresolution method, whose basic purpose is to concentrate computationaleffort on zones of strong variation of the solution. Time adaptivity isachieved by two alternative devices, namely locally varying time stepping and aRunge-Kutta-Fehlberg-type adaptive time integration. A series of numericalexamples demonstrates thatthese methods are efficient and sufficiently accurateto simulate the electrical activity in myocardial tissue with affordableeffort. In addition, an optimalthreshold for discarding non-significantinformation in the multiresolution representation of the solution is derived,and the numerical efficiency and accuracy of the method is measured in terms ofCPU time speed-up, memory compression, and errors in different norms.

A multiresolution space-time adaptive scheme for the bidomain model in electrocardiology