Improved Discretization Methods for Modeling Wavefront Conduction in Nonuniform Cardiac Tissue

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Investigations into the relative roles of tissue structure and membraneExcitability recovery on creating conditions for arrhythmias in the heart have proven tobe extremely challenging. Computer models of wavefront propagation have beenimportant to the inquiry by allowing effects to be isolated and by providing access tosome of the parameters that cannot be monitored or controlled in a given experimentalsetup. Due to limitations in the traditionally employed numerical methods, however,these computer models have either ignored or greatly simplified the effects of structuraland geometrical non-uniformities on the activation process. Consequently, mostmechanisms for arrhythmogenesis derived from them are generally based on theeffects of non-uniformities of membrane properties in tissue with assumed uniformmaterial properties. For macroscopic models of the heart to have greater predictiveability they must be able to incorporate the effects of diseased-induced tissue structureinhomogeneities on conduction and potential timecourses. The objectives of this proposal are to develop improved discretization schemes for robustly modelingconduction in regions with spatially varying material and membrane properties. Theseobjectives will be accomplished by creating a unified meltherhatical and computationalframework for simulation that will allow different numerical methods to be directlycompared. The simulation system, BIDOSIM, will use a module-based paradigm fromwhich a single "sun-time environment" can be created. This approach will allow any advances made in any one component to lead directly to an advancement of the wholeprogram. This modularity will thus enable developers from different disciplines to focuson their own area of expertise (i.e model description, numerical integration methods,parallelization) without needing to simultaneously work on the other areas. BIDOSIMwill be used to evaluate the use of structured and unstructured finite volume methods,that involve quadrilateral and triangular grids, to discretize the computational domainsof interest. The speed, accuracy and ability of both types of methods will be examinedusing explicit and implicit time stepping algorithms. To ensure that the spatialdiscretization methods are able to accommodate any advances in the dynamical models of the ion fluxes across the membrane state-of-the-art kinetic models, such as the Lucfludy II ventricular and Nygren atrial models, will be evaluated over a range of physiological conditions. Finally, strategies for using spatially adaptive gridding in regions with abrupt changes in tissue properties, such as those expected in diseased myocardium, will be developed. Such adaptation will allow significantly fewer grid points and enable the ability to distinguish better artifact from true behavior. The development of the overall software package will be enhanced through feedback from an outside group of users and dissemination will be facilitated through partnerships with two national centers, NCSA and the Center for Bioelectric Field Simulation.