We propose to develop, construct, and refine mathematical and computational multi-scale models which will link macroscopic electrical impulse propagation in the heart to underlying membrane-based sub-cellular ionic currents and other intercellular and intracellular metabolic processes, in ways which preserve anatomical architecture of the heart. Such a model will incorporate more realistic physiology and anatomy while avoiding many of the spatial averaging problems of current bi-domain models. Individual sub-cellular and membrane parameters cannot be measured during propagation. By creating propagating models which include these parameters, we seek to create a new understanding of electrical impulse propagation in the heart and in other excitable tissue, such as nerve and muscle. Moreover similar techniques can also be used to model abnormal electrical activity in the brain, which contributes to epilepsy, and abnormal electrical activity in the gastrointestinal tract, a major cause of GI motility disorders. Most previous large scale models of this type have incorporated various simplifications of the cellular architecture in the interest of computational efficiency. Such assumptions have produced results which have not always withstood close experimental scrutiny. In order to allow for fundamentally important tissue architectural complexities, we will continue the development of new modeling techniques which bridge across scales and which employ high order explicit time-integrators so that they can run efficiently using parallel computation on distributed memory clusters of multiprocessors. This will allow for efficient simulations of an entire ventricle or whole heart without averaging out the effects of the discrete cellular nature of the heart. Since both the sub-cellular and macro aspects of these studies can be treated with varying degrees of complexity, we will incorporate modular libraries, starting with the library developed using cellML, an XML derived modeling language, under the IUPS Physiome project. These modular libraries can be used to make trade-offs between complexity and speed of execution which are appropriate for a given model. We have already had substantial success at employing newer explicit numerical integration techniques in both physical and biological problems. In order to further exploit these newer techniques in a biological environment in a way which is efficient and scalable, new university collaborations have been formed between the Biomedical Engineering Department, located at the Health-Science Center in Memphis, and the Mathematics Department, located on the main campus in Knoxville. We will create a modest sized cluster of parallel computers at each of the performance sites with the ability to link them across the network with very high performance communications channels. Software developed in this more coarsely linked, clustered environment will be useful for constructing even larger scale models to run in computational grid environments of hundreds to thousands of processors and associated distributed memory. PUBLIC HEALTH RELEVANCE After 50 years of experimentation and modeling, it is still not known whether lethal cardiac arrhythmias usually arise from a single "irritable" focus (enhanced automaticity) and are then propagated to the rest of the heart or, alternatively, that the primary abnormality is a disorder of propagation itself (reentry). Similarly, in the neurosciences, it is not really known how often epilepsy is due to a single "irritable" focus in the brain and how often the primary disorder is in the propagation of impulses through connecting fibers of the brain itself. We seek support to develop modeling tools based on newer mathematical techniques and newer knowledge of anatomy and physiology to try to answer these questions.