MATHEMATICAL MODELING AND SIMULATION

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This subproject is one of many research subprojects utilizing the resources provided by a Center grant funded by NIH/NCRR. The subproject and investigator (PI) may have received primary funding from another NIH source, and thus could be represented in other CRISP entries. The institution listed is for the Center, which is not necessarily the institution for the investigator. MATHEMATICAL MODELING AND SIMULATION Subproject Description As a Center, we have established expertise in the area of simulation in bioelectric fields, have built on that expertise in the current funding period, and propose to continue to make this form of simulation a centerpiece of our future research activities. At the start of the Center, our focus was on passive electrical characteristics of the torso and head and their response to endogenous bioelectric sources (the heart and brain); we solved both forward problems based on known sources as well as inverse problems, in which we sought to identify and localize bioelectric sources from measurements on (or outside) the body surface. In recent years, we have also begun to simulate the bioelectric activity itself and thus to study the nature of bioelectric sources; these sources are highly dynamic and increased knowledge of their behavior will help improve our ability to predict the consequences of their function and disfunction in disease. We propose to continue this research, with emphasis on simulating the effects of myocardial ischemia and defibrillation on the heart and epilepsy and deep brain stimulation in the brain. In order to translate the discoveries and computational developments within the Center to the broader biomedical user community, we will continue to develop, publish, release, and support software that will incorporate models of dynamic bioelectric sources as well as the tools with which to create efficient solutions to the associated forward and inverse problems. One application of the simulation of bioelectric activity has been in the computation of the spread of excitation in microscopic models of myocardial tissue. The goal of this research was to address a long standing gap in the multiscale modeling of cardiac electrophysiology between the very evolved and well characterized behavior of cardiac cell membranes and the simulation of electrical activity in the whole heart. Simulation of the heart has advance mainly because there exist models at each of the meaningful scales, from stochastic models of ion channels to whole heart and torso. However, there is a need for simplification at each transition of scale and hence a requirement that results at one scale find an associated expression at the next. For example, a model of tissue must be able to incorporate the effects of changes in the behavior of the cell in order to mimic or predict pathophysiology of the mechanisms of pharmaceutics. It is also essential, and until recently a significant omission, in this translation across scales that changes in microscopic structure find expression in tissue level models. We have addressed this omission. The approach we have developed, which we have named "microdomain" modeling, is meant to incorporate structural information at the microscopic scale and then general parameters that feed into the tissue level simulation framework known as the "bidomain" approach. Each microdomain model we have created contains a modest number (30--150) of cardiac myocytes surrounded by a discrete extracellular space, which is also an explicit part of the model. The information for these models comes from microscopy and histology together with basic conductivities of electrolytes and the gap junctions that link myocytes. By tessellating the microdomain into millions of finite elements, it is possible to compute bulk values for both intracellular and extracellular, anisotropic conductivities, which are the equivalent parameters in the bidomain. The bidomain is the product of a homogenization process that removes this level of detail, incorporating it in a few tissue parameters. In this way, it is possible to include the effects of, for example, myocardial ischemia on changes in extracellular space on a small, microdomain and then compute the required bidomain parameters to predict the response of the whole heart to ischemia. In the past year, we have expanded the scope of the microdomain models to 132 cells, which is now large enough to represent the spread of activation and measure conduction velocities both along and across he fiber direction. This new model is the basis for one journal article submitted and a second nearing completion of final review. The novel aspect of especially the second article is that it describes a comparison of the spread of excitation in a microdomain and in a bidomain model with the same physical size and characteristics. We were able to show that under a reasonable range of conditions, i.e., varying parameters such as extracellular space and gap junction conductivities to represent both normal and ischemic myocardium, both models generate the same results. However, this is only true if the bulk conductivity parameters of the bidomain are derived from the microdomain simulations. Thus, we have developed a means of linking explicitly variations in microscopic geometry or electrical conductivity with the resulting variations in associated bidomain parameters, a link that was previously only possible through very coarse approximation. These two articles, along with two previous journal publications describing the passive characteristics of the microdomain, should form a solid body of work that, along with the conferences at which we continue to present these results, will establish this approach. The software required to carry out the simulations represents a merging of SCIRun and the Cardiowave software developed by the Duke Computational Electrophysiology group and is available through the CIBC website.