This subproject is one of many research subprojects utilizing theresources provided by a Center grant funded by NIH/NCRR. The subproject andinvestigator (PI) may have received primary funding from another NIH source,and thus could be represented in other CRISP entries. The institution listed isfor the Center, which is not necessarily the institution for the investigator.We consider two applications with vast potential to exploit the Grid for societal benefit, in conjunction with Grid tool developers who have NSF funding together with us, in part to use these applications as a testbed for Grid monitoring and allocation algorithmic and software development. Inverse problems and image registration problems offer interesting resource assessment and allocation challenges, having real-time aspects. The need to process noninvasive imaging data to invert for properties of a biological medium from surface measurements, and to register medical images, arises in variety of research and clinical settings. A variety of inversion and registration techniques exist that are formulated as optimization problems subject to particular constraints and regularizations. Three-dimensional versions of these problems are computationally complex and often require parallel implementation of an individual task. Ensembles of these parallel tasks further exploit the concurrency of the Grid. In this development project, we specifically consider distributed parameter identification problems for the FitzHugh-Nagumo model of electrocardiology. The model describes the evolution of electrical potentials and ion concentrations in heart tissues. The mathematical problem is to reconstruct physical parameters in the system through partial knowledge of its solutions on the boundary of the domain. We present a parallel algorithm of Newton-Krylov type that combines Newton's method for numerical optimization with Krylov subspace solvers for the resulting Karush-Kuhn-Tucker system. We have shown by numerical simulations that parameter reconstruction can be performed from measurements taken on the boundary of the domain only. We need to do wide parameter sweeps to understand the effects of both physical and algorithmic parameters on the quality of reconstructions, to influence practice and possibly to stimulate theory.
Showing the most recent 10 out of 292 publications
