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by Mauro Perego
This talk concerns mathematical and numerical modeling of two medical
applications: cerebral focal ischemia and action potential propagation.
Cerebral ischemia can be caused by an artery occlusion. As a consequence
of occlusion, focal ischemia occours with possible tissue degeneration. A
major problem while treating the ischemia is that pharmacological
reperfusion of the brain could lead to hemorrhage. The proposed model
includes a space dependent description of the blood dynamics considering
the brain as a porous medium and a description of tissue byochemics:
tissue metabolism (ATP synthesis, oxygen partial pressure and glucose
consumption), ionic disorder (spreading depression phenomenon) and tissue
damage caused by the reduction in the flow rate. 3D simulations on simple
geometries are presented.
Action potential propagation in the myocardial tissue is described using
the Bidomain macroscopic model, coupled with models for the ionic cell
currents (Rogers-McCulloch, Luo-Rudy). Since solving the Bidomain model is
very expensive, methods to reduce its computational costs without losing
accuracy are investigated. In particular we present a preconditioner for
the Bidomain system based on the simplified Monodomain model. A posteriori
error estimator based on the Monodomain solution and adaptive modeling
strategies are presented as well. This is a joint work with L.
Gerardo-Giorda, F. Nobile, L. Mirabella and A. Veneziani.
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