Fluid dynamics problems encountered in engineering disciplines typically involve boundaries whose positions are known in advance. Examples are the fixed boundaries of flow in conduits or the moving boundary presented by an engine-driven propellor. By contrast, fluid dynamics problems encountered in biological disciplines involve flexible boundaries whose position is the result of the boundaries' interactions with the fluid in which it is immersed. This interaction also plays a critcal role in determining the fluid motion as well. Knowing the boundary position in advance greatly simplifies computational fluid dynamics in engineering; not knowing it in advance greatly complicates computational fluid dynamics in biology.

We have developed the "Immersed Boundary Method," a general approach which simplifies the computation of flows in the presence of moving elastic boundaries. We have applied this approach to the study of flow in the chambers and nearby great vessels of the human heart.

This talk will describe the Immersed Boundary Method (briefly) and the construction of a three-dimensional computer model of the human heart (based on the observed fiber anatomy of mammals). Results of computations of blood flow in the model (including some computer-generated videos) will be shown.

This is joint work with Charles S. Peskin, Courant Institute of Mathematical Sciences, New York University

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  1998-1999 Mathematics in Biology