Thursday, May 13

The John von Neumann Lecture:
The Immersed Boundary Method for Biological Fluid Dynamics

2:00 PM-3:00 PM
Room: Capitol Center/South
Chair: Gilbert Strang, SIAM President, and Massachusetts Institute of Technology

Biofluid dynamics is characterized by the interaction of elastic incompressible tissue with viscous incompressible fluid. In some cases the elastic tissue is active, like muscle, which means that it can act a source of mechanical energy. The Immersed Boundary Method is both a mathematical formulation and a computational method for the biofluid dynamic problem. In the immersed boundary formulation, the equations of fluid dynamics are used in an unconventional way, to describe not only the fluid but also the immersed elastic tissue with which it interacts. In the computational scheme that is motivated by this formulation, the fluid equations are solved on a fixed (Eulerian) cubic lattice, and elastic forces are computed from a Lagrangian representation of the immersed elastic tissue, the material points of which move freely through the cubic lattice of the fluid computation. The two components of this Eulerian/Lagrangian scheme are linked by a smoothed version of the Dirac delta function, which is used to apply elastic forces to the fluid, and to interpolate the fluid velocity at the representative material points of the elastic tissue. This methodology has been applied to the heart and its valves; the inner ear; the swimming of fish, sperm, and micro-organisms; the deformation and locomotion of cells; the clotting of blood; the collapse of thin-walled veins; and the regulatory contractions of muscular arterioles. Video animations depicting the results of some immersed boundary computations will be shown.

Charles S. Peskin
Courant Institute of Mathematical Sciences
New York University

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MMD, 2/2/99