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Thursday, May 13

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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*

Additional information regarding the The John von Neumann Lecture
appears at archive.siam.org/prizes/vonneu.htm.

*MMD, 2/2/99*