### Math Biology Seminar Abstracts

Wednesday April 23, 2003

## "Comparing closures for a multiple scale, continuum model of platelet aggregation."

Bob Guy

Dept. of Mathematics,
University of Utah

Abstract:
A continuum model of platelet aggregation in large arteries is
presented. The blood and aggregating platelets are treated as a
single fluid with varying material properties to account for links
between platelets. There are two distinct spatial scales, the scale
of the fluid and the much smaller scale of platelet--platelet
interactions. Activated platelets interact to form elastic links on
the smaller scale. These links influence the fluid flow by the
addition of an extra stress.

The presence of two spatial scales makes the problem extremely
difficult to analyze or to simulate. However, under the assumptions
that the links act as linear springs with zero resting length and the
breaking rate of the links is independent of the strain, the equations
on the platelet scale can be eliminated in favor of an evolution
equation for the stress tensor. Some approximations for allowing the
breaking rate of a link to depend on its length while only working
with variables on the fluid length scale are presented. These
approximations are compared with the exact solution for simple flows
and compared with numerical results for more complicated flows.

For more information contact J. Keener, 1-6089

E-mail:
keener@math.utah.edu