[Acmsmajors] This week's Undergraduate Mathematical Sciences
miller at math.washington.edu
Tue Jan 10 10:25:03 PST 2006
Undergraduate Mathematical Sciences Seminar
Speaker: Kirsten Fagnan, UW Applied Mathematics Graduate Student
Title: Numerical Modeling of Extracorporeal Shock Wave Therapy with Finite
Abstract: Extracorporeal Shock Wave Therapy (ESWT) is a noninvasive technique
for the treatment of a variety of musculoskeletal conditions such as delayed
union of fractures, plantar fascitis and calcified tendonitis of the shoulder.
Shock waves were first used medically as lithotripsy to pulverize hardened
calcified deposits such as kidney stones. This technique was first use beyond
lithotripsy to treat calcifications in the shoulder as these deposits are
similar to renal calculi. Later it was shown to improve bone regeneration in
the treatment of non-unions. In lithotripsy, a shock wave is generated in a
liquid bath, focused through the use of an ellipsoid reflector and it then
propagates into the body where it strikes the area of interest. Current
numerical models are limited to simplified situations because the
structure of the wave is highly nonlinear and therefore difficult to
model with traditional finite difference and finite element techniques.
I would like to use finite volume methods to capture this nonlinear
behavior and model the shock wave propagation in bone and tissue. This
approach has been successfully applied to many problems in acoustic or
elastic wave propagation in heterogeneous media.
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