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NJIT Mathematical Biology Seminar

Tuesday, September 21, 2010, 2:30pm
Cullimore Hall 611
New Jersey Institute of Technology

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Shape optimization for tumor location

Cristina Turner

Department of Matheamtics, FAMaF, Universidad Nacional de Cordoba

n non-invasive thermal diagnostics, accurate correlations between the thermal image on skin sur- face and interior human physiology are often desired, which require general solutions of the bioheat equation. In this work an estimation methodology to determine unknown geometrical parameters of an embedded tumor is proposed. We de.ned a functional that represents the mismatch between a measured experimental temperature pro.le, may be obtained by infrared thermography, at the skin surface and the solution of an appropriate boundary problem. This functional is related with the geometrical parameters through the solution of the boundary problem, in such a way that .nding the minimum of this functional form also means to .nd the unknown geometrical parameters of the embedded tumor. The Barzilai and Borwein gradient method was implemented to solve the optimiza- tion problem of .nding the optimal geometric parameters and sensitivity analysis using the adjoint method was considered to compute the shape derivative of the functional.