THE METHOD OF FUNDAMENTAL SOLUTIONS FOR THE INVERSE TIME-DEPENDENT PERFUSION COEFFICIENT PROBLEM

THE METHOD OF FUNDAMENTAL SOLUTIONS FOR THE INVERSE TIME-DEPENDENT PERFUSION COEFFICIENT PROBLEM

F. S. Shahsahebi, J. Damirchi, A. Janmohammadi

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Abstract

This paper deals with an inverse problem associated with the bio-heat equa- tion in living tissue in the human body. The inverse problem consists of the identication of time-dependent perfusion coecient when the exact and noisy measurements of tem- perature at a xed space point x are specied. The numerical method for the retrieval of the unknown perfusion coecient is based on the method of fundamental solutions (MFS). By introducing the fundamental solution of the heat equation and theoretical properties of these solutions, the MFS is used in conjunction with the Tikhonov regular- ization method. The choice of the regularization parameter is based on L-curve criteria to obtain a stable solution. Our numerical approach for numerical dierentiation of discrete noisy data is focused on the iterated Tikhonov method due to ill-posedness of problem. Numerical results show the eciency and applicability of the proposed algorithm in approximation of unknown perfusion coecient.

Keywords

Inverse Parabolic Problem, Ill-Posed Problem, Regularization Method, The MFS Method.