Numerical Solution of Bioheat Transfer Model using Generalized Wavelet Collocation Method

Abstract

In this article, we develop a a generalized wavelet collocation method based on a Haar wavelet to facilitate the solution of modified Pennes bio-heat transfer model during thermal therapy. The process of heat transfer in living biological tissue is studied under various coordinate systems. Contrary to the existing operational matrix methods based on orthogonal functions, we construct the Haar wavelet operational matrices of integration without using the block pulse functions. The temperature distribution inside a living biological tissue has been investigated for different estimations of thermal conductivity, antenna power constant, and surface
temperature. The numerical results obtained shows that the desired temperature occur faster in spherical symmetric coordinate as compared to axisymmetric coordinate where as temperature in axisymmetric coordinate occur faster in comparison to cartesian coordinate. The performance and accuracy of the proposed technique is elucidates by a comparison of the numerical outcomes with homotopy perturbation method and the exact solution of the model.

Key words and phrases. Bio-heat model; Coordinate system; Haar wavelet; Collocation method; Operational matrices.

2000 Mathematics Subject Classification. 42C40, 80M22, 35Q79, 65T60