GENERALIZED FINITE DIFFERENCE METHOD FOR BIOHEAT TRANSFER ANALYSIS ON SKIN TISSUE WITH TUMORS

Bioheat transfer analysis is widely used in clinical medical treatment and diagnosis, such as cryosurgery, tumor hyperthermia, disease diagnosis and so on. The presence of a tumor inside healthy skin tissues makes the temperature increment in the vicinity of the tumor. This characteristic is often used to detect tumor growth in skin tissue. Therefore it is necessary to do some numerical investigation on bioheat transfer analysis. Considering the skin tissue containing tumor, a novel meshless collocation method-generalized finite difference method (GFDM) is applied to Pennes bioheat equation, which can be used to describe the heat transfer process of the skin tissue containing tumors. Based on Taylor expansion and moving least squares method, the derivative of physical quantity at each discrete node can be expressed by the linear combination of physical quantities and weight coefficients at several adjacent nodes in the GFDM. Then the linear system of equations is constructed with the unknown physical quantities at discrete nodes. The proposed method not only has the advantages without mesh and numerical integration, but also overcomes the problem of highly ill-conditioned resultant matrix in most meshless collocation methods. It provides a possibility for the application of this kind of methods in large-scale engineering numerical calculation. The GFDM numerical model for simulating the bioheat transfer process in skin tissue with tumors is first introduced. Then the numerical accuracy and convergence of the GFDM are verified through some benchmark examples with/without regular-shaped tumors. Finally the effects of the arbitrary-shaped tumor including the location, geometry and size on the thermal behavior inside the skin tissue are investigated.