Transient bioheat transfer analysis in biological tissues by fundamental-solution-based numerical methods

Abstract

Taylor's expansion approach was applied to linearize the nonlinear term in the original nonlinear bioheat transfer governing equation. Then the DRM and the MFS was established to obtain the particular and homogeneous solutions. The influence of blood perfusion rate on temperature distribution in the skin tissue was analysed by changing the coefficients in the three expressions of blood perfusion rate. Numerical results showed that the variation of blood perfusion rate plays a significant role in the temperature distribution within the skin tissue. Finally, a meshless numerical scheme combining the operator splitting method (OSM), the RBF interpolation and the MFS was developed for solving transient nonlinear bioheat problems in two-dimensional skin tissue. In the numerical scheme, the nonlinearity caused by the temperature-dependent blood perfusion rate (TDBPR) is taken into consideration. In the procedure, the OSM is used to separate the Laplacian operator and the nonlinear source term, and then second-order time-stepping schemes are employed for approximating two splitting operators in order to convert the original governing equation into a linear nonhomogeneous Helmholtz-type governing equation (NHGE) at each time step. The full fields consisting of the particular and homogeneous solutions are enforced to fit the NHGE at interpolation points and the boundary conditions at boundary collocations to determine unknowns at each time step. The proposed method was verified by comparison with other methods. Furthermore, the sensitivity of the coefficients in cases of a linear and an exponential relationship of TDBPR was investigated to reveal their bioheat effect on the skin tissue.