A Combination of Laplace Transform and Meshless Method for Analysing Thermal Behaviour of Skin Tissues

A novel numerical model is developed for evaluating the temperature distribution on a two- dimensional skin tissue. The method is based on a combination of Laplace transform and meshless method as well as on the Pennes bio-heat equation. It is the first time to combine Laplace transform and RBF-MFS to study the performance of heat transfer in skin tissue governed by Pennes equation. First, Laplace transform of Pennes bio- heat equation is applied to handle the derivative of time variable. Then, the particular solution is approximated by a linear combination of radial basis functions, and the homogeneous solution is approximately determined by the method of fundamental solution. The multi-subdomain RBF-MFS technique is implemented for analyzing problems containing different materials and/or multi- connected regions. The last step of the algorithm is the inverse Laplace transforms from Laplace domain to time domain. The efficiency and availability of the proposed method is assessed by several examples including healthy tissue, tissue with tumour and burned tissue.