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Temperature determination in the tissue with a tumor using MRBEM and FEM

Paruch M., Dziewoński M., Kokot G.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2005

Vol. 4, nr 1

195-203

The numerical algorithms based on the boundary element method and finite element method are used for the temperature field computations in the non homogenous domain being the composition of healthy tissue and the tumor region. The three dimensional problem is considered. Thermophysical parameters of sub-domains, in particular the perfusion coefficients, thermal conductivities and the metabolic heat sources are different. From the mathematical point of view the problem is described by the system of two Poisson's equations with temperature-dependent source functions. These equations are supplemented by the adequate boundary conditions. The algorithms discussed allow, among others, to determine the temperature distribution on the surface of the skin. In the final part of the paper the examples of computations are shown.

Modelling of thermal processes occuring in the tissue with a tumor with regard to parameter sensitivity analysis

Majchrzak E., Paruch M., Drozdek J.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2004

Vol. 3, nr 1

133--142

The numerical algorithm based on the multiple reciprocity boundary element method is used for the temperature field computations in the non-homogeneous domain of healthy tissue and the tumor region. The thermophysical parameters of tumor, in particular the perfusion rate, the metabolic heat source and the thermal conductivity are essentially bigger than for healthy tissue. From the mathematical point of view the problem is described by the system of two Poisson's equations supplemented by the adequate boundary conditions. The main subject of the paper is the sensitivity analysis of temperature distribution with respect to the thermal parameters of tumor region and healthy tissue. In the final part of the paper the examples of computations are shown.