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Numerical solution of bioheat transfer equation by means of the dual reciprocity BEM

100%

Drozdek J. , Majchrzak E.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2007

tom Vol. 6, nr 1

47-56

Application of the standard boundary element method for numerical solution of the bioheat transfer equation requires discretization not only the boundary but also the interior of the domain considered. It results from the presence of internal heat sources in the biological tissue (metabolic and perfusion sources). In this paper the variant of the BEM which is connected only with the boundary discretization is presented. It is the essential advantage of the algorithm proposed in comparison with the classical one. As example, the problem of temperature field computations in heating biological tissue domain is solved.

Application of the dual reciprocity boundary element method for numerical modelling of solidification process

80%

Majchrzak E. , Drozdek J. , Kałuża G. , Poteralska J.

tom Vol. 8, iss. 4

99-104

The dual reciprocity boundary element method is applied for numerical modelling of solidification process. This variant of the BEM is connected with the transformation of the domain integral to the boundary integrals. In the paper the details of the dual reciprocity boundary element method are presented and the usefulness of this approach to solidification process modelling is demonstrated. In the final part of the paper the examples of computations are shown.

Heating of tissue by means of the electric field : numerical model basing on the BEM

80%

Majchrzak E. , Drozdek J. , Paruch M.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2008

tom Vol. 7, nr 1

99-110

The domain of tissue is subjected to the action of electrodes located on the skin surface. External electric field causes the heat generation in tissue domain. The distribution of electric potential in domain considered is described by the Laplace equation, while the temperature field is described by the Pennes equation. These problems are coupled by source function being the additional component in Pennes equation and resulting from the electric field action. The coupled problem is solved using the boundary element method. 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

80%

Majchrzak E. , Paruch M. , Drozdek J.

tom 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.