Showing papers by "Ewa Majchrzak published in 2011"

Identification of electromagnetic field parameters assuring the cancer destruction during hyperthermia treatment

Abstract: Electromagnetic field induced by two external electrodes and temperature field resulting from electrode action in the domain of biological tissue being a composition of healthy region and a tumour is considered. To warrant the optimum conditions of tumour destruction, the magnetic nanoparticles are embedded in this region. It is assumed that the temperature which assures an effect of destruction should be higher than 42°C. In this article, the problems relating to the electrodes’ electric potential identification and the simultaneous identification of potential and number of nanoparticles introduced to the tumour region are discussed. Additional information necessary to solve the task results from the postulated temperature inside the tumour region assuring its destruction. The problem has been solved using both the gradient method and evolutionary algorithm. The boundary element method is applied to solve the coupled problem connected with the heating of biological tissues.

Numerical Modelling of Hyperthermia and Hypothermia Processes

Abstract: In the paper the results of different numerical solutions of bioheat transfer problems are presented. The base of numerical algorithms constitute the models containing the bioheat transfer equation (or equations) and the adequate geometrical, physical, boundary and initial conditions. In the first part of the paper the solutions concerning the transient temperature field in the biological tissue subjected to the strong external heat sources (freezing, burns) are presented. Next, the examples of sensitivity analysis application in the range of bioheat transfer are discussed. In the final part of the paper the inverse problems are formulated and the example concerning the identification of thermal parameters is shown.

Numerical modelling of the cancer destruction during hyperthermia treatment

Abstract: Electromagnetic field induced by two external elect rodes and temperature field resulting from electrod es action in 3D domain of biological tissue is considered. To assure the opti mum conditions of destruction the magnetic nanoparticles are introduced to the tumor-domain analyzed. External electric field caus es the heat generation in tissue domain. The distri bution of electric potential in domain considered is described by the Laplace equat ion, while the temperature field is described by th e Pennes equation. These problems are coupled by source function being the a dditional component in Pennes equation and resultin g from the electric field action. The problem is solved by means of the bound ary element method. In the final part of the paper the examples of computations are shown.

Shape sensitivity analysis. Implicit approach using boundary element method

Abstract: The Laplace equation (2D problem) supplemented by b oundary conditions is analyzed. To estimate the changes of temperature in the 2D domain due to the change of local geometry of the boundary, the implicit method of sensitivity analysis is used. In the final part of the paper, the example of numerical c omputations is shown. Introduction To estimate the changes of temperature in a 2D doma in due to the change of local geometry of the boundary, the methods of sensit ivity analysis can be applied [1-5]. There are two basic approaches to sensitivit y analysis using boundary element formulation: the continuous approach and the d iscretized one [6]. In the continuous approach (explicit differentiation method), the analytical expressions for sensitivities are derived and then they are calcula ted numerically using the BEM. They have the form of boundary integrals with integ rands that depend only on the variables of the primary as well as additional prob lems. The implicit differentiation method, which belongs to the discretized approach, is based on the differentiation of algebraic boundary element matrix equations. The derivatives of boundary element system matrices can be calculated either analy tical or semi-analytically. In the paper the implicit differentiation method of se n itivity analysis for a steady state problem is presented 2 2 2 2 ( , ) ( , ) ( , ) : 0 ∂ ∂ ∈Ω λ + λ = ∂ ∂ T x y T x y x y x y (1) where λ [W/(mK)] is the thermal conductivity, T is the temperature and x, y are the geometrical co-ordinates. Equation (1) is s upplemented by boundary conditions Please cite this article as: Ewa Majchrzak, Katarzyna Freus, Sebastian Freus, Shape sensitivity analysis. Implicit approach using boundary element method, Scientific Research of the Institute of Mathematics and Computer Science, 2011, Volume 10, Issue 1, pages 151-161. The website: http://www.amcm.pcz.pl/ E. Majchrzak, K. Freus, S. Freus 152 1 2 3 ( , ) : ( , ) ( , ) : ( , ) ( , ) ( , ) : ( , ) ( , ) [ ( , ) ] ∞ ∈Γ = ∈Γ = −λ ⋅ ∇ = ∈Γ = −λ ⋅ ∇ = α − b b x y T x y T x y q x y T x y q x y q x y T x y T x y T n n (2) where Tb is the known boundary temperature, qb is the known boundary heat flux, α [W/(m K)] is the heat transfer coefficient and T∞ is the ambient temperature. 1. Boundary element method for Laplace equation The boundary integral equation for the problem desc ribed by equations (1), (2) is the following [7, 8] ( , ) : ( , ) ( , ) ( , , , ) ( , )d = ( , , , ) ( , )d B T T x y q x y q x y T x y ∗ Γ ∗ Γ ξ η ∈Γ ξ η ξ η + ξ η Γ ξ η Γ ∫ ∫ (3) where ( , ) (0,1) ξ η ∈ B is the coefficient connected with the local shape o f the boundary, ( ξ,η) is the observation point, ( , ) ( , ), ( , , , ) ∗ = −λ ⋅ ∇ ξ η q x y T x y T x y n is the fundamental solution 1 1 ( , , , ) ln 2 ∗ ξ η = πλ T x y r (4) where r is the distance between points ( ξ,η) and (x,y) 2 2 ( ) ( ) = − ξ + − η r x y (5) Function ( , , , ) ∗ ξ η q x y is defined as follows: ( , , , ) ( , , , ) ∗ ∗ ξ η = −λ ⋅ ∇ ξ η q x y T x y n (6) and it can be calculated analytically 2 ( , , , ) 2 ∗ ξ η = π d q x y r (7) where ( ) ( ) = − ξ + − η x y d x n y n (8) while nx, ny are the directional cosines of normal outward vecto r n. Shape sensitivity analysis. Implicit approach using boundary element method 153 2. Numerical realization of boundary element method In numerical realization of the BEM, the boundary i s d vided into N boundary elements and integrals appearing in equation (3) ar e substituted by the sums of integrals over these elements

Application of General Boundary Element Method for Numerical Solution of Bioheat Transfer Equation

Abstract: The heat transfer processes proceeding in domain of living tissue are discussed. The typical model of bioheat transfer bases, as a rule, on the well known Pennes equation (heat diffusion equation with additional terms corresponding to the perfusion and metabolic heat sources). Here, the other approach basing on the dual-phase-lag equation (DPLE) is considered. This equation is supplemented by the adequate boundary and initial conditions. To solve the problem the general boundary element method is adapted. The examples of computations for 2D problem are presented in the final part of the paper.

Numerical analysis of heat transfer in countercurrent blood flow and biological tissue

Abstract: Bioheat transfer in biological tissue is described by the Pennes equation, while the change of blood temperature along the artery an d vein is described by ordinary differential equations, at the same time the counte rcurrent blood flow is taken into account. The coupling of these equations results from the bo undary conditions given by the blood vessel walls. There are two methods used here in or der to calculate the temperatures along the blood vessels and across biological tissue. To solve the Pennes equation, the Multiple Reciprocity Boundary Element Method (MRBEM) is appl ied. It should be pointed out that this method does not require discretisation of the int rior of the domain. The second method used in this paper is the Finite Difference Method (FDM) and it is applied to calculate the temperatures along the blood vessels, and it comple ments the previous one. It is important to note that the diameter of an artery is smaller t han of a vein, which results from the physiological characteristics of these blood vessel s. In the final part of the paper, the results of the computations are shown and conclusions are f ormulated. 1. Governing equations Biological tissue is heated by a pair of blood vess els located at the central part of the tissue cylinder, as shown in Figure 1. Fig. 1. Pair of blood vessels (Krogh-type tissue cy linder) Γ Γ Γ

Axisymmetric modeling of ultrashort-pulse laser interactions with thin metal film

Abstract: The hyperbolic two-temperature model is used in order to describe the heat propagation in metal film subjected to an ultrashort-pulse laser heating. An axisymmetric heat source with Gaussian temporal and spatial distributions has been taken into account. At the stage of numerical computations the finite difference method is used. In the final part of the paper the examples of computations are shown.