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1
Content available remote Solving the dual-phase lag bioheat transfer equation by the generalized finite difference method
Turchan Ł.
Archives of Mechanics
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2017
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Vol. 69, nr 4-5
389--407
EN
The modeling of bioheat transfer process described by the dual-phase lag equation is considered. The basic equation is supplemented by the appropriate boundary-initial conditions. In the central part of the cylindrical domain the heated sub-domain is located. In this region the additional component determining the capacity of an internal heat source is taken into account. At the stage of numerical computations the generalized finite difference method (GFDM) is used. The GFDM nodes distribution is generated in a random way (with some limitations). The examples of computations for different nodes distribution and comparison with the classical finite difference method are presented. In the final part of the paper the conclusions are formulated.
2
Content available 1D generalized dual-phase lag equation. Sensitivity analysis with respect to the porosity
Kałuża G., Majchrzak E., Turchan Ł.
Journal of Applied Mathematics and Computational Mechanics
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2016
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Vol. 15, nr 1
49--58
EN
Thermal processes occurring in the heated tissue are described by the 1D generalized dual-phase lag equation supplemented by appropriate boundary and initial conditions. Using the sensitivity analysis method, the additional problem connected with the porosity is formulated. Both problems are solved by means of the explicit scheme of the finite difference method. In this way it is possible to estimate the temperature changes due to the perturbation of porosity. In the final part of the paper, the example of computation is shown and the conclusions are formulated.
3
Content available remote Modeling of skin tissue heating using the generalized dual phase-lag equation
Majchrzak E., Turchan Ł., Dziatkiewicz J.
Archives of Mechanics
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2015
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Vol. 67, nr 6
417--437
EN
This paper concerns the numerical modeling of skin tissue heating. To describe the analyzed process the system of three generalized dual phase-lag equations corresponding to the successive layers of the skin: epidermis, dermis and sub-cutaneous region is applied. On the surfaces between the layers the ideal thermal contact is assumed, on the skin surface the Neumann condition describing the external heating of tissue can be accepted, and on the remaining surfaces the no-flux condition is taken into account. Initial temperature of the tissue and the blood is known. The problem is solved using the explicit scheme of finite difference method. In the final part of the paper the results of computations are shown.
4
Content available Numerical analysis of artificial hyperthermia treatment
Turchan Ł., Majchrzak E.
Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska
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2014
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nr 1
48--53
EN
This paper presents numerical modelling of artificial hyperthermia treatment. Presented model takes into account not only the temperature distributions but also the thermal dose parameter. Obtaining of temperature distributions takes advantage of the generalized dual phase lag equation. For computer calculations the parallelized algorithm was prepared.
PL
Artykuł dotyczy numerycznego modelowania zabiegu sztucznej hipertermii. Analiza skuteczności zabiegu jest rozpatrywana nie tylko na podstawie czasoprzestrzennych rozkładów temperatury, ale także w oparciu o parametr dawki termicznej. Do modelowania przepływu ciepła w rozpatrywanym obszarze wykorzystano uogólnione równanie z dwoma czasami opóźnień. Na potrzeby obliczeń numerycznych napisano autorski program oparty o obliczenia równoległe.
5
Content available Solution of dual phase lag equation by means of the boundary element method using discretization in time
Majchrzak E., Turchan Ł.
Journal of Applied Mathematics and Computational Mechanics
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2013
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Vol. 12, nr 4
89--95
EN
The dual phase lag equation describing the temperature field in a 3D domain is considered. This equation supplemented by boundary and initial conditions is solved by means of the boundary element method using discretization in time, while at the same time the Dirichlet and Neumann boundary conditions are taken into account. Numerical realization of the BEM for the constant boundary elements and constant internal cells is presented. The example of computations concerns the temperature field distribution in a heated domain. The conclusions connected with the proper choice of time step and discretization of the domain considered are formulated.
6
Content available remote Numerical analysis of tissue heating using the bioheat transfer porous model
Majchrzak E., Turchan Ł.
Computer Assisted Methods in Engineering and Science
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2013
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Vol. 20, no. 2
123--131
EN
The paper concerns the modelling of artificial hyperthermia. The 3D domain including healthy tissue and tumor region is considered. Heat transfer processes proceeding in this domain are described by the Pennes model and next by the porous one. The external heating of tissue is taken into account by the introduction of internal source function to the equation considered. Both models are supplemented by the same geometrical, physical, boundary and initial conditions. At the stage of numerical simulation the explicit scheme of finite difference method is used. The examples of computations show the similarities and differences of solutions and allow to formulate the conclusions connected with the applications of the results obtained in the hyperthermia therapy.
7
Content available remote The Finite Difference Method for transient convection-diffusion problems
Majchrzak E., Turchan Ł.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2012
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Vol. 11, nr 1
63-72
EN
The convection-diffusion equation (1D problem) is considered. At first, the unknown temperature T is expanded into a Taylor series with respect to time taking into account its three components. Next, using the convection-diffusion equation and equation obtained from the differentiation of this equation, the way of temperature T computations is shown. In this new equation the high order derivatives with respect to spatial co-ordinate appear and the approximation of these derivatives is also discussed. The explicit scheme is used and the stability criteria are formulated. Finally, the results of computations are shown.
8
Analiza numeryczna temperatury i dawki termicznej w czasie zabiegu hipertermii
Majchrzak E., Turchan Ł.
Modelowanie Inżynierskie
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2011
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T. 10, nr 41
237-242
PL
Rozpatrywano obszar zdrowej tkanki �(sześcian) z centralnie umieszczonym podobszarem (sześcian) zmienionym chorobowo. Założono, że w celu destrukcji obszaru �, jest on przez pewien czas (czas ekspozycji) sztucznie nagrzewany. Zadanie opisano równaniem Pennesa uzupełnionym warunkami brzegowo-początkowymi. Na podstawie otrzymanych rozkładów temperatury wyznaczono dawkę termiczną TD.
EN
The domain of healthy tissue (cube) within centrally located pathological changed sub-domain (cube) has been considered. To destroy the tumor region , the temporary heating of this sub-domain has been assumed. The problem analysed has been described by the Pennes equation supplemented by boundary and initial conditions. Thermal dose assuring the proper effect of treatment has been estimated on the basis of calculated temperature distribution.
9
Content available remote Boundary element method for 3D Fourier-Kirchhoff heat transfer equation
Majchrzak E., Turchan Ł.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2010
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Vol. 9, nr 1
121-130
EN
The 3D heat transfer problem (steady state) is considered. The equation describing the thermal processes contains the convective term (substantial derivative). The problem is solved by means of the boundary element method. The numerical model for constant boundary elements and constant internal cells is presented. In the final part of the paper the examples of computations are shown. The numerical results obtained by means of the BEM are compared with analytical solution and the very good compatibility can be observed.
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