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1

Analysis of the effect of external heating in the human tissue: A finite element approach

Sannyal Mridul, Mukaddes Abul, Rahman Md. Matiar, Mithu M. A. H.

Polish Journal of Medical Physics and Engineering

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2020

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Vol. 26, Iss. 4

251--262

EN

Thermal therapy which involves either raising or lowering tissue temperature to treat malignant cells needs precise acknowledgment of thermal history inside the biological system to ensure effective treatment. For this purpose, this study presents a two-dimensional unsteady finite element model (FEM) of the bioheat transfer problem based on Pennes bio-heat equation to analyze the thermal response of tissue subject to external heating. Crank-Nikolson scheme was used for the unsteady solution. A finite element code was developed using C language to calculate results. The obtained numerical result was compared with the analytical and other numerical results available in the literature. A good agreement was found from the comparison. Temperature distribution inside the human body due to constant and sinusoidal spatial and surface heating were analyzed. Response to point heating was also investigated. Moreover, a sensitivity analysis was carried out to know the effect of various parameters, i.e. blood temperature, thermal conductivity, and blood perfusion rate on tissue temperature. The outcome of this study will be helpful for the researchers and physicians involved in the thermal treatment of human tissue.

2

Cattaneo-Vernotte bio-heat transfer equation. Identification of external heat flux and relaxation time in domain of heated skin tissue

Mochnacki Bohdan, Paruch Marek

Computer Assisted Methods in Engineering and Science

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2018

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Vol. 25, no. 2-3

71--80

EN

A cylindrical skin tissue domain subjected to an external heat flux is considered. Thermal processes in the domain considered are described by the Cattaneo-Vernotte equation supplemented by the appropriate boundary and initial conditions. The aim of considerations is the identification of external heat flux and relaxation time on the basis of ‘measured’ heating/cooling curves at the set of selected points located on the surface of the skin. The direct problem is solved using the implicit scheme of the Finite Difference Method (FDM), while at the stage of the inverse problem solution, the evolutionary algorithm is applied. In the final part of the paper the examples of computations are presented.

3

Numerical analysis of thermal processes in the system protective clothing – biological tissue subjected to an external heat flux

Mochnacki B., Duda M.

Journal of Applied Mathematics and Computational Mechanics

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2016

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Vol. 15, nr 2

85--93

EN

The non-homogeneous fragment of biological tissue is considered. Its shape roughly corresponds to the fragment of cross-section of the upper or lower limb. The tissue domain is protected by a layer of protective clothing. The purpose of numerical computations is to examine the effectiveness of the clothing insulation layer on the action of the external heat fluxes of differing intensity. Thermal processes in the tissue domain are described by the system of the Pennes equations. This system is supplemented by the appropriate boundary-initial conditions and the energy equations determining the transient temperature field in the fabric and air gap sub-domains (the air gap is treated as a solid body). At the stage of numerical computations, the program MSC. Marc has been used. In the final part of the paper, the examples of numerical simulations and also the conclusions are presented.

4

Simulations of thermal processes in tooth proceeding during cold pulp vitality testing

Ciesielski M., Mochnacki B., Siedlecki J.

Acta of Bioengineering and Biomechanics

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2016

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Vol. 18, no. 3

33--41

EN

Purpose: This paper deals with the mathematical modeling of the thermal processes occurring in the tooth, during a very brief contact (a few seconds) with a very cold liquid on a part of the tooth crown. In this way one can simulate a heat transfer in tooth proceeding during a dental diagnostic test - pulp vitality testing. The impact of rapid ambient thermal changes acting on the tooth can cause toothache. Methods: The mathematical model: a system of partial differential equations with initialboundary conditions (the axially-symmetrical problem) and their numerical solutions using the control volume method is discussed. Results: Simulation results of the kinetics of the temperature changes inside the tooth are presented. The example of the control volume mesh (using the Voronoi polygons) well describing the shape of a molar tooth is given. Conclusions: The simulation results (the temperature distribution in the tooth at any moment of the simulation time and the kinetics of temperature variation at the points of the considered tooth domain) can help dentists in the selection of an appropriate method of treatment.

5

Bioheat transfer equation : the problem of FDM explicit scheme stability

Tuzikiewicz W., Duda M.

Journal of Applied Mathematics and Computational Mechanics

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2015

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Vol. 14, nr 4

139--144

EN

In the paper the problem of explicit FDM scheme stability for the bio-heat transfer equation (the Pennes equation) is discussed. To formulate the appropriate condition the von Neumann approach is applied. The first chapter contains the known derivation of FDM stability condition for the Fourier equation. In the second part, a similar condition is found for the case of the bio-heat transfer equation containing both the perfusion and metabolic heat sources.

6

Sensitivity analysis and inverse problems in bio-heat transfer modelling

Majchrzak E., Mochnacki B.

Computer Assisted Mechanics and Engineering Sciences

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2006

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Vol. 13, No. 1

85-108

EN

In the paper the problems connected with numerical modelling of bio-heat transfer processes are discussed. The mathematical model of phenomena discussed bases on the Pennes equation, at the same time the steady and transient tasks are considered. The basic equation is supplemented by the adequate geometrical, physical, boundary and (in the case of transient heat transfer) initial conditions. In the first part of the paper the examples of direct solutions are discussed. Next the possibilities of sensitivity analysis applications in the domain of bio-heat transfer are presented. In the final part the selected solutions of inverse problems are shown. On the stage of numerical simulations both in the case of direct and inverse problems, as a rule, the different variants of the boundary element method have been used.

7

Analysis of thermal processes occuring in tissue with a tumor region using bem

Majchrzak E., Mochnacki B.

Journal of Theoretical and Applied Mechanics

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2002

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Vol. 40 nr 1

101-112

EN

In the paper a numerical algorithm based on the boundary element method is used for temperature field computations in the non-homogeneous domain being a composition of healthy tissue and a tumor region. Thermophysical parameters of subdomains, in particular the perfusion coefficients and metabolic heat sources are different. From the mathematical point of view the problem is described by a system of two Poisson's equations with temperature-dependent source functions. These equations are supplemented by adequate boundary conditions. The discussed algorithm allows one to determine the temperature distribution on the surface of the skin. In this way it is possible to analyse the dependence brtween the geometrical features of the tumor region and the external thermal effects. The results can be useful as the information for noninvasive diagnostics. In the final part of the paper examples of computations are shown.

PL

Algorytm numeryczny bazujący na metodzie elementów brzegowych wykorzystano do obliczeń rozkładów remperatury w obszarze niejednorodnym, składającym się ze zdrowej tkanki i podobszaru nowotworowego. Parametry termofizyczne tych podobszarów są zróżnicowane, a w szczególności różnią się współczynniki perfuzji krwi oraz składniki źródłowe związane z metabolizmem. Z matematycznego punktu widzenia rozważane zagadnienie opisane jest układem dwóch równań z zależnymi od temperatury składnikami źródłowymi. Równania te uzupełniają odpowiednie warunki brzegowe. Przedstawiony algorytm pozwala określić rozkład temperatury na powierzchni tkanki skórnej. W ten sposób można analizować zależności między wielkością, kształtem i położeniem podobszaru nowotworowego, a zewnętrznymi efektami termicznymi. Uzyskane wyniki mogą być przydatne w diagnostyce nieinwazyjnej. W końcowej części artykułu przedstawiono przykłady obliczeń.

8

Numerical modelling of bio-heat transfer using the boundary element method

Majchrzak E.

Journal of Theoretical and Applied Mechanics

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1998

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nr 2

437-455

EN

Numerical models of heat transfer processes proceeding in a biological tissue subjected to a strong external thermal interaction are discussed. In this case one can consider diametrically different phenomena; such as burns resulting from thermal contact of the skin with an external heat source, or the freezing process of biological tissue used in cryosurgery. From the mathematical point of view these processes belong to the group of boundary-initial problems described by the diffusion equation and adequate boundary-initial conditions. At the stage of numerical realization the boundary element method can be applied and such an approach is discussed in this paper.

PL

W pracy przedstawiono opisy matematyczne i modele numeryczne procesów cieplnych zachodzących w tkance biologicznej poddanej silnym termicznym oddziaływaniom zewnętrznym. Można tu rozpatrywać skrajnie różne zjawiska, takie jak oparzenia wynikające z kontaktu skóry z zewnętrznym źródłem ciepła, lub też proces zamrażania tkanki w czasie zabiegu kriochirurgicznego. Z matematycznego punktu widzenia procesy te należą do grupy zadań brzegowo-początkowych opisanych równaniami dyfuzji i odpowiednimi warunkami jednoznaczności. Na etapie realizacji numerycznej można wykorzystać metodę elementów brzegowych i takie właśnie podejście jest prezentowane w niniejszej pracy.