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1
Content available remote Modelling the tumor temperature distribution in anatomically correct female breast phantom
Gas Piotr, Miaskowski Arkadiusz, Dobrowolski Dariusz
Przegląd Elektrotechniczny
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2020
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R. 96, nr 2
146--149
EN
The presented paper focuses on a numerical analysis of temperature in the anatomical model of the female breast with a strictly defined level of power generated by the EMF source in pathological tissue saturated with ferrofluid. The aim of this study was to examine the effect of blood perfusion rate models on the resultant tumor temperature. The four tumor perfusion models were subjected to comparative analysis: constant, linear, nonlinear and completely free of blood flow. The authors have shown that taking into account the various temperature dependences of blood perfusion models within the treated tissue might play an important role in the complex process of female breast cancer treatment planning.
PL
Przedstawiona praca skupia się na numerycznej analizie temperatury w anatomicznym modelu gruczołu piersiowego kobiety o ściśle określonym poziomie mocy generowanej przez źródło PEM w patologicznej tkance nasyconej ferrofluidem. Celem tej pracy było zbadanie wpływu perfuzji krwi na wypadkową temperaturę guza. Analizie porównawczej poddano cztery modele perfuzji w guzie: stały, liniowy, nieliniowy oraz model całkowicie pozbawiony przepływu krwi. Autorzy pracy wykazali, że uwzględnienie różnych zależności temperaturowych dla modeli perfuzji krwi w leczonej tkance, może odgrywać istotną rolę w złożonym procesie planowania leczenia nowotworów piersi.
2
Content available Comparison of bio-heat transfer numerical models based on the Pennes and Cattaneo-Vernotte equations
Ciesielski M., Duda M., Mochnacki B.
Journal of Applied Mathematics and Computational Mechanics
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2016
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Vol. 15, nr 4
33--38
EN
The homogeneous soft tissue domain subjected to an external heat source is considered. Thermal processes in this domain are described using the well known Pennes equation and next the Cattaneo-Vernotte one. Within recent years the prevailing view is that the Cattaneo-Vernotte equation better describes the thermal processes proceeding in the biological tissue (it results from the specific internal tissue structure). Appearing in this equation the delay time of heat flux with respect to the temperature gradient (τq) is of the order of several seconds and the different values of τq are taken into account. At the stage of numerical modeling the finite difference method is used. In the final part of the paper, the examples of computations are shown.
3
Content available remote Mathematical modelling of heat transport in a section of human forearm
Nowakowska O., Buliński Z.
Computer Assisted Methods in Engineering and Science
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2015
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Vol. 22, no. 4
347--363
EN
The paper presents numerical analysis of heat transfer in the human forearm and influence of its internal structure on the temperature distribution inside. For this purpose three geometrical models of a human forearm were developed: model containing continuous muscle tissue only, model in which muscle tissue and bones were considered and model which contained muscle tissue bones and main blood vessels. In those models heat transfer in the muscle tissues and bones were described by Pennes bioheat equation, while for blood flowing through main vessels (artery and vein) full set of governing equations were solved. Moreover, simplified one-dimensional description of skin was developed in order to reduce model complexity. Results obtained with all models were confronted against each other to reveal influence of the main blood vessels on the temperature distribution in a forearm.
4
Content available remote Inverse heat transfer problems: an application to bioheat transfer
Rojczyk M., Orlande H. R. B., Colaço M. J., Szczygieł I., Nowak A. J., Białecki R. A., Ostrowski Z.
Computer Assisted Methods in Engineering and Science
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2015
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Vol. 22, no. 4
365--383
EN
In this work, we applied the Markov chain Monte Carlo (MCMC) method for the estimation of parameters appearing in the Pennes’ formulation of the bioheat transfer equation. The inverse problem of parameter estimation was solved with the simulated transient temperature measurements. A one-dimensional (1D) test case was used to explore the capabilities of using the MCMC method in bioheat transfer problems, specifically for the detection of skin tumors by using surface temperature measurements. The analysis of the sensitivity coefficients was performed in order to examine linear dependence and low sensitivity of the model parameters. The solution of the direct problem was verified with a commercial code. The results obtained in this work show the ability of using inverse heat transfer analysis for the detection of skin tumors.
5
Content available Temperature field in burned and healthy tissue : sensitivity analysis with respect to the thermal parameters
Freus K., Freus S., Majchrzak E.
Journal of Applied Mathematics and Computational Mechanics
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2014
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Vol. 13, nr 3
47--58
EN
A non-homogeneous system being the composition of burn wound and healthy tissue is considered. The heat exchange between sub-domains and environment is described by the system of partial differential equations (the Pennes equations) supplemented by the assumed boundary conditions. Additional problems associated with sensitivity analysis with respect to thermal parameters occurring in the mathematical model are formulated. Both the basic problem and additional ones concerning the sensitivity with respect to selected parameters are solved using the boundary element method. In the final part of the paper the results of computations are shown.
6
Content available Determination of the temperature field in burned and healthy skin tissue using the boundary element method. Part 2
Freus K., Freus S.
Journal of Applied Mathematics and Computational Mechanics
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2013
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Vol. 12, nr 3
47--54
EN
In the paper, the position of the boundary between burned and healthy tissue is described by the NURBS curve. The temperature field in the domain is calculated by means of the boundary element method. The influence of discretization on the temperature distribution in the burned and healthy skin tissue is analysed. Different numbers of boundary elements and internal cells are taken into account. In the final part of the paper the examples of computations are shown.
7
Content available Determination of the temperature field in burned and healthy skin tissue using the boundary element method. Part 1
Freus K., Freus S., Majchrzak E.
Journal of Applied Mathematics and Computational Mechanics
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2013
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Vol. 12, nr 3
39--46
EN
In the paper the burned and healthy layers of skin tissue are considered. The temperature distribution in these layers is described by the system of two Pennes equations. The governing equations are supplemented by the boundary conditions. On the external surface the Robin condition is known. On the surface between burned and healthy skin the ideal contact is considered, while on the internal surface limiting the system the body temperature is taken into account. The problem is solved by means of the boundary element method.
8
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.
9
Content available An interval finite difference method for the bioheat transfer problem described by the pennes equation with uncertain parameters
Jankowska M. A., Sypniewska-Kamińska G.
Mechanics and Control
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2012
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Vol. 31, no. 2
77-84
EN
In this paper the transient bioheat transfer problem given by the one-dimensional Pennes equation with mixed boundary conditions is considered. The model assumes the heat transfer between the skin and its surroundings in the case of a natural and forced convection. For computations the interval finite difference method of Crank--Nicolson type together with the floating-point interval arithmetic is used. In this way, uncertain geometric and thermophysical parameters can be represented in the form of intervals as well as the resultant temperature distribution over time.
PL
W pracy rozważa się nieustalone zagadnienie przepływu biociepła w skórze opisane równaniem Pennesa z mieszanymi warunkami brzegowymi. W modelu uwzględniono wymianę ciepła między skórą a otoczeniem zarówno w przypadku konwekcji swobodnej, jak i wymuszonej. Do obliczeń wykorzystano przedziałową metodę różnic skończonych typu Cranka-Nicolsona oraz zmiennopozycyjną arytmetykę przedziałową. W ten sposób nieprecyzyjnie określone wartości parametrów geometrycznych i termofizycznych mogą być reprezentowane w postaci przedziałów, podobnie jak wynikowy rozkład temperatury w czasie.
10
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.
11
Content available remote Numerical modelling of tissue heating by means of the electromagnetic field
Majchrzak E., Paruch M.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2010
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Vol. 9, nr 1
89-97
EN
Electromagnetic field induced by two external electrodes and temperature field resulting from electrodes action in 3D domain of biological tissue is considered. 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 boundary element method is applied to solve the coupled problem connected with the biological tissue heating. In the final part of the paper the examples of computations are shown.
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