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1

Hyperthermia process control induced by the electric field in order to cancer destroying

Paruch M.

Acta of Bioengineering and Biomechanics

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2014

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Vol. 16, no. 4

123--130

EN

Purpose: The paper presents numerical modeling of the artificial hyperthermia induced by the electric field in order to destroy the abnormal tissue. In particular, the possibility of process control in order to increase the temperature of only the tumor tissue was discussed. Due to the fact, that the external electrodes which generate the additional heat, heats not only the area of the tumor, but also healthy tissue which surrounds the tumor, increasing the temperature inside the cancer is possible by introducing the paramagnetic nanoparticles into the interior. Additionally, the proper selection of voltage on the electrodes and the number of nanoparticles will achieve the optimal effect of hyperthermia treatment. Methods: The multiple reciprocity BEM is applied to solve the coupled problem connected with the biological tissue heating. In order to determine the appropriate values of the parameters the inverse problem has been formulated, connected with simultaneous identification of the voltage of the electrodes and the number of nanoparticles, which is solved using the evolutionary algorithm. Results: The changes of the voltage of electrodes cause the changes of temperature in the entire domain considered, but the possibilities of temperature field control (e.g. a concentration of maximum temperature at the central point of tumor) are rather unrealizable, because the maximum temperature we could observe in the neighbourhood of the electrodes. Conclusions: The idea consisting in the introduction of nanoparticles to the tumor region (for the concentrated energy deposition at the target tissue) is very effective. We obtain the maximum temperature exactly in the tumor domain.

2

Estimation of relaxation and thermalization times in microscale heat transfer model

Mochnacki B., Paruch M.

Journal of Theoretical and Applied Mechanics

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2013

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Vol. 51 nr 4

837--845

EN

The energy equation corresponding to the dual phase lag model (DPLM) results from the generalized form of the Fourier law, in which the two ‘delay times’ (relaxation and thermalization time) are introduced. The DPLM should be used in the case of microscale heat transfer analysis, in particular when thermal processes are characterized by extremely short duration (e.g. ultrafast laser pulse), considerable temperature gradients and very small dimensions (e.g. thin metal film). In this paper, the problem of relaxation and thermalization time identification is discussed, at the same time the heat transfer processes proceeding in the domain of a thin metal film subjected to a laser beam are analyzed. The solution presented bases on the application of evolutionary algorithms. The additional information concerning the transient temperature distribution on a metal film surface is assumed to be known. At the stage of numerical realization, the finite difference method (FDM) is used. In the final part of the paper, an example of computations is presented.

3

Cattaneo-Vernotte equation : identification of relaxation time using evolutionary algorithms

Mochnacki B., Paruch M.

Journal of Applied Mathematics and Computational Mechanics

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2013

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Vol. 12, nr 4

97--102

EN

The Cattaneo-Vernotte equation describing the heat conduction process in domain of solid body results from the generalization of the well - known Fourier law, in which the delay time’ (relaxation time τq) is introduced. The Cattaneo-Vernotte equation should be, among others, used in a case of microscale heat transfer analysis when the thermal processes are characterized by the extremely short duration (e.g. ultrafast laser pulse), the considerable temperature gradients and the very small dimensions (e.g. thin metal film). In the paper the problem of relaxation time identification is considered. In particular, the heat conduction process proceeding in domain of thin metal film subjected to a laser pulse is analyzed. The inverse problem solution is obtained using the evolutionary algorithms. The information concerning the time-dependent temperature distribution on the surface of metal film is assumed to be known. At the stage of numerical computations the finite difference method (FDM) is applied. In the final part of the paper the example of computations is shown.

4

Application of evolutionary algorithms for identification of dual phase lag model parameters

Mochnacki B., Paruch M.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

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2011

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Vol. 10, nr 1

189-198

EN

The dual phase lag model (DPLM) based on the generalized form of Fourier law, in particular the introduction of two 'delay times' (relaxation time τq and thermalization time τT) leads to the considered form of energy equation. This equation should be applied in the case of microscale heat transfer modeling. In particular, DPLM constitutes a good approximation of thermal processes which are characterized by extremely short duration (e.g. ultrafast laser pulse), extreme temperature gradients and geometrical features of the domain considered (e.g. thin metal film). In this paper, the identification problem of two of the above mentioned positive constants τq, τT is discussed and the thermal processes proceeding in the domain of thin metal film subjected to a laser beam are analyzed. At the stage of computations connected with the identification problem solution, evolutionary algorithms are used. To solve the problem, additional information concerning the transient temperature distribution on a metal film surface is assumed to be known.

5

Estimation of dual phase lag model parameters using the evolutionary algorithms

Mochnacki B., Paruch M.

Archives of Foundry Engineering

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2011

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Vol. 11, iss. 3 spec.

277--281

EN

Generalization of Fourier law, in particular the introduction of two ‘delay times’ (relaxation time τq and thermalization time τT) leads to the new form of energy equation called the dual-phase-lag model (DPLM). This equation should be applied in a case of microscale heat transfer modeling. In particular, DPLM constitutes a good approximation of thermal processes which are characterized by extremely short duration (e.g. ultrafast laser pulse), extreme temperature gradients and geometrical features of domain considered (e.g. thin metal film). The aim of considerations presented in this paper is the identification of two above mentioned positive constants τq, τT. They correspond to the relaxation time, which is the mean time for electrons to change their energy states and the thermalization time, which is the mean time required for electrons and lattice to reach equilibrium. In this paper the DPLM equation is applied for analysis of thermal processes proceeding in a thin metal film subjected to a laser beam. At the stage of computations connected with the identification problem solution the evolutionary algorithms are used. To solve the problem the additional information concerning the transient temperature distribution on a metal film surface is assumed to be known.

6

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.

7

Numerical modelling of temperature field in the tissue with a tumor subjected to the action of two external electrodes

Majchrzak E., Paruch M.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

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2009

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Vol. 8, nr 1

137-145

EN

The domain of tissue with a tumor subjected to the action of electrodes located on the skin surface is considered. External electric field causes the heat generation in the domain analyzed. The distribution of electric potential is described by the system of Laplace's equations, while the temperature field is described by the system of Pennes' equations. On the contact surface between healthy tissue and tumor region the ideal electric and ideal thermal contacts are assumed. To assure the optimum conditions of tumor destruction the magnetic nanoparticles are introduced to the tumor region. The aim of investigations is to determine the temperature field in the domain considered for different size and positions of external electrodes, in other words to choose such electrodes which assure the cancer destruction. To solve the coupled problem connected with the biological tissue heating the boundary element method is used. In the final part of the paper the examples of computations are shown.

8

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

Majchrzak E., Drozdek J., Paruch M.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

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2008

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Vol. 7, nr 1

99-110

EN

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.

9

Application of evolutionary algorithm for cast iron latent heat identification

Mendakiewicz J., Paruch M.

Archives of Foundry Engineering

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2008

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Vol. 8, iss. 4

115-120

EN

In the paper the cast iron latent heat in the form of two components corresponding to the solidification of austenite and eutectic phases is assumed. The aim of investigations is to estimate the values of austenite and eutectic latent heats on the basis of cooling curve at the central point of the casting domain. This cooling curve has been obtained both on the basis of direct problem solution as well as from the experiment. To solve such inverse problem the evolutionary algorithm (EA) has been applied. The numerical computations have been done using the finite element method by means of commercial software MSC MARC/MENTAT. In the final part of the paper the examples of identification are shown.

10

The modelling of heating a tissue subjected to external electromagnetic field

Majchrzak E., Dziatkiewicz G., Paruch M.

Acta of Bioengineering and Biomechanics

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2008

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Vol. 10, nr 2

31-36

EN

The boundary element method (BEM) is used to solve the coupled problem connected with the biological tissue heating. The tissue treated as a non-homogeneous domain (healthy tissue and tumor region) is subjected to external electromagnetic field. The thermal effect is produced by electrodes that touches the skin surface. External electromagnetic field generates the internal temperature field, which can be modelled by using the volumetric internal heat sources in the tissue domain (this source function constitutes one of components of the Pennes equation). In the paper, both BEM application to coupled bioheat transfer problems and numerical results of computations are theoretically considered. The successive examples show the different input data determining the electromagnetic field parameters.

11

Numerical simulation of bioheat transfer process in the human eye using finite element method

Paruch M.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

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2007

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Vol. 6, nr 1

199-204

EN

In this paper the finite element method is used for the numerical simulation of two dimensional transient bioheat transfer process in the human eye. The human eye is modelling as a composition of several homogeneous regions. On the outer surface the heat radiation is assumed, on the inner surface the Robin condition is accepted. In the final part of the paper the results of computations are shown.

12

Application of evolutionary algorithms in identification of solidification parameters

Majchrzak E., Mendakiewicz J., Paruch M.

Journal of Achievements in Materials and Manufacturing Engineering

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2007

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Vol. 23, nr 2

67-70

EN

Purpose: The casting-mould system is considered. Additionally, it is assumed that part of internal parameters determining the course of thermal processes, e.g. volumetric specific heat of mould, mould thermal conductivity, casting thermal conductivity and the like is unknown. Formulated in this way an inverse problem can be solved using different methods and in this paper the possibility of evolutionary algorithms application is presented. To solve the problem knowledge of cooling/heating curves at selected set of points from casting/mould domain is necessary. The evolutionary algorithm allows to minimize the fitness function containing the differences between the 'measured' cooling curves and the same curves found on the basis of boundary initial problem numerical solution for the assumed set of parameters. The calculated cooling/heating curves have been found using explicit scheme of finite difference method. It turned out that the algorithm proposed gives sufficiently exact results of identification and it can be successfully applied in the scope of thermal theory of foundry process. Design/methodology/approach: In this work numerical modelling of solidification process is applied. A cast iron solidifying in a sand mould is analyzed. The information concerning the courses of cooling/heating curves at the selected set of points from the domain considered is used in order to identify the unknown parameters of the process analyzed. Findings: Application of evolutionary algorithms gives sufficiently exact results of identification of solidification parameters. Research limitations/implications: Further work requires an introducing of real temperature measurements to the model presented. Practical implications: The paper shows the possibilities of solidification parameters identification on the basis of temperature measurements. Originality/value: The evolutionary algorithms presented allow to identify the parameters of solidification process e.g. volumetric specific heat of mould, mould thermal conductivity, casting thermal conductivity and the like.

13

Numerical simulation of the freezing process in biological tissue with tumor

Dziewoński M., Paruch M.

Zeszyty Naukowe Katedry Mechaniki Stosowanej / Politechnika Śląska

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2006

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z. 26

87-92

EN

In the paper the numerical simulation of freezing process of tissue with tumor is presented. In particular the action of external cylindrical cryoprobe is analyzed. On the stage of numerical simulations the finite element method (FEM) is applied. The computations have been done using the MSC MARC/MENTAT code supplemented by additional procedures taking into account the cyclic boundary conditions and temperature-dependent thermophysical parameters of the tissue and tumor [2].

14

Computer implementation of the dual reciprocity BEM for 2D Poisson's equation

Majchrzak E., Drozdek J., Ładyga E., Paruch M.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

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2006

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Vol. 5, nr 1

95-105

EN

In this paper the variant of the boundary element method called dual reciprocity BEM is presented. On the stage of numerical computations the DRBEM application for the Poisson equation allows to avoid the discretization of the interior of the domain considered. In the final part of the paper the results of computations are shown.

15

Numerical simulation of tumor region identification on the basis of skin surface temperature

Paruch M., Majchrzak E.

Acta of Bioengineering and Biomechanics

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2006

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Vol. 8, nr 2

143-150

EN

In the paper, the inverse problem consisting in the simultaneous estimation of the unknown geometrical parameters of the tumor region based on a local skin surface temperature is solved. The problem of thermal processes proceeding in the domain considered is described by the system of the Pennes equations and boundary conditions given on the outer and contact surfaces. In the stage of numerical solution, the evolutionary algorithm coupled with the multiple reciprocity boundary element method has been applied.

16

Temperature determination in the tissue with a tumor using MRBEM and FEM

Paruch M., Dziewoński M., Kokot G.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

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2005

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Vol. 4, nr 1

195-203

EN

The numerical algorithms based on the boundary element method and finite element method are used for the temperature field computations in the non homogenous domain being the composition of healthy tissue and the tumor region. The three dimensional problem is considered. Thermophysical parameters of sub-domains, in particular the perfusion coefficients, thermal conductivities and the metabolic heat sources are different. From the mathematical point of view the problem is described by the system of two Poisson's equations with temperature-dependent source functions. These equations are supplemented by the adequate boundary conditions. The algorithms discussed allow, among others, to determine the temperature distribution on the surface of the skin. In the final part of the paper the examples of computations are shown.

17

Sensitivity analysis of temperature field with respect to the radius of internal hole

Majchrzak E., Kałuża G., Paruch M.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

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2005

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Vol. 4, nr 1

165-172

EN

The domain (2D problem) with internal hole of radius R is considered. The temperature field in this domain is described by the Laplace equation supplemented by adequate boundary conditions. The aim of investigations is to estimate the changes of temperature due to change of radius R. In order to solve the problem, the boundary element method is used and the implicit differentiation method of sensitivity analysis is applied. In the final part of the paper the example of numerical computations is shown.

18

Modelling of thermal processes occuring in the tissue with a tumor with regard to parameter sensitivity analysis

Majchrzak E., Paruch M., Drozdek J.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

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2004

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Vol. 3, nr 1

133--142

EN

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.

19

Sensitivity analysis of temperature field in the tissue with a tumor

Majchrzak E., Paruch M., Drozdek J.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

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2003

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Vol. 2, nr 1

93--98

EN

The numerical algorithm based on the boundary element method is used for the temperature field computations in the non-homogeneous domain of healthy tissue and the tumor region. Thermophysical parameters of tumor region, in particular the perfusion coefficient and the metabolic heat source are essentially bigger than for healthy tissue. The values of these parameters are assumed to be constant. 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 constant source functions in the sub-domains considered. In the final part the examples of computations are shown.