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Electrosurgical resection of colorectal polyps - mathematical modelling of processes during medical treatment

Siedlecki Jarosław

Journal of Applied Mathematics and Computational Mechanics

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2023

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Vol. 22, nr 3

43--56

EN

The colonoscopic electrosurgical polypectomy is a very popular surgical procedure in which the colon polyps are removed. In this work, the mathematical description of the electrical and thermal processes proceeding during this procedure has been proposed. The mathematical model contains the specification of the considered domain’s geometry, the system of the partial differential equations that governs heat transfer in the considered particular sub-domains (i.e. polyp, colon and electrode) with the adequate initial-boundary conditions, the system of the differential equations for determination of the electrical potential distribution in the tissue sub-domains, and the definition of the Arrhenius tissue damage integral. Next, the example results of numerical simulations for the proper and incorrect positions of the polyp in the colon are presented. The conclusions are also provided. The proposed research can be helpful for the surgeons to choose the optimal set parameters of the electric current during the endoscopy procedure.

2

Numerical modeling of biological tissue heating : admissible thermal dose

Ciesielski M., Mochnacki B., Szopa R.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

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2011

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Vol. 10, nr 1

11-20

EN

The cylindrical domain of skin tissue subjected to an external heat flux is considered (shape of domain is determined by form of function describing Neumann boundary condition on external surface of the system). The first version of numerical simulations concerns the heterogeneous multi-layered skin tissue domain (epidermis, dermis, subcutaneous region). The thermophysical parameters of successive layers are assumed to be different, but constant. The second version of computations concerns the homogeneous domain, but the mean values of the thermophysical parameters are temperature-dependent (non-linear task). Knowledge of the spatial, time-dependent temperature field allows one to determine the so-called thermal dose and also the degree of tissue destruction. The algorithm presented can be useful in medical practice, among others, at the stage of the hyperthermia therapy scheme.

3

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.

4

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.

5

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.

6

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.