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2 Journal of Applied Mathematics and Computational Mechanics

2 Siedlecki J.

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

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Siedlecki J.

Journal of Applied Mathematics and Computational Mechanics

2023

tom Vol. 22, nr 3

43--56

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.

The fourth-order ordinary differential equation with the fractional initial/boundary conditions

100%

Siedlecki J.

Journal of Applied Mathematics and Computational Mechanics

2020

tom Vol. 19, nr 1

79--87

The initial/boundary value problem for the fourth-order homogeneous ordinary differential equation with constant coefficients is considered. In this paper, the particular solutions an ordinary differential equation with respect to the set of boundary conditions are studied. At least one of the boundary conditions is described by a fractional derivative. Finally, a few illustrative examples of particular solutions to the considered problem are shown.