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Numerical modeling of tissue laser irradiation with uncertain parameters using the interval finite pointset method

Korczak Anna

Journal of Applied Mathematics and Computational Mechanics

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2024

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Vol. 23, nr 2

41--53

EN

In the following paper, the numerical analysis of thermal processes occurring in biological tissue with uncertain parameters is presented. The heat transfer model is based on the Pennes equation, where interval heat sources are introduced. The model is assumed to be transient and one-dimensional. Additionally, analysed tissue is exposed to laser irradi ation, and the internal heat sources resulting from laser irradiation based on the Beer law are taken into account. Moreover, the perfusion rate and the effective scattering coefficient are treated as variables dependent on tissue damage. For numerical calculations, the interval version of the Finite Pointset Method has been used. All calculations are performed due to the direct interval arithmetic rules. The paper is concluded by presenting the obtained results

2

Analysis of ultrashort laser pulse irradiation with 2d thin metal films using the fuzzy lattice Boltzmann method

Piasecka-Belkhayat Alicja, Korczak Anna

Journal of Theoretical and Applied Mechanics

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2020

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Vol. 58 nr 1

209--219

EN

This paper presents the numerical modelling of heat transfer in two-dimensional metal films. The mathematical model of the problem analyzed consists on fuzzy coupled lattice Boltzmann equations for electrons and phonons supplemented by adequate boundary-initial conditions. In this model, the standard two-dimensional 9-speed lattice (D2Q9) is used. The main concept behind this work was to use the fuzzy lattice Boltzmann method (FLBM) to analyze the thermal process proceeding in a thin metal film. The application of α-cuts allows one to simplify mathematical operations in the fuzzy numbers set. Additionally, the trapezoidal approximation of fuzzy relaxation times and boundary conditions is considered. In the final part of the paper, the results of numerical computations are shown.

3

Modelling of biological tissue damage process with application of interval arithmetic

Korczak Anna, Jasiński Marek

Journal of Theoretical and Applied Mechanics

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2019

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Vol. 57 nr 1

249--261

EN

In the paper, the numerical analysis of thermal processes proceeding in a 2D soft biological tissue subjected to laser irradiation is presented. The transient heat transfer is described by the bioheat transfer equation in Pennes formulation. The internal heat source resulting from the laser-tissue interaction based on the solution of the diffusion equation is taken into account. Thermophysical and optical parameters of the tissue are assumed as directed intervals numbers. At the stage of numerical realization. the interval finite difference method has been applied. In the final part of the paper, the results obtained are shown.

4

Application of the interval Lattice Boltzmann method for a numerical modeling of 2D thin metal films irradiated by ultrashort laser pulses

Piasecka-Belkhayat Alicja, Korczak Anna

Journal of Applied Mathematics and Computational Mechanics

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2019

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Vol. 18, nr 4

63--71

EN

In the paper, the two-dimensional numerical modelling of heat transfer in thin metal films irradiated by ultrashort laser pulses using the D2Q9 scheme is considered. In the mathematical description, the relaxation times and the boundary conditions for phonons and electrons are given as interval numbers. The problem has been formulated using the interval coupled lattice Boltzmann equations for electrons and phonons. The solution has been obtained by means of the interval lattice Boltzmann method using the rules of directed interval arithmetic. Examples of numerical computations are presented in the final part of the paper.