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1

Modeling of photochemical and photothermal effects in soft tissue subjected to laser irradiation

Jasiński Marek, Zadoń Maria

Computer Assisted Methods in Engineering and Science

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2024

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Vol. 31, no. 1

29--50

EN

The purpose of this study is to analyze the phenomena that occur in biological tissueduring photodynamic therapy (PDT). Under the influence of the laser, triplet oxygen istransformed into singlet oxygen, which is cytotoxic to cancer tissue. The impact of thelaser on the tissue may also be accompanied by changes in the thermophysical parameters,e.g., perfusion, which can affect the supply of oxygen to the tissue and, consequently,the outcome of the therapy. The proposed model uses the optical diffusion equation,the Pennes bioheat transfer equation, and reactions equations for PDT. The connectionbetween bioheat transfer and PDT models is taken into account through the respectiverelationships between perfusion rate, capillary blood velocity, and the maximum oxygensupply rate. Furthermore, a method is proposed to model abnormal vascular patterns inthe tumor subdomain. The boundary element method and the finite difference methodwere used in the numerical implementation stage.

2

Modeling of the influence of elevated temperature on oxygen distribution in soft tissue

Jasiński Marek, Zadoń Maria

Engineering Transactions

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2023

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Vol. 71, iss. 3

287--306

EN

The purpose of the study was to analyze the combined model of bioheat transfer and oxygen distribution in tissue during exposition to the external heat impulse. The effect of temperature and thermal damage to the tissue on the values of its thermophysical parameters was taken into account. The variable value of the perfusion coefficient affects the blood velocity in the capillary and thus the distribution of the partial oxygen pressure in the tissue. Various models of the oxygen dissociation curves were also considered and a sensitivity analysis was performed for the parameters of the oxygen distribution model. In the numerical realization stage, the finite difference method and the shooting method were used.

3

Numerical analysis of the thermal damage process of the tissue-blood vessel system and distribution of oxygen in the tissue

Jasiński Marek

Journal of Theoretical and Applied Mechanics

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2022

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Vol. 60 nr 2

199--212

EN

The paper presents a numerical analysis of the thermal damage process taking place in biological tissue containing a blood vessel during laser irradiation. The internal heat source resulting from laser irradiation based on the solution of the optical diffusion equation is taken into account. The investigation was concerned with the influence of tissue denaturation and oxygen content in blood on temperature distribution. The analysis of oxygen transport to the tissue is treated as a part of the analysis of thermal damage processes. At the stage of numerical computations, the boundary element method and the finite difference method were used.

4

Numerical analysis of thermal damage and oxygen distribution in laser irradiated tissue

Jasiński Marek

Journal of Applied Mathematics and Computational Mechanics

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2022

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Vol. 21, nr 2

51--62

EN

A numerical analysis of the thermal damage process that proceeds in biological tissue during laser irradiation is presented. Heat transfer in the tissue is assumed to be transient and two-dimensional. The internal heat source resulting from the laser irradiation based on the solution of optical diffusion equation is taken into account. Changes in tissue oxygen distribution resulting from temperature changes are analyzed using the Krogh cylinder model with Michaelis-Menten kinetics. A Hill model was used to describe the oxyhemoglobin dissociation curve. At the stage of numerical realization, the boundary element method and the finite difference method have been applied.

5

Numerical analysis of biological tissue heating using the dual-phase lag equation with temperature - dependent parameters

Majchrzak Ewa, Stryczyński Mikołaj

Journal of Applied Mathematics and Computational Mechanics

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2022

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Vol. 21, nr 3

85--98

EN

The dual-phase lag equation is formulated for the case when the thermophysical parameters occurring in this equation are temperature-dependent. The axial-symmetrical domain of biological tissue heated by an external heat source is considered. The problem is solved using the implicit scheme of the finite difference method. At the stage of numerical computations, the analytical relationships taken from the literature describing changes in parameters are taken into account.

6

Mathematical modeling of the phenomena that occur in a biological tissue containing photosensitizer

Jasiński Marek, Zadoń Maria

Journal of Applied Mathematics and Computational Mechanics

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2022

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Vol. 21, nr 4

40--51

EN

The aim of the study is to analyze photothermal and photochemical phenomena that occur during photodynamic therapy (PDT). In this type of therapy, under the influence of the laser, reactions take place related to the transformation of triplet oxygen form into its singlet form which is cytotoxic to the tissue. The increases in temperature resulting from the laser-tissue interaction during PDT are not big; however, they can lead to changes in tissue perfusion, which can affect oxygen delivery to the tissue. The proposed model uses optical diffusion equation, Pennes bioheat transfer equation, and reactions equations for PDT. The main findings of the analysis show the impact of temperature on the value of the perfusion coefficient and triplet oxygen distributions at the end of the treatment procedure.

7

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.

8

Phase-lag effects in skin tissue during transient heating

Kumar R., Vashishth A. K., Ghangas S.

International Journal of Applied Mechanics and Engineering

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2019

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Vol. 24, no. 3

603--623

EN

A three-phase-lag (TPL) model is proposed to describe heat transfer in a finite domain skin tissue with temperature dependent metabolic heat generation. The Laplace transform method is applied to solve the problem. Three special types of heat flux are applied to the boundary of skin tissue for thermal therapeutic applications. The depth of tissue is influenced by the different oscillation heat flux. The comparison between the TPL and dual-phase-lag (DPL) models is analyzed and the effects of phase lag parameters […] and material constant […] on the tissue temperature distribution are presented graphically.

9

Identification of boundary heat flux assuring the destruction of target region of biological tissue application of the generalized dual-phase lag model and gradient method

Turchan Łukasz, Majchrzak Ewa

Computer Assisted Methods in Engineering and Science

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2019

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Vol. 26, no. 1

21--34

EN

In this paper, an axially symmetrical biological tissue domain subjected to an external heat source is analyzed. The thermal processes occurring in the domain considered are described using the generalized dual-phase lag model supplemented by the Neumann boundary conditions and the appropriate initial conditions. The problem of tissue heating is solved using the implicit scheme of the finite difference method. The obtained solution allows one to determine the local and temporary values of the Arrhenius integral. Next, the inverse problem related to the identification of the boundary heat flux assuring the postulated destruction of the tissue target region is considered. The problem is solved using the gradient method. In the final part of the paper, the results of computations and the conclusions are presented.

10

Modelling of thermal damage process in soft tissue subjected to laser irradiation

Jasiński M.

Journal of Applied Mathematics and Computational Mechanics

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2018

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Vol. 17, nr 2

29--41

EN

The numerical analysis of thermal damage process proceeding in biological tissue during laser irradiation is presented. Heat transfer in the tissue is assumed to be transient and two-dimensional. The internal heat source resulting from the laser irradiation based on the solution of the diffusion equation is taken into account. The tissue is regarded as a homogeneous domain with perfusion coefficient and effective scattering coefficient treated as dependent on tissue injury. At the stage of numerical realization, the boundary element method and the finite difference method have been used. In the final part of the paper the results of computations are shown.

11

Thermal modelling and screening method for skin pathologies using active thermography

Strąkowska M., Strąkowski R., Strzelecki M., De Mey G., Więcek B.

Biocybernetics and Biomedical Engineering

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2018

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Vol. 38, no. 3

602--610

EN

This paper presents a novel screening approach of human skin pathologies using Active IR Thermography. The inputs of the proposed algorithm are the values of the physical parameters of the skin. Parameters are estimated based on dynamic thermographic measurements of human skin and the developed thermal model of the tissue. The calculations were based on the inverse thermal modelling. Classification was done using Support Vector Machine, Linear Discriminant Analysis and k-Nearest Neighbours classifiers. As an example, one presented the results of screening for psoriasis.

12

Solving the dual-phase lag bioheat transfer equation by the generalized finite difference method

Turchan Ł.

Archives of Mechanics

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2017

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Vol. 69, nr 4-5

389--407

EN

The modeling of bioheat transfer process described by the dual-phase lag equation is considered. The basic equation is supplemented by the appropriate boundary-initial conditions. In the central part of the cylindrical domain the heated sub-domain is located. In this region the additional component determining the capacity of an internal heat source is taken into account. At the stage of numerical computations the generalized finite difference method (GFDM) is used. The GFDM nodes distribution is generated in a random way (with some limitations). The examples of computations for different nodes distribution and comparison with the classical finite difference method are presented. In the final part of the paper the conclusions are formulated.

13

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.

14

Cattaneo-Vernotte bioheat transfer equation. Stability conditions of numerical algorithm based on the explicit scheme of the finite difference method

Mochnacki B., Tuzikiewicz W.

Journal of Applied Mathematics and Computational Mechanics

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2016

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Vol. 15, nr 4

137-144

EN

The Cattaneo-Vernotte (CVE) equation is considered. This equation belongs to the group of hyperbolic PDE. Supplementing this equation by two additional terms corresponding to perfusion and metabolic heat sources one can apply the CVE as a mathematical model describing the heat transfer processes proceeding in domain of the soft tissue. Such an approach is recently often preferred substituting the classical Pennes model. At the stage of numerical computations the different numerical methods of the PDE solving can be used. In this paper the problems of stability conditions for the explicit scheme of the finite difference method (FDM) are discussed. The appropriate condition limiting the admissible time step have been found using the von Neumann analysis.

15

1D generalized dual-phase lag equation. Sensitivity analysis with respect to the porosity

Kałuża G., Majchrzak E., Turchan Ł.

Journal of Applied Mathematics and Computational Mechanics

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2016

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Vol. 15, nr 1

49--58

EN

Thermal processes occurring in the heated tissue are described by the 1D generalized dual-phase lag equation supplemented by appropriate boundary and initial conditions. Using the sensitivity analysis method, the additional problem connected with the porosity is formulated. Both problems are solved by means of the explicit scheme of the finite difference method. In this way it is possible to estimate the temperature changes due to the perturbation of porosity. In the final part of the paper, the example of computation is shown and the conclusions are formulated.

16

Sensitivity of transient temperature field in domain of forearm insulated by protective clothing with respect to perturbations of external boundary heat flux

Mochnacki B., Ciesielski M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2016

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Vol. 64, nr 3

591--598

EN

The problem discussed in the paper is numerical modeling of thermal processes in the domain of biological tissue secured by a layer of protective clothing being in thermal contact with the environment. The cross-section of the forearm (2D problem) is treated as non-homogeneous domain in which the sub-domains of skin tissue, fat, muscle and bone are distinguished. The air gap between skin tissue and protective clothing is taken into account. The process of external heating is determined by Robin boundary condition and sensitivity analysis with respect to the perturbations of heat transfer coefficient and ambient temperature is also discussed. Both the basic boundary-initial problem and the sensitivity problems are solved by means of control volume method using Voronoi polygons.

17

Modelling of thermal damage in laser irradiated tissue

Jasiński M.

Journal of Applied Mathematics and Computational Mechanics

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2015

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Vol. 14, nr 4

67--78

EN

In the paper the numerical analysis of thermal processes proceeding in the 2D homogeneous biological tissue subjected to laser irradiation is presented. In particular, the influence of necrotic changes in tissue on the values of the perfusion coefficient and effective scattering coefficient are discussed. The transient heat transfer is described by the bioheat transfer equation in the Pennes formulation. As a model of light distribution in tissue, the first-order scattering approach has been used. At the stage of numerical realization the 1st scheme of the boundary element method has been applied.

18

3D model of thermal interactions between human forearm and environment

Duda M., Mochnacki B.

Journal of Applied Mathematics and Computational Mechanics

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2015

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Vol. 14, nr 3

17--23

EN

Thermal processes in the domain of a human forearm are considered. The external surface of forearm is in the direct thermal contact with the environment. The steady state problem is considered. From the mathematical point of view, the task is described by the system of the Poisson-type equations, the boundary conditions given on the contact surface between tissue sub-domains, the boundary conditions determining heat transfer between blood vessels and tissue and the boundary conditions on the external surface of the system. The non-homogeneous forearm domain is reconstructed as accurately as possible (3D task). At the stage of numerical modelling, the finite element method has been used. In the final part of the paper the example of computations is presented.

19

Validation of a numerical model of locally cooled tissues

Buliński P., Ostrowski Z., Adamczyk W., Fityka A., Nowak A. J.

Computer Assisted Methods in Engineering and Science

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2015

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Vol. 22, no. 4

305--314

EN

Measurements of heat transfer and temporal temperature distribution can be used as input in the diagnostic tools and methods of skin lesions, with special attention paid to malignant melanoma identification. Such approach requires mutual use of skin temperature and heat flux measurements combined with numerical simulation. A mild skin cooling process by a brass compress is considered in this paper. The temperature distribution on the skin and the heat flux between metal and tissues are measured. They are used in the course of validation study of the proposed numerical model. A numerical model of heat transfer in living tissues is described by Pennes’ bioheat equation augmented with additional models of passive thermoregulation and vasoconstriction effects. The information regarding material properties of tissues and cooling compress involved in the simulation is essential to accurately solve this problem. Therefore, the main purpose of this work is to determine the accurate material property information by means of laboratory experiments.

20

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.