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1

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.

2

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.

3

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.

4

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.

5

Comparison of three In silico models of heat transfer in human body exposed to mild cooling

Buliński P., Ostrowski Z., Adamczyk W.

Studia Informatica

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2016

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Vol. 37, nr 3A

31--42

EN

The comparison of three numerical models of skin undergoing thermal stimulation in a human forearm is presented. Small brass compress is used to cool tissues, followed by the analysis of the skin temperature recovery process. In silico generated results are validated against in vivo measurements on 8 male adults.

PL

W pracy przedstawiono porównanie trzech modeli numerycznych tkanek przedramienia poddanych stymulacji termicznej. Chłodzenie skóry zrealizowano za pomocą mosiężnego kompresu. Analizowano proces powrotu schłodzonej skóry do warunków równowagi termicznej. Wyniki symulacji in silico porównano z pomiarami in vivo wykonanymi dla grupy 8 dorosłych mężczyznach.

6

Numerical analysis of thermal processes in the system protective clothing – biological tissue subjected to an external heat flux

Mochnacki B., Duda M.

Journal of Applied Mathematics and Computational Mechanics

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2016

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Vol. 15, nr 2

85--93

EN

The non-homogeneous fragment of biological tissue is considered. Its shape roughly corresponds to the fragment of cross-section of the upper or lower limb. The tissue domain is protected by a layer of protective clothing. The purpose of numerical computations is to examine the effectiveness of the clothing insulation layer on the action of the external heat fluxes of differing intensity. Thermal processes in the tissue domain are described by the system of the Pennes equations. This system is supplemented by the appropriate boundary-initial conditions and the energy equations determining the transient temperature field in the fabric and air gap sub-domains (the air gap is treated as a solid body). At the stage of numerical computations, the program MSC. Marc has been used. In the final part of the paper, the examples of numerical simulations and also the conclusions are presented.

7

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.

8

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.

9

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.

10

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.

11

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.

12

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.

13

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.

14

Numerical analysis of tissue heating using the bioheat transfer porous model

Majchrzak E., Turchan Ł.

Computer Assisted Methods in Engineering and Science

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2013

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Vol. 20, no. 2

123--131

EN

The paper concerns the modelling of artificial hyperthermia. The 3D domain including healthy tissue and tumor region is considered. Heat transfer processes proceeding in this domain are described by the Pennes model and next by the porous one. The external heating of tissue is taken into account by the introduction of internal source function to the equation considered. Both models are supplemented by the same geometrical, physical, boundary and initial conditions. At the stage of numerical simulation the explicit scheme of finite difference method is used. The examples of computations show the similarities and differences of solutions and allow to formulate the conclusions connected with the applications of the results obtained in the hyperthermia therapy.

15

Analysis of thermal processes proceeding in the skin tissue subjected to freezing

Majchrzak E., Kałuża G.

Zeszyty Naukowe Katedry Mechaniki Stosowanej / Politechnika Śląska

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2006

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z. 26

225-230

EN

The freezing process of skin tissue is described by the strongly non-linear bioheat transfer equation in which the additional term controlling the evolution of latent heat appears. Using the approach called 'the one domain method' finally one obtains the partial differential equation containing the substitute thermal capacity of tissue. The boundary and initial conditions determine the thermal interaction between the tissue and cryoprobe tip. In the paper we consider the external cylindrical cryoprobe. In order to estimate the influence of cryoprobe geometry on the course of the process the shape sensitivity analysis has been applied. In particular the direct approach is used (explicit differentiation method). The results of numerical modelling (the boundary element method is applied) allow to formulate the essential practical conclusions concerning the course of cryosurgery treatments.

16

Parameter sensitivity analysis of burn integrals using the adjoint approach

Majchrzak E., Jasiński M.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

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2004

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Vol. 3, nr 1

115--120

EN

In the paper the numerical analysis of thermal processes proceeding in the domain of biological tissue subjected to an external heat source is presented. Heat transfer in the skin tissue was assumed to be transient and one-dimensional. The degree of the skin burn can be predicted on the basis of so called Henriques integrals and the main subject of the paper is the sensitivity analysis of these integrals with respect to the thermophysical parameters. Here the adjoint approach of parameter sensitivity analysis has been applied. On the stage of numerical computations the boundary element method has been used. In the final part of the paper the results obtained are shown.

17

Phased array optimizing characteristics in HIFU device

Chen Q., Xiong B., Chen Y.

Archives of Acoustics

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2003

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Vol. 28, no. 2

109-116

EN

For the high intensity focused ultrasound (HIFU) phased array frequency distribution pattern size and amount of the elements may affect the performance and cost of the HIFU device. In this paper an inner holed spherical shell with 96 transducer elements was designed basing on the Ebbini pseudo-inverse matrix and Penns bioheat equation. The phased array has a lower grating-lobe level and a higher intensity gain suitable for deep heating. The experiments with the array usung 16 elements show that the phased array design produces a large dynamic scan scale with least elements and a high heat focus.