Identification of Laser Intensity Assuring the Destruction of Target Region of Biological Tissue Using the Gradient Method and Generalized Dual-Phase Lag Equation

Majchrzak, Ewa; Turchan, Łukasz; Jasiński, Marek

doi:10.1007/s40997-018-0225-2

Cited by 15 publications

(7 citation statements)

References 35 publications

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“…where w 0 is the initial perfusion coefficient while Arr denotes the Arrhenius injury integral (Majchrzak et al, 2019;Paruch, 2020)…”

Section: Governing Equationsmentioning

confidence: 99%

“…The earliest of bioheat transfer equations, but probably still the most widely used, is the Pennes equation (Abraham and Sparrow, 2007;Paruch, 2017). The newest equations, such as GDPL equation (generalized dual-phase lag equation), take into account a heterogeneous structure of biological tissue (Dombrovski, 2012; Majchrzak et al, 2019).…”

Section: Introductionmentioning

confidence: 99%

“…For this purpose, radiative transport equation is usually taken into account, which can be solved by the statistical Monte Carlo approach or one of several modifications in the discrete ordinates method (Dombrovski, 2012; Friebel et al, 2006;Jacques and Pogue, 2008). It is also possible to approximate the light transport using the optical diffusion equation (Korczak and Jasiński, 2019;Majchrzak et al, 2019).…”

Section: Introductionmentioning

confidence: 99%

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

Jasiński¹

2022

Journal of Theoretical and Applied Mechanics

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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.

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“…where w 0 is the initial perfusion coefficient while Arr denotes the Arrhenius injury integral (Majchrzak et al, 2019;Paruch, 2020)…”

Section: Governing Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Jasiński¹

2022

Journal of Theoretical and Applied Mechanics

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“…The latest research and opinions [14,15,28,29] related to the bio-heat transfer problems proceedings in the living biological tissues prove that the bio-heat models should be described by the non-Fourier heat conduction models, among others, by the modified Pennes equation derived from the Cattaneo-Vernotte model or from the dual phase lag model. In the Cattaneo-Vernotte model, the relaxation time appears, while in the second model, the thermalizaton time additionally occurs.…”

Section: Future Research Planmentioning

confidence: 99%

Mathematical Modelling of Thermal and Electrical Processes in the Polyp-Colon System During Electrosurgical Polypectomy

Ciesielski¹,

Siedlecki²,

Janik³

2020

IJHT

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In this paper, the mathematical model of the electrical and thermal processes proceeding during the electrosurgical polypectomy is considered. During a colonoscopy, the endoscopist can remove abnormal growths (polyps) inside the large intestine (the colon). In the electrosurgical polypectomy procedure, a polypectomy snare is tightened around the base of the polyp. Next, the electric current flows for a short moment of time from the snare loop (the first electrode), through the polyp-colon tissues and the other body tissues, to the second electrode placed on the patient's skin. Both electrodes are connected to the electrosurgical generator unit. This medical surgery allows to cut off the polyp stalk from the colon wall. The systems of the partial differential equations that describe the thermal and electrical processes with the appropriate initial-boundary conditions are proposed. The examples of numerical simulations related to two duty cycles of the electrosurgical generator unit are presented. Simulation results can be helpful for the surgeons to choose the optimal heating time and to set other parameters of the electric current that flows by tissues during the endoscopy procedure.

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“…To estimate the degree of tissue destruction the Arrhenius integral, which describes the relationship between temperature and tissue damage, is used [39][40][41][42][43][44], where the relation between the tissue death with the temperature and the treatment time is given by…”

Section: Arrhenius Scheme-a Model Of Tissue Destructionmentioning

confidence: 99%

Mathematical Modeling of Breast Tumor Destruction Using Fast Heating during Radiofrequency Ablation

Paruch

2019

Materials

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In oncology, hyperthermia is understood as a planned, controlled technique of heating cancerous changes in order to destroy their cells or stop their growth. In clinical practice, hyperthermia is used in combination with radiotherapy, chemotherapy, or immunological therapy. During the hyperthermia, the tissue is typically exposed to a temperature in the range of 40-45 • C, the exception is thermoablation, during which the temperatures reach much higher values. Thermoablation is characterized by the use of high temperatures up to 90 • C. The electrode using the radiofrequency is inserted into the central area of the tumor. Interstitial thermoablation is used to treat, among others, breast and brain cancer. The therapy consists of inducing coagulation necrosis in an area that is heated to very high temperatures. Mathematical modeling is based on the use of a coupled thermo-electric model, in which the electric field is described by means of the Laplace equation, while the temperature field is based on the Pennes equation. Coupling occurs at the level of the additional source function in the Pennes equation. The temperature field obtained in this way makes it possible to calculate the Arrhenius integral as a determinant of the destruction of biological tissue. As a result of numerical calculations regarding the temperature field and the Arrhenius integral, it can be concluded that, with the help of numerical tools and mathematical modeling, one can simulate the process of destroying cancerous tissue.

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Identification of Laser Intensity Assuring the Destruction of Target Region of Biological Tissue Using the Gradient Method and Generalized Dual-Phase Lag Equation

Cited by 15 publications

References 35 publications

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

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

Mathematical Modelling of Thermal and Electrical Processes in the Polyp-Colon System During Electrosurgical Polypectomy

Mathematical Modeling of Breast Tumor Destruction Using Fast Heating during Radiofrequency Ablation

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