Nonlocal thermal effects on biological tissues and tumors

El-Nabulsi, Rami Ahmad; Anukool, Waranont

doi:10.1016/j.tsep.2022.101424

Cited by 6 publications

(3 citation statements)

References 93 publications

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“…which is introduced into the equation describing the bioheat transfer in the tissue domain [6,7,9]. In the current work, a description based on the Pennes bioheat transfer equation with adequate boundary initial conditions is used [11][12][13][14][15] 2 0 : ,…”

Section: Governing Equationsmentioning

confidence: 99%

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

Jasiński¹,

Zadoń²

2022

J. Appl. Math. Comput. Mech.

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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.

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Section: Governing Equationsmentioning

confidence: 99%

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

Jasiński¹,

Zadoń²

2022

J. Appl. Math. Comput. Mech.

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“…We use the Pennes bio-heat equation, which integrates heat conduction and perfusion to calculate total body heat. [20][21][22][23][24][25] .…”

Section: Introductionmentioning

confidence: 99%

Velocity and Blood Perfusion’s Impact on Transient Bioheat Transfer in Human Skin, a Numerical Investigation

Hasnain,

AlRajhi,

Saqib

et al. 2023

Preprint

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We used fundamental-solution-based numerical methods, notably the finite volume method, to solve the two-dimensional transient bioheat transfer problem in this study. The modified Chen and Holmes (CH) bioheat transfer equation governs this problem, providing a solid physical and physiological foundation. The equation is derived from the fundamental principle of energy conservation and takes into consideration the thermal energy produced by metabolic processes occurring within the tissue. Both the Pennes model and the Chen-Holmes model are utilized for the analysis of Bioheat transfer. Instead of Pennes’ equation, the CH model includes a convective heat transfer term that accounts for thermal interactions between blood vessels and tissues and a conductive term that accounts for enhanced tissue conductive heat transfer as a function of blood perfusion rate. We used a uniform velocity term to analyze temperature profiles to explore the effects of altering parameters across time. Convective results match the literature, proving accuracy and boosting our trust in the proposed approach.

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“…To start, we introduce the following nonlocal Schrödinger integro-differential equation: [22,26,41,42]…”

mentioning

confidence: 99%

Generalized uncertainty principle from long-range kernel effects: The case of the Hawking black hole temperature

El-Nabulsi

Anukool

2023

Chinese Phys. B

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We prove the existence of an analogy between spatial long range interactions which are of convolution-type introduced in non-relativistic quantum mechanics and the generalized uncertainty principle predicted from quantum gravity theories. As an illustration, black holes temperatures effects are discussed. It was observed that for specific choices of the moment's kernels, cold black holes may emerge in the theory.

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Nonlocal thermal effects on biological tissues and tumors

Cited by 6 publications

References 93 publications

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

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

Velocity and Blood Perfusion’s Impact on Transient Bioheat Transfer in Human Skin, a Numerical Investigation

Generalized uncertainty principle from long-range kernel effects: The case of the Hawking black hole temperature

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