A revised approach for an exact analytical solution for thermal response in biological tissues significant in therapeutic treatments

Dutta, Jaideep; Kundu, Balaram

doi:10.1016/j.jtherbio.2017.03.015

Cited by 22 publications

(10 citation statements)

References 35 publications

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“…To originate the exact thermal behaviour of skin tissue under a therapeutic heating in accordance with the practical aspects, the initial temperature of skin tissue must be as a function of spatial coordinates due to highly non-uniform and non-homogeneous structures of tissue, and metabolic heat generation rate. Dutta and Kundu 45 established the implementation of spatially dependent initial condition of biological heat transfer under a therapeutic heating by quantifying 52.8% error involved (based on thermal wave modelling) in comparison with a constant initial condition for a specific set of boundary conditions.…”

Section: Mathematical Modellingmentioning

confidence: 99%

Two-dimensional hybrid analytical approach for the investigation of thermal aspects in human tissue undergoing regional hyperthermia therapy

Dutta

Kundu

2020

Proceedings of the Institution of Mechanical Engineers, Part C:

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The formation of the present work is based on the development of the exact analytical solution of two-dimensional temperature response by employing the hyperbolic heat conduction bioheat model in a single-layered human skin tissue subjected to the regional hyperthermia therapy (RHT) for cancer treatment. The mathematical approach has been utilized as a hybrid form of ‘separation of variables’ and ‘finite integral transform’ method. Three kinds of surface heat fluxes (constant, sinusoidal and cosine) have been employed as an external heat source on the therapeutic surface of the square-shaped skin tissue of 100 mm × 100 mm. An innovative form of initial condition (spatially dependent) has been implemented in the present mathematical formulation as skin tissues are highly non-homogeneous and non-uniform in structure. The present research outcome indicates that cosine heat flux would be a suitable alternative for the sinusoidal heat flux. The impact of the relaxation time lag has been clearly noted in the thermal response with the waveform-like behaviour and it justifies the postulate of hyperbolic heat conduction. The two-dimensional temperature of the skin tissue has been observed in the range of 48.1 ℃–40 ℃ (in decreasing order). Estimated peak temperatures are in the proposed spectrum of hyperthermia therapy for an exposure time of 100 s, and this fact is true in an agreement with the medical protocol of the cancer treatment. The accuracy of the mathematical modelling and in-house computer codes are justified with the published numerical models and the maximum deviation of the thermal response has been noticed in order of 1.5–3%. The two-dimensional surface thermal contours have provided a glimpse of heat flow in the physical domain of skin tissue under different heating conditions and this research output may be beneficial to establish the theoretical standard of the regional hyperthermia treatment for cancer eradication.

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Section: Mathematical Modellingmentioning

confidence: 99%

Two-dimensional hybrid analytical approach for the investigation of thermal aspects in human tissue undergoing regional hyperthermia therapy

Dutta

Kundu

2020

Proceedings of the Institution of Mechanical Engineers, Part C:

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“…A further study can be carried out to simulate all physical quantities above mentioned and tissue damage in realistic anisotropic media with arbitrary shapes, electrode arrays with different geometry and arbitrary shape of the electrode. As the solution (44) is obtained for constant initial condition, it would be interesting to know how the solution (44) changes when spatially dependent initial condition is used, as reported in [5].…”

Section: Remarks On Generalized Pennes Equationmentioning

confidence: 99%

“…During application of these therapies, tissue heating arises due to conduction losses (i.e., resistive heating from ion movement) [4]. Thermal spread in biological tissue may be measured using an infrared thermograph device [5]. Images of surface temperature and false-positive and false-negative constitute limitations of the infrared thermography method [6,7].…”

Section: Introductionmentioning

confidence: 99%

“…It has been used when the internal heat generation of tissue is produced by its metabolism [17]. Additionally, Pennes bioheat equation permits to describe the energy conservation equation for biological heat transfer on the basis of the classical Fourier's law of heat conduction [5]. Analytic modeling of temperature distribution is based on solving the linear bioheat transfer equation for tissue, which is the general heat equation for conduction, with added terms for heat sources [8][9][10]18].…”

Section: Introductionmentioning

confidence: 99%

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Analytical solution of the bioheat equation for thermal response induced by any electrode array in anisotropic tissues with arbitrary shapes containing multiple-tumor nodules

Oria¹,

Cabrales

Reyes

2019

Rev. Mex. Fís.

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The Pennes bioheat transfer equation is the most used model to calculate the temperature induced in a tumor when physical therapies like electrochemical treatment, electrochemotherapy and/or radiofrequency are applied. In this work, a modification of the Pennes bioheat equation to study the temperature distribution induced by any electrode array in an anisotropic tissue containing several nodules (primary or metastatic) with arbitrary shape is proposed. For this, the Green functions approach is generalized to include boundaries among two or more media. The analytical solution we obtain in a very compact way, under quite general suppositions, allows calculating the temperature distributions in the tumor volumes and their surfaces, in terms of heat sources, initial temperature and calorific sources at the boundary of tumors.

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“…The focus of the study was to find a solution to the inverse problem of dealing with the estimation of state variables, like the temperature distribution in the tissues. Dutta and Kundu developed a revised exact analytical solution of the thermal profile of 1‐D PBHE for living tissues influenced in thermal therapeutic treatments. The separation of variables technique is used to obtain the analytical solution.…”

Section: Introductionmentioning

confidence: 99%

Fundamental solution of steady and transient bio heat transfer equations especially for skin burn and hyperthermia treatments

Deka

Bhanja

Nath

2018

Heat Trans. Asian Res.

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In the field of bio heat transfer, as of now, the main concern of researchers lies in the proper and accurate thermal damage of the diseased tissues without destroying or damaging the neighboring healthy tissues during the tumor treatment. The present work aims to develop a new approach toward solving the bio heat transfer equations for the skin burn and hyperthermia treatments. Both analytical and numerical solutions are proposed. For the analytical study, a differential transform method is used to solve steady and unsteady state heat equations. The finite volume method is adopted to solve these equations numerically, which provides a better scope to solve the highly nonlinear complex equations. To obtain a complete solution, a code is developed in MATLAB and MATHEMATICA. The variation of different parameters, such as perfusion constant, space heating, surface step heating, and thermal conductivity, with time were observed. Apart from the above analysis of temperature distribution during skin burn through the spilling of hot beverage, its numerical solution was also performed for this problem at different boundary conditions. It was observed that with the help of the temperature distribution, depending on the time and the severity of the burn, different ranges of depths of the burn can be determined.

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A revised approach for an exact analytical solution for thermal response in biological tissues significant in therapeutic treatments

Cited by 22 publications

References 35 publications

Two-dimensional hybrid analytical approach for the investigation of thermal aspects in human tissue undergoing regional hyperthermia therapy

Two-dimensional hybrid analytical approach for the investigation of thermal aspects in human tissue undergoing regional hyperthermia therapy

Analytical solution of the bioheat equation for thermal response induced by any electrode array in anisotropic tissues with arbitrary shapes containing multiple-tumor nodules

Fundamental solution of steady and transient bio heat transfer equations especially for skin burn and hyperthermia treatments

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