Numerical solution of non-linear dual-phase-lag bioheat transfer equation within skin tissues

Kumar, Dinesh; Kumar, P.; Rai, K.N.

doi:10.1016/j.mbs.2017.08.009

Cited by 37 publications

(18 citation statements)

References 27 publications

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“…For θ = 1, that is, in the general case for Equation (43), the roots are to be computed using cubic formulas. Here we do not develop the algebra, as it goes beyond the purpose of this work.…”

Section: Three-equation System: Meso3mentioning

confidence: 99%

“…Applications can be also found in the biomedical sector, such as in medical treatments, where the temperature of the nano-constructs injected in the treated tissues can be controlled to perform cryosurgery [41] or treat hyperthermia [42]. Non-Fourier phenomena also appear in localized and pulsed heat transfer through skin tissues and blood vessels, where non-linear dual-phase-lag models are typically used [43].…”

Section: Introductionmentioning

confidence: 99%

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Mesoscopic Moment Equations for Heat Conduction: Characteristic Features and Slow–Fast Mode Decomposition

Bergamasco

Alberghini

Fasano

et al. 2018

Entropy

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Abstract:In this work, we derive different systems of mesoscopic moment equations for the heat-conduction problem and analyze the basic features that they must hold. We discuss two-and three-equation systems, showing that the resulting mesoscopic equation from two-equation systems is of the telegraphist's type and complies with the Cattaneo equation in the Extended Irreversible Thermodynamics Framework. The solution of the proposed systems is analyzed, and it is shown that it accounts for two modes: a slow diffusive mode, and a fast advective mode. This latter additional mode makes them suitable for heat transfer phenomena on fast time-scales, such as high-frequency pulses and heat transfer in small-scale devices. We finally show that, if proper initial conditions are provided, the advective mode disappears, and the solution of the system tends asymptotically to the transient solution of the classical parabolic heat-conduction equation.

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Section: Three-equation System: Meso3mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Mesoscopic Moment Equations for Heat Conduction: Characteristic Features and Slow–Fast Mode Decomposition

Bergamasco

Alberghini

Fasano

et al. 2018

Entropy

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“…However, because the inner structure of the human body is inhomogeneous, the physiological parameters depend on local tissue temperature. Some researchers [ 8 , 9 , 10 ] considered the perfusion term to be a function of the temperature in local tissue. Similarly, some authors [ 11 , 12 ] assumed a metabolic heat source in their model, and this was also a function of the temperature in local tissue.…”

Section: Introductionmentioning

confidence: 99%

“…The treatment techniques such as hyperthermia, thermal ablation, cryoablation, and cryosurgery are used for selectively destroying the tumor in living skin tissue. Thermal therapy is an ideal modality for the treatment of infected cells using different types of external heat sources like electromagnetic irradiation [ 6 , 10 , 12 , 13 ], magnetic nanoparticles (MNPs) [ 15 , 16 ], etc.…”

Section: Introductionmentioning

confidence: 99%

“…Several researchers studied the temperature distribution in skin tissues using the DPL bioheat transfer model, undertaking different types of volumetric heat sources. They solved the DPLBHT model using the finite element Legendre wavelet Galerkin method [ 15 ] and used the FERK (4,5) method [ 10 , 12 , 13 ] and finite difference-decomposition method [ 6 ]. The development of the reconfigurable distributed multiple-input multiple-output technique in a practical communication environment was proposed by Do and Haas [ 35 ].…”

Section: Introductionmentioning

confidence: 99%

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A Study on Non-Linear DPL Model for Describing Heat Transfer in Skin Tissue during Hyperthermia Treatment

Sharma

Kumar²

2020

Entropy

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The article studies the simulation-based mathematical modeling of bioheat transfer under the Dirichlet boundary condition. We used complex non-linear dual-phase-lag bioheat transfer (DPLBHT) for analyzing the temperature distribution in skin tissues during hyperthermia treatment of infected cells. The perfusion term, metabolic heat source, and external heat source were the three parts of the volumetric heat source that were used in the model. The non-linear DPLBHT model predicted a more accurate temperature within skin tissues. The finite element Runge–Kutta (4,5) (FERK (4,5)) method, which was based on two techniques, finite difference and Runge–Kutta (4,5), was applied for calculating the result in the case of our typical non-linear problem. The paper studies and presents the non-dimensional unit. Thermal damage of normal tissue was observed near zero during hyperthermia treatment. The effects of the non-dimensional time, non-dimensional space coordinate, location parameter, regional parameter, relaxation and thermalization time, metabolic heat source, associated metabolic heat source parameter, perfusion rate, associated perfusion heat source parameter, and external heat source coefficient on the dimensionless temperature profile were studied in detail during the hyperthermia treatment process.

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Numerical solution of nonlinear dual‐phase‐lag model for analyzing heat transfer in tissue during thermal therapy

Sharma

Singh

Kumar³

2021

Comp and Math Methods

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This article deals with mathematical modeling and simulation of heat transfer in tissue under periodic boundary condition using nonlinear dual-phase-lag-bioheat-transfer (DPLBHT). We have taken the temperature dependent blood perfusion and metabolic heat source as exponent variation in nonlinear DPLBHT model, both are experimentally validated function of temperature. In this article we applied finite difference method and Runge-Kutta (4,5) scheme to solve nonlinear problem. In particular case the exact solution is obtained and compared with numerical scheme and both are in good agreement. Effect of different parameters are discussed in detail such as blood perfusion rate, dimensionless heat source parameters, relaxation, and thermalization time on dimensionless temperature. The whole article is analyzed in dimensionless form.

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Numerical solution of non-linear dual-phase-lag bioheat transfer equation within skin tissues

Cited by 37 publications

References 27 publications

Mesoscopic Moment Equations for Heat Conduction: Characteristic Features and Slow–Fast Mode Decomposition

Mesoscopic Moment Equations for Heat Conduction: Characteristic Features and Slow–Fast Mode Decomposition

A Study on Non-Linear DPL Model for Describing Heat Transfer in Skin Tissue during Hyperthermia Treatment

Numerical solution of nonlinear dual‐phase‐lag model for analyzing heat transfer in tissue during thermal therapy

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