Analytical analysis of the Pennes bioheat transfer equation with sinusoidal heat flux condition on skin surface

Shih, Tzu Ching; Yuan, Peng; Lin, Win-Li; Kou, Hong-Sen

doi:10.1016/j.medengphy.2006.10.008

Cited by 191 publications

(72 citation statements)

References 20 publications

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“…The results were obtained for x = 0.0001 and t = 0.25, for three different time intervals. Since the analytical solution was derived for α = 1 [36], we used a value of α closer to 1 (α = 0.999). As shown, a good agreement was obtained between the numerical and the analytical solutions.…”

Section: Methodology Assessmentmentioning

confidence: 99%

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Fractional Pennes’ Bioheat Equation: Theoretical and Numerical Studies

Ferrás

Ford

Morgado

et al. 2015

FCAA

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In this work we provide a new mathematical model for the Pennes' bioheat equation, assuming a fractional time derivative of single order. Alternative versions of the bioheat equation are studied and discussed, to take into account the temperature-dependent variability in the tissue perfusion, and both finite and infinite speed of heat propagation. The proposed bioheat model is solved numerically using an implicit finite difference scheme that we prove to be convergent and stable. The numerical method proposed can be applied to general reaction diffusion equations, with a variable diffusion coefficient. The results obtained with the single order fractional model, are compared with the original models that use classical derivatives.MSC 2010 : 35R11, 65N99, 92-08

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Section: Methodology Assessmentmentioning

confidence: 99%

“…Pennes' [33] bioheat transfer equation (see also [30], [1], [36], [31], [24], [25]), which describes the thermal distribution in human tissue, taking into account the influence of blood flow, (see Fig. 1) is given by, In order to overcome Pennes' bioheat model limitations, other models have been proposed in the literature.…”

Section: Introductionmentioning

confidence: 99%

Fractional Pennes’ Bioheat Equation: Theoretical and Numerical Studies

Ferrás

Ford

Morgado

et al. 2015

FCAA

View full text Add to dashboard Cite

show abstract

“…He assumed that all heat transfer between the tissue and the blood occurs in the capillaries and neglected the local effects of thermally significant blood vessels appearing in the domain under consideration [4]. He also assumed a constant rate blood perfusion of the form "V.s" where V and s are respectively the perfusion rate per unit volume of tissues and the density of the blood.…”

Section: Introductionmentioning

confidence: 99%

Transient State Finite Element Model to Analyse Thermal Variations in Peripheral Region of Human Limb undergoing Healing after Surgery

Gupta¹,

Shakya²

2014

IOSRJM

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“…Shih et al [34] and Yuan et al [35] suggested. Using this technique, Liu and Xu [36] analyzed the influences that a sinusoidal heat flux source placed on the skin surface have on the temperature inside it, and Tjahjono [37] analytically analyzed the heating temperature of a slab embedded with gold NPs due to a constant magnetic flux.…”

Section: Introductionmentioning

confidence: 99%

An Analytic Analysis of the Diffusive-Heat-Flow Equation for Different Magnetic Field Profiles for a Single Magnetic Nanoparticle

Dana

Gannot

2012

Journal of Atomic, Molecular, and Optical Physics

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This study analytically analyzes the changes in the temperature profile of a homogenous and isotropic medium having the same thermal parameters as a muscular tissue, due to the heat released by a single magnetic nanoparticle (MNP) to its surroundings when subject to different magnetic field profiles. Exploring the temperature behavior of a heated MNP can be very useful predicting the temperature increment of it immediate surroundings. Therefore, selecting the most effective magnetic field profile (MFP) in order to reach the necessary temperature for cancer therapy is crucial in hyperthermia treatments. In order to find the temperature profile caused by the heated MNP immobilized inside a homogenous medium, the 3D diffusive-heat-flow equation (DHFE) was solved for three different types of boundary conditions (BCs). The change in the BC is caused by the different MF profiles (MFP), which are analyzed in this article. The analytic expressions are suitable for describing the transient temperature response of the medium for each case. The analysis showed that the maximum temperature increment surrounding the MNP can be achieved by radiating periodic magnetic pulses (PMPs) on it, making this MFP more effective than the conventional cosine profile.

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Analytical analysis of the Pennes bioheat transfer equation with sinusoidal heat flux condition on skin surface

Cited by 191 publications

References 20 publications

Fractional Pennes’ Bioheat Equation: Theoretical and Numerical Studies

Fractional Pennes’ Bioheat Equation: Theoretical and Numerical Studies

Transient State Finite Element Model to Analyse Thermal Variations in Peripheral Region of Human Limb undergoing Healing after Surgery

An Analytic Analysis of the Diffusive-Heat-Flow Equation for Different Magnetic Field Profiles for a Single Magnetic Nanoparticle

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