Temperature response in skin tissue during hyperthermia based on three-phase-lag bioheat model using RBF meshfree method

Abstract

Various non-Fourier heat conduction models have been proposed to overcome the paradox of the infinite propagation speed of heat signals in Fourier’s law. The three-phase-lag (TPL) heat model is a non-Fourier model based on the linearized theory of coupled thermoelasticity that combines heat flux, temperature gradient, and thermal displacement gradient. The present paper proposes a novel method with meshfree and spectral nature to solve the two-dimensional three-phase lag (TPL) bioheat model for tissue heating during hyperthermia. In the space domain, radial basis functions (RBFs) and, in the time direction, shifted Chebyshev polynomials are employed to solve the model. The use of Chebyshev polynomials in the time direction enables one to get the solution in the whole time domain simultaneously with fewer nodes. Further, there is no need for background meshes in space due to the meshless nature of RBFs, and the proposed method is equally applicable to irregular domains. The proposed method is validated with the existing semi-analytical solution of the TPL model in one spatial dimension and found to be in good agreement. The temperature profile and the impact of various parameters, such as phase lag times, blood perfusion rate, and heat source parameters on heat transfer in tissue, have also been discussed.

Keywords:

• Bioheat model
• Chebyshev polynomial
• irregular domain
• radial basis function
• three-phase lag

Declaration

Conflict of interest

The authors have no conflicts of interest to declare that are relevant to the content of this article.

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Additional information

Funding

The first author acknowledges the financial support received from University Grant Commission as junior research fellowship (JRF) (Ref: 1069(CSIR-UGC NET Dec 2018)) during the preparation of this manuscript. The second author acknowledges the financial support received from Science & Engineering Research Board (SERB), India via project no.: MTR/2021/000538.