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Analytical and numerical temperature distribution in a 3-D triple-layer skin tissue subjected to a multi-point laser beam. (English) Zbl 1479.78020

Summary: In the present study, the temporal and spatial variation of temperature in a three-dimensional triple-layer skin tissue under the laser heating is determined. Using the method of separation of variables along with the Laplace transform, the so-called Pennes bio-heat equation is analytically solved in a 3D triple-layer tissue in which each layer has its own thermo-physical properties. The laser heating of the skin, with both single and multiple laser beams, is modelled based on time-dependent Gaussian-shaped irradiance distributions with exponential axial attenuation. For the presented solution approach, it can be shown that the laser can be considered as an arbitrary function of time such as pulses with a specified time interval with each desired spatial distribution. Besides the analytical solution, the governing equations are solved numerically by using the standard finite element method and the results are compared with the analytical solution to investigate the effects of laser heating on human skin. The effects of using single and multiple-point laser beams on the temperature increment are investigated. A good agreement between both analytical and numerical solutions is observed. The obtained results indicate that a better temperature distribution in the skin tissue is obtained; whenever, a multi-point laser is employed.

MSC:

78A60 Lasers, masers, optical bistability, nonlinear optics
78A48 Composite media; random media in optics and electromagnetic theory
80A19 Diffusive and convective heat and mass transfer, heat flow
92C05 Biophysics
35Q60 PDEs in connection with optics and electromagnetic theory
35Q79 PDEs in connection with classical thermodynamics and heat transfer
35Q92 PDEs in connection with biology, chemistry and other natural sciences
44A10 Laplace transform
78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
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