Eigenvalue analysis of thermo-mechanical relaxation times in viscoelastic skin tissue

Abstract

This study investigates the thermoviscoelastic behavior of skin tissue under applied heat flux. The analysis uses the Pennes bioheat transfer model and the Kelvin-Voigt model for viscoelastic materials. A governing equation for biothermoviscoelasticity is provided with relevant initial and boundary conditions for a single-layer skin model of finite thickness. Temperature, displacement, and stress in the tissue are computed using a Laplace-transform eigenvalue method, then converted back to the time domain with MATLAB. To understand the effects of the viscosity coefficient, relaxation times of viscosity and thermal conduction, and the characteristic time of pulsing heat flux on the temperature profiles and mechanical deformation, parametric studies are conducted. Displacement, temperature and stress are plotted and presented. In combination, these measures assess the tissue response and provide a theoretical framework to support model refinement and the optimization of thermal therapy.