Thermoviscoelastic response of skin tissue via fractional Pennes bioheat and fractional viscoelasticity

Abstract

In this paper, the thermoviscoelastic response of skin tissue, as a typical class of viscoelastic biological tissue, subject to thermal shock is studied based on the fractional Kelvin-Voigt model and fractional Pennes bioheat conduction. A time-fractional biothermoviscoelastic governing equation is derived and initial-boundary value conditions are given for monolayer skin tissue of finite thickness. The temperature change and thermal stress of viscoelastic skin tissue are obtained by the Laplace transform and its inversion using matlab software. The influences of viscosity coefficient, relaxation times, fractional-order viscosity/heat parameter, and blood perfusion rate of skin tissue on the temperature distribution and the elastic displacement are analyzed. The numerical results show that fractional-order viscosity does not affect temperature, whereas fractional-order heat flow does. Moreover, fractional-order heat flow affects the sensitivity of blood perfusion rate to the thermodynamic response.

Keywords:

• Bioheat transfer
• biothermoviscoelastic response
• fractional viscoelasticity
• skin tissue

Disclosure statement

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (Grant Nos. 12102485 and 11872379).