Dynamic response of porous viscoelastic living tissue under fractional-order Moore–Gibson–Thompson thermoelasticity theory
Soumik Das, Rachaita Dutta, Abhik Sur, Eduard‐Marius Craciun
Abstract
Purpose This paper aims to analyze the thermo-mechanical interactions in living tissue. This study also aims to improve the understanding of heat transport dynamics and their coupled biomechanical responses during thermal therapies by incorporating higher order fractional time derivatives and Eringen’s nonlocal elasticity. Design/methodology/approach A novel bio-thermoelastic model is developed. This model uses a higher order fractional Moore–Gibson–Thompson (MGT) approach for heat propagation and Eringen’s nonlocal elasticity for the constitutive behavior of viscoelastic tissue with voids. Analytical solutions for displacements, temperature, void volume fractions and stresses have been established using normal mode analysis. Numerical simulations illustrate the effects of fractional-order parameters, nonlocality, viscoelasticity and temporal variations. Findings The fractional-order parameter significantly impacts thermophysical values, increasing the strength of each physical field. Nonlocal theory influences the size of biophysical quantities. The fractional MGT theory more accurately represents heat transport in tumor cells than the classical Pennes model. It eliminates non-physical results by predicting thermo-mechanical wave propagation within tissue over a finite spatial range. Research limitations/implications This study does not incorporate interstitial fluid flow, chemical messenger synthesis and diffusion, multi-scale human tissue modeling, or large deformation effects for cancerous cells. Practical implications The findings offer critical insights for thermal therapies such as hyperthermia and laser surgery, where precise thermal shock is essential for controlled destruction of pathological tissues while minimizing collateral damage. The parametric analysis can optimize key design parameters, enhancing the precision of hyperthermia protocols. Originality/value This work develops an analytical framework that integrates higher order fractional time derivatives with Eringen’s nonlocal elasticity and viscoelasticity while also considering porosity within bio-thermoelastic models. This approach provides a more comprehensive understanding of thermo-mechanical interactions in living tissue compared to conventional models.