Incorporating temperature-dependent properties into the modeling of photo-thermo-mechanical interactions in cancer tissues

Abstract

The interaction between laser beams and biological tissue is notably characterized by the photo-thermo-mechanical mechanism. Modeling the behavior of biological tissue has proven to be highly beneficial in the medical field, encompassing various applications such as the diagnosis and treatment of diverse human ailments. Examining alterations in tumor temperature and their distribution when exposed to a heat source, like a laser beam, and improving heat absorption rates through nanoparticles, presents a substantial challenge. This challenge becomes particularly complex when cancer characteristics are influenced by temperature changes. Therefore, this study delves into the coupled mechanical and thermal behaviors of cancer tissue through coupled nonlinear thermo-mechanical equations with variable coefficients.The derivation of two nonlinear coupled equations, accounting for temperature distribution and motion, is based on non-Fourier heat conduction, considering dual phase lags and a Zener-type thermo-viscoelastic constitutive model for cancer tumors. This formulation takes into account variable thermo-mechanical characteristics. To address the nonlinearity stemming from variable coefficients, the governing equations are solved simultaneously in the spatial and temporal domains. This is achieved through an approach involving initial and boundary conditions, employing a semi-numerical-analytical technique using a Galerkin-based reduced order model and Laplace transform in each time step. The coefficients are updated at subsequent steps. The study thoroughly investigates the approach of subjecting tissue to a heating source and explores the effects of phase lags.