State-space Approach Based on Fractional Three-Phase-lag Thermoelasticity of Biological Tissue in Nanoparticle-Assisted Hyperthermia

Gold nanoparticles, serving as a photothermal agent, are often embedded in tumor tissue to enhance the efficacy of laser hyperthermia. This paper investigates the thermomechanical response of a two-layer semi-infinite biological tissue composed of tumor tissue embedded with gold nanoparticles and normal tissue under laser irradiation. By incorporating the Pennes bioheat equation, a fractional three-phase-lag (FTPL) thermoelastic model is formulated to address the problem. The gold nanoparticles affect the laser absorption and scattering at the tumor site. The exact analytical solution of the fractional thermomechanical coupling problem is obtained by coupling the state-space method with the Laplace transformation. The influence of the FTPL model parameters, the convective cooling coefficient at the boundary, the gold nanoparticle concentration, and the laser parameters on the thermomechanical behavior are analyzed. This study establishes a unified thermomechanical coupling solution framework via the state-space method for laser hyperthermia, and provide valuable insights for the application and development of gold nanoparticles in biological thermal therapy.