Analytical solution for thermal response and thermal damage in two-dimensional biological tissue under a moving laser...

This paper presents an analytical study on the thermal response and thermal damage evolution in two-dimensional biological tissue subjected to a moving Gaussian laser source. A bio-heat transfer model incorporating the dual-phase-lag (DPL) constitutive relation is developed, accounting for blood perfusion and metabolic heat generation. The governing equation is solved by Laplace transform combined with eigenfunction expansion, and the time-domain solution is obtained via the Stehfest numerical inversion algorithm. The semi-analytical framework is validated against finite difference solutions, confirming its accuracy and efficiency. Results reveal an asymmetric, teardrop-shaped temperature field and the progressive development of reversible and irreversible thermal damage zones quantified by the Arrhenius integral. Parametric analysis shows that increasing laser speed reduces peak temperature and thermal damage, while a smaller beam radius intensifies energy concentration and localizes damage. This work provides an efficient theoretical tool for optimizing parameters in laser-based medical procedures.