A semi-analytical dual-phase-lag model for the thermal and mechanical responses of skin tissue under continuous laser irradiation

The aim of this study is to establish a one-dimensional semi-analytical framework that sequentially couples the dual-phase-lag non-Fourier heat transfer theory with generalized linear thermoelasticity to predict the transient temperature, displacement, and stress responses of skin tissue under continuous-wave laser irradiation, and to quantify how the phase-lag parameters, intrinsic tissue properties and laser characteristics govern the thermomechanical safety boundaries of laser thermotherapy. The governing equations are decoupled by the separation of variables method and Duhamel's integral, and the resulting series solutions agree with COMSOL finite-element benchmarks to within 0.12% for the peak temperature and 5% for the peak stress. The results reveal three primary modulation mechanisms. First, an increase in the heat flux phase lag reduces both the surface peak temperature and the maximum compressive stress, whereas an increase in the temperature gradient phase lag promotes deeper energy diffusion and elevates the temperature and thermal expansion strain in sub-surface tissues. Second, the intrinsic tissue properties exert a dual damping effect: a higher tissue density attenuates both the thermal and mechanical responses, whereas increased microcirculatory blood perfusion provides only limited cooling against extreme temperature peaks. Third, the laser characteristics govern the safety boundaries: longer wavelengths substantially reduce the surface temperature and compressive stress, whereas a higher power density nonlinearly escalates the induced mechanical stress and the associated risk of tissue damage. The proposed model provides theoretical support for the preliminary determination of laser thermotherapy safety thresholds and the optimization of personalized treatment protocols, while the reported stress-based thresholds remain theoretical predictions that require experimental and clinical validation.