Dual-phase-lag thermoelastic analysis of laser-irradiated biological tissue with blood perfusion: a multilayer spherical model.

A dual-phase-lag (DPL) thermoelastic bioheat transfer model incorporating blood perfusion and metabolic heating is developed for the transient analysis of laser-irradiated spherical tumor tissue. The two-layer system (tumor core embedded in normal tissue) is solved semi-analytically in the Laplace domain, and the time-domain results are recovered via Stehfest inversion with NS = 12 terms. The laser transient is posed about a solved pre-exposure metabolic-perfusion equilibrium, so metabolism is not activated artificially at irradiation onset. Derivation from the DPL heat-flux law and complete energy balance shows that the heat-flux-lag operator acts on perfusion and every source term. A Vieta-stable characteristic root and no-division mode normalization remove the cancellation-sensitive elastic-dispersion divisor. An independent radial finite-difference solver reproduces the semi-analytical fields to within 0.0161% for temperature and 0.858% for stress, the laser-increment energy residual stays below 0.00198%, the steady-baseline residual is 0.000136%, and seventy-digit controls show no consequential floating-point loss. Within the numerical reporting window below the imposed 100 °C ceiling (1≤ t ≤ 20 s), the solved baseline is 40.083 °C at the tumor center and the main uniform-source near-center temperature reaches 87.07 °C at 20 s. Radius, finite-boundary, perfusion, phase-lag and equal-power radially decaying source sensitivities delimit where geometry and source idealization affect the predictions. The mechanical coefficients and laser load are legacy/illustrative benchmark inputs, so the framework is intended as a reproducible solver benchmark rather than a patient-specific treatment model.