Fractional two-temperature dual-phase-lag bioheat transfer under electromagnetic heating: An analytical-physics-informed neural network framework

This study develops a hybrid semi-analytical and physics-informed neural-network framework for transient thermoelastic heat transfer in biological tissue subjected to electromagnetic heating. The formulation combines a fractional two-temperature dual-phase-lag bioheat model with thermoelastic coupling, blood perfusion, temperature-dependent metabolic heat generation, and an effective Maxwell–Ohm Joule-heating source. The governing equations are solved in the Laplace domain and numerically inverted to generate reference temperature, displacement, and stress fields, which are subsequently used to constrain and evaluate a physics-informed neural network. In response to recent experimental evidence on non-Fourier heat transfer in skin, the heat-flux and temperature-gradient phase lags are restricted to an experimentally informed sub-second domain, with baseline values 𝜏 𝑞 = 0 . 2 5 s and 𝜏 𝑇 = 0 . 1 0 s . The results show that fractional thermal memory, conductive–thermodynamic temperature non-equilibrium, and finite-rate transport modify thermal penetration and the timing and magnitude of the thermoelastic response, with the strongest effects concentrated in the rapidly heated near-surface region. The corrected PINN reproduces the semi-analytical thermal and mechanical fields with close field-level agreement within the validated parameter domain, enabling rapid repeated evaluation without replacing the underlying physics-based reference model. Arrhenius post-processing links the corrected transient temperature histories to exposure-time- and depth-dependent thermal-damage measures. The framework therefore provides a computationally efficient tool for sensitivity analysis and model-based thermal-safety assessment. The fractional order and phase-lag parameters are treated as effective, tissue- and protocol-dependent quantities; direct experimental calibration and validation of the complete fractional TTDPL–electromagnetic–thermoelastic model remain necessary before clinical interpretation.