Photo-thermal Bidirectional Coupling Model for Transcranial Photobiomodulation

Abstract

BackgroundAccurate optical-field simulation is critical for precise dosage delivery in transcranial photobiomodulation (tPBM). Current simulations neglect photon absorption-induced tissue heating which leads to temperature-dependent alterations of the optical field, thus fails to account for the bidirectional photo-thermal coupling effect. ObjectiveThis paper aims to establish a dynamic photo-thermal couple model that rigorously quantifies the bidirectional interaction between tissue heating and light propagation, and improves the optical dose prediction. ModelWe propose a Photo-Thermal bidirectional coupling Model (PTM). First, the Pennes Bioheat Equation (PBE) is employed to model the thermal response induced by photon absorption. Second, a Real-time temperature-dependent Absorption coefficient Model (RAM) is newly developed to quantify the thermal effect. Third, the PBE and RAM are integrated into the photon diffusion equation, forming the PTM. Finally, this coupled framework is solved temporally by an unconditionally stable Crank-Nicolson scheme. SimulationsBenchmarking against an analytical solution (two-layer cylindrical domain) demonstrates that PTM reduces the temperature prediction error by over 2.35% compared to the uncoupled baseline. Simulations using a realistic head model reveal that, compared to PTM, uncoupled modeling underestimates energy deposition by 150 J/m3 and overestimates photon fluence by 3 J/m2 within just one minute, and such discrepancies will be amplified with increasing exposure duration and power. Furthermore, the PTM identifies a 1.43-mm advantage in penetration depth for pulsed-wave over continuous-wave modality under iso-energy conditions, a key insight enabled by the coupled modeling approach. ConclusionThe PTM provides a high-fidelity simulation framework that captures the dynamic, bidirectional photo-thermal coupling in tPBM, explicitly quantifying the thermal feedback ignored by current models and thereby enabling more reliable treatment optimization and safer clinical translation.