Einas M.A. Widaa
Physical Science Department, Faculty of Science, Taif University, P.O. Box. 11099, Turaba 21945, Kingdom of Saudi Arabia
Mohamed Yahia Shirgawi
Department of physics, Faculty of Art and Science at AL Muznab, AL Qassim University, AL Muznab, Kingdom of Saudi Arabia
Abeer Mohammed Khairy Ahmed
Department of physics, Faculty of Art and Science at AL Muznab, AL Qassim University, AL Muznab, Kingdom of Saudi Arabia
Mohammed Ismail Adam Saleh
Physics Department, Faculty of Science, Al-Baha University, Al-Baha P.O. Box 1988, Kingdom of Saudi Arabi
Musa Ibrahim Babiker Hussein
Physics Department, Faculty of Science, Al-Baha University, Al-Baha P.O. Box 1988, Kingdom of Saudi Arabi
Ebtisam A. Yousef
Department of Physical Sciences, Physics Division, College of Science, Jazan University, P.O. Box 114, Jazan 45142, Saudi Arabia
Manahil A. Mohammed Ashmaig
Mathematics Department, Faculty of Science Qassim University, Buraydah 51452, Saudi
A.H. Abdelrahman
Department of Physics, College of Science, Qassim University, 51452 Buridah, Saudi Arabia
Najwa Idris A. Ahmed
Department of Physics, College of Science, Qassim University, 51452 Buridah, Saudi Arabia
This study presents a unified quantum–biophysical model for describing light–tissue interaction in photodynamic and diagnostic applications. The framework combines the time-dependent Schrödinger equation with Maxwell’s electromagnetic coupling, allowing the representation of photon dynamics, energy localization, and absorption in complex biological media. The optical potential and damping terms are introduced to model refractive and absorptive properties, respectively, leading to analytical expressions for the quantum absorption coefficient ( ), relaxation time ( ), and Photodynamic Therapy Index (PDTI). The model predicts that light intensity decays exponentially with depth, while higher absorption coefficients yield faster relaxation and stronger surface energy deposition—characteristics desirable for shallow photodynamic therapy. A Klein–Gordon relativistic extension is proposed for high-energy photon regimes such as UV or X-ray interactions. The developed theoretical framework provides a data-free, physics-based approach to estimate and optimize biphotonic efficiency. It establishes a foundation for future integration with Physics-Informed Neural Networks (PINNs) to retrieve tissue-dependent parameters from imaging data, bridging quantum theory and medical photonics in a mathematically consistent way.
