Photodynamic Therapy (PDT) Mathematical and Physical Principles Underlying Photodynamic Therapy A Precision Approach to Skin Treatment

Abstract

Photodynamic Therapy (PDT) is a highly targeted and minimally invasive treatment that leverages the principles of mathematics and physics to treat various skin conditions. Its mechanism involves light absorption, energy transfer, and the generation of reactive oxygen species (ROS) to selectively destroy diseased cells while sparing healthy tissues. The process begins with the absorption of light, governed by the Beer-Lambert Law, which determines how light penetrates the skin and interacts with the photosensitizer. Energy transfer occurs as photons excite the photosensitizer, producing ROS through quantum efficiency and energy conversion processes. Tissue optics and scattering dynamics, modeled by radiative transport equations, further elucidate how light diffuses through skin layers. Additionally, Fick’s Laws of Diffusion describe ROS distribution and their interaction with cellular targets. Mathematical models incorporating light intensity, photosensitizer concentration, and oxygen availability allow precise calculation of PDT dosimetry. This integration of physics and mathematics provides a foundation for optimizing PDT efficacy and expanding its clinical applications.