Mathematical Modeling And Verification Study On Photodynamic Therapy For Port Wine Stains

Objective This study aims to establish a systemic mathematical model and a simulation method of Photodynamic Therapy (PDT) for Port Wine Stains (PWS) through analyzing effect of correlative factors (such as laser, photosensitizer, oxygen) and their interaction applying mathematical method. And it is verified by experimental work.Methods & Results In the first part, the mathematical model of PDT for PWS is established through mathematical method on the basis of the next three aspects: (1) The distribution model of laser in tissue: The Monte Carlo method is applied, considering the complex pathology structure of PWS. (2) The concentration model of photosensitizer includes two parts: The concentration in microvasculature varies according to pharmacokinetics; The photosensitizer diffuses in tissue due to Fick's law, and is affected by photobleaching simultaneously. (3) The concentration model of oxygen in tissue: Oxygen diffusion is given by Fick's law, and singlet oxygen (¹O₂) generation causes the oxygen consumption.The mathematic model of ¹O₂ is established on the basis of above three models. The generation rate of ¹O₂ is calculated by Lambert-Beer's law and quantum yields equation of ¹O₂. Then, the systemic simulation methods are established by finite difference method.In the second part, the production and distribution of ¹O₂ in vessel and tissue are simulated on an ideal tissue model which is a cube containing a cylindrical vessel. More attention has been paid on the spatial and temporal rule of ¹O₂ distribution, as well as the impact of each factor in mathematical model. The results showed: (1) Most of ¹O₂ is produced in vascular wall and blood near the wall. (2) The production of ¹O₂ is non-linear with the dose of laser and photosensitizer through the direct and indirect effect (photobleaching and effect of oxygen). (3) The target tissue selective effect of...