Photodynamic therapy: computer modeling of diffusion and reaction phenomena

We have developed a transient, one-dimensional mathematical model for the reaction and diffusion phenomena that occurs during photodynamic therapy (PDT). This model is referred to as the PDTmodem program. The model is solved by the Crank-Nicholson finite difference technique and can be used to predict the fates of important molecular species within the intercapillary tissue undergoing PDT. The following factors govern molecular oxygen consumption and singlet oxygen generation within a tumor: (1) photosensitizer concentration; (2) fluence rate; and (3) intercapillary spacing. In an effort to maximize direct tumor cell killing, the model allows educated decisions to be made to insure the uniform generation and exposure of singlet oxygen to tumor cells across the intercapillary space. Based on predictions made by the model, we have determined that the singlet oxygen concentration profile within the intercapillary space is controlled by the product of the drug concentration, and light fluence rate. The model predicts that at high levels of this product, within seconds singlet oxygen generation is limited to a small core of cells immediately surrounding the capillary. The remainder of the tumor tissue in the intercapillary space is anoxic and protected from the generation and toxic effects of singlet oxygen. However, at lower values of this product, the PDT-induced anoxic regions are not observed. An important finding is that an optimal value of this product can be defined that maintains the singlet oxygen concentration throughout the intercapillary space at a near constant level. Direct tumor cell killing is therefore postulated to depend on the singlet oxygen exposure, defined as the product of the uniform singlet oxygen concentration and the time of exposure, and not on the total light dose.