A theoretical study of light fractionation and dose-rate effects in photodynamic therapy

The efficacy of photodynamic therapy is dependent upon the optical dose rate or upon the fractionation schedule on the light. These effects are thought to be limited by the time required for oxygen diffusion from the capillaries, since this therapy can consume oxygen faster than it can be supplied to tissues distant from the blood vessels. Oxygen diffusion and consumption by metabolic and photochemical mechanisms have been modeled here to compare theoretical predictions with experimental results of varying light fractionations and delivered dose rates. The mathematics of the problem have been described in the literature, and the present study extends these calculations to allow a more direct and quantitative comparison with fractionation experiments, using both analytical and numerical arguments. The optimum fraction time was found to depend only on the intercapillary spacing and not on the intensity of irradiation or the concentration of photosensitizer. The calculations indicate that experimentally observed optimum fractionation times of 30 and 60 s correspond to a distance from capillary to cell of approximately 1 mm. These results suggest that the fractionated light irradiation experiments need careful interpretation, and some possible reasons for longer optimum fractionation times are discussed.