A transient one-dimensional mathematical model is presented to help visualize the qualitative and quantitative effects on inter-capillary tissue undergoing photodynamic therapy (PDT). The model is solved by a Crank-Nicholson finite difference formulation to provide time-dependent concentrations of the Type II mechanism's photo-oxidation species in the tissue surrounding a capillary. The time-dependent solution allows educated decisions to be made as to the optimum timing of light fractionation (on/off) cycles. Qualitative and quantitative optimization of the PDT process is considered along with a case study of data in the literature, the main goal being to provide optimized light therapy regimens for eventual clinical use.
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Henning et al. (1995) studied this question.
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