Aspects of Mathematical Modeling in Photodynamic Therapy

This contribution examines the effects of oxygen diffusion and transport on the observed kinetics during Photodynamic Therapy in a spherical cell model and also provides a theoretical background for the qualitative and quantitative characterization of different aspects of basic cellular decision making processes. The logical design and computational algorithms consider the decision-making process of a single cell in response to PDT treatment, and can be adjusted to accommodate and provide important insights into cellular response to other treatments, such as radiation, chemotherapy, neurodegeneration, etc., by applying the principles introduced here. Moreover, this study includes the introduction of predator prey dynamical systems for the study of PDT survival curves in the time domain and points towards an axiomatic foundation of biological behavior of PDT treated cells, according to the current line of research in the field, that will assess various experimental data.