Macroscopic Modeling of the singlet oxygen production during PDT.

Photodynamic therapy (PDT) dose, D, is defined as the absorbed dose by the photosensitizer during photodynamic therapy. It is proportional to the product of photosensitizer concentration and the light fluence. This quantity can be directly characterized during PDT and is considered to be predictive of photodynamic efficacy under ample oxygen supply. For type-II photodynamic interaction, the cell killing is caused by the reaction of cellular acceptors with singlet oxygen. The production of singlet oxygen can be expressed as ηD, where η is the singlet oxygen quantum yield and is a constant under ample oxygen supply. For most PDT, it is desirable to also take into account the effect of tissue oxygenation. We have modeled the coupled kinetics equation of the concentrations of the singlet oxygen, the photosensitizers in ground and triplet states, the oxygen, and tissue acceptors along with the diffusion equation governing the light transport in turbid medium. We have shown that it is possible to express η as a function of local oxygen concentration during PDT and this expression is a good approximation to predict the production of singlet oxygen during PDT. Theoretical estimation of the correlation between the tissue oxygen concentration and hemoglobin concentration, oxygen saturation, and blood flow is presented.