Study of tissue oxygen supply rate in a macroscopic photodynamic therapy singlet oxygen model

An appropriate expression for the oxygen supply rate (Γ(s)) is required for the macroscopic modeling of the complex mechanisms of photodynamic therapy (PDT). It is unrealistic to model the actual heterogeneous tumor microvascular networks coupled with the PDT processes because of the large computational requirement. In this study, a theoretical microscopic model based on uniformly distributed Krogh cylinders is used to calculate Γ(s) = g (1 - [³O₂]/[³O₂]₀) that can replace the complex modeling of blood vasculature while maintaining a reasonable resemblance to reality; g is the maximum oxygen supply rate and [³O₂]/[³O₂]₀ is the volume-average tissue oxygen concentration normalized to its value prior to PDT. The model incorporates kinetic equations of oxygen diffusion and convection within capillaries and oxygen saturation from oxyhemoglobin. Oxygen supply to the tissue is via diffusion from the uniformly distributed blood vessels. Oxygen can also diffuse along the radius and the longitudinal axis of the cylinder within tissue. The relations of Γ(s) to [³O₂]/[³O₂]₀ are examined for a biologically reasonable range of the physiological parameters for the microvasculature and several light fluence rates (ϕ). The results show a linear relationship between Γ(s) and [³O₂]/[³O₂]₀, independent of ϕ and photochemical parameters; the obtained g ranges from 0.4 to 1390 μM/s.