A theoretical comparison of macroscopic and microscopic modeling of singlet oxygen during Photofrin and HPPH mediated-PDT.

Mathematic models were developed to simulate the complex dynamic process of photodynamic therapy (PDT). Macroscopic or microscopic modeling of singlet oxygen (1O2) is particularly of interest because it is the major cytotoxic agent causing biological effects during PDT. Our previously introduced macroscopic PDT model incorporates the diffusion equation for the light propagation in tissue and the macroscopic kinetic equations for the production of the 1O2. The distance-dependent distribution of 3O2 and reacted 1O2 can be numerically calculated using finite-element method (FEM). We recently improved the model to include microscopic kinetic equations of oxygen diffusion from uniformly distributed blood vessels and within tissue. In the model, the cylindrical blood capillary has radius in the range of 2-5 μm and a mean length of 300 μm, and supplies oxygen into tissue. The blood vessel network is assumed to form a 2-D square grid perpendicular to a linear light source. The spacing of the grid is 60 μm. Oxygen can also diffuse along the radius and the longitudinal axial of the cylinder within tissue. The oxygen depletion during Photofrin-PDT can be simulated using both macroscopic and microscopic approaches. The comparison of the simulation results have reasonable agreements when velocity of blood flow is reduced during PDT.