Modeling light fluence rate distribution in optically heterogeneous prostate photodynamic therapy using a kernel method.

To accurately calculate light fluence rate distribution for light dosimetry in prostate photodynamic therapy (PDT), heterogeneity of optical properties has to be taken into account. Previous study has shown that a finite-element method (FEM) can be an efficient tool to deal with the optical heterogeneity. However, the calculation speed of the FEM is not suitable for real time treatment planning. In this paper, two kernel models are developed. Because the kernels are based on analytic solutions of the diffusion equation, calculations are much faster. We derived our extensions of kernel from homogeneous medium to heterogeneous medium assuming spherically symmetrical heterogeneity of optical properties. The kernel models are first developed for a point source and then extended for a linear source, which is considered a summation of point sources uniformly spaced along a line. The kernel models are compared with the FEM calculation. In application of the two kernel models to a heterogeneous prostate PDT case, both kernel models give improved light fluence rate results compared with those derived assuming homogeneous medium. In addition, kernel model 2 predicts reasonable light fluence rates and is deemed suitable for treatment planning.