A diffusion equation based algorithm for determination of the optimal number of fibers used for breast cancer treatment planning in photodynamic therapy

Abstract

It is essential in interstitial Photodynamic therapy (iPDT) treatment planning to ensure a homogeneous distribution within a tumor volume using cylindrical diffusing fibers while keeping the surrounding tissue intact. Light distribution is simulated through two algorithms based on the diffusion equation assuming diffusers as light sources. The first algorithm analyzes the diffusion equation and studies the effects of different variables (optical properties, delivered power, diffuser length, and position). Next, optical properties of breast were applied to estimate the volume that receives accepted light dose from one diffuser. In the second algorithm, multiple diffusers were simulated in order to find the relation between the volume and the number of required diffusers which are needed to cover cubical or cylindrical volume with sufficient light dose. Throughout this study, real values of optical properties, clinical laser power, and treatment time were considered to evaluate sufficient light doses. This study is in agreement with previous works in that optical properties are the major factors influencing light distribution in iPDT. It is shown that for a homogeneous phantom mimicking breast cancer and cubical or cylindrical shape, the number of required fibers N equal W×L or D2 respectively.

Keywords

• ipdt, diffusion equation, cylindrical diffuser fiber, sufficient light dose, breast cancer