Light Dosimetry at Tissue Surfaces for Oblique Incident Circular Fields.

Oblique incident light fields are sometimes unavoidable for photodynamic therapy of skin cancers, e.g., for large fields on uneven surface. We have performed Monte-Carlo simulation for circular fields (R = 0.25, 0.35, 0.5, 1, 2, 3, and 8 cm) for reduced scattering coefficient μs' = 10 cm-1 and attenuation coefficient μa = 0.1 - 1.0 cm-1. We used anisotropy g = 0.9 and the index of refraction n = 1.4 for all Monte-Carlo simulations. Compared to a broad beam of normal incidence, the peak fluence rate along the central-axis for a slanted beam is increased for otherwise the same geometrical conditions and optical properties. The effective attenuation coefficient is slightly decreased for a slanted beam compared to a normal incident beam. The beam profile for a slanted beam at a fixed depth is no longer symmetrical but is higher towards the lateral side of beam incidence. Since the broad beam with finite radius R can be considered as a convolution of a pencil beam, solution for a slanted pencil beam can be used to determine the light fluence distribution for circular beams with oblique beam incidence. An analytical solution can be obtained for the pencil beam obliquely incident on a semi-infinite medium. The solution can be approximated using the diffusion or P3 theory with one point source or two point sources located at appropriate depths with appropriate weights along the beam pathlength inside the phantom, with corresponding image sources to fulfill the extended boundary condition. The analytical solution agrees well with Monte-Carlo Simulation at depths z > 2cosθ t /μ' t , θt is the incident angle after refraction at the interface. Measurements using an isotropic detector were made in a liquid phantom composed of intralipid and ink to verify the Monte-Carlo simulation results.