A study of the radiative transfer equation using a spherical harmonics-nodal collocation method

- The diffusion approximation to the radiative transfer equation has limited validity.
- The PL equations for the radiative transfer problem are studied.
- These equations are spatially discretized using a nodal collocation method.
- Different 1D and 2D benchmark problems of light propagation in tissue are solved.

Optical tomography has found many medical applications that need to know how the photons interact with the different tissues. The majority of the photon transport simulations are done using the diffusion approximation, but this approximation has a limited validity when optical properties of the different tissues present large gradients, when structures near the photons source are studied or when anisotropic scattering has to be taken into account. As an alternative to the diffusion model, the PL equations for the radiative transfer problem are studied. These equations are discretized in a rectangular mesh using a nodal collocation method. The performance of this model is studied by solving different 1D and 2D benchmark problems of light propagation in tissue having media with isotropic and anisotropic scattering.