Light Transport in Biological Tissue Using Three-dimensional Frequency-domain Simplified Spherical Harmonics Equations

The accuracy of the commonly used diffusion approximation as used in diffuse optical tomography is known to be limited in cases involving strong absorption and in these situations a higher ordered approximation is necessary. In this study, a light transport model has been developed based upon the three-dimensional frequency-domain simplified spherical harmonics (SP(N)) approximation for orders up to N = 7. The SP(N) data are tested against a semi-infinite multi-layered Monte Carlo model. It has been shown that the SP(N) approximation for higher orders (N >1) provides an increase in accuracy over the diffusion equation specifically near sources and at boundaries of regions with increased optical absorption. It is demonstrated that the error of fluence calculated near the sources between the diffusion approximation and the SP(N) model (N = 7) can be as large as 60%, therefore limiting the use of the diffusion approximation for small animal imaging and in situations where optical changes near sources are critical for tomographic reconstructions.