Spatially varying optical property reconstruction using a finite element diffusion equation approximation

A finite element reconstruction algorithm for optical data based on a diffusion equation approximation is presented. A frequency domain approach is adopted and a unified formulation for three combinations of boundary observables and conditions is described. A multidetector, multisource measurement and excitation strategy is simulated, which includes a distributed model of the light source that illustrates the flexibility of the methodology to modeling adaptations. Simultaneous reconstruction of both absorption and scattering coefficients for a tissue-like medium is achieved for all three boundary data types. The algorithm is found to be computationally practical, and can be implemented without major difficulties in a workstation computing environment. Results using simulated data suggest that qualitative images can be produced that readily highlight the location of absorption and scattering heterogeneities within a circular background region of close to 4 cm in diameter over a range of contrast levels. Absorption images appear to more closely identify the true size of the heterogeneity; however, both the absorption and scattering reconstructions have difficulty with sharp transitions at increasing depth. Quantitatively, the reconstructions are not accurate, suggesting that absolute optical imaging involving simultaneous recovery of both absorption and scattering profiles in multicentimeter tissues geometries may prove to be extremely difficult.