Effects due to geometry and boundary conditions in multiple light scattering

Three-dimensional simulation of near-infrared diffusion in tissue: boundary condition and geometry analysis for finite-element image reconstruction

Imaging of tissue with near-infrared spectral tomography is emerging as a practicable method to map hemoglobin concentrations within tissue. However, the accurate recovery of images by using modeling methods requires a good match between experiments and the model prediction of light transport in tissue. We illustrate the potential for a match between (i) three-dimensional (3-D) frequency-domain diffusion theory, (ii) two-dimensional diffusion theory, (iii) Monte Carlo simulations, and (iv) experimental data from tissue-simulating phantoms. Robin-type boundary conditions are imposed in the 3-D model, which can be implemented with a scalar coupling coefficient relating the flux through the surface to the diffuse fluence rate at the same location. A comparison of 3-D mesh geometries for breast imaging indicates that relative measurements are sufficiently similar when calculated on either cylindrical or female breast shapes, suggesting that accurate reconstruction may be achieved with the simpler cylindrical mesh. Simulation studies directly assess the effects from objects extending out of the image plane, with results suggesting that spherically shaped objects reconstruct at lower contrast when their diameters are less than 15-20 mm. The algorithm presented here illustrates that a 3-D forward diffusion model can be used with circular tomographic measurements to reconstruct two-dimensional images of the interior absorption coefficient.

Boundary conditions for light propagation in diffusive media with nonscattering regions

The diffusion approximation proves to be valid for light propagation in highly scattering media, but it breaks down in the presence of nonscattering regions. We present a compact expression of the boundary conditions for diffusive media with nonscattering regions, taking into account small-index mismatch. Results from an integral method based on the extinction theorem boundary condition are contrasted with both Monte Carlo and finite-element-method simulations, and a study of its limit of validity is presented. These procedures are illustrated by considering the case of the cerebro-spinal fluid in the brain, for which we demonstrate that for practical situations in light diffusion, these boundary conditions yield accurate results.

Theory of a fixed scatterer embedded in a turbid medium: numerical results

Based on a previous theory of diffuse photon density waves by Furutsu [J. Opt. Soc. Am. A 15, 1371 (1998)], several sets of figures are prepared to detect a fixed scatterer (object) embedded in a turbid layer, such as a tumor in tissue, with a source and a detector placed independently along the boundaries on different sides. The relative total intensity of the wave is introduced such that it is reduced to 1 in the case of no scatterer and usually less than that, owing to a shadowing by the scatterer. Sets of curves are presented to demonstrate shadow images of the scatterer observed along the layer boundaries depending on the scatterer's location.

Does the photon-diffusion coefficient depend on absorption?

We investigate the controversy over the precise form of the photon diffusion coefficient and suggest that it is largely independent of absorption, i.e., Do = v/3mu(s)'. After presentation of the general theoretical arguments underlying this assertion, Monte Carlo simulations are performed and explicitly reveal that the absorption independent diffusion coefficient gives better agreement with theory than the traditionally accepted photon diffusion coefficient, D(mu)a = v/3(mu(s) + mu(a)). The importance of resolving this controversy for the proper characterization of the material optical properties is discussed.