Identification of the Functional Form of Nonlinear Effects of Localized Finite Absorption in a Diffusing Medium

H. L. Graber et al. (1995)


A linear perturbation model for reconstructing images of absorption (Σa) and scattering (Σs) cross sections of a highly scattering medium is presented. Two factors limiting the accuracy of images reconstructed from linear perturbation models are described. These are self-shadowing effect of a single perturbation and the mutual coupling effect of two perturbations. A relaxation method to numerically solve the diffusion equation for a slab geometry and to compute the flux of diffuse light crossing both surfaces of an intially nonabsorbing (Σs= 1.0, Σa= 0.0) slab, as the Σa in one or two cells of the medium is increased. When a single voxel was perturbed, it was found that: 1) for all voxel locations considered, a plot of change in light flux vs. change in Σa deviates significantly from a straight line when the addtional Σa exceeds ~0.1; 2) the rate at which the flux perturbation approaches its limiting value as Σa increases is independent of the location of the perturbed voxel. When two voxels were perturbed simultaneously, it was found that: 1) the distance separating two voxels is the most important determinant of the maximal mutual coupling effect they can have; 2) the maximal mutual coupling effect falls rapidly as the distance between two voxels increases; 3) if both perturbed voxels are lie in the same layer (i.e., depth), the rate at which the mutual coupling effect approaches its limiting value as the Σa perturbations increase is independent of the detector location; 4) when the perturbed voxels are different layers, there is a small but significant difference between the effects of mutual coupling on the diffuse transmission and on the diffuse reflectance. Low-order rational functions are sufficient for modeling both the self-shadowing and mutual coupling effects. Methods for modifying image reconstruction algorithms to incoporate corrections for these two effects are discussed.