Nonlinear effects of localized absorption perturbations on the light distribution in a turbid medium

A theoretical model of photon propagation in a scattering medium is presented, from which algebraic formulas for the detector-reading perturbations (delta R) produced by one or two localized perturbations in the macroscopic absorption cross section (delta mu a) are derived. Examination of these shows that when delta mu a is titrated from very small to large magnitudes in one voxel, the curve traced by the corresponding delta R values is a rectangular hyperbola. Furthermore, while delta Rinfinity identical to lim delta mu a-->infinity delta R is dependent on the location of the detector with respect to the source and the voxel, the ratio delta R/ delta Rinfinity is independent of the detector location. We also find that when delta mu a is varied in two voxels simultaneously, the quantity delta R (delta mu a,1 [symbol: see text] delta mu a,2) is a bilinear rational function of the delta mu aS. These results apply not only in the case of steady-state illumination and detection but to time-harmonic measurements as well. The validity of the theoretical formulas is demonstrated by applying them to the results of selected numerical diffusion computations. Potential applications of the derived expressions to image-reconstruction problems are discussed.