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

H. L. Graber et al. (1998)

Summary

A theoretical model of photon propagation in a scattering medium is presented, from which algebraic formulas for the detector-

A theoretical model of photon propagation in a scattering medium is presented, from which algebraic formulas for the detector-readings perturbations (ΔR) produced by one or two localized perturbations in the macroscopic absorption cross section Δμa are derived. Examination of these shows that when Δμa is “titrated” from very small to large magnitudes in one voxel, the curve traced by the corresponding ΔR values is a rectangular hyperbola. Furthermore, while  is dependent on the location of the detector with respect to the source and the voxel, the ratio ΔRR is independent of the detector location. We also find that when Δμa is varied in two voxels simultaneously, the quantity ΔRμa,1 ∧ Δμa,2) is a bilinear rational function of the Δμas. These results apply not only in the case of steady-state illumination and detection but extend 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.