Statistics of Penetration Depth of Photons Re-emitted from Irradiated Tissue

A theory is developed which relates quasi-elastic light scattering measurements to blood flow in tissue micro-vasculature. We assume that the tissue matrix surrounding the blood cells is a strong diffuser of light and that moving erythrocytes, therefore, are illuminated by a spatially distributed source. Because the surrounding tissue is considered to be stationary, Doppler shifts in the frequency of the scattered light arise only from photon interactions with the moving blood cells. The theory implies that the time decay of the photon autocorrelation function scales proportionally with cell size and inversely with mean translational speed. Analysis of multiple interactions of photons with moving cells indicates the manner in which spectral measurements additionally are sensitive to changes in blood volume. Predictions are verified by measurements of particle flow in model tissues.

To allow the determination of scattering and absorption parameters of a turbid material from reflection measurements the relation of these parameters to the reflection has been described by two theoretical approaches. One approach is based on the diffusion theory which has been extended to include anisotropic scattering. This results in a reflection formula in which the scattering and absorption are described by one parameter each. As a second more general approach a Monte Carlo model is applied. Comparison of the results indicates the range of values of the scattering and absorption parameters where the computationally fast diffusion approach is applicable.

Various characteristics of photon diffusion in turbid biological media are examined. Applications include the interpretation of data acquired with laser Doppler blood-flow monitors and the design of protocols for therapeutic excitation of tissue chromophores. Incident radiation is assumed to be applied at an interface between a turbid tissue and a transparent medium, and the reemission of photons from that interface is analyzed. Making use of a discrete lattice model, we derive an expression for the joint probability gamma(n, rho)d2 rho that a photon will be emitted in the infinitesimal area d2 rho centered at surface point rho = (x, y), having made n collisions with the tissue. Mathematical expressions are obtained for the intensity distribution of diffuse surface emission, the probability of photon absorption in the interior as a function of depth, and the mean path length of detected photons as a function of the distance between the site of the incident radiation and the location of the detector. We show that the depth dependence of the distribution of photon absorption events can be inferred from measured parameters of the surface emission profile. Results of relevant computer simulations are presented, and illustrative experimental data are shown to be in accord with the theory.