Using the method of images, we examine the three boundary conditions commonly applied to the surface of a semi-infinite turbid medium. We find that the image-charge configurations of the partial-current and extrapolated-boundary conditions have the same dipole and quadrupole moments and that the two corresponding solutions to the diffusion equation are approximately equal. In the application of diffusion theory to frequency-domain photon-migration (FDPM) data, these two approaches yield values for the scattering and absorption coefficients that are equal to within 3%. Moreover, the two boundary conditions can be combined to yield a remarkably simple, accurate, and computationally fast method for extracting values for optical parameters from FDPM data. FDPM data were taken both at the surface and deep inside tissue phantoms, and the difference in data between the two geometries is striking. If one analyzes the surface data without accounting for the boundary, values deduced for the optical coefficients are in error by 50% or more. As expected, when aluminum foil was placed on the surface of a tissue phantom, phase and modulation data were closer to the results for an infinite-medium geometry. Raising the reflectivity of a tissue surface can, in principle, eliminate the effect of the boundary. However, we find that phase and modulation data are highly sensitive to the reflectivity in the range of 80-100%, and a minimum value of 98% is needed to mimic an infinite-medium geometry reliably. We conclude that noninvasive measurements of optically thick tissue require a rigorous treatment of the tissue boundary, boundary approach.

Amplitude-modulated light launched into multiple-scattering media, e.g., tissue, results in the propagation of density waves of diffuse photons. Photon density wave characteristics in turn depend on modulation frequency () and media optical properties. The damped spherical wave solutions to the homogeneous form of the diffusion equation suggest two distinct regimes of behavior: (1) a highfrequency dispersion regime where density wave phase velocity V has a /; dependence and (2) a low-frequency domain where V, is frequency independent. Optical properties are determined for various tissue phantoms by fitting the recorded phase () and modulation (m) response to simple relations for the appropriate regime. Our results indicate that reliable estimates of tissuelike optical properties can be obtained, particularly when multiple modulation frequencies are employed.

The major use of the fluorescence recovery after photobleaching (FRAP) technique is to measure the translational motion of the molecular components in various condensed media. In a conventional laser spot photobleaching experiment, a photomultiplier is used to measure the total brightness levels of the bleached region in the sample, so no spatial information can be directly obtained. In video-FRAP, a series of images after photobleaching is acquired, allowing the spatial character of the recovery to be determined; this permits direct detection of both anisotropic diffusion and flow. To utilize all of the available image data to determine the transport coefficients, a two-dimensional spatial Fourier transform analysis of the images after photobleaching was employed. The change in the transform between two time points reflects the action of diffusion during the interim. An important advantage of this method, which involves taking the ratio of image transforms at different time points, is that it does not require a specific initial condition to be created by laser photobleaching. The ability of the analysis to extract transport coefficients from computer-simulated diffusional recovery is assessed in the presence of increasing amounts of noise. Experimental data analysis from the diffusion of proteins in viscous solutions and from the diffusion of protein receptors on cell surfaces demonstrate the feasibility of the Fourier analysis to obtain transport coefficients from the video FRAP measurement.