Properties of Photon Density Waves in Multiple-Scattering Media

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 (ω) 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 Vp has a ω dependence and (2) a low-frequency domain where Vp is frequency independent. Optical properties are determined for various tissue phantoms by fitting the recorded phase (Φ) 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

Frequency-Domain Photon Migration in Turbid Media

An analytical model is presented for the propagation of diffuse photon density waves in turbid media. The frequency- and wavelength-dependence of photon density waves are measured using Frequency-domain Photon Migration (FDPM). Media optical properties, including absorption, transport, and fluorescence relaxation times are calculated from experimental results

Optical Property Measurements in Turbid Media Using Frequency Domain Photon Migration

In frequency domain photon migration (FDPM), amplitude-modulated light is launched into a turbid medium, e.g. tissue, which results in the propagation of density waves of diffuse photons. Variations in the optical properties of the medium perturb the phase velocity and amplitude of the diffusing waves. These parameters can be determined by measuring the phase delay and demodulation amplitude of the waves with respect to the source. More specifically, the damped spherical wave solutions to the homogeneous form of the diffusion equation yield expressions for phase (φ) and demodulation (m) as a function of source distance, modulation frequency, absorption coefficient (β), and effective scattering coefficient (Бeff). In this work,we present analytical expressions for the variable dependence of φ and m on modulation frequency. A simple method for extracting absorption coefficients from φ and m vs. frequency plots is applied to the measurement of tissue phantoms. Using modulation frequencies between 5 MHz and 250 MHz, absorption coefficients as low as 0.024cm -l are measured in the presence of effective scattering coefficients as high as 144cm -1. Our results underscore the importance of employing multiple modulation frequencies for the quantitative determination of optical properties

Tissue Characterization and Imaging Using Photon Density Waves

The optical properties of brain tissues have been evaluated by measuring the phase velocity and attenuation of harmonically modulated light. The phase velocity for photon density waves at 650-nm wavelength has been found to be in the range of 5 to 12% of the corresponding velocity in a nonscattering medium, and the optical penetration depth was in the range 2.9 to 5.2 mm. These results are used to predict the resolution of optical imaging of deep tissue structures by diffusely propagating incoherent photons. The results indicate that structures of a few millimeters in linear dimension can be identified at 10 mm depth provided that proper wavelength and time resolution are selected. This depth can possibly be enlarged to 30 mm in the case of tissues with very low scattering such as in the case of the neonatal human brain

Optical Properties of Human Uterus at 630 nm

The optical properties of normal and fibriotic human uteri were determined using frequency-domain and steady-state techniques

Photomedicine of the endometrium: experimental concepts

Gynaecological photomedicine offers new diagnostic and therapeutic methods based on the interaction of light with the reproductive organs. One example is photodynamic therapy (PDT) in which photosensitizers are applied systemically or topically for selective endometrial ablation. Several studies describing the potential use of PDT for this application are reviewed. Basic experimental and clinical aspects of PDT, such as photosensitizer types, application modes, irradiation parameters, optical properties of tissues and photodegradation of photosensitizers are discusse

Boundary Conditions for the Diffusion Equation in Radiative Transfer

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, and we suggest a unified partial-current-extrapolated boundary approach

Phase Velocity Limit of High-Frequency Photon Density Waves

In frequency-domain photonmigration (FDPM), two factors make high modulation frequencies desirable. First, with frequencies as high as a few GHz, the phase lag versus frequency plot has sufficient curvature to yield both the scattering and absorption coefficients of the tissue under examination. Second, because of increased attenuation, highfrequency photon density waves probe smaller volumes, an asset in small volume in vivo or in vitro studies. This trend toward higher modulation frequencies has led us to reexamine the derivation of the standard diffusion equation (SDE)from the Boltzman transport equation. We find that a second-order time-derivative term, ordinarily neglected in the derivation, can be significant above 1GHzfor some biological tissue. The revised diffusion equation, including the second-order time-derivative, is often termed the PI equation. We compare the dispersion relation of the PI equation with that of the SDE. The PI phase velocity is slower than that predicted by the SDE; in fact, the SDE phase velocity is unbounded with increasing modulation frequency, while the PI phase velocity approaches c/sqrt(3) in the high frequency limit. We emphasize that the phase velocity c/sqrt(3) is attained only at modulation frequencies with periods shorter than the mean time between scatterings of a photon, a frequency regime that probes the medium beyond the applicability of diffusion theory. Finally we caution that values for optical properties deduced from FDPM data at high frequencies using the SDE can be in error by 30% or more