Intensity-modulated light launches traveling photon-density waves into optically diffusive media. In the presence of a fluorophore, excitation photon density waves generate fluorescence photon-density waves that can be quantitatively described using diffusion theory. We examine a number of limiting cases of the fluorescence photon-density wave to clarify its physical meaning and its implications in quantitative fluorescence spectroscopy of diffusive media. Our discussion may guide the development of experimental protocols for quantitative fluorescence spectroscopy in optically diffusive media.

The reconstruction of the location and optical properties of objects in turbid media requires the solution of the inverse problem. Iterative solutions to this problem can require large amounts of computing time and may not converge to a unique solution. Instead, we propose a fast, simple method for approximately solving this problem in which calculated effective absorption and reduced scattering coefficients are backprojected to create an image of the objects. We reconstructed images of objects with centimeter dimensions embedded in a diffusive medium with optical characteristics similar to those of human tissue. Data were collected by a frequency-domain spectrometer operating at 120 MHz with a laser diode light source emitting at 793 nm. Intensity and phase of the incident photon density wave were collected from linear scans at different projection angles. Although the positions of the objects are correctly identified by the reconstructed images, the optical parameters of the objects are recovered only qualitatively.

We have studied light migration in highly scattering media theoretically and experimentally, using the diffusion approximation in a semi-infinite-geometry boundary condition. Both the light source and the detector were located on the surface of a semi-infinite medium. Working with frequency-domain spectroscopy, we approached the problem in three areas: (1) we derived theoretical expressions for the measured quantities in frequency-domain spectroscopy by applying appropriate boundary conditions to the diffusion equation; (2) we experimentally verified the theoretical expressions by performing measurements on a macroscopically homogeneous medium in quasi-semi-infinite-geometry conditions; (3) we applied Monte Carlo methods to simulate the semi-infinite-geometry boundary problem. The experimental results and the confirming Monte Carlo simulation show that the diffusion approximation, under the appropriate boundary conditions, accurately estimates the optical parameters of the medium. © 1994 Optical Society of America.

The Green's function for the diffusion equation is widely used to describe photon transport in turbid media. We have performed aseries of spectroscopy experiments on a number of uniform turbid media with different optical properties (absorption coefficient in the range 0.03-0.14 cm(-1), reduced scattering coefficient in the range 5-22 cm(-1)). Our experiments have been conducted in the frequency domain, where the measured parameters are the dc intensity (I(dc)), ac amplitude (I(ac)), and phase (?) of the light intensity wave. In an infinite medium, the Green's function predicts a linear dependence of ln(rI(dc)) and ? on the source-detector separation r. Our measurements show that the intercepts of these straight lines predicted by the Green's function do not agree with the experimental results. To reproduce the experimental results, we have introduced an effective photon source whose spatial extent and source strength depend on the optical properties of the medium. This effective source term has no effect on the slopes of the straight lines predicted by the Green'sfunction at large values of r.

The predictions of the frequency-domain standard diffusion equation (SDE) model for light propagation in an infinite turbid medium diverge from the more complete [Formula Presented] approximation to the linear Boltzmann transport equation at intensity modulation frequencies greater than several hundred MHz. The [Formula Presented] approximation is based on keeping only the terms l=0 and l=1 in the expansion of the angular photon density in spherical harmonics, and the nomenclature [Formula Presented] approximation is used since the spherical harmonics of order l=1 can be written in terms of the first order Legendre polynomial, which is traditionally represented by the symbol [Formula Presented]. Frequency-domain data acquired in a quasi-infinite turbid medium at modulation frequencies ranging from 0.38 to 3.2 GHz using a superheterodyning microwave detection system were analyzed using expressions derived from both the [Formula Presented] aproximation equation and the SDE. This analysis shows that the [Formula Presented] approximation provides a more accurate description of the data over this range of modulation frequencies. Some researchers have claimed that the [Formula Presented] approximation predicts that a light pulse should propagate with an average speed of c/ √3 in a thick turbid medium. However, an examination of the Green’s function that we obtained from the frequency-domain [Formula Presented] approximation model indicates that a photon density wave phase velocity of c/ √3 is only asymptotically approached in a regime where the light intensity modulation frequency aproaches infinity. The Fourier transform of this frequency-domain result shows that in the time domain, the [Formula Presented] approximation predicts that only the leading edge of the pulse (i.e., the photons arriving at the detector at the earliest time) approaches a speed of c/√3. © 1996 The American Physical Society.

Light spectroscopy in the frequency-domain has been used to study the optical properties of biological tissues. We have analyzed the possibility of using light emitting diodes (LEDs) as intensity modulated light sources for frequency-domain spectroscopy. The use of LEDs presents several advantages: One LED's output covers a spectral region of about 80 nm, and commercially available LEDs allow for the coverage of the spectral range from 550 to 900 nm, which is a region of interest in near infrared medical applications; the light output of an LED is stable with respect to that of lasers and lamps; the wide angular disthbution make LEDs safe for in vivo studies. Furthermore, LED frequency-domain spectroscopy is a relatively inexpensive technique. We describe some circuits we used to modulate the intensity of LEDs at radio frequency, and point out the possibility of building a multi-source spectrometer. Some applications of LED frequency-domain spectroscopy, both in vitro and in vivo, are shown.

We have measured the local blood flow (BF) and oxygen consumption (OC) in the human calf muscle using near-infrared spectroscopy during venous occlusion. Venous occlusion was achieved by inflating a pneumatic cuff around the thigh of the subject. We have investigated the influence of the inflation time and cuff pressure on the recovered values of BF and OC. We have found that if the cuff pressure is increased from a threshold pressure (approximately 30 mm Hg) to a critical pressure (approximately 45 mm Hg) in less than about 6 s, one measures the same values of BF and OC independent of the total inflation time and final cuff pressure. We also report nine-pixel spatial maps of BF and OC to show that this technique can lead to spatially resolved measurements of blood flow and oxygen consumption in tissues.

We have developed an instrument for non-invasive optical imaging of the human brain that produces on-line images with a temporal resolution of 160 ms. The imaged quantities are the temporal changes in cerebral oxy-hemoglobin and deoxy-hemoglobin concentrations. We report real-time videos of the arterial pulsation and motor activation recorded on a 4 x 9 cm 2 area of the cerebral cortex in a healthy human subject. This approach to optical brain imaging is a powerful tool for the investigation of the spatial and temporal features of the optical signals collected on the brain.

We have measured the optical absorption and scattering coefficient spectra of a multiple-scattering medium (i.e., a biological tissue-simulating phantom comprising a lipid colloid) containing methemoglobin by using frequency-domain techniques. The methemoglobin absorption spectrum determined in the multiple-scattering medium is in excellent agreement with a corrected methemoglobin absorption spectrum obtained from a steady-state spectrophotometer measurement of the optical density of a minimally scattering medium. The determination of the corrected methemoglobin absorption spectrum takes into account the scattering from impurities in the methemoglobin solution containing no lipid colloid. Frequency-domain techniques allow for the separation of the absorbing from the scattering properties of multiple-scattering media, and these techniques thus provide an absolute measurement of the optical absorption spectra of the methemoglobin/lipid colloid suspension. One accurately determines the absolute methemoglob in absorption spectrum in the frequency domain by extracting the scattering and absorption coefficients from the phase shift Φ and average light intensity DC (or Φ and the amplitude of the light-intensity oscillations AC) data with relationships provided by diffusion theory, but one determines it less accurately by using the Φ and modulation M (M ≡ AC/DC) data and the diffusion theory relationships. In addition to the greater uncertainty in the absorption and scattering coefficients extracted from the Φ and M data, the optical parameters extracted from the Φ and M data exhibit systematically inaccurate behavior that cannot be explained by random noise in the system. Possible reasons for the systematically lower accuracy of the methemoglobin absorption spectrum obtained from Φ and M data are discussed.

We have investigated the accuracy of the frequency-domain, diffusion equation Green's function in modeling optical signals in turbid media. Our optical measurements were conducted in strongly scattering media having absorption coefficients in the range 0.035-0.14 cm-1 and reduced scattering coefficients in the range 5-22 cm-1. The optical signal was both delivered to and collected from the sample by means of optical fibers. We have verified that the r-independent factor in the Green's function does not agree with the experimental data. This discrepancy shows that the photons launched in the medium by an optical fiber cannot be modeled by a point source located at a fixed position. These results have no influence on multi-distance measurement protocols (which only employ the r-dependent part of the solution), while they must be considered when calibration measurements on a known sample are performed.