Light propagation in strongly scattering media can be described by the diffusion approximation to the Boltzmann transport equation. We have derived analytical expressions based on the diffusion approximation that describe the photon density in a uniform, infinite, strongly scattering medium that contains a sinusoidally intensity-modulated point source of light. These expressions predict that the photon density will propagate outward from the light source as a spherical wave of constant phase velocity with an amplitude that attenuates with distance r from the source as exp(-ar)/r. The properties of the photon-density wave are given in terms of the spectral properties of the scattering medium. We have used the Green's function obtained from the diffusion approximation to the Boltzmann transport equation with a sinusoidally modulated point source to derive analytic expressions describing the diffraction and the reflection of photon-density waves from an absorbing and/or reflecting semi-infinite plane bounded by a straight edge immersed in a strongly scattering medium. The analytic expressions given are in agreement with the results of frequency-domain experiments performed in skim-milk media and with Monte Carlo simulations. These studies provide a basis for the understanding of photon diffusion in strongly scattering media in the presence of absorbing and reflecting objects and allow for a determination of the conditions for obtaining maximum resolution and penetration for applications to optical tomography.

Near-infrared (NIR) optical properties of turbid media, e.g., tissue, can be accurately quantified noninvasively using methods based on diffuse reflectance or transmittance, such as frequency domain photon migration (FDPM). Factors which govern the accuracy and sensitivity of FDPM-measured optical properties include instrument performance, the light propagation model, and fitting algorithms used to calculate optical properties from measured data. In this article, we characterize instrument, model, and fitting uncertaintics of an FDPM system designed for clinical use and investigate how each of these factors affects the quantification of NIR absorption (μa) and reduced scattering (μs′) parameters in tissue phantoms. The instrument is based on a 500 MHz, multiwavelength platform that sweeps through 201 discrete frequencies in as little as 675 ms. Phase and amplitude of intensity modulated light launched into tissue, i.e., diffuse photon density waves (PDW), are measured with an accuracy of ±0.30° and ±3.5%, while phase and amplitude precision are ±0.025° and ±0.20%, respectively. At this level of instrument uncertainty, simultaneous fitting of frequency-dependent phase and amplitude nonlinear model functions derived from a photon diffusion approximation provides an accurate and robust strategy for determining optical properties from FDPM data, especially for media with high absorption. In an optical property range that is characteristic of most human tissues in the NIR (5×10−3<μa<5×10−2 mm−1, 0.5<μs′<2 mm−1), we theoretically and experimentally demonstrate that the multifrequency, simultaneous-fit approach allows μa and μs′ to be quantified with an accuracy of ±5% and ±3%, respectively. Although exceptionally high levels of precision can be obtained using this approach (<1% of the estimated absorption and scattering values), we show that the absolute accuracy of optical property measurements is highly dependent on specific factors associated with instrument performance, model function relevance, and details of the fitting strategy used to calculate μa and μs′.

Near infrared diffuse optical spectroscopy and diffuse optical imaging are promising methods that eventually may enhance or replace existing technologies for breast cancer screening and diagnosis. These techniques are based on highly sensitive, quantitative measurements of optical and functional contrast between healthy and diseased tissue. In this study, we examine whether changes in breast physiology caused by exogenous hormones, aging, and fluctuations during the menstrual cycle result in significant alterations in breast tissue optical contrast. A noninvasive quantitative diffuse optical spectroscopy technique, frequencydomain photon migration, was used. Measurements were performed on 14 volunteer subjects by using a hand-held probe. Intrinsic tissue absorption and reduced scattering parameters were calculated from frequency-domain photon migration data. Wavelength-dependent absorption (at 674, 803, 849, and 956 nm) was used to determine tissue concentration of oxyhemoglobin, deoxyhemoglobin, total hemoglobin, tissue hemoglobin oxygen saturation, and bulk water content. Results show significant and dramatic differences in optical properties between menopausal states. Average premenopausal intrinsic tissue absorption and reduced scattering values at each wavelength are 2.5-to 3-fold higher and 16 -28% greater, respectively, than absorption and scattering for postmenopausal subjects. Absorption and scattering properties for women using hormone replacement therapy are intermediate between premenopausal and postmenopausal populations. Physiological properties show differences in mean total hemoglobin (7.0 M, 11.8 M, and 19.2 M) and water concentration relative to pure water (10.9%, 15.3%, and 27.3%) for postmenopausal, hormone replacement therapy, and premenopausal subjects, respectively. Because of their unique, quantitative information content, diffuse optical methods may play an important role in breast diagnostics and improving our understanding of breast disease.

The absorption and scattering coefficient of a macroscopically homogeneous strongly scattering medium (lipid emulsion) containing Methylene Blue is quantitatively measured in the spectral range from 620 to 700 nm. We conduct the measurements in the frequency domain by using a light-emitting diode (LED) whose intensity is modulated at a frequency of 60 MHz. We derive an analytical expression for the absorption and scattering coefficients that is based on a two-distance measurement technique. A comparison with other measurement protocols such as measurement at two modulation frequencies shows that the two-distance method gives a better determination of the scattering and absorption coefficients. This study highlights the efficiency and ease of use of the LED technique, which lends itself to in vivo spectroscopy of biological tissues.

A 1-GHz multifrequency, multiwavelength frequency-domain photon migration instrument is used to measure quantitatively the optical absorption ͑ a ͒ and effective optical scattering ͑ s Ј͒ of normal and malignant tissues in a human subject. Large ellipsoidal ͑ϳ10-cm major axis, ϳ6-cm minor axes͒ subcutaneous malignant lesions were compared with adjacent normal sites in the abdomen and back. Absorption coefficients recorded at 674, 811, 849, and 956 nm were used to calculate tissue hemoglobin concentration ͑oxyhemoglobin, deoxyhemoglobin, and total͒, water concentration, hemoglobin oxygen saturation, and blood volume fraction in vivo. Our results show that the normal and the malignant tissues measured in the patient have clearly resolvable optical and physiological property differences that may be broadly useful in identifying and characterizing tumors.

SUMMARYA multiwavelength, high bandwidth (1 GHz) frequency-domain photon migration (FDPM) instrument has been developed for quantitative, non-invasive measurements of tissue optical and physiological properties. The instrument produces 300 kHz to 1 GHz photon density waves (PDWs) in optically turbid media using a network analyser, an avalanche photodiode detector and four amplitude-modulated diode lasers (674 nm, 811 nm, 849 nm and 956 nm). The frequency-dependence of PDW phase and amplitude is measured and compared to analytically derived model functions in order to calculate absorption, µ a , and reduced scattering, µ s , parameters. The wavelength-dependence of absorption is used to determine tissue haemoglobin concentration (total, oxy-and deoxy-forms), oxygen saturation and water concentration. We present preliminary results of non-invasive FDPM measurements obtained from normal and tumour-containing human breast tissue. Our data clearly demonstrate that physiological changes caused by the presence of small (about 1 cm diameter) palpable lesions can be detected using a handheld FDPM probe.

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The predictions of the frequency-domain standard diffusion equation (SDE) model for light propagation in an infinite turbid medium diverge from the more complete P& approxI'matron to the linear Boltzmann transport equation at intensity modulation frequencies greater than several hundred MHz.The P& approximation is based on keeping only the terms 1=0 and 1=1 in the expansion of the angular photon density in spherical harmonics, and the nomenclature P& approximation is used since the spherical harmonics of order 1=1 can be written in terms of the first order Legendre polynomial, which is traditionally represented by the symbol P&. 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 P& aproximation equation and the SDE. This analysis shows that the P& approximation provides a more accurate description of the data over this range of modulation frequencies. Some researchers have claimed that the P& 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 P, 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 P & 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. PACS number(s): 05.60.+w