Joseph Fishkin

A multiwavelength, high bandwidth frequency-domain photon migration 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 in optically turbid media using a network analyzer, an avalanche photodiode detector and four amplitude-modulated diode lasers. The frequency-dependence of PDW phase and amplitude is measured and compared to analytically derived model functions in order to calculate absorption, μ, and reduced scattering, μ, parameters. The wavelength-dependence of absorption is used to determine tissue haemoglobin concentration, oxygen saturation and water concentration. We present preliminary results of non-invasive FDPM measurements obtained from normal and turnout-containing human breast tissue. Our data clearly demonstrate that physiological changes caused by the presence of small palpable lesions can be detected using a handheld FDPM probe.

The basic principles of a non-contact, near-infrared technique for the mapping of layered tissues are discussed theoretically and verified experimentally. The propagation properties of diffuse photon-density waves in tissues depend on the optical properties of the tissue. When a layered medium is irradiated by amplitude modulated light, the difference in optical properties between the layers is evident in the phase and amplitude of the diffuse reflection coefficient, which is a result of the interference of the partial waves propagating in the different layers. Thus, diffuse photon- density waves are applicable to the analysis of the structure of layered tissue. The probing depth is determined by the modulation frequency of the incident light. For modulation frequencies between several hundred megahertz and a few gigahertz, this allows us to analyze the properties of muscle tissue of up to 4-8 mm below the surface. Experimental results based on chicken breast muscle are given. As an example, the technique might be of use for evaluating the depth of necrosis and the blood volume fraction in deep burns.

A 1-GHz multifrequency, multiwavelength frequency-domain photon migration instrument is used to measure quantitatively the optical absorption and effective optical scattering of normal and malignant tissues in a human subject. Large ellipsoidal 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 total!, 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. © 1997 Optical Society of America.

The predictions of the frequency-domain standard diffusion equation model for light propagation in an infinite turbid medium diverge from the more complete P1 approximation to the linear Boltzmann transport equation at intensity modulation frequencies greater than several hundred MHz. The P1 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 P1 approximate is used since he spherical harmonics of order l = 1 can be written in terms of the first order Legendre polynomial which is traditionally represented by the symbol P1. 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 P1 aproximation equation and the SDE This analysis shows that the P1 approximation provides a more accurate description of the data over this range of modulation frequencies. Some researchers have claimed that the P1 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 P1 approximation model indicates that a photon density wave phase velocity of c/√3 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 P1 approximation predicts that only the leading edge of the pulse appreaches a speed of c/√3.

We describe an approach that combines clinical ultrasound and photon migration techniques to enhance the sensitivity and information content of diffuse optical tomography. Measurements were performed on a postmenopausal woman with a single 1.8×0.9 cm malignant ductal carcinoma in situ approximately 7.4 mm beneath the skin surface. The ultrasound-derived information about tumor geometry enabled us to segment the breast tissue into tumor and background regions. Optical data was obtained with a multifrequency, multiwavelength hand-held frequency-domain photon migration backscattering probe. The optical properties of the tumor and background were then computed using the ultrasound-derived geometrical constraints. An iterative perturbative approach, using parallel processing, provided quantitative information about scattering and absorption simultaneously with the ability to incorporate and resolve complex boundary conditions and geometries. A three to four fold increase in the tumor absorption coefficient and nearly 50% reduction in scattering coefficient relative to background was observed. Calculations of the mean physiological parameters reveal fourfold greater tumor total hemoglobin concentration [Hbtot] than normal breast and tumor hemoglobin oxygen saturation values of 63%. Comparison of semi-infinite to heterogeneous models shows superior tumor/background contrast for the latter in both absorption and scattering. Sensitivity studies assessing the impact of tumor size and refractive index assumptions, as well as scan direction, demonstrate modest effects on recovered properties.

This essay argues that we ought to think differently about unequal opportunity. Instead of focusing only on overall prospects in life, we ought to train our attention on the particular moments of decision and the particular developmental processes that shape, in different respects, the trajectories of people’s lives. A new wave of research in the social sciences makes possible this shift in focus, which will have profound implications for our understanding of both the concept of equal opportunity itself and its applications in public policy and law