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Isotropic scattering coefficient measurements were made of monodisperse polystyrene lattices of two different diameters of 144 nm and 223 nm and at volume fractions ranging from 0.15 to 0.22, using frequency domain photon migration measurements at wavelengths of 660, 685, 785 and 828 nm. The isotropic scattering coefficient measurements were shown to be sensitive to the changing ionic strength (0.5-4 mM, NaCl equiv.) of the dispersions exhibiting hindered scattering owing to structure at the lowest ionic strength values. Monte Carlo simulations and numerical solution of the Ornstein Zernike equations were used to compute isotropic scattering coefficients for comparison to measured values. The interaction potential was modeled as a hard sphere Yukawa potential and the Hypernetted Chain closure was used to solve the OZ equation. Effective particle charges were found after renormalization of the bare particle charge and used to predict the isotropic scattering coefficient. The model data were found to follow similar trends as experimental measurements. The refractive index of the particles has found to be an important factor for predicting experimental isotropic scattering coefficient values., (Published by Elsevier Inc.)

A variety of biomedical imaging techniques such as optical and fluorescence tomography, electrical impedance tomography, and ultrasound imaging can be cast as inverse problems, wherein image reconstruction involves the estimation of spatially distributed parameter(s) of the PDE system describing the physics of the imaging process. Finite element discretization of imaged domain with tetrahedral elements is a popular way of solving the forward and inverse imaging problems on complicated geometries. A dual-adaptive mesh-based approach wherein, one mesh is used for solving the forward imaging problem and the other mesh used for iteratively estimating the unknown distributed parameter, can result in high resolution image reconstruction at minimum computation effort, if both the meshes are allowed to adapt independently. Till date, no efficient method has been reported to identify and resolve intersection between tetrahedrons in independently refined or coarsened dual meshes. Herein, we report a fast and robust algorithm to identify and resolve intersection of tetrahedrons within nested dual meshes generated by 8-similar subtetrahedron subdivision scheme. The algorithm exploits finite element weight functions and gives rise to a set of weight functions on each vertex of disjoint tetrahedron pieces that completely cover up the intersection region of two tetrahedrons. The procedure enables fully adaptive tetrahedral finite elements by supporting independent refinement and coarsening of each individual mesh while preserving fast identification and resolution of intersection. The computational efficiency of the algorithm is demonstrated by diffuse photon density wave solutions obtained from a single- and a dual-mesh, and by reconstructing a fluorescent inclusion in simulated phantom from boundary frequency domain fluorescence measurements.

Frequency domain photon migration (FDPM) technique was employed to investigate the structure factors of dense, polydisperse colloidal suspensions. The angle-integrated structure factors, [S(q)], extracted from FDPM measurements of scattering properties at volume fractions ranging from 0.05 to 0.4, were compared with the values predicted from the polydisperse hard sphere Percus-Yevick (HSPY) model, as well as decoupling approximation (DA) and local monodisperse approximation (LMA) models that incorporated independently measured particle size information. Results show that the polydisperse HSPY model is the most suitable for accounting for particle interactions which predominantly arise from volume exclusion effects. Furthermore, the influence of size polydispersity upon [S(q)] is most significant at high volume fractions. The static structure factors at small wave vector q, S(0), were also assessed from dual wavelength FDPM measurements by using the small wave number approximation as well as the local monodisperse approximation. The measured S(0) agrees well with the values predicted by the polydisperse HSPY model.

The isotropic scattering coefficients of 143-nm diameter polystyrene latex suspensions were measured using frequency-domain photon migration (FDPM) at 687 and 828 nm as a function of volume fraction (0.05-0.3) and ionic strength (1.0 to 120 mM NaCl equivalents) in order to derive the angle-integrated structure factor, S(q), and structure factor at zero wave vector, S(0). The effective surface charges of the dispersions were estimated by fitting the measured isotropic scattering coefficients at each wavelength as a function of volume fraction to the solution of the Orstein-Zernike integral equation using the hard sphere Yukawa potential model and mean spherical approximation as a closure relation. The estimates of surface charges were comparable at both wavelengths, but decreased with ionic strength. At 120 mM NaCl equivalents, the values of S(0) obtained from FDPM matched those predicted by the Percus-Yevick model, and decreased with volume fraction, consistent with prediction by the Carnahan-Starling equation.

Frequency domain photon migration (FDPM) measurements were conducted to assess particle interactions of concentrated, monodisperse, polystyrene samples obtained directly from industry by using multiple scattering light. The angle-integrated static structure factor, S(q), and static structure factor at small wave vector q, S(0), were obtained from FDPM measurements at high volume fractions ranging from 0.05 to 0.3, and were compared with those obtained from the monodisperse hard sphere Percus-Yevick (HSPY) model. Effects of different colloid sizes on structure factor evaluated at two different wavelengths were also investigated. Results show that the monodisperse HSPY model is suitable for accounting for particle interactions and local microstructures in these colloidal suspensions. Upon using the HSPY model, particle sizes of polystyrene suspensions were recovered from FDPM measurements at high volume fractions (up to 0.3), which agree well with the DLS measurement of diluted sample ( approximately 0.001). The study of polydispersity effect shows that the FDPM method can be successfully used for recovering the mean particle size of polydisperse colloidal suspension with low polydispersity (<16%) under the assumption of monodisperse hard sphere systems.

Time-dependent measurements of light propagation were conducted in aqueous dispersions of 523 nm diameter polystyrene at concentrations between 0.1 and 0.4 solids volume fraction in order to assess how particle correlation is influenced by depletion interactions arising from the addition of soluble polyethyleneoxide (PEO). In the absence of polymer, the transport scattering length can be predicted from Mie scattering theory and the Percus-Yevick (P-Y) model for static structure of a dense hard-sphere colloidal solution. Depletion forces arising from the addition of PEO of varying molecular weights influenced the spatial ordering of the dispersion and caused a further increase in the transport scattering length beyond that predicted by hard-sphere static structure factor but similar to that predicted by the mean sphere approximation (MSA) to the P-Y model described by Ye et al. (1996). Onset of flocculation occurred with increased PEO addition and correlated with PEO molecular weight. Phase separation was noted by no further change in the transport scattering length, except when flocculation was induced by the highest molecular weight PEO. The use of time-dependent measurements of light propagation in dense systems provides an alternative to small-angle light, neutron, and X-ray scattering characterization of interaction potentials in dense, multiply scattering samples and promises further fruitful investigation of colloidal particle interactions in suspensions. Copyright 1999 Academic Press.

In summary, Table II is a listing of the pitfalls and advantages of using Monte Carlo simulations and numerical solution of the diffusion equation to describe photon migration in tissues. Judicious use of these techniques to describe the solution to the forward imaging problem may allow determination of the best theoretical resolution and the smallest detectable volume for the range of optical property differences expected in situ or imposed by contrast agent administration. Furthermore, an understanding of the forward imaging problem through these numerical techniques also contributes to our understanding of the most efficient solution to the inverse imaging problem.