Frequency-domain Photon Migration Research Articles

Application of frequency domain photon migration to particle size analysis and monitoring of pharmaceutical powders.

The frequency domain photon migration (FDPM) technique was employed to determine mean particle size of pharmaceutical powders. Results show that the FDPM-measured scattering coefficient increases linearly with reciprocal mean particle size of powdered samples. In contrast to near-infrared spectroscopy techniques, FDPM technique enables determination of scattering and absorption separately so that it does not require data pretreatment and chemometric calibration models. In addition, this unique advantage provides more detailed information about powder samples, which can be used as a potential tool for on-line monitoring of not only variation of active pharmaceutical ingredient concentrations from changes in the absorption coefficient but also variation of particle sizes from changes in the scattering coefficient.

Sensitivity and depth penetration of continuous wave versus frequency-domain photon migration near-infrared fluorescence contrast-enhanced imaging.

The development of near-infrared fluorescent contrast agents and imaging techniques depends on the deep penetration of excitation light through several centimeters of tissue and the sensitive collection of the re-emitted fluorescence. In this contribution, the sensitivity and depth penetration of various fluorescence-enhanced imaging studies is surveyed and compared with current studies using continuous wave (CW) and frequency-domain photon migration (FDPM) measurements with planar wave illumination of modulated excitation light at 100 MHz and area collection of reemitted fluorescent light using a previously developed modulated intensified charge-coupled device camera system. Fluorescence was generated from nanomolar to micromolar solutions of indocyanine green (ICG) in a 100 microL volume submerged at 1-4 cm depths in a 1% Liposyn solution to mimic tissue scattering properties. Enhanced depth penetration and sensitivity are achieved with optimal filter rejection of excitation light, and FDPM rejection of background light is not achieved using CW methods. We show the ability to detect as few as 100 fmol of ICG from area illumination of 785 nm light (5.5 mW/cm2) and FDPM area collection of 830 nm fluorescent light generated from 3 cm below the phantom surface. The lowered noise floor of FDPM measurements enables greater sensitivity and penetration depth than comparable CW measurements.

Sensitivity and depth penetration of continuous wave versus frequency-domain photon migration near-infrared fluorescence contrast-enhanced imaging

Sensitivity and depth penetration of continuous wave versus frequency-domain photon migration near-infrared fluorescence contrast-enhanced imaging

Near-infrared fluorescence contrast-enhanced imaging with intensified charge-coupled device homodyne detection: measurement precision and accuracy.

Fluorescence frequency-domain photon migration (FDPM) through tissue refers to the propagation of intensity-modulated fluorescent light that originates from tissue-laden fluorophores following illumination with an intensity-modulated excitation light source. FDPM measurements of modulation amplitude and phase are ultimately employed in an inversion algorithm for tomographic reconstruction of interior optical and fluorescent property maps that delineate disease enhanced with fluorescent contrast agent. Because the inverse problem is underdetermined, measurement precision and accuracy crucially impact its solution. Reported here are the precision and accuracy of FDPM measurements acquired using an intensified CCD homodyne detection system. By introducing 32 phase delays between the oscillators used to modulate the intensifier gain and light source intensity at 100 MHz, mean precision is maximized at +/-0.46% and +/-0.26 deg for measurements of modulation amplitude and phase, respectively. Measurement precision improves when the number of phase delays increases. Measurements of fluorescence modulation amplitude and phase, acquired from the surface of a tissue phantom at distances ranging between 0.71 and 3.6 cm from an incident excitation point source, exhibit a mean accuracy of 17% and 1.9 deg, respectively. Measurement accuracy deteriorates with increasing distance from the point source, but for distances up to 1.0 cm from the point source, measurements of fluorescence modulation amplitude and phase exhibit a mean accuracy of 5.4% and 0.30 deg, respectively.

Modification of Electrostatic Interaction by Rhodamine 6G Adsorption on Polystyrene Latex as Assessed by Frequency Domain Photon Migration

To demonstrate assessment of electrostatic interactions using first principles models, the isotropic scattering coefficients of negatively charged polystyrene latex were measured with frequency domain photon migration (FDPM) as the effective surface charge was changed by adsorbing positively charged surfactant, Rhodamine 6G (R6G). Measurements were conducted on dense suspensions (volume fraction = 0.186) at an ionic strength of 5 mM NaCl equivalent with varying amounts of positively charged R6G adsorbed on the particle surface. The FDPM measurements of isotropic scattering were then fitted to a model prediction obtained by solving the Ornstein−Zernike integral equation using the hard sphere Yukawa interaction model with mean spherical approximation as closure. The results show that the parameter estimate of surface charge decreased with adsorbed R6G showing the ability to use multiply scattered light to characterize electrostatic interaction in dense suspensions.

Influence of the refractive index-mismatch at the boundaries measured in fluorescenceenhanced frequency-domain photon migration imaging

Over the past decade, developments towards near-infrared (NIR) optical tomography involve the recovery of interior optical maps from boundary measurements using the first principles of light propagation models. The refractive-index mismatch parameter in the boundary condition of the light propagation model, namely the diffusion equation, can significantly impact model prediction of measurements and therefore image recovery. In this contribution, the influence of refractive-index mismatch parameter between predictions and referenced measurements of fluorescence-enhanced frequency-domain photon migration (FDPM) are established; its greater influence on emission over excitation predictions are demonstrated, and the methods to accurately determine refractive index mismatch parameter from basic principles are reviewed.

Three-dimensional, Bayesian image reconstruction from sparse and noisy data sets: near-infrared fluorescence tomography.

A method for inverting measurements made on the surfaces of tissues for recovery of interior optical property maps is demonstrated for sparse near-infrared (NIR) fluorescence measurement sets on large tissue-simulating volumes with highly variable signal-to-noise ratio. A Bayesian minimum-variance reconstruction algorithm compensates for the spatial variability in signal-to-noise ratio that must be expected to occur in actual NIR contrast-enhanced diagnostic medical imaging. Image reconstruction is demonstrated by using frequency-domain photon migration measurements on 256-cm(3) tissue-mimicking phantoms containing none, one, or two 1-cm(3) heterogeneities with 50- to 100-fold greater concentration of Indocyanine Green dye over background levels. The spatial parameter estimate of absorption owing to the dye was reconstructed from only 160 to 296 surface measurements of emission light at 830 nm in response to incident 785-nm excitation light modulated at 100 MHz. Measurement error of acquired fluence at fluorescent emission wavelengths is shown to be highly variable. Convergence and quality of image reconstructions are improved by Bayesian conditioning incorporating (i) experimentally determined measurement error variance, (ii) recursively updated estimates of parameter uncertainty, and (iii) dynamic zonation. The results demonstrate that, to employ NIR fluorescence-enhanced optical imaging for large volumes, reconstruction approaches must account for the large range of signal-to-noise ratio associated with the measurements.

Assessment of Small-Angle and Angle-Averaged Structure Factor for Monitoring Electrostatic Colloidal Interactions Using Multiply Scattered Light

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.

Volume of pharmaceutical powders probed by frequency-domain photon migration measurements of multiply scattered light.

Using probability distribution analysis to describe the propagation of multiply scattered light between a point source and point detector located a known distance apart, mathematical expressions predicting the volume of sampled powder were determined for infinite and semi-infinite powder beds and then compared to experimental measurements of frequency-domain photon migration (FDPM). Our results show that the volume of powder sampled varies with optical properties and, when using FDPM techniques, with modulation frequency. For a typical measurement in lactose powder, the volume of powder sampled by multiply scattered light propagating between a 1000-microm-diameter point source and point detector pair separated by 8 mm is predicted to be 1.8 and 1.5 cm3 at modulated frequencies of 50 and 100 MHz, respectively. Experimental measurements in lactose powder confirm the predictions.

Three-dimensional fluorescence enhanced optical tomography using referenced frequency-domain photon migration measurements at emission and excitation wavelengths

The ultimate success of near-infrared optical tomography rests on the precise measurement of light propagation within tissues or random media, the accurate prediction of these measurements from a light propagation model, and an efficient three-dimensional solution of the inverse imaging problem. To date, optical tomography algorithms have focused on frequency-domain photon migration (FDPM) measurements of phase-delay and amplitude attenuation, which are reported relative to the incident light, even though phase-delay and amplitude of incident light are nearly impossible to measure directly. In this contribution, we examine referenced, fluorescence-enhanced frequency-domain photon migration measured at excitation and/or emission wavelengths and report on a measurement strategy to minimize measurement and calibration error for efficient coupling of data to a distorted Born iterative imaging algorithm. We examine three referencing approaches and develop associated inversion algorithms for (1) normalizing detected emission FDPM data to the predicted emission wave arising from a homogeneous medium, (2) referencing detected emission FDPM data to that detected at a reference point, and (3) referencing detected emission FDPM data to detected excitation FDPM data detected at a reference point. Our results show the latter approach to be practical while reducing the nonlinearity of the inverse problem. Finally, in light of our results, we demonstrate the method for eliminating the influence of source strength and instrument functions for effective fluorescence-enhanced optical tomography using FDPM.

Assessment of Electrostatic Interactions in Dense Colloidal Suspensions with Multiply Scattered Light

The electrostatic repulsive force between particles impacts the static structure of colloidal systems and dramatically hinders visible light scattering. In this investigation, we employed frequency domain photon migration (FDPM) to measure the isotropic scattering coefficients of dialyzed polystyrene latex suspensions at 687 and 828 nm as a function of ionic strengths between 1 and 120 mM NaCl equivalents. Measured isotropic scattering coefficients increased with decreasing ionic strength of the suspensions, suggesting that changes in electrostatic interactions can be evaluated in ensemble measurements of visible light scattering. At 120 mM NaCl equivalents, the isotropic scattering coefficients were accurately predicted by Mie theory with the Percus−Yevick (PY) polydisperse model to account for hard-sphere (HS) interactions. At lower ionic strengths, the isotropic scattering coefficients at varying colloidal volume fractions were regressed to scattering theory which incorporated the mean spherical approximation (MSA) with the hard sphere Yukawa (HSY) interaction for monodisperse suspensions in order to yield an effective surface charge given the size and ionic strength. The estimates of surface charges obtained from scattering data at 687 and 828 nm were consistently similar but varied with ionic strength. A three-component MSA primary model (PM) was used in an attempt to account for sample polydispersity but yielded poor fit and estimates of effective surface charges which varied for data taken at the two wavelengths.

Precise analysis of frequency domain photon migration measurement for characterization of concentrated colloidal suspensions

Frequency domain photon migration (FDPM) is a new method for characterization of concentrated colloidal suspensions using multiply scattered light. The ability of FDPM to determine size and interaction characteristics of the particulate phase of colloidal suspensions depends largely upon the accuracy and precision of FDPM-measured optical properties. In this work, FDPM measurements at multiple modulation frequencies and multiple source-to-detector distances are systematically analyzed for obtaining accurate and precise scattering properties of colloidal suspensions. Two different data analysis methods, multifrequency (MF) nonlinear regression and multidistance (MD) linear regression, and corresponding various strategies for fitting to the optical diffusion equation are investigated. The accuracy and precision of estimated scattering coefficients by different approaches are compared. Results show that MD linear regression with simultaneous regression of average intensity and phase shift or amplitude and phase shift data provides the best data analysis method since it provides not only accurate estimated parameters but also an accurate estimation of their uncertainties. Finally, an important criterion, derived from the photon diffusion model, is proposed for checking the consistency of measurement data and optimizing experimental conditions for FDPM characterization of multiply scattering materials.

Investigation of Particle Interactions in Dense Colloidal Suspensions Using Frequency Domain Photon Migration: Bidisperse Systems

The frequency domain photon migration (FDPM) technique was employed for investigation of particle interactions of dense, bidisperse, polystyrene samples of differring volume ratios of small to large particle sizes. The particle interactions of bidisperse systems were evaluated from the angular integrated structure factors, 〈S(q)〉 , which were extracted from FDPM measurements of scattering properties at high volume fractions ranging from 0.1 to 0.3. The FDPM-measured 〈S(q)〉 were then compared with theoretical predictions using the full binary hard sphere Percus−Yevick (HSPY) model, as well as the decoupling approximation (DA) and the local monodisperse approximation (LMA) models. The influence of differing volume ratios of colloid sizes on structure factors at differing wavelengths was also investigated. Results show that the interactions between small and large particles significantly impact the structure factors as well as the scattering properties in dense bidisperse colloidal suspensions. Furthermore, ...

Investigation of Particle Interactions in Concentrated Colloidal Suspensions Using Frequency Domain Photon Migration: Monodisperse Systems

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 (∼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.

Noninvasive monitoring of hemodynamic stress using quantitative near-infrared frequency-domain photon migration spectroscopy.

Hemorrhagic hypovolemia and inotropic agent administration were used to manipulate cardiac output (CO) and oxygen delivery in rabbits to investigate the correlation between noninvasive frequency domain photon migration (FDPM) spectroscopy and invasive hemodynamic monitoring parameters. Frequency-domain photon migration provides quantitative measurements of light absorption and reduced scattering (mu(a) and mu(s)(prime prime or minute), respectively) in tissue. Wavelength dependent mu(a) values were used to calculate in vivo tissue concentration of deoxyhemoglobin [Hb], oxyhemoglobin [HbO(2)], total hemoglobin [TotHb], and water [H(2)O] as well as mixed arterial-venous oxygen saturation (S(t)O(2)) in tissue. FDPM-derived physiologic properties were correlated with invasive measurements of CO and mean pulmonary artery pressure (mPAP), FDPM-derived [TotHb] and S(t) O(2) correlated significantly with hemorrhaged volume (HV), mPAP, and CO. Correlation coefficients for [TotHb] vs HV, mPAP, and CO were -0.77, 0.86, and 0.70, respectively. Correlation coefficients of S(t)O( 2) vs HV, mPAP, and CO were -0.71, 0.55, and 0.61, respectively. Dobutamine induced changes resulted in correlation coefficients between FDPM-derived and invasively measured physiologic parameters that are comparable to those induced by hypovolemia. FDPM spectroscopy is sensitive to changes in mPAP and CO of as little as 15%. These results suggest that FDPM spectroscopy may be used in clinical settings to noninvasively monitor central hemodynamic parameters and to directly assess oxygenation of tissues.

Spectroscopy enhances the information content of optical mammography.

Near-infrared (NIR) diffuse optical spectroscopy and imaging may enhance existing technologies for breast cancer screening, diagnosis, and treatment. NIR techniques are based on quantitative measurements of functional contrast between healthy and diseased tissue. In this study we measured the spectral dependence of tissue absorption (mu(a)) and reduced scattering (mu'(s)) in the breasts of 30 healthy women and one woman with a fibroadenoma using a seven-wavelength frequency-domain photon migration probe. Subjects included pre- and postmenopausal women between the ages of 18 and 64. Multi-spectral measurements were used along with a four-component fit to determine the concentrations of de-oxy and oxy-hemoglobin, water and lipids in breast. The scattering spectral shape was also quantified. Our measurements demonstrate that the measured concentrations of NIR analytes correlate well with known breast physiology. Although the tissue scattering at a single wavelength was found to have little value as a functional parameter, the dependence of the scattering on wavelength provided key insights into breast composition and physiology. Lipids and scattering spectra in the breast were found to increase and decrease, respectively, with increasing body mass index. Simple calculations are also provided to demonstrate potential penalties from ignoring the contributions of water and lipids in breast measurements. Finally, water is shown to be a possible indicator for detecting a fibroadenoma, whereas the hemoglobin saturation was found to be a poor indicator. Multi-spectral measurements, compared to measurements restricted to one or two wavelengths, provide additional information that may be useful in managing breast disease.

Optical property measurements of turbid media in a small-volume cuvette with frequency-domain photon migration

A frequency-domain photon migration (FDPM) technique is developed for quantitative measurement of the absorption and reduced scattering coefficients of highly turbid samples in a small-volume (0.45-ml) reflective cuvette. We present both an analytical model for the FDPM cuvette and its experimental verification, using calibrated phantoms and suspensions of living cells. FDPM model fits to experimental data demonstrate that the reduced scattering (mu(s)?) and absorption (mu(a)) coefficients can be derived with accuracies of 5-10% and 10-15%, respectively. Changing the cuvette wall reflectivity alters the frequency-dependent behavior of photon density waves (PDWs). For highly reflective wall boundaries (R(eff) >/= 90-95%), PDW confinement leads to substantial enhancement in both amplitude and phase compared with identical samples in infinite media. Results from experiments on microsphere suspensions are compared with predictions from Mie theory to assess the potential of this method to interpret scattering properties in terms of scatterer size and density. Optical property measurements of biological cell suspensions are reported, and the possibility of optically monitoring cell physiology in a carefully controlled environment is demonstrated.

Approach for Particle Sizing in Dense Polydisperse Colloidal Suspension Using Multiple Scattered Light

Direct particle sizing of colloidal suspensions at high solid concentrations is difficult due to confounding effects of multiple scattering and particle interactions. In this work, the frequency domain photon migration (FDPM) technique, based upon multiple light scattering, is extended for particle sizing of colloidal suspensions at high volume fractions by combining an appropriate model to account for particle interactions. FDPM measurements of isotropic scattering coefficients were conducted to assess the effect of particle interactions of polydisperse polystyrene samples at high volume fractions ranging from 1% to 40%. The isotropic scattering coefficients were then compared with the theoretical predictions which include the full polydisperse hard sphere Percus−Yevick (HSPY) model as well as the decoupling approximation and the local monodisperse approximation models to account for excluded volume effects. Results show that the polydisperse HSPY model is suitable for accounting for particle interactions which predominately arise from volume exclusion effects and which influence light scattering. Upon use of the polydisperse HSPY model to predict static structure factors, the particle size distribution (PSD) of polydisperse polystyrene suspensions was recovered at high volume fractions up to 40% at two different wavelengths. Our inversion results agree well with PSD measured by dynamic light scattering at a diluted sample of the same suspensions (∼0.01% volume of solids).

Inversion algorithms for particle sizing with photon migration measurement

AbstractA new linear inverse method is demonstrated for recovery of particle‐size distribution (PSD) and volume fraction of opaque colloidal suspensions from frequency domain photon migration (FDPM) measurement of multiply scattered light. To deal with the ill posedness of PSD retrieving problem, the size distribution is approximated by the B‐spline expansion. Tikhonov regularization, along with both nonnegativity and smoothing constraints, in which the L‐curve method is employed to choose a regularization parameter, are also used to ensure the stable and realistic solution. The algorithm is tested using synthetic FDPM measurements at a variety of size distributions, and results are compared using other inverse methods. The influences of model and measurement error are investigated. To demonstrate our inversion approach, PSD and volume fraction of opaque titanium dioxide suspensions are recovered from actual FDPM measurements. This work demonstrates the ability of FDPM method to characterize colloidal suspensions.

Three-dimensional unconstrained and constrained image-reconstruction techniques applied to fluorescence, frequency-domain photon migration

The development of near-infrared (NIR) optical imaging for biomedical optical imaging is hampered by the computational intensiveness of large-scale three-dimensional (3-D) image reconstruction and the potential lack of endogenous contrast for detection of relevant tissue features. In this contribution the inverse optical imaging problem is formulated in three dimensions in a noncompressive geometry as a simple-bound constrained minimization problem in order to recover the interior fluorescence properties of exogenous contrast agent from frequency-domain photon migration measurements at the boundary. The solution of the forward optical diffusion problem for the frustum shape containing fluorescence inclusions of 10:1 contrast is accomplished by use of the Galerkin finite-element formulation. The inverse approach employs the truncated Newton method with trust region and a modification of automatic reverse differentiation to speed the computation of the optimization problem. The image-reconstruction results confirm that the constrained minimization may offer a more logical approach for the 3-D optical imaging problem than unconstrained optimization.