Frequency-domain method for measuring spectral properties in multiple-scattering media: methemoglobin absorption spectrum in a tissuelike phantom

In vivo monitoring of hemoglobin derivatives in a rat thermal injury model using spectral diffuse reflectance imaging

INTRODUCTION

To demonstrate the feasibility of our previously proposed Diffuse reflectance spectral imaging (DRSI) method for in vivo monitoring of oxygenated hemoglobin, deoxygenated hemoglobin, methemoglobin, tissue oxygen saturation, and methemoglobin saturation in a rat scald burn wound model and assess whether the method could be used for differentiating the burn depth groups in rats based on the hemoglobin parameters.

METHODOLOGY

Superficial dermal burns (SDBs), deep dermal burns (DDBs), and deep burns (DBs) were induced in rat dorsal skin using a Walker-Mason method. An approach based on multiple regression analysis for spectral diffuse reflectance images aided by Monte Carlo simulations for light transport was used to quantify the hemoglobin parameters. Canonical discriminant analysis (CDA) was performed to discriminate SDB, DDB, and DB.

RESULTS

CDA using the total hemoglobin concentration, tissue oxygen saturation, and methemoglobin saturation as the independent variables showed good performance for discriminating the SDB, DDB, and DB groups immediately after burn injury and the SDB group from the DDB and DB groups 24-72 h after burn injury.

CONCLUSIONS

The DRSI method with multiple regression analysis for quantification of oxygenated hemoglobin, deoxygenated hemoglobin, and methemoglobin proved to be reliable for monitoring these hemoglobin derivatives in the rat experimental burn injury model. The parameters of tissue oxygen saturation, methemoglobin saturation, and total hemoglobin concentration are promising for the differentiating the degree of burn injury using CDA.

In Vivo Transcutaneous Monitoring of Hemoglobin Derivatives Using a Red-Green-Blue Camera-Based Spectral Imaging Technique

Cyanosis is a pathological condition that is characterized by a bluish discoloration of the skin or mucous membranes. It may result from a number of medical conditions, including disorders of the respiratory system and central nervous system, cardiovascular diseases, peripheral vascular diseases, deep vein thrombosis, and regional ischemia. Cyanosis can also be elicited from methemoglobin. Therefore, a simple, rapid, and simultaneous monitoring of changes in oxygenated hemoglobin and deoxygenated hemoglobin is useful for protective strategies against organ ischemic injury. We previously developed a red-green-blue camera-based spectral imaging method for the measurements of melanin concentration, oxygenated hemoglobin concentration (C_HbO), deoxygenated hemoglobin concentration (C_HbR), total hemoglobin concentration (C_HbT) and tissue oxygen saturation (StO₂) in skin tissues. We leveraged this approach in this study and extended it to the simultaneous quantifications of methemoglobin concentration (C_metHb), C_HbO, C_HbR, and StO₂. The aim of the study was to confirm the feasibility of the method to monitor C_metHb, C_HbO, C_HbR, C_HbT, and StO₂. We performed in vivo experiments using rat dorsal skin during methemoglobinemia induced by the administration of sodium nitrite (NaNO₂) and changing the fraction of inspired oxygen (FiO₂), including normoxia, hypoxia, and anoxia. Spectral diffuse reflectance images were estimated from an RGB image by the Wiener estimation method. Multiple regression analysis based on Monte Carlo simulations of light transport was used to estimate C_HbO, C_HbR, C_metHb, C_HbT, and StO₂. C_metHb rapidly increased with a half-maximum time of less than 30 min and reached maximal values nearly 60 min after the administration of NaNO₂, whereas StO₂ dramatically dropped after the administration of NaNO₂, indicating the temporary production of methemoglobin and severe hypoxemia during methemoglobinemia. Time courses of C_HbT and StO₂, while changing the FiO₂, coincided with well-known physiological responses to hyperoxia, normoxia, and hypoxia. The results indicated the potential of this method to evaluate changes in skin hemodynamics due to loss of tissue viability and vitality.

Transcutaneous monitoring of hemoglobin derivatives during methemoglobinemia in rats using spectral diffuse reflectance

SIGNIFICANCE

Untreated methemoglobinemia may cause severe hypoxemia and even death when methemoglobin levels in the blood stream exceed 70%. Although CO-oximetry can be used to monitor the response to treatment for methemoglobinemia, it is costly and requires an invasive procedure for collecting blood samples from patients. A pulse CO-oximeter with a contact probe can be used to continuously and non-invasively measure the percentage of methemoglobin, as well as the percutaneous oxygen saturation. In terms of the prevention of infectious diseases, however, it is desirable to monitor methemoglobin and oxygen saturation levels in a non-contact manner. Diffuse reflectance spectral imaging is promising as a non-contact, non-invasive, and cost-effective clinical diagnostic tool for methemoglobinemia.

AIM

To demonstrate the feasibility of visible spectral diffuse reflectance for in vivo monitoring of hemoglobin derivatives and evaluating methemoglobin production and reduction as well as hypoxemia during methemoglobinemia in rats.

APPROACH

A new imaging approach based on the multiple regression analysis aided by Monte Carlo simulations for light transport was developed to quantify methemoglobin, oxygenated hemoglobin, and deoxygenated hemoglobin using a hyperspectral imaging system. An in vivo experiment with rats exposed to sodium nitrite (NaNO2) at different doses was performed to confirm the feasibility of the method for evaluating the dynamics of methemoglobin, oxygenated hemoglobin, and deoxygenated hemoglobin during methemoglobinemia. Systemic physiological parameters, including the percutaneous arterial oxygen saturation, heart rate (HR), and pulse distention, were measured by a commercially available pulse oximeter, and the results were compared to those obtained by the proposed method.

RESULTS

Both the methemoglobin concentration and methemoglobin saturation rapidly increased with a half-maximum time of <20  min. They reached their maximal values nearly 60 min after the administration of NaNO2. Tissue oxygen saturation dramatically dropped to a minimum of 33.7  %    ±  0.4  %  , 23.1  %    ±  5.6  %  , 8.8  %    ±  1.7  %  , and 9.7  %    ±  5.1  %   on average for NaNO2 doses of 25, 37.5, 50, and 75 mg/kg, respectively. Changes in methemoglobin concentration and tissue oxygen saturation are indicative of the temporary production of methemoglobin and severe hypoxemia during methemoglobinemia. Profound increases in the HR and pulse distention implied an elevated cardiac output caused by tachycardia and the resultant increase in peripheral blood volume to compensate for the hypoxia and hypoxemia during methemoglobinemia. This was in agreement with the time course of the peripheral hemoglobin volume concentration obtained by the proposed method.

CONCLUSIONS

The proposed method is capable of the in vivo non-contact simultaneous evaluation of methemoglobin levels and hypoxemia during methemoglobinemia, and that it has potential as a tool for the diagnosis and management of methemoglobinemia.

Review of early development of near-infrared spectroscopy and recent advancement of studies on muscle oxygenation and oxidative metabolism

Near-infrared spectroscopy (NIRS) has become an increasingly valuable tool to monitor tissue oxygenation (Toxy) in vivo. Observations of changes in the absorption of light with Toxy have been recognized as early as 1876, leading to a milestone NIRS paper by Jöbsis in 1977. Changes in the absorption and scatting of light in the 700-850-nm range has been successfully used to evaluate Toxy. The most practical devices use continuous-wave light providing relative values of Toxy. Phase-modulated or pulsed light can monitor both absorption and scattering providing more accurate signals. NIRS provides excellent time resolution (~ 10 Hz), and multiple source-detector pairs can be used to provide low-resolution imaging. NIRS has been applied to a wide range of populations. Continued development of NIRS devices in terms of lower cost, better detection of both absorption and scattering, and smaller size will lead to a promising future for NIRS studies.

Combined multi-distance frequency domain and diffuse correlation spectroscopy system with simultaneous data acquisition and real-time analysis

Frequency domain near infrared spectroscopy (FD-NIRS) and diffuse correlation spectroscopy (DCS) have emerged as synergistic techniques for the non-invasive assessment of tissue health. Combining FD-NIRS oximetry with DCS measures of blood flow, the tissue oxygen metabolic rate can be quantified, a parameter more closely linked to underlying physiology and pathology than either NIRS or DCS estimates alone. Here we describe the first commercially available integrated instrument, called the "MetaOx", designed to enable simultaneous FD-NIRS and DCS measurements at rates of 10 + Hz, and offering real-time data evaluation. We show simultaneously acquired characterization data demonstrating performance equivalent to individual devices and sample in vivo measurements of pulsation resolved blood flow, forearm occlusion hemodynamic changes and muscle oxygen metabolic rate monitoring during stationary bike exercise.

Probe for evaluating the absorbing and transport scattering properties of turbid fluids using low-cost time-of-flight technology

A probe is described that when immersed into a highly scattering fluid provides a measurement of its scattering and absorbing properties at a single optical wavelength. It uses recently available low-cost proximity sensor modules to estimate the mean flight times of photons diffusely transmitted between near-infrared sources and detectors at two different separations. The probe has been designed with a specific application for enabling the rapid and efficient production of fluids, which mimic the optical properties of biological tissues. The potential of the device is demonstrated using precalibrated solutions of intralipid, an intravenous nutrient, and absorbing dye. It is shown that a combination of time-of-flight measurements at two source–detector separations can uniquely specify the absorption coefficient and the transport scattering coefficient.

Light distribution modulated diffuse reflectance spectroscopy

Typically, a diffuse reflectance spectroscopy (DRS) system employing a continuous wave light source would need to acquire diffuse reflectances measured at multiple source-detector separations for determining the absorption and reduced scattering coefficients of turbid samples. This results in a multi-fiber probe structure and an indefinite probing depth. Here we present a novel DRS method that can utilize a few diffuse reflectances measured at one source-detector separation for recovering the optical properties of samples. The core of innovation is a liquid crystal (LC) cell whose scattering property can be modulated by the bias voltage. By placing the LC cell between the light source and the sample, the spatial distribution of light in the sample can be varied as the scattering property of the LC cell modulated by the bias voltage, and this would induce intensity variation of the collected diffuse reflectance. From a series of Monte Carlo simulations and phantom measurements, we found that this new light distribution modulated DRS (LDM DRS) system was capable of accurately recover the absorption and scattering coefficients of turbid samples and its probing depth only varied by less than 3% over the full bias voltage variation range. Our results suggest that this LDM DRS platform could be developed to various low-cost, efficient, and compact systems for in-vivo superficial tissue investigation.

Artificial neural networks for retrieving absorption and reduced scattering spectra from frequency-domain diffuse reflectance spectroscopy at short source-detector separation

Diffuse reflectance spectroscopy (DRS) based on the frequency-domain (FD) technique has been employed to investigate the optical properties of deep tissues such as breast and brain using source to detector separation up to 40 mm. Due to the modeling and system limitations, efficient and precise determination of turbid sample optical properties from the FD diffuse reflectance acquired at a source-detector separation (SDS) of around 1 mm has not been demonstrated. In this study, we revealed that at SDS of 1 mm, acquiring FD diffuse reflectance at multiple frequencies is necessary for alleviating the influence of inevitable measurement uncertainty on the optical property recovery accuracy. Furthermore, we developed artificial neural networks (ANNs) trained by Monte Carlo simulation generated databases that were capable of efficiently determining FD reflectance at multiple frequencies. The ANNs could work in conjunction with a least-square optimization algorithm to rapidly (within 1 second), accurately (within 10%) quantify the sample optical properties from FD reflectance measured at SDS of 1 mm. In addition, we demonstrated that incorporating the steady-state apparatus into the FD DRS system with 1 mm SDS would enable obtaining broadband absorption and reduced scattering spectra of turbid samples in the wavelength range from 650 to 1000 nm.

Cerebral metabolic rate of oxygen (CMRO2) assessed by combined Doppler and spectroscopic OCT

A method of measuring cortical oxygen metabolism in the mouse brain that uses independent quantitative measurements of three key parameters: cerebral blood flow (CBF), arteriovenous oxygen extraction (OE), and hemoglobin concentration ([HbT]) is presented. Measurements were performed using a single visible light spectral/Fourier domain OCT microscope, with Doppler and spectroscopic capabilities, through a thinned-skull cranial window in the mouse brain. Baseline metabolic measurements in mice are shown to be consistent with literature values. Oxygen consumption, as measured by this method, did not change substantially during minor changes either in the fraction of inspired oxygen (FiO2) or in the fraction of inspired carbon dioxide (FiCO2), in spite of larger variations in oxygen saturations. This set of experiments supports, but does not prove, the validity of the proposed method of measuring brain oxygen metabolism.

Measuring tumor cycling hypoxia and angiogenesis using a side-firing fiber optic probe

Hypoxia and angiogenesis can significantly influence the efficacy of cancer therapy and the behavior of surviving tumor cells. There is a growing demand for technologies to measure tumor hypoxia and angiogenesis temporally in vivo to enable advances in drug development and optimization. This paper reports the use of frequency-domain photon migration with a side-firing probe to quantify tumor oxygenation and hemoglobin concentrations in nude rats bearing human head/neck tumors administered with carbogen gas, cycling hypoxic gas or just room air. Significant increase (with carbogen gas breathing) or decrease (with hypoxic gas breathing) in tumor oxygenation was observed. The trend in tumor oxygenation during forced cycling hypoxia (CH) followed that of the blood oxygenation measured with a pulse oximeter. Natural CH was also observed in rats under room air. The studies demonstrated the potential of the technology for longitudinal monitoring of tumor CH during tumor growth or in response to therapy.

Higher-order modulations of fs laser pulses for GHz frequency domain photon migration system

Except the fundamental modulation frequency, by higher-order-harmonic modulations of mode-locked laser pulses and a simple frequency demodulation circuit, a novel approach to GHz frequency-domain-photon-migration (FDPM) system was reported. With this novel approach, a wide-band modulation frequency comb is available without any external modulation devices and the only electronics to extract the optical attenuation and phase properties at a selected modulation frequency in FDPM systems are good mixers and lock-in devices. This approach greatly expands the frequency range that could be achieved by conventional FDPM systems and suggests that our system could extract much more information from biological tissues than the conventional FDPM systems. Moreover, this demonstration will be beneficial for discerning the minute change of tissue properties.

Assessment of brain oxygenation in term and preterm neonates using near infrared spectroscopy

PURPOSE

The aim of this study was to determine brain oxygenation in full-term and preterm neonates using near infrared spectroscopy.

MATERIAL AND METHODS

A total of 88 full-term and preterm newborn infants without hypoxic-ischaemic disorders admitted to the NICU were examined using NIRS on the first day of life and on day 28 of life. Additional measurements were taken at the end of the first week of life in the premature neonates group. Measurements of oxyhaemoglobin (HbO2), deoxyhaemoglobin (Hb), total haemoglobin (HbT) concentration and tissue oxygen saturation (Ox) were performed in 5 brain regions. Right and left frontal areas, the occipital area and right and left temporal areas were measured.

RESULTS

In full-term healthy neonates a marked decrease in HbO, Hb and HbT values was observed on day 28 of life in all brain regions except the occipital area. In the neonatal period the greatest changes in brain oxygenation occurred in the right and left frontal regions of the brain. In preterm neonates constant values of HbO2 and Ox were observed in the first 28 days of life. In preterm newborn infants, as well as in full term newborn infants, similar Ox and HbO2 values were obtained on day 28 of life.

CONCLUSIONS

NIRS is a safe method and can be used to evaluate brain oxygenation in newborn infants. The results of these measurements are in accordance with changes in brain oxygenation in the first month of life, which are predicated on the basis of the neonate's physiology.

Regional and hemispheric asymmetries of cerebral hemodynamic and oxygen metabolism in newborns

Understanding the evolution of regional and hemispheric asymmetries in the early stages of life is essential to the advancement of developmental neuroscience. By using 2 noninvasive optical methods, frequency-domain near-infrared spectroscopy and diffuse correlation spectroscopy, we measured cerebral hemoglobin oxygenation (SO(2)), blood volume (CBV), an index of cerebral blood flow (CBF(i)), and the metabolic rate of oxygen (CMRO(2i)) in the frontal, temporal, and parietal regions of 70 premature and term newborns. In concordance with results obtained using more invasive imaging modalities, we verified both hemodynamic (CBV, CBF(i), and SO(2)) and metabolic (CMRO(2i)) parameters were greater in the temporal and parietal regions than in the frontal region and that these differences increased with age. In addition, we found that most parameters were significantly greater in the right hemisphere than in the left. Finally, in comparing age-matched males and females, we found that males had higher CBF(i) in most cortical regions, higher CMRO(2i) in the frontal region, and more prominent right-left CBF(i) asymmetry. These results reveal, for the first time, that we can detect regional and hemispheric asymmetries in newborns using noninvasive optical techniques. Such a bedside screening tool may facilitate early detection of abnormalities and delays in maturation of specific cortical areas.

Reference optical phantoms for diffuse optical spectroscopy. Part 1--Error analysis of a time resolved transmittance characterization method

Development, production quality control and calibration of optical tissue-mimicking phantoms require a convenient and robust characterization method with known absolute accuracy. We present a solid phantom characterization technique based on time resolved transmittance measurement of light through a relatively small phantom sample. The small size of the sample enables characterization of every material batch produced in a routine phantoms production. Time resolved transmittance data are pre-processed to correct for dark noise, sample thickness and instrument response function. Pre-processed data are then compared to a forward model based on the radiative transfer equation solved through Monte Carlo simulations accurately taking into account the finite geometry of the sample. The computational burden of the Monte-Carlo technique was alleviated by building a lookup table of pre-computed results and using interpolation to obtain modeled transmittance traces at intermediate values of the optical properties. Near perfect fit residuals are obtained with a fit window using all data above 1% of the maximum value of the time resolved transmittance trace. Absolute accuracy of the method is estimated through a thorough error analysis which takes into account the following contributions: measurement noise, system repeatability, instrument response function stability, sample thickness variation refractive index inaccuracy, time correlated single photon counting system time based inaccuracy and forward model inaccuracy. Two sigma absolute error estimates of 0.01 cm(-1) (11.3%) and 0.67 cm(-1) (6.8%) are obtained for the absorption coefficient and reduced scattering coefficient respectively.

Temperature-dependent optical properties of Intralipid measured with frequency-domain photon-migration spectroscopy

We present the temperature dependence of absorption and reduced scattering coefficients of 1.8% Intralipid measured by frequency-domain photon-migration spectroscopy between 710 and 850 nm. These measurements were made in the physiologically relevant 30 to 40 degrees C temperature range. The temperature coefficients for absorption were consistent during heating and cooling and follow closely other reported results. The change in absorption coefficient at 740 nm suggests that a minimum temperature change of 4 degrees C is observable within the error limits. We found that the reduced scattering coefficient shows a hysteresis with temperature at 740 nm. The temperature coefficient for reduced scattering determined from heating cycle measurements agrees with theory and other measurements within the error limits.

Thermal coagulation-induced changes of the optical properties of normal and adenomatous human colon tissues in vitro in the spectral range 400-1,100 nm

The absorption coefficients, the reduced scattering coefficients and the optical penetration depths for native and coagulated human normal and adenomatous colon tissues in vitro were determined over the range of 400-1,100 nm using a spectrophotometer with an internal integrating sphere system, and the inverse adding-doubling method was applied to calculate the tissue optical properties from diffuse reflectance and total transmittance measurements. The experimental results showed that in the range of 400-1,100 nm there were larger absorption coefficients (P < 0.01) and smaller reduced scattering coefficients (P < 0.01) for adenomatous colon tissues than for normal colon tissues, and there were smaller optical penetration depths for adenomatous colon tissues than for normal colon tissues, especially in the near-infrared wavelength. Thermal coagulation induced significant increase of the absorption coefficients and reduced scattering coefficients for the normal and adenomatous colon tissues, and significantly reduced decrease of the optical penetration depths for the normal and adenomatous colon tissues. The smaller optical penetration depth for coagulated adenomatous colon tissues is a disadvantage for laser-induced thermotherapy (LITT) and photodynamic therapy (PDT). It is necessary to adjust the application parameters of lasers to achieve optimal therapy.

Progress of near-infrared spectroscopy and topography for brain and muscle clinical applications

This review celebrates the 30th anniversary of the first in vivo near-infrared (NIR) spectroscopy (NIRS) publication, which was authored by Professor Frans Jobsis. At first, NIRS was utilized to experimentally and clinically investigate cerebral oxygenation. Later it was applied to study muscle oxidative metabolism. Since 1993, the discovery that the functional activation of the human cerebral cortex can be explored by NIRS has added a new dimension to the research. To obtain simultaneous multiple and localized information, a further major step forward was achieved by introducing NIR imaging (NIRI) and tomography. This review reports on the progress of the NIRS and NIRI instrumentation for brain and muscle clinical applications 30 years after the discovery of in vivo NIRS. The review summarizes the measurable parameters in relation to the different techniques, the main characteristics of the prototypes under development, and the present commercially available NIRS and NIRI instrumentation. Moreover, it discusses strengths and limitations and gives an outlook into the "bright" future.

Investigation of light propagation models to determine the optical properties of tissue from interstitial frequency domain fluence measurements

Four models, standard diffusion approximation (SDA), single Monte Carlo (SMC), delta-P1, and isotropic similarity (ISM), are developed and evaluated as forward calculation tools in the estimation of tissue optical properties. The inverse calculation uses the ratio of the fluences and phase difference at two locations close to an intensity modulated isotropic source to recover the reduced scattering coefficient mus' and the absorption coefficient mua. Diffusion theory allows recovery of optical properties (OPs) within 5% for media with mus'mua>10. The performance of the delta-P1 model is similar to SDA, with limited enhanced accuracy. The collimation approximation may limit the use of the delta-P1 model for spherical geometry, and/or the fluence may not be accurately calculated by this model. The SMC model is the best, recovering OPs within 10% regardless of the albedo. However, the necessary restriction of the searched OPs space is inconvenient. The performance of ISM is similar to that of diffusion theory for media with mus'mua>10, and better for 1<mus'mua<10, i.e., determines absorption within 5% and reduced scattering within 20%. In practice, satisfactory estimates (within 5 to 10%) can be achieved using SDA to recover mus' and ISM to recover mua for media with mus'mua>5.

Evaluation of Ingredient Concentration in Powders Using Two-Speed Photon Migration Theory and Measurements

Two-speed photon migration in densely packed powder blends wherein the particle diameters are much larger than the incident wavelength are simulated with (i) dynamic simulation of particle sedimentation for generating powder structure, (ii) the complete-random-mixture model for predicting the active pharmaceutical ingredient (API) distribution within the powder bed, and (iii) Monte Carlo for tracking the photon trajectories. The simulation results reveal that while both absorption and isotropic scattering coefficients increase with solid-volume fraction ranging from 0.12 to 0.64, the absorption-to-isotropic-scattering ratio is (i) independent of the solid-volume fraction for particle refractive index ranging from 1.2 to 1.8 and (ii) linearly dependent upon the API volume concentration ranging from 0% to 5%. Frequency domain photon migration measurements of resin powder beds of varying particle size verified the developed simulation method. Measurements of lactose powder beds of varying particle size, solid-volume fraction, and ferric oxide particles content verified the simulation results that evidence independence of the absorption-to-isotropic-scattering ratio upon solid-volume fraction.

Noninvasive in vivo monitoring of methemoglobin formation and reduction with broadband diffuse optical spectroscopy

We present noninvasive, quantitative in vivo measurements of methemoglobin formation and reduction in a rabbit model using broadband diffuse optical spectroscopy (DOS). Broadband DOS combines multifrequency frequency-domain photon migration (FDPM) with time-independent near infrared (NIR) spectroscopy to quantitatively measure bulk tissue absorption and scattering spectra between 600 nm and 1,000 nm. Tissue concentrations (denoted by brackets) of methemoglobin ([MetHb]), deoxyhemoglobin ([Hb-R]), and oxyhemoglobin ([HbO2]) were determined from absorption spectra acquired in "real time" during nitrite infusions in nine pathogen-free New Zealand White rabbits. As little as 30 nM [MetHb] changes were detected for levels of [MetHb] that ranged from 0.80 to 5.72 microM, representing 2.2 to 14.9% of the total hemoglobin content (%MetHb). These values agreed well with on-site ex vivo cooximetry data (r2= 0.902, P < 0.0001, n = 4). The reduction of MetHb to functional hemoglobins was also carried out with intravenous injections of methylene blue (MB). As little as 10 nM changes in [MB] were detectable at levels of up to 150 nM in tissue. Our results demonstrate, for the first time, the ability of broadband DOS to noninvasively quantify real-time changes in [MetHb] and four additional chromophore concentrations ([Hb-R], [HbO2], [H2O], and [MB]) despite significant overlapping spectral features. These techniques are expected to be useful in evaluating dynamics of drug delivery and therapeutic efficacy in blood chemistry, human, and preclinical animal models.

Evaluation of photon migration using a two speed model for characterization of packed powder beds and dense particulate suspensions

A two-speed photon diffusion equation is developed for light propagation in a powder bed of high volume fraction or dense particulate suspension, whereby the light speed is impacted by the refractive index difference between particles and the suspending medium. The equation is validated using Monte Carlo simulation of light propagation coupled with dynamic simulation of particle sedimentation for the non-uniform arrangement of powder particles. Frequency domain experiments at 650 nm for a 77-microm-diameter resin-powder and 50-microm-diameter lactose-powder beds as well as resin-water and lactose-ethanol suspensions confirm the scattering and absorption coefficients derived from the two-speed diffusion equation.

Impact of excipient particle size on measurement of active pharmaceutical ingredient absorbance in mixtures using frequency domain photon migration

A system of dual-component powder mixtures, varying in excipient particle size and concentration of active pharmaceutical ingredient (API), is analyzed using frequency domain photon migration (FDPM) techniques. The results show that the FDPM-measured absorption coefficient increases linearly with increasing API concentration whereas the isotropic scattering coefficient shows no sensitivity to changes in API concentration. It is further seen that the absorption coefficient of blends, owing to the API, is not only linearly dependent on its concentration, but that this relationship is furthermore related to the excipient particle size. Finally, a comparison between near-infrared absorbance and FDPM-measured isotropic scattering as a function of reciprocal particle size is made to highlight FDPM as a powerful particle sizing tool without need for calibration. Overall, this study presents FDPM as a comprehensive method for detection of API concentration independent of excipient particle size.

Determination of optical properties in semi-infinite turbid media using imaging measurements of frequency-domain photon migration obtained with an intensified charge-coupled device

Frequency-domain photon migration measurements across the surface of a tissue-mimicking, semi-infinite phantom are acquired via an intensified charge-coupled device (ICCD) detection system and used in conjunction with the diffusion approximation to determine the optical properties. The absorption and reduced scattering coefficients are determined least accurately when relative measurements of average light intensity I(rel)dc are employed either alone or in a combination with relative modulation amplitude data I(rel)ac and/or relative phase shift data theta(rel). The absorption and reduced scattering coefficients are found accurate to within 15 and 11%, respectively, of the values obtained from standard single-pixel measurements when theta(rel) measurements are employed alone or in combination with I(rel)ac data.

Fluorescence lifetime spectroscopy for pH sensing in scattering media

Fluorescence lifetime spectroscopy in the presence of tissuelike scattering is demonstrated from measurements of phase and modulation ratio as a function of modulation frequency using a pH-sensitive dye, Carboxy Seminaphthofluorescein-1 (C-SNAFL-1). From the optical diffusion equation describing the propagation and generation of fluorescence within solutions of 0.5 microM C-SNAFL-1 containing 2.0% (by volume) of Intralipid as a scatterer, the values of the average lifetime of C-SNAFL-1 were determined as the solution pH varied between 5 and 9. Average lifetime values were found to match those measured using traditional phase-modulation measurement in nonscattering media. Furthermore, the robustness of the spectroscopic technique was demonstrated by conducting lifetime measurements at varying scatterer concentrations (1.5-3.0 vol % Intralipid). These results confirm the approach for analytical sensing in scattering media via fluorescence lifetime kinetics in order to track changes in analyte concentrations.

Measurement of Low-Dose Active Pharmaceutical Ingredient in a Pharmaceutical Blend Using Frequency-Domain Photon Migration

Frequency-domain photon migration (FDPM) measurements of time-dependent light propagation are conducted to provide the powder absorbance for quantitative prediction of terazosin as the active pharmaceutical ingredient (API) in a low-dose (0.72 wt %) oral tablet formulation. Calibration of the FDPM-derived powder absorbance at discrete wavelengths of 514, 650, 687, and 785 nm was performed for API contents ranging between 0 and 1.5 wt % in mixtures showing maximum sensitivity at 650 nm. The relative standard deviation (RSD) of FDPM absorption coefficient measurement at 650 nm in a well-mixed 1.08 wt % terazosin blend was <1.6%, of which no more than 0.12% arose from FDPM instrumental error and the remainder was attributable to the complete-random-mixture model. The applicability of FDPM as an on-line sensor for powder-blending operations was further evaluated by analyzing grab samples taken directly from five locations of a 2-cu-ft Gallay blender at intervals of 5 min within the blending process. FDPM results indicate that homogeneity was largely achieved in the first 10 min, during which the RSD of API content across five sampling locations decreased from 27% to 8%, and the RSD decreased to 5% after 25 min of blending. Evolution of homogeneity within the blending process assessed through FDPM measurements was fit to the first-order model of particle blending further evidencing applicability for monitoring powder-blending processes.

Validating the assumption to the interference approximation by use of measurements of absorption efficiency and hindered scattering in dense suspensions

Frequency domain photon migration (FDPM) measurements were employed to accurately quantify optical properties of both the suspending fluid and particles within dense polystyrene suspensions of 143- or 226-nm mean diameter at varying concentrations (5-30% by volume). The measured absorption coefficients varied linearly with particle volume fraction whereas the isotropic scattering coefficients varied nonlinearly in agreement with the prediction that utilizes the hard-sphere structure factor model. These results validate the interference approximation of light scattering to describe light propagation accurately within dense suspensions. Furthermore, owing to the accuracy of FDPM absorption measurements, the imaginary refractive indices for both particles and their suspending fluid were determined and were found to compare favorably with literature values.

Characterization of Pigment Particle Absorption Efficiencies Using Frequency Domain Photon Migration

Time-dependent measurements of multiply scattered light were made using frequency domain photon migration (FDPM) techniques in polystyrene latex as a function of ppm pigment concentration (by weight) in order to determine the wavelength-dependent absorption efficiencies for three different pigment particles. The results demonstrate that the absorption spectra of pigment particles within their dispersing vehicles concur with the complementary color chart. FDPM offers a first-principles method for assessing optical characteristics of pigments within their dispersing vehicles and without the need to resort to conventional measurement of diffuse reflectance from coatings and data analysis using phenomenological theory.

Characterizing point spread functions of two-photon fluorescence microscopy in turbid medium

In recent years, fluorescence microscopy based on two-photon excitation has become a popular tool for biological and biomedical imaging. Among its advantages is the enhanced depth penetration permitted by fluorescence excitation with the near-infrared photons, which is particularly attractive for deep-tissue imaging. To fully utilize two-photon fluorescence microscopy as a three-dimensional research technique in biology and medicine, it is important to characterize the two-photon imaging parameters in a turbid medium. We investigated the two-photon point spread functions (PSFs) in a number of scattering samples. Gel samples containing 0.1-microm fluorescent microspheres and Liposyn III were used as phantoms mimicking the turbid environment often found in tissue. A full characterization of the two-photon PSFs of a water and oil immersion objective was completed in samples composed of 0, 0.25, 0.5, 1, and 2% Liposyn III. Our results show that up to depths of about 100 (oil) and 200 microm (water), the presence of scatterers (up to 2% Liposyn III) does not appreciably degrade the PSF widths of the objectives.

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.

Measurement of diffusion parameters using a sinusoidal iontophoretic source in rat cortex

A new method was developed to extract diffusion parameters in brain tissue using a sinusoidal iontophoretic point source of tetramethylammonium operated at different frequencies. The resulting steady state oscillating extracellular concentration of this probe molecule was continuously monitored using an ion-selective microelectrode located about 100 microm from the source. Because the probe molecules must diffuse through the extracellular space (ECS), the oscillating concentration at the recording location will develop a phase lag and an amplitude attenuation relative to the sinusoidal source. These two components of the signal can be analyzed to determine the tortuosity factor lambda and the ECS volume fraction alpha. The method also measures the nonspecific clearance rate constant kappa. In brain slices this reflects washout of diffusing molecules. Values of alpha (0.18+/-0.05) and lambda (1.67+/-0.08) obtained from this frequency method in rat cortical slices were similar to those obtained by the real-time iontophoretic method employing a square pulse source. The relative merits of the frequency method compared to the pulse method are discussed.

Fluorescence lifetime spectroscopy in multiply scattering media with dyes exhibiting multiexponential decay kinetics

To investigate fluorescence lifetime spectroscopy in tissue-like scattering, measurements of phase modulation as a function of modulation frequency were made using two fluorescent dyes exhibiting single exponential decay kinetics in a 2% intralipid solution. To experimentally simulate fluorescence multiexponential decay kinetics, we varied the concentration ratios of the two dyes, 3,3-diethylthiatricarbocyanine iodide and indocynanine green (ICG), which exhibit distinctly different lifetimes of 1.33 and 0.57 ns, respectively. The experimental results were then compared with values predicted using the optical diffusion equation incorporating 1) biexponential decay, 2) average of the biexponential decay, as well as 3) stretched exponential decay kinetic models to describe kinetics owing to independent and quenched relaxation of the two dyes. Our results show that while all kinetic models could describe phase-modulation data in nonscattering solution, when incorporated into the diffusion equation, the kinetic parameters failed to likewise predict phase-modulation data in scattering solutions. We attribute the results to the insensitivity of phase-modulation measurements in nonscattering solutions and the inaccuracy of the derived kinetic parameters. Our results suggest the high sensitivity of phase-modulation measurements in scattering solutions may provide greater opportunities for fluorescence lifetime spectroscopy.

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.

In vivo near-infrared spectroscopy

Interrogation of tissue with light offers the potential for noninvasive chemical measurement, and penetration with near-infrared wavelengths (750-1000 nm) is greater than with visible light. Specific absorption by clinically relevant compounds such as oxy- and deoxyhemoglobin and the intracellular respiratory enzyme cytochrome oxidase enable in vivo measurement of these to be performed safely and conveniently. This is the basis of in vivo near-infrared spectroscopy (ivNIRS). Multiple scattering of the interrogating beam by tissues leads to an optical path that is considerably longer than the simple physical pathlength and this complicates the analysis. Modeling of photon propagation through tissues with, for example, finite element and Monte Carlo methods, is assisting in improving the ivNIRS methodology. Instrumentation has advanced from simple continuous wave approaches, through time-resolved methods based on either time-domain or frequency-domain approaches, to spatially resolved measurement based on diffuse reflectance. Initial clinical applications were for monitoring the brain in the neonate and fetus and muscle in adults. Currently, use in adults and children for neurological assessments are of growing interest.

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 ( 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.

Zeeman laser-scanning confocal microscopy in turbid media

A novel Zeeman laser-scanning confocal microscope (ZLSCM) is proposed. It has the same configuration as the conventional laser-scanning confocal microscope (LSCM) in which a Zeeman laser in conjunction with a Glan-Thompson analyzer is used. In our system, the analyzer with the bandpass filter, which act simultaneously as a polarization gate and a coherence gate, enhance the collection efficiency of the weak-scattering photons and simultaneously suppress the multiple-scattering photons. The improvement in depth resolution of a ZLSCM in a scattering medium compared with that of a conventional LSCM is discussed and demonstrated experimentally.

Quantifying the absorption and reduced scattering coefficients of tissuelike turbid media over a broad spectral range with noncontact Fourier-transform hyperspectral imaging

Absorption (mu(a)) and reduced scattering (mu(s)') spectra of turbid media were quantified with a noncontact imaging approach based on a Fourier-transform interferometric imaging system (FTIIS). The FTIIS was used to collect hyperspectral images of the steady-state diffuse reflectance from turbid media. Spatially resolved reflectance data from Monte Carlo simulations were fitted to the recorded hyperspectral images to quantify mu(a) and mu(s)' spectra in the 550-850-nm region. A simple and effective calibration approach was introduced to account for the instrument response. With reflectance data that were close to and far from the source (0.5-6.5 mm), mu(a) and mu(s)' of homogeneous, semi-infinite turbid phantoms with optical property ranges comparable with those of tissues were determined with an accuracy of +/-7% and +/-3%, respectively. Prediction accuracy for mu(a) and mu(s)' degraded to +/-12% and +/-4%, respectively, when only reflectance data close to the source (0.5-2.5 mm) were used. Results indicate that reflectance data close to and far from the source are necessary for optimal quantification of mu(a) and mu(s)'. The spectral properties of mu(a) and mu(s)' values were used to determine the concentrations of absorbers and scatterers, respectively. Absorber and scatterer concentrations of two-chromophore turbid media were determined with an accuracy of +/-5% and +/-3%, respectively.

Polarized optical coherence imaging in turbid media by use of a Zeeman laser

A method that uses a Zeeman laser in conjunction with a Glan-Thompson analyzer to image an object in a turbid medium is proposed. A heterodyne signal is generated only when the scattering photons are partially polarized, and the spatial coherence is not seriously degraded after the signal propagates in the turbid medium. A system combining polarization discrimination with optical coherence detection to image the object in a scattering medium is successfully demonstrated. The medium is a solution of polystyrene microspheres measuring 1.072 mum in diameter suspended in distilled water contained in a 10-mm-thick quartz cuvette. The advantages of this optical system, including better selectivity of the weak partially polarized scattering photons and better imaging ability in higher-scattering media, are discussed.

Quantifying the properties of two-layer turbid media with frequency-domain diffuse reflectance

Noncontact, frequency-domain measurements of diffusely reflected light are used to quantify optical properties of two-layer tissuelike turbid media. The irradiating source is a sinusoidal intensity-modulated plane wave, with modulation frequencies ranging from 10 to 1500 MHz. Frequency-dependent phase and amplitude of diffusely reflected photon density waves are simultaneously fitted to a diffusion-based two-layer model to quantify absorption (mu(a)) and reduced scattering (mu(s)') parameters of each layer as well as the upper-layer thickness (l). Study results indicate that the optical properties of two-layer media can be determined with a percent accuracy of the order of +/-9% and +/-5% for mu(a) and mu(s)', respectively. The accuracy of upper-layer thickness (l) estimation is as good as +/-6% when optical properties of upper and lower layers are known. Optical property and layer thickness prediction accuracy degrade significantly when more than three free parameters are extracted from data fits. Problems with convergence are encountered when all five free parameters (mu(a) and mu(s)' of upper and lower layers and thickness l) must be deduced.

Frequency-domain photon migration measurements for quantitative assessment of powder absorbance: A novel sensor of blend homogeneity

The measurement and analysis of frequency-domain photon migration (FDPM) measurements of powder absorbance in pharmaceutical powders is described in the context of other optical techniques. FDPM consists of launching intensity-modulated light into a powder and detecting the phase delay and amplitude modulation of the re-emitted light as a function of the modulation frequency. From analysis of the data using the diffusion approximation to the radiative transport equation, the absorption coefficient can be obtained. Absorption coefficient measurements of riboflavin in lactose mixtures are presented at concentrations of 0.1 to 1% (w/w) at near-infrared wavelengths where solution absorption cross sections are difficult to accurately measure using traditional transmission measurements in nonscattering solutions. FDPM measurements in powders enabled determinations of absorption coefficients that increase linearly with concentration (w/w) according to Beer-Lambert relationship. The extension of FDPM for monitoring absorbance of low-dose and ultralow-dose powder blending operations is presented.

Probing Static Structure of Colloid-Polymer Suspensions with Multiply Scattered Light

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.

Investigation of static structure factor in dense suspensions by use of multiply scattered light

Near-infrared, frequency-domain photon migration measurements of phase shift are used to derive accurate values of isotropic scattering coefficients in concentrated, interacting suspensions of aqueous polystyrene microspheres with volume concentrations ranging from 1% to 45% by solids and mean diameters ranging from 135 to 500 nm. Under conditions of high ionic strength, the isotropic scattering coefficient can be quantitatively predicted by the Percus-Yevick model for hard-sphere interactions and Mie theory. In addition, the attractive interactions between scatterers arising from the addition of soluble poly(ethylene glycol) with molecular weights of 100 and 600 K cause hindered scattering. The increases in static structure and decreases in isotropic scattering coefficient agree with that predicted by Mie theory and the depletion interaction model developed by Asakura and Oosawa [J. Chem. Phys. 22, 1255 (1954)]. These results demonstrate the success of monitoring interaction between particles by use of multiple-scattered light and the necessity of incorporating models for these interactions when predicting scattering of dense, concentrated suspensions.

Separation of changes in light scattering and chromophore concentrations during cortical spreading depression in rats

We used near-infrared spectroscopy to separate tissue scattering changes from changes in cerebral oxyhemoglobin and deoxyhemoglobin and the redox state of cytochrome- c -oxidase. A separate term of the transport scattering coefficient (micro(s)(?)) was included in a modified Lambert-Beer equation. It is shown by diffusion equation analysis that there is a simple relationship between the differential path-length factor (D(a)) and its scattering equivalent (D(s)) . The method was applied to cortical spreading depression (CSD) data recorded through the skulls of rats. Biphasic changes in micro(s)(?)of +/-0.1mm(-1)were observed during CSD's that spread with a velocity of ~5mm/min . The method proposed has the promise to permit monitoring of scattering changes noninvasively in humans during cortical activation or pathophysiological conditions.

Effect of the scattering delay on time-dependent photon migration in turbid media

We modified the diffusion approximation of the time-dependent radiative transfer equation to account for a finite scattering delay time. Under the usual assumptions of the diffusion approximation, the effect of the scattering delay leads to a simple renormalization of the light velocity that appears in the diffusion equation. Accuracy of the model was evaluated by comparison with Monte Carlo simulations in the frequency domain for a semi-infinite geometry. A good agreement is demonstrated for both matched and mismatched boundary conditions when the distance from the source is sufficiently large. The modified diffusion model predicts that the neglect of the scattering delay when the optical properties of the turbid material are derived from normalized frequency- or time-domain measurements should result in an underestimation of the absorption coefficient and an overestimation of the transport coefficient. These observations are consistent with the published experimental data.

Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration

A 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 of PDW phase and amplitude is measured and compared to analytically derived model functions in order to calculate absorption, mu a, and reduced scattering, mu 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.

Measurement of particle-size distribution and volume fraction in concentrated suspensions with photon migration techniques

The determination of the particle size distribution and the volume fraction in concentrated suspensions from the multiwavelength measurement of isotropic-scattering coefficients by use of frequency-domain photon migration techniques is demonstrated for three different polydisperse polystyrene suspensions. When a Newton-type inverse algorithm is used, the successful recovery of the particle size distribution, in the form of a Weibull function, and the volume fraction of polystyrene suspensions is achieved. Our results are in excellent agreement with dynamic light-scattering size distribution measurements. On consideration of the particle mass conservation as an additional constraint penalty term in the inverse algorithm, it is shown that the quality of the particle size distribution reconstruction can be improved. Because no calibration is needed, photon migration techniques are especially suited for on-line measurement of the particle size distribution and the volume fraction in the chemical- and the pharmaceutical-based industries.

Predictions and measurements of scattering and absorption over broad wavelength ranges in tissue phantoms

Predictions from Mie theory regarding the wavelength dependence of scattering in tissue from the near UV to the near IR are discussed and compared with experiments on tissue phantoms. For large fiber separations it is shown that rapid, simultaneous measurements of the elastic scatter signal for several fiber separations can yield the absorption coefficient and reduced scattering coefficient. With this information, the size of the scattering particles can be estimated, and this is done for Intralipid. Measurements made at smaller source detector separations support Mie theory calculations, demonstrating that the sensitivity of elastic scatter measurements to morphological features, such as scatterer size, is enhanced when the distance between the source and detector fibers is small.