Correlation between blood glucose concentration in diabetics and noninvasively measured tissue optical scattering coefficient

Machine Learning Method and Hyperspectral Imaging for Precise Determination of Glucose and Silicon Levels

This article introduces an algorithm for detecting glucose and silicon levels in solution. The research focuses on addressing the critical need for accurate and efficient glucose monitoring, particularly in the context of diabetic management. Understanding and monitoring silicon levels in the body is crucial due to its significant role in various physiological processes. Silicon, while often overshadowed by other minerals, plays a vital role in bone health, collagen formation, and connective tissue integrity. Moreover, recent research suggests its potential involvement in neurological health and the prevention of certain degenerative diseases. Investigating silicon levels becomes essential for a comprehensive understanding of its impact on overall health and well-being and paves the way for targeted interventions and personalized healthcare strategies. The approach presented in this paper is based on the integration of hyperspectral data and artificial intelligence techniques. The algorithm investigates the effectiveness of two distinct models utilizing SVMR and a perceptron independently. SVMR is employed to establish a robust regression model that maps input features to continuous glucose and silicon values. The study outlines the methodology, including feature selection, model training, and evaluation metrics. Experimental results demonstrate the algorithm's effectiveness at accurately predicting glucose and silicon concentrations and showcases its potential for real-world application in continuous glucose and silicon monitoring systems.

In Vivo Near-Infrared Noninvasive Glucose Measurement and Detection in Humans

In optical noninvasive glucose detection, how to detect the glucose-caused signals from the constant human variations and disturbed probing conditions is always the biggest challenge. Developing effective measurement strategies is essential to realize the detection. A near-infrared (NIR) spectroscopy-based strategy is studied to effectively solve the in vivo measurement issues, obtaining clean blood glucose-caused signals. Two solutions composing our strategy are applied to the NIR spectroscopy-based measurement system to acquire clean raw signals in the data collection, which are a customized high signal-to-noise ratio multi-ring InGaAs detector to reduce the influence of human variations, and a fixing and aiming method to reproduce a consistent measurement condition. Seventeen cases of glucose tolerance test (GTT) on healthy and diabetic volunteers were conducted to validate the strategy. The human experiment results clearly show that the expected blood glucose changes have been detected at 1550 nm. The average correlation coefficient of the 17 cases of GTT between light signal and glucose reference reaches 0.84. The proposed measurement strategy is verified feasible for the glucose detecting in vivo. The strategy provides references to further studies and product developments for the NIR spectroscopy-based glucose measurement and references to other optical measurements in vivo.

Single-pulse, Kerr-effect Mueller matrix LiDAR polarimeter

We present a novel light detection and ranging (LiDAR) polarimeter that enables measurement of 12 of 16 sample Mueller matrix elements in a single, 10 ns pulse. The new polarization state generator (PSG) leverages Kerr phase modulation in a birefringent optical fiber, creating a probe pulse characterized by temporally varying polarization. Theoretical expressions for the Polarization State Generator (PSG) Stokes vector are derived for birefringent walk-off and no walk-off and incorporated into a time-dependent polarimeter signal model employing multiple polarization state analyzers (PSA). Polarimeter modeling compares the Kerr effect and electro-optic phase modulator-based PSG using a single Polarization State Analyzer (PSA) and a scattering sample yielding similarly good performance for both. We include results from an experimental demonstration of the Kerr effect PSG.

Specialized source-detector separations in near-infrared reflectance spectroscopy platform enable effective separation of diffusion and absorption for glucose sensing

We present an approach for accurate glucose sensing in turbid media using a spectrally resolved reflectance setup. Our proposed reflectance setup uses specialized source-detector separations (SDSs) to enable an effective separation of diffusion and absorption signals. Additionally, we adjust the selected SDSs to their optimal values to acquire maximum sensitivity to glucose in the two signals. The separation can help to enhance the sensitivity to glucose both for the diffusion and absorption signals, as they always suppress each other by causing opposite effects on the reflected diffuse light intensity. Monte Carlo simulations and experiments for glucose sensing are used to test the method. The acquired optimal SDSs could provide a reference for noninvasive blood glucose sensing.

Sugar Concentration Measurement System Using Radiofrequency Sensor

A sugar solution measurement system was developed based on the dielectric properties of the sucrose molecule. An ac conductivity and tan δ study as a function of the frequency was performed to find the suitable frequency range for the measuring system. The results indicate that it is possible to obtain a better response of the sensor using the frequencies as the maxima peak in tan δ appears. Developed setup for sucrose solution was appropriate to measure in a 0.15 to 1 g/mL range with an experimental error of about 3%. The proposed system improves the measurement time over some other methods.

Fasting blood glucose levels in patients with different types of diseases

Normal human physiology is dependent on a tight control of the fasting blood glucose (FBG) levels. The islets of pancreas maintains FBG levels within a narrow range of 4-6mmol/L by secreting various hormones, especially insulin and glucagon. However, the hormone secretions by the islets of pancreas are governed by a collective effort among pancreas-islet axis, brain-islet axis, liver-islet axis, gut-islet axis, and adipocyte/myocyte-islet axis. Furthermore, the damage of pancreas, vascular system, brain, liver, intestine, adipose, muscle, and other organs and tissues might affect FBG levels through insulin resistance or impaired insulin signaling, which is the hallmark of type 2 diabetes. In this study, 320,572 clinical lab test results of FBG levels from healthy individuals and patients with 64 different types of diseases during the past 5 years in our hospital were retrieved and analyzed. Based on the mean (SD), median, and p (-Log₁₀p) values, we found 57/64 diseases including type 2 diabetes, pancreatitis, diabetic nephropathy, and pancreatic cancer had significantly (p<0.05, -Log₁₀p>1.30) increased whereas 6/64 diseases including preeclampsia, Wilms' tumor, and lupus erythematous had significantly decreased FBG levels compared to that of healthy controls. These data indicated that the increased FBG levels might be a general pathophysiological property of diseased tissues or organs and the increased FBG levels might be a consequence but not the cause for either prediabetes or type 2 diabetes.

Scattering-independent glucose absorption measurement using a spectrally resolved reflectance setup with specialized variable source-detector separations

We report a novel approach for the accurate measurement of glucose absorption in turbid media using a spectrally resolved reflectance setup. Our proposed reflectance setup with specialized variable source-detector separations enables scattering-independent absorption measurement, which is critical to in vivo long-term glucose concentration monitoring. Starting from the first-order approximation of the radiative transfer equation (RTE), we developed a scattering-independent glucose absorption measurement method and then evaluated this approach by Monte Carlo simulations as well as tissue-mimicking phantom studies in which glucose concentration was accurately measured. Our study demonstrates the potential of our proposed scattering-independent absorption measurement technique as an effective tool to quantify glucose levels in turbid media, which is an important step towards future in vivo long-term glucose concentration monitoring in human subjects.

Estimating the refractive index of oxygenated and deoxygenated hemoglobin using genetic algorithm - support vector regression model

BACKGROUND AND OBJECTIVES

The refractive index of hemoglobin plays important role in hematology due to its strong correlation with the pathophysiology of different diseases. Measurement of the real part of the refractive index remains a challenge due to strong absorption of the hemoglobin especially at relevant high physiological concentrations. So far, only a few studies on direct measurement of refractive index have been reported and there are no firm agreements on the reported values of refractive index of hemoglobin due to measurement artifacts. In addition, it is time consuming, laborious and expensive to perform several experiments to obtain the refractive index of hemoglobin. In this work, we proposed a very rapid and accurate computational intelligent approach using Genetic Algorithm/Support Vector Regression models to estimate the real part of the refractive index for oxygenated and deoxygenated hemoglobin samples.

METHODS

These models utilized experimental data of wavelengths and hemoglobin concentrations in building highly accurate Genetic Algorithm/Support Vector Regression model (GA-SVR).

RESULTS

The developed methodology showed high accuracy as indicated by the low root mean square error values of 4.65 × 10^-4 and 4.62 × 10^-4 for oxygenated and deoxygenated hemoglobin, respectively. In addition, the models exhibited 99.85 and 99.84% correlation coefficients (r) for the oxygenated and deoxygenated hemoglobin, thus, validating the strong agreement between the predicted and the experimental results CONCLUSIONS: Due to the accuracy and relative simplicity of the proposed models, we envisage that these models would serve as important references for future studies on optical properties of blood.

Noninvasive measurement of glucose concentration on human fingertip by optical coherence tomography

A method is proposed for determining the glucose concentration on the human fingertip by extracting two optical parameters, namely the optical rotation angle and the depolarization index, using a Mueller optical coherence tomography technique and a genetic algorithm. The feasibility of the proposed method is demonstrated by measuring the optical rotation angle and depolarization index of aqueous glucose solutions with low and high scattering, respectively. It is shown that for both solutions, the optical rotation angle and depolarization index vary approximately linearly with the glucose concentration. As a result, the ability of the proposed method to obtain the glucose concentration by means of just two optical parameters is confirmed. The practical applicability of the proposed technique is demonstrated by measuring the optical rotation angle and depolarization index on the human fingertip of healthy volunteers under various glucose conditions.

Characterization of the Optical Properties of Turbid Media by Supervised Learning of Scattering Patterns

Fabricated tissue phantoms are instrumental in optical in-vitro investigations concerning cancer diagnosis, therapeutic applications, and drug efficacy tests. We present a simple non-invasive computational technique that, when coupled with experiments, has the potential for characterization of a wide range of biological tissues. The fundamental idea of our approach is to find a supervised learner that links the scattering pattern of a turbid sample to its thickness and scattering parameters. Once found, this supervised learner is employed in an inverse optimization problem for estimating the scattering parameters of a sample given its thickness and scattering pattern. Multi-response Gaussian processes are used for the supervised learning task and a simple setup is introduced to obtain the scattering pattern of a tissue sample. To increase the predictive power of the supervised learner, the scattering patterns are filtered, enriched by a regressor, and finally characterized with two parameters, namely, transmitted power and scaled Gaussian width. We computationally illustrate that our approach achieves errors of roughly 5% in predicting the scattering properties of many biological tissues. Our method has the potential to facilitate the characterization of tissues and fabrication of phantoms used for diagnostic and therapeutic purposes over a wide range of optical spectrum.

Differential Mueller matrix polarimetry technique for non-invasive measurement of glucose concentration on human fingertip

A differential Mueller matrix polarimetry technique is proposed for obtaining non-invasive (NI) measurements of the glucose concentration on the human fingertip. The feasibility of the proposed method is demonstrated by detecting the optical rotation angle and depolarization index of tissue phantom samples containing de-ionized water (DI), glucose solutions with concentrations ranging from 0~500 mg/dL and 2% lipofundin. The results show that the extracted optical rotation angle increases linearly with an increasing glucose concentration, while the depolarization index decreases. The practical applicability of the proposed method is demonstrated by measuring the optical rotation angle and depolarization index properties of the human fingertips of healthy volunteers.

Optical detection of glucose concentration in samples with scattering particles

An optical-based method is proposed for measuring the glucose concentration of samples containing scattering particles. In the proposed approach, a Stokes-Mueller reflection-based polarimetry technique is used to solve the Mueller matrices of a turbid glucose sample with circular birefringence and depolarization properties given six incident lights with different polarization states. Using an error function defined as the difference between the simulated output Stokes vectors and the experimental ones, a genetic algorithm is used to inversely derive the optical rotation and depolarization parameters of the experimental sample corresponding to the glucose concentration and scattering depolarization effect, respectively. The validity of the proposed method is demonstrated using glucose samples containing 0.02 ml and 0.04 ml lipofundin, respectively.

Non-invasive method to detect the changes of glucose concentration in whole blood using photometric technique

A non-invasive method is developed to monitor rapid changes in blood glucose levels in diabetic patients. The system depends on an optical cell built with a LED that emits light of wavelength 535nm, which is a peak absorbance of hemoglobin. As the glucose concentration in blood decreases, its osmolarity also decreases and the Red Blood Cells (RBCs) swell and decrease the path length absorption coefficient. Decreasing absorption coefficient increases the transmission of light through the whole blood. The system was tested with a constructed optical cell that held whole blood in a capillary tube. As expected the light transmitted to the photodiode increases with decreasing glucose concentration. The average response time of the system was between 30-40 seconds.

Continuous noninvasive monitoring of changes in human skin optical properties during oral intake of different sugars with optical coherence tomography

The objective of this study was to evaluate the effects of blood glucose concentration (BGC) on in vivo human skin optical properties after oral intake of different sugars. In vivo optical properties of human skin were measured with a spectral domain optical coherence tomography (SD-OCT). Experimental results show that increase of BGC causes a decrease in the skin attenuation coefficient. And the maximum decrements in mean attenuation coefficient of skin tissue after drinking glucose, sucrose and fructose solution are 47.0%, 36.4% and 16.5% compared with that after drinking water, respectively (p < 0.05). The results also show that blood glucose levels of the forearm skin tissue are delayed compared with finger-stick blood glucose, and there are significant differences in the time delays after oral intake of different sugars. The time delay between mean attenuation coefficient and BGC after drinking glucose solution is evidently larger than that after drinking sucrose solution, and that after drinking sucrose solution is larger than that after drinking fructose solution. Our pilot studies indicate that OCT technique is capable of non-invasive, real-time, and sensitive monitoring of skin optical properties in human subjects during oral intake of different sugars.

Polarization sensitive optical low-coherence reflectometry for blood glucose monitoring in human subjects

A device based on polarization sensitive optical low-coherence reflectometry is developed to monitor blood glucose levels in human subjects. The device was initially tested with tissue phantom. The measurements with human subjects for various glucose concentration levels are found to be linearly dependent on the ellipticity obtainable from the home-made phase-sensitive optical low-coherence reflectometry device. The linearity obtained between glucose concentration and ellipticity are explained with theoretical calculations using Mie theory. A comparison of results with standard clinical methods establishes the utility of the present device for non-invasive glucose monitoring.

Time-domain fluorescence-guided diffuse optical tomography based on the third-order simplified harmonics approximation

Extensive efforts have been made to integrate diffuse optical tomography (DOT) with other imaging modalities, such as magnetic-resonance imaging and x-ray computerized tomography, for its performance improvement. However, the experimental apparatus is in general intricate and costly due to adoption of the physically distinct radiation regimes. In this study, a time-domain fluorescence-guided DOT methodology that incorporates a priori localization information provided by diffuse fluorescence tomography (DFT) is investigated in an attempt to optimize recovery of the optical property distributions. The methodology is based on a specifically designed multichannel time-correlated single-photon-counting DOT/DFT system as well as a featured-data image reconstruction scheme that is developed within the framework of the generalized pulse spectrum technique and employs the third-order simplified harmonics approximation to the radiative transfer equation as the forward model. We have validated the methodology using phantom experiments and demonstrated that, with the guidance of fluorescence a priori, the quantitativeness and spatial resolution of the recovered optical target can be considerably improved in terms of the absorption and scattering images.

In vivo spatial frequency domain spectroscopy of two layer media

Monitoring of tissue blood volume and local oxygen saturation can inform the assessment of tissue health, healing, and dysfunction. These quantities can be estimated from the contribution of oxyhemoglobin and deoxyhemoglobin to the absorption spectrum of the dermis. However, estimation of blood related absorption in skin can be confounded by the strong absorption of melanin in the epidermis and epidermal thickness and pigmentation varies with anatomic location, race, gender, and degree of disease progression. Therefore, a method is desired that decouples the effect of melanin absorption in the epidermis from blood absorption in the dermis for a large range of skin types and thicknesses. A previously developed inverse method based on a neural network forward model was applied to simulated spatial frequency domain reflectance of skin for multiple wavelengths in the near infrared. It is demonstrated that the optical thickness of the epidermis and absorption and reduced scattering coefficients of the dermis can be determined independently and with minimal coupling. Then, the same inverse method was applied to reflectance measurements from a tissue simulating phantom and in vivo human skin. Oxygen saturation and total hemoglobin concentrations were estimated from the volar forearms of weakly and strongly pigmented subjects using a standard homogeneous model and the present two layer model.

Experimental validation of Mueller matrix differential decomposition

Mueller matrix differential decomposition is a novel method for retrieving the polarimetric properties of general depolarizing anisotropic media [N. Ortega-Quijano and J. L. Arce-Diego, Opt. Lett. 36, 1942 (2011), R. Ossikovski, Opt. Lett. 36, 2330 (2011)]. The method has been verified for Mueller matrices available in the literature. We experimentally validate the decomposition for five different experimental setups with different commutation properties and controlled optical parameters, comparing the differential decomposition with the forward and reverse polar decompositions. The results enable to verify the method and to highlight its advantages for certain experimental applications of high interest.

Spatial frequency domain spectroscopy of two layer media

Monitoring of tissue blood volume and oxygen saturation using biomedical optics techniques has the potential to inform the assessment of tissue health, healing, and dysfunction. These quantities are typically estimated from the contribution of oxyhemoglobin and deoxyhemoglobin to the absorption spectrum of the dermis. However, estimation of blood related absorption in superficial tissue such as the skin can be confounded by the strong absorption of melanin in the epidermis. Furthermore, epidermal thickness and pigmentation varies with anatomic location, race, gender, and degree of disease progression. This study describes a technique for decoupling the effect of melanin absorption in the epidermis from blood absorption in the dermis for a large range of skin types and thicknesses. An artificial neural network was used to map input optical properties to spatial frequency domain diffuse reflectance of two layer media. Then, iterative fitting was used to determine the optical properties from simulated spatial frequency domain diffuse reflectance. Additionally, an artificial neural network was trained to directly map spatial frequency domain reflectance to sets of optical properties of a two layer medium, thus bypassing the need for iteration. In both cases, the optical thickness of the epidermis and absorption and reduced scattering coefficients of the dermis were determined independently. The accuracy and efficiency of the iterative fitting approach was compared with the direct neural network inversion.

Detecting glucose-induced changes in in vitro and in vivo experiments with optical coherence tomography

Optical clearing is a well-known phenomenon. It is based on the matching of refractive indices of a bulk material and scattering particles. The same principle is also used in scattering-based optical measurements of different constituents, such as glucose. By registering changes in scattering, it is possible to evaluate changes in the concentration of a solvent. This work describes the use of optical coherence tomography (OCT) to monitor glucose-induced changes in the optical properties of samples. Intralipid, mouse skin tissue, and mice (C57BL) are used as samples. Differences between in vitro and in vivo measurement conditions, the effect of glucose on the samples' optical properties, as well as possible problems in OCT experiments are discussed. A comparison of OCT signals from mouse skin samples and mice in vivo shows that the intensity of backscattered radiation is stronger in a living animal than in cultured tissue. Moreover, the effect of glucose on the scattering properties is larger in an in vivo case than in an in vitro case. In comparison with tissue, the effect of glucose is the smallest in Intralipid. The results increase the value of using cultured tissue in developing optical sensing techniques.

Polarization-based diffuse reflectance imaging for noninvasive measurement of glucose

BACKGROUND

The ability to measure glucose concentration through noninvasive approaches would impact the treatment of diabetes significantly. Polarization-based optical approaches have received considerable interest because of their potential medical applications. Glucose, a chiral molecule, has the ability to rotate the plane of linearly polarized light, commonly referred to as optical activity, as well as changing the refractive index of the media, which therefore affects the overall scattering coefficient in a given media. The magnitude of each effect is related to the concentration of glucose. Although most previous studies have reported on the use of polarimetry in the aqueous humor of the eye because of its nonscattering nature, one would also expect that glucose concentration could be measured in more turbid media such as tissue through a similar approach. This study investigated how each of these effects is correlated to glucose concentration in a physiological range for highly scattering biological media.

METHODS

A custom-designed imaging polarimeter was used to image highly scattering Intralipid-based media containing different concentrations of glucose. Model formation and glucose prediction were performed through the use of partial least squares (PLS) regression. Further insight into the differences between polarization-based image measurements and encoding of glucose information was provided through the use of principal component analysis (PCA).

RESULTS

When coupled with PLS regression, in vitro polarization measurements yielded highly correlated glucose predictions in both calibration and independent validation, 0.999 and 0.998, respectively. Through the use of PCA, it appears that the majority of the image-based signal yielding the most significant glucose information is attributable to changes in the overall scattering coefficient due to glucose concentration and, to a lesser degree, effects of optical activity.

CONCLUSIONS

This study showed how polarimetric-based imaging coupled with PLS regression can be used to quantify glucose concentration in highly scattering media. Such methods may potentially be able to extend the use of noninvasive in vivo polarimetric measurements, normally acquired in the anterior chamber of the eye, to other preferred sensing sites such as the skin.

Affinity-based turbidity sensor for glucose monitoring by optical coherence tomography: toward the development of an implantable sensor

We investigated the feasibility of constructing an implantable optical-based sensor for seminoninvasive continuous monitoring of analytes. In this novel sensor, analyte concentration-dependent changes induced in the degree of optical turbidity of the sensing element can be accurately monitored by optical coherence tomography (OCT), an interferometric technique. To demonstrate proof-of-concept, we engineered a sensor for monitoring glucose concentration that enabled us to quantitatively monitor the glucose-specific changes induced in bulk scattering (turbidity) of the sensor. The sensor consists of a glucose-permeable membrane housing that contains a suspension of macroporous hydrogel particles and concanavalin A (ConA), a glucose-specific lectin, that are designed to alter the optical scattering of the sensor as a function of glucose concentration. The mechanism of modulation of bulk turbidity in the sensor is based on glucose-specific affinity binding of ConA to pendant glucose residues of macroporous hydrogel particles. The affinity-based modulation of the scattering coefficient was significantly enhanced by optimizing particle size, particle size distribution, and ConA concentration. Successful operation of the sensor was demonstrated under in vitro condition where excellent reversibility and stability (160 days) of prototype sensors with good overall response over the physiological glucose concentration range (2.5-20 mM) and good accuracy (standard deviation 5%) were observed. Furthermore, to assess the feasibility of using the novel sensor as one that can be implanted under skin, the sensor was covered by a 0.4 mm thick tissue phantom where it was demonstrable that the response of the sensor to 10 mM glucose change could still be measured in the presence of a layer of tissue shielding the sensor aiming to simulate in vivo condition. In summary, we have demonstrated that it is feasible to develop an affinity-based turbidity sensor that can exhibit a highly specific optical response as a function of changes in local glucose concentration and such response can be accurately monitored by OCT suggesting that the novel sensor can potentially be engineered to be used as an implantable sensor for in vivo monitoring of analytes.

Correlation between collagen solubility and skin optical clearing using sugars

BACKGROUND AND OBJECTIVE

Light scattering from collagen within skin limits light-based therapeutics while increasing the risk of epidermal thermal injury. Specific chemicals show the ability to reduce light scattering by reversibly altering the optical properties of skin. This study examines the correlation between collagen solubility and the optical clearing potential (OCP) of sugars and sugar-alcohols using in vitro rodent skin.

MATERIALS AND METHODS

Collagen solubility in dextrose, fructose, sucrose, and sorbitol was measured using near-UV spectroscopy. Light transmittance, reflectance, and rodent skin thickness were measured (giving skin reduced scattering coefficient) before and after exposure of the dermal surface to sugars and sugar-alcohols. OCP was calculated as the ratio of reduced scattering coefficients before and after exposures.

RESULTS

Dextrose, fructose, sucrose, and sorbitol had at least twice the collagen solubility and twice the OCP as compared to glycerol. In general, collagen solubility correlated with each agent's ability to optically clear rodent skin.

CONCLUSION

These results demonstrate that sugar and sugar-alcohol interaction with collagen are a primary event in tissue optical clearing.

Measurement of the absorption and scattering properties of turbid liquid foods using hyperspectral imaging

A hyperspectral imaging system in line scanning mode was used for measuring the absorption and scattering properties of turbid food materials over the visible and near-infrared region of 530-900 nm. An instrumental calibration procedure was developed to compensate for the nonuniform instrument response of the imaging system. A nonlinear curve-fitting algorithm for a steady-state diffusion theory model was proposed to determine absorption (mua) and reduced scattering coefficients (mu's) from the spatially resolved hyperspectral reflectance profiles. The hyperspectral imaging system provided good measurement of mua and mu's for the simulation samples made of Intralipid scattering material and three absorbers (blue dye, green dye, and black ink) with average fitting errors of 16% and 11%, respectively. The optical properties of the fruit and vegetable juices and milks were determined. Values of the absorption and reduced scattering coefficient at 600 nm were highly correlated to the fat content of the milk samples with the correlation coefficient of 0.995 and 0.998, respectively. Compared to time-resolved and frequency-domain techniques, the hyperspectral imaging technique provides a faster and simpler means for measuring the optical properties of turbid food and agricultural products.

Effects of assuming constant optical scattering on measurements of muscle oxygenation by near-infrared spectroscopy during exercise

The aim of this study was to examine the effects of assuming constant reduced scattering coefficient (μ[Formula: see text]) on the muscle oxygenation response to incremental exercise and its recovery kinetics. Fifteen subjects (age: 24 ± 5 yr) underwent incremental cycling exercise. Frequency domain near-infrared spectroscopy (NIRS) was used to estimate deoxyhemoglobin concentration {[deoxy(Hb+Mb)]} (where Mb is myoglobin), oxyhemoglobin concentration {[oxy(Hb+Mb)]}, total Hb concentration (Total[Hb+Mb]), and tissue O2 saturation (Sti[Formula: see text]), incorporating both continuous measurements of μ[Formula: see text] and assuming constant μ[Formula: see text]. When measuring μ[Formula: see text], we observed significant changes in NIRS variables at peak work rate Δ[deoxy(Hb+Mb)] (15.0 ± 7.8 μM), Δ[oxy(Hb+Mb)] (−4.8 ± 5.8 μM), ΔTotal[Hb+Mb] (10.9 ± 8.4 μM), and ΔSti[Formula: see text](−11.8 ± 4.1%). Assuming constant μ[Formula: see text] resulted in greater ( P < 0.01 vs. measured μ[Formula: see text]) changes in the NIRS variables at peak work rate, where Δ[deoxy(Hb+Mb)] = 24.5 ± 15.6 μM, Δ[oxy(Hb+Mb)] = −9.7 ± 8.2 μM, ΔTotal[Hb+Mb] = 14.8 ± 8.7 μM, and ΔSti[Formula: see text]= −18.7 ± 8.4%. Regarding the recovery kinetics, the large 95% confidence intervals (CI) for the difference between those determine measuring μ[Formula: see text] and assuming constant μ[Formula: see text] suggested poor agreement between methods. For the mean response time (MRT), which describes the overall kinetics, the 95% confidence intervals were MRT − [deoxy(Hb+Mb)] = 26.7 s; MRT − [oxy(Hb+Mb)] = 11.8 s, and MRT − Sti[Formula: see text]= 11.8 s. In conclusion, μ[Formula: see text] changed from light to peak exercise. Furthermore, assuming a constant μ[Formula: see text] led to an overestimation of the changes in NIRS variables during exercise and distortion of the recovery kinetics.

Evaluation of a fiberoptic-based system for measurement of optical properties in highly attenuating turbid media

Background

Accurate measurements of the optical properties of biological tissue in the ultraviolet A and short visible wavelengths are needed to achieve a quantitative understanding of novel optical diagnostic devices. Currently, there is minimal information on optical property measurement approaches that are appropriate for in vivo measurements in highly absorbing and scattering tissues. We describe a novel fiberoptic-based reflectance system for measurement of optical properties in highly attenuating turbid media and provide an extensive in vitro evaluation of its accuracy. The influence of collecting reflectance at the illumination fiber on estimation accuracy is also investigated.

Methods

A neural network algorithm and reflectance distributions from Monte Carlo simulations were used to generate predictive models based on the two geometries. Absolute measurements of diffuse reflectance were enabled through calibration of the reflectance system. Spatially-resolved reflectance distributions were measured in tissue phantoms at 405 nm for absorption coefficients (μ_a) from 1 to 25 cm^-1 and reduced scattering coefficients (μ′s MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacuaH8oqBgaqbamaaBaaaleaacqqGZbWCaeqaaaaa@3007@) from 5 to 25 cm^-1. These data and predictive models were used to estimate the optical properties of tissue-simulating phantoms.

Results

By comparing predicted and known optical properties, the average errors for μ_a and μ′s MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacuaH8oqBgaqbamaaBaaaleaacqqGZbWCaeqaaaaa@3007@ were found to be 3.0% and 4.6%, respectively, for a linear probe approach. When bifurcated probe data was included and samples with μ_a values less than 5 cm^-1 were excluded, predictive errors for μ_a and μ′s MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacuaH8oqBgaqbamaaBaaaleaacqqGZbWCaeqaaaaa@3007@ were further reduced to 1.8% and 3.5%.

Conclusion

Improvements in system design have led to significant reductions in optical property estimation error. While the incorporation of a bifurcated illumination fiber shows promise for improving the accuracy of μ′s MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacuaH8oqBgaqbamaaBaaaleaacqqGZbWCaeqaaaaa@3007@ estimates, further study of this approach is needed to elucidate the source of discrepancies between measurements and simulation results at low μ_a values.

In vivo study of glucose-induced changes in skin properties assessed with optical coherence tomography

Recently, our in vivo studies demonstrated a strong correlation between blood glucose concentration and the slope of the optical coherence tomography (OCT) signal when the probing beam was scanned over a straight line. To improve the sensitivity of OCT for blood glucose monitoring, two-dimensional (2D) lateral scanning of the OCT probing beam was proposed. Depth-dependent changes in pig skin properties with variation of blood glucose concentration were revealed due to significant suppression of speckle noise and motion artefacts in 2D scanning mode. The correlation coefficient of the OCT signal slope with blood glucose concentration varied periodically in the range from -0.9 to +0.9 depending on depth. The period of variation of the correlation coefficient was 100-150 microm that corresponded to the distance between neighbour collagen bundles. We also observed a decrease of skin thickness by 10 +/- 7.5 microm with an increase of blood glucose concentration by 277 +/- 56 mg dl(-1). Mechanisms of glucose-induced changes in skin properties owing to tissue layer shift caused by dehydration associated with the glucose osmotic effect were considered.

Angular measurements of light scattered by turbid chiral media using linear Stokes polarimeter

The effects of turbid chiral media on light polarization are studied in different directions around the scattering samples using a refined linear Stokes polarimeter, which simplifies the signal analysis, and allows for the detailed investigations of scattered light. Because no moving parts are involved in a measurement at a specific detection direction, the determination accuracy of polarization states is increased. The results show that light depolarization increases with both turbidity and detection angle for low and moderately turbid samples; however, the angular dependence decreases with increasing turbidity. When the turbidity is increased to approximately 100 cm(-1), the depolarization becomes higher in the forward than in the backward direction. Polarization sensitive Monte Carlo simulations are used to verify some experimental observations. The results also demonstrate that surviving linear polarization fraction and overall intensity are more sensitive to the increase of glucose concentration in backward than in the forward direction in highly turbid media, indicating that backward geometry may be preferable for potential glucose detection in a biomedical context. Comparison measurements with optically inactive glycerol suggest that the refractive index matching effect, and not the chiral nature of the solute, dominates the observed optical rotation engendered by glucose in highly turbid media.

Collagen solubility correlates with skin optical clearing

Biomedical optics and photomedicine applications are challenged by the turbidity of most biological tissue systems. Nonreactive, biocompatible chemical agents can induce a reversible reduction in optical scattering of collagenous tissues such as human skin. Herein we show that a chemical agent's tissue optical clearing potential is directly related to its collagen solubility, providing a rational design basis for effective, percutaneous formulations.

Noninvasive and minimally invasive methods for transdermal glucose monitoring

Noninvasive and minimally invasive techniques for monitoring glucose via the skin are reviewed. These approaches rely either on the interaction of electromagnetic radiation with the tissue or on the extraction of fluid across the barrier. The structure and physiology of the skin make the technical realization of transdermal glucose monitoring a difficult challenge. The techniques involving transdermal fluid extraction circumvent and/or compromise the barrier function of skin's outermost and least permeable layer, the stratum corneum, by the application of physical energy. While sonophoresis and microporation methods, for example, are in relatively early-stage development, a device using reverse iontophoresis [the GlucoWatch Biographer (Cygnus, Inc., Redwood City, CA)] is already commercially available. Optical techniques to monitor glucose are truly noninvasive. The tissue is irradiated, the absorbed or scattered radiation is analyzed, and the information is processed, to provide a measure proportional to the concentration of glucose in the dermal tissue. These techniques include near-infrared and Raman spectroscopy, polarimetry, light scattering, and photoacoustic spectroscopy. By contrast, impedance spectroscopy measures changes in the dielectric properties of the tissue induced by blood glucose variation. Large-scale studies in support of efficacy of these methodologies are as yet unavailable. At present, therefore, transdermal fluid extraction technologies are offering greater promise in terms of practical and realizable devices for patient use. The truly noninvasive allure of the optical approach assures continued and intense research activity--for the moment, however, an affordable, efficient, and portable system is not on the immediate horizon.

Non-invasive glucose measurement technologies: an update from 1999 to the dawn of the new millennium

There are three main issues in non-invasive (NI) glucose measurements: namely, specificity, compartmentalization of glucose values, and calibration. There has been progress in the use of near-infrared and mid-infrared spectroscopy. Recently new glucose measurement methods have been developed, exploiting the effect of glucose on erythrocyte scattering, new photoacoustic phenomenon, optical coherence tomography, thermo-optical studies on human skin, Raman spectroscopy studies, fluorescence measurements, and use of photonic crystals. In addition to optical methods, in vivo electrical impedance results have been reported. Some of these methods measure intrinsic properties of glucose; others deal with its effect on tissue or blood properties. Recent studies on skin from individuals with diabetes and its response to stimuli, skin thermo-optical response, peripheral blood flow, and red blood cell rheology in diabetes shed new light on physical and physiological changes resulting from the disease that can affect NI glucose measurements. There have been advances in understanding compartmentalization of glucose values by targeting certain regions of human tissue. Calibration of NI measurements and devices is still an open question. More studies are needed to understand the specific glucose signals and signals that are due to the effect of glucose on blood and tissue properties. These studies should be performed under normal physiological conditions and in the presence of other co-morbidities.

Glucose and mannitol diffusion in human dura mater

An in vitro experimental study of the control of the human dura mater optical properties at administration of aqueous solutions of glucose and mannitol has been presented. The significant increase of the dura mater optical transmittance under action of immersion liquids has been demonstrated. Diffusion coefficients of glucose and mannitol in the human dura mater tissue at 20 degrees C have been estimated as (1.63 +/- 0.29) x 10(-6)cm(2)/s and as (1.31 +/- 0.41) x 10(-6) cm(2)/s, respectively. Experiments show that administration of immersion liquids allows for the effective control of tissue optical characteristics that make dura mater more transparent, thereby increasing the ability of light penetration through the tissue.

Monitoring blood glucose changes in cutaneous tissue by temperature-modulated localized reflectance measurements

BACKGROUND

Most proposed noninvasive methods for glucose measurements do not consider the physiologic response of the body to changes in glucose concentration. Rather than consider the body as an inert matrix for the purpose of glucose measurement, we exploited the possibility that noninvasive measurements of glucose can be approached by investigating their effects on the skin's thermo-optical response.

METHODS

Glucose concentrations in humans were correlated with temperature-modulated localized reflectance signals at wavelengths between 590 and 935 nm, which do not correspond to any near-infrared glucose absorption wavelengths. Optical signal was collected while skin temperature was modulated between 22 and 38 degrees C over 2 h to generate a periodic set of cutaneous vasoconstricting and vasodilating events, as well as a periodic change in skin light scattering. The method was tested in a series of modified meal tolerance tests involving carbohydrate-rich meals and no-meal or high-protein/no-carbohydrate meals.

RESULTS

The optical data correlated with glucose values. Changes in glucose concentrations resulting from a carbohydrate-rich meal were predicted with a model based on a carbohydrate-meal calibration run. For diabetic individuals, glucose concentrations were predicted with a standard error of prediction <1.5 mmol/L and a prediction correlation coefficient 0.73 in 80% of the cases. There were run-to-run differences in predicted glucose concentrations. Non-carbohydrate meals showed a high degree of scatter when predicted by a carbohydrate meal calibration model.

CONCLUSIONS

Blood glucose concentrations alter thermally modulated optical signals, presumably through physiologic and physical effects. Temperature changes drive cutaneous vascular and refractive index responses in a way that mimics the effect of changes in glucose concentration. Run-to-run differences are attributable to site-to-site structural differences.

Precision of measurement of tissue optical properties with optical coherence tomography

Accurate and noninvasive measurement of tissue optical properties can be used for biomedical diagnostics and monitoring of tissue analytes. Noninvasive measurement of tissue optical properties (total attenuation and scattering coefficients, optical thickness, etc.) can be performed with the optical coherence tomography (OCT) technique. However, speckle noise substantially deteriorates the accuracy of the measurements with this technique. We studied suppression of speckle noise for accurate measurement of backscattering signal and scattering coefficient with the OCT technique. Our results demonstrate that the precision of measurement of backscattering signals with the OCT technique can be 0.2% for homogeneously scattering media and 0.7% for skin, if spatial averaging of speckle noise is applied. This averaging allows us to achieve the precision of tissue scattering coefficient measurements of approximately +/-0.8%. This precision can be further improved by a factor of 2-3, upon optimization of OCT operating parameters.

Specificity of noninvasive blood glucose sensing using optical coherence tomography technique: a pilot study

Noninvasive monitoring of blood glucose concentration in diabetic patients would significantly reduce complications and mortality associated with this disease. In this paper, we experimentally and theoretically studied specificity of noninvasive blood glucose monitoring with the optical coherence tomography (OCT) technique. OCT images and signals were obtained from skin of Yucatan micropigs and New Zealand rabbits. Obtained results demonstrate that: (1) several body osmolytes may change the refractive index mismatch between the interstitial fluid (ISF) and scattering centres in tissue, however the effect of the glucose is approximately one to two orders of magnitude higher; (2) an increase of the ISF glucose concentration in the physiological range (3-30 mM) may decrease the scattering coefficient by 0.22% mM(-1) due to cell volume change; (3) stability of the OCT signal slope is dependent on tissue heterogeneity and motion artefacts; and (4) moderate skin temperature fluctuations (+/- 1 degree C) do not decrease accuracy and specificity of the OCT-based glucose sensor, however substantial skin heating or cooling (several degrees C) significantly change the OCT signal slope. These results suggest that the OCT technique may provide blood glucose concentration monitoring with sufficient specificity under normal physiological conditions.

Reflectance-based determination of optical properties in highly attenuating tissue

Accurate data on in vivo tissue optical properties in the ultraviolet A (UVA) to visible (VIS) range are needed to elucidate light propagation effects and to aid in identifying safe exposure limits for biomedical optical spectroscopy. We have performed a preliminary study toward the development of a diffuse reflectance system with maximum fiber separation distance of less than 2.5 mm. The ultimate objective is to perform endoscopic measurement of optical properties in the UVA to VIS. Optical property sets with uniformly and randomly distributed values were developed within the range of interest: absorption coefficients from 1 to 25 cm(-1) and reduced scattering coefficients from 5 to 25 cm(-1). Reflectance datasets were generated by direct measurement of Intralipid-dye tissue phantoms at lambda=675 nm and Monte Carlo simulation of light propagation. Multivariate calibration models were generated using feed-forward artificial neural network or partial least squares algorithms. Models were calibrated and evaluated using simulated or measured reflectance datasets. The most accurate models developed-those based on a neural network and uniform optical property intervals-were able to determine absorption and reduced scattering coefficients with root mean square errors of +/-2 and +/-3 cm(-1), respectively. Measurements of ex vivo bovine liver at 543 and 633 nm were within 5 to 30% of values reported in the literature. While our technique for determination of optical properties appears feasible and moderately accurate, enhanced accuracy may be achieved through modification of the experimental system and processing algorithms.

Temperature modulation of the visible and near infrared absorption and scattering coefficients of human skin

We determine temperature effect on the absorption and reduced scattering coefficients (mu(a) and mu(s)(')) of human forearm skin. Optical and thermal simulation data suggest that mu( a) and mu(s)(') are determined within a temperature-controlled depth of approximately 2 mm. Cutaneous mu(s)(') change linearly with temperature. Change in mu(a) was complex and irreversible above body normal temperatures. Light penetration depth (delta) in skin increased on cooling, with considerable person-to-person variations. We attribute the effect of temperature on mu(s)(') to change in refractive index mismatch, and its effect on mu(a) to perfusion changes. The reversible temperature effect on mu (s)(' ) was maintained during more than 90 min. contact between skin and the measuring probe, where temperature was modulated between 38 and 22 degrees C for multiple cycles While temperature modulated mu(s)(' ) instantaneously and reversibly, mu(a) exhibited slower response time and consistent drift. There was a statistically significant upward drift in mu(a) and a mostly downward drift in mu( s)(') over the contact period. The drift in temperature-induced fractional change in mu(s)(') was less statistically significant than the drift in mu(s)('). Deltamu( s)(') values determined under temperature modulation conditions may have less nonspecific drift than mu(s)(') which may have significance for noninvasive determination of analytes in human tissue.

Analysis of the picosecond magneto-optical phenomena in scattering media of biological interest

The behaviour of a magneto-optically active biological-like medium under picosecond optical excitation is analysed. The new technique is based on the fact that photons trapped in multiple scattering events inside the magneto-optical medium leave the medium with larger induced rotation angles, as they travel longer distances. Two- and three-dimensional displacements of the photons in the medium are separately analysed. The dependence of this effect on the applied magnetic field strength, the value of the magneto-optical constant of the medium and the standard deviation of the statistical distribution of the photons scattered inside the turbid medium are studied. The best values for the magnetic field and optical parameters of the biological medium are proposed for the experimental observation of the picosecond magneto-optical phenomena in scattering media of biological origin. We also make some prospective studies to evaluate the potential application of the magneto-optical effect as a tool for optical tissue biopsy. Values for the optimum magnetic field intensities and for the expected experimental sensitivity in diverse conditions are reported.

Determination of glucose concentration in a scattering medium based on selected wavelengths by use of an overtone absorption band

A method and device for measuring glucose concentration in a scattering medium have been developed. A spectral range of 800-1800 nm is considered for wavelength selection because of its deeper penetration into biological tissue and the presence of a glucose absorption band. An algorithm based on selected wavelengths is proposed to minimize interference from other components. The optimal distance between the light source and the detector for diffuse reflectance measurement minimizes the influence of medium scattering. The proposed algorithm and measuring device are tested with a solution containing milk with added glucose. Glucose concentrations between 0 and 2000 mg/dl are determined with a correlation coefficient of 0.977. We also investigate the influence of concentration variations of other substances such as water, hemoglobin, albumin, and cholesterol when they are mixed in a scattering medium.

Monte Carlo model and single-scattering approximation of the propagation of polarized light in turbid media containing glucose

We present a single-scattering model as well as a Monte Carlo model of the effect of glucose on polarized light in turbid media. Glucose alters the Mueller-matrix patterns of diffusely backscattered and forward-scattered light because glucose molecules rotate the polarization plane of linearly polarized light. For example, the angles of rotation in Mueller-matrix elements S21 and S12 are linearly related to the concentration of glucose and increase with the source-detector distance. In the nondiffusion regime, the two models agree well with each other. In the diffusion regime, the single-scattering model is invalid, but there still exists a linear relationship between the angles of rotation in the Mueller-matrix elements and the concentration of glucose, which is predicted by the Monte Carlo model.

Haemoglobin oxygenation of a two-layer tissue-simulating phantom from time-resolved reflectance: effect of top layer thickness

A dual wavelength time-resolved reflectance system was developed for monitoring haemoglobin saturation noninvasively. At each wavelength, the time-resolved reflectance data were fitted to a diffusion model of light propagation in a homogeneous, semi-infinite medium to yield the absolute scattering and absorption coefficients. The absorption coefficients were then used to calculate haemoglobin saturation. A two-layer phantom containing human erythrocytes in a scattering solution in the bottom layer was used to study system performance under more realistic conditions. The top layer was chosen to simulate either skin or fat and the oxygenation of the bottom layer, which corresponded to muscle, was controlled. The thickness of the fat layer was varied from 1.5 to 10 mm to investigate the effects of increasing the top layer thickness. These results, obtained with the simple diffusion model, were compared with simultaneous measurements of oxygenation made directly in the bottom layer. Errors in estimating haemoglobin saturation with this method ranged from 5-11% depending on the thickness of the top layer and its optical properties.

Dynamic optical coherence tomography in studies of optical clearing, sedimentation, and aggregation of immersed blood

The concept of refractive-index matching to enhance the optical penetration depth of whole blood is discussed on the basis of in vitro studies that used the technique of near-infrared optical coherence tomography. It was found that optical clearing of blood is defined not only by refractive-index matching but also by changes in the size of red blood cells and in their aggregation ability when chemicals are added. For example, in whole blood diluted to twice its volume by saline with the addition of 6.5% glycerol, the total attenuation coefficient was reduced from 4.2 to 2.0 mm(-1), and the optical penetration at 820 nm was correspondingly increased to 117%. For the other agents tested (glucose, dextrans, propylene glycol, and trazograph) the enhancement of penetration was 20-150.5%. In the blood sedimentation study, regular or irregular oscillations or jumps of the red-blood cell-plasma boundary were observed. The 1-min time period of regular oscillations correlated well with the kinetics of the aggregation process as described by the two subsequent stages of formation of linear and three-dimensional aggregates. The results also showed that optical clearing of blood by osmotic agents is potentially useful not only in blood sedimentation and aggregation studies but also in intravascular optical coherence tomography imaging techniques.

Experimental verification of the effect of refractive index mismatch on the light fluence in a turbid medium

Diffusion theory is often used to model the transport of light within tissue. It can be used to calculate the light fluence rate in tissue, for example, during photodynamic therapy, or to measure the absorption and scattering properties of tissue. For both of these applications, the influence of the interface between the tissue and the exterior medium on the fluence rate inside the tissue must be known in order to make accurate calculations. We present an experimental investigation of the effect of the refractive index mismatch at the tissue interface on the internal light fluence rate and on the spatially resolved diffuse reflectance as the boundary conditions of the tissue/external medium are changed. The effects of changing the relative refractive index at the boundary are compared to predictions of diffusion theory. The effect of the refractive index mismatch is predicted correctly by diffusion theory.

Determination of the optical properties of two-layer turbid media by use of a frequency-domain hybrid monte carlo diffusion model

The general two-layer inverse problem in biomedical photon migration is to estimate the absorption and scattering coefficients of each layer as well as the top-layer thickness. We attempted to solve this problem, using experimental and simulated spatially resolved frequency-domain (FD) reflectance for optical properties typical of skin overlying muscle or skin overlying fat in the near infrared. Two forward models of light propagation were used: a two-layer diffusion solution [Appl. Opt. 37, 779 (1998)] and a hybrid Monte Carlo (MC) diffusion model [Appl. Opt. 37, 7401 (1998)]. MC-simulated FD reflectance data were fitted as relative measurements to the hybrid and the pure diffusion models. It was found that the hybrid model could determine all the optical properties of the two-layer media studied to ~5%. Also, the same accuracy could be achieved by means of fitting MC-simulated cw reflectance data as absolute measurements, but fitting them as relative ones is an ill-posed problem. In contrast, two-layer diffusion could not retrieve the top-layer optical properties as accurately for FD data and was ill-posed for both relative and absolute cw data. The hybrid and the pure diffusion models were also fitted to experimental FD reflectance measurements from two-layer tissue-simulating phantoms representative of skin-on-fat and skin-on-muscle baseline optical properties. Both the hybrid and the diffusion models could determine the optical properties of the lower layer. The hybrid model demonstrated its potential to retrieve quantitatively the transport scattering coefficient of skin (the upper layer), which was not possible with the pure diffusion model. Systematic discrepancies between model and experiment may compromise the accuracy of the deduced top-layer optical properties. Identifying and eliminating such discrepancies is critical to practical application of the method.