Modified Beer-Lambert Law Research Articles

Assessment of variations in air-dry wood density using time-of-flight near-infrared spectroscopy

Non-destructive measurement of wood density using reflectance and transmittance near-infrared spectroscopy (NIRS) has already been reported by several researchers. However, these methods do not allow an independent determination of the spectral contributions of the absorption and scattering effects. In this study, time-of-flight NIRS (TOF-NIRS) was used to measure wood density of seven softwood and hardwood species. A curve fitting procedure was used to resolve the diffusion equation and compute the absorption (µa) and reduced scattering coefficients () from the time-resolved profiles (TRPs) acquired from the wood samples. Statistical parameters were also computed from TRPs and correlated with the wood air-dry density as well as with both optical coefficients. A simple linear regression model was built to relate air-dry wood density to µa (R2 = 0.56, root mean square error [RMSE] = 0.047 g/cm3, p value < 0.05). Results obtained were in good agreement with the modified Beer–Lambert law for turbid media. The square root of the / ratio (which was well correlated with the photons mean path length) was used to correct for the distortion due to scattering in absorbance NIR spectra acquired using reflectance spectroscopy. This research demonstrates the potential of TOF-NIRS to assess wood density and to correct reflectance spectra for scattering effects.

Extraordinary High Microwave Absorption Cross Section of Ultralong Carbon Nanotubes

The microwave-induced heating of nanoparticles has been actively studied in pursuit of more efficient microwave absorbers. Here we systematically investigated the microwave absorption cross section of conductive particles (Al), magnetic particles (Fe3O4), and carbon nanotubes with different lengths. The particles were suspended in silicone oil and irradiated with a microwave at 2.45 GHz using a single-mode microwave reactor. The experimentally measured heating rate was analytically modeled based on the modified Lambert–Beer law to obtain the microwave absorption cross section per mass. The microwave-induced heating rate was primarily dependent on optical absorbance, which is proportional to the mass concentration of suspended particles. Under the similar optical absorbance, longer nanotubes provided greater microwave absorption cross section which could be described by the short dipole antenna theory. The microwave absorption cross section of 5 mm long multiwalled carbon nanotubes was ∼4080 times greater ...

The application of extended modified Lambert Beer model for measurement of blood carboxyhemoglobin and oxyhemoglobin saturation

This work presents the use of extended Modified Lambert Beer (MLB) model for accurate and continuous monitoring of percent blood carboxyhemoglobin (COHb) (SCO) and oxyhemoglobin (OxyHb) saturation ( SO 2) via a fitting procedure. This quantification technique is based on the absorption characteristics of hemoglobin derivatives in the wavelength range of 520–600 nm to give the best estimates of the required parameters. A comparison of the performance of the developed model and MLB law is made using attenuation data from Monte Carlo simulations for a two-layered skin model. The results revealed a lower mean absolute error of 0.4% in the values estimated by the developed model as compared to 10% that is given by the MLB law. This study showed that the discussed approach is able to provide consistent and accurate measurement of blood SO 2 and SCO across different skin pigmentations suggesting that it may potentially be used as an alternative means for clinical diagnosis of carbon monoxide ( CO ) poisoning.

WIRELESS DISTRIBUTED ACQUISITION SYSTEM FOR NEAR INFRARED SPECTROSCOPY – WDA-NIRS

The wireless distributed acquisition system for near infrared spectroscopy (WDA-NIRS) is a portable, ultra-compact, continuous wave (CW) NIRS system. Its main advantage is that it allows continuous synchronized multi-site hemodynamic monitoring. The WDA-NIRS system calculates online changes in hemoglobin concentration based on modified Beer–Lambert law and the tissue oxygenation index based on the spatial-resolved spectroscopy method. It consists of up to seven signal acquisition units, sufficiently small to be easily attached to any part of the body. These units are remotely synchronized by a PC base station for independent acquisition of NIRS signals. Each acquisition module can be freely adapted to individual requirements such as local skin properties and the microcirculation of interest, e.g., different muscles, brain, skin, etc. For this purpose, the light emitted by each LED can be individually, interactively or automatically adjusted to local needs. Furthermore, the user can freely create an emitter time-multiplexing protocol and choose the detector sensitivity most suitable to a particular situation. The potential diagnostic value of this advanced device is demonstrated by three typical applications.

Continuous correction of differential path length factor in near-infrared spectroscopy

In continuous-wave near-infrared spectroscopy (CW-NIRS), changes in the concentration of oxyhemoglobin and deoxyhemoglobin can be calculated by solving a set of linear equations from the modified Beer-Lambert Law. Cross-talk error in the calculated hemodynamics can arise from inaccurate knowledge of the wavelength-dependent differential path length factor (DPF). We apply the extended Kalman filter (EKF) with a dynamical systems model to calculate relative concentration changes in oxy- and deoxyhemoglobin while simultaneously estimating relative changes in DPF. Results from simulated and experimental CW-NIRS data are compared with results from a weighted least squares (WLSQ) method. The EKF method was found to effectively correct for artificially introduced errors in DPF and to reduce the cross-talk error in simulation. With experimental CW-NIRS data, the hemodynamic estimates from EKF differ significantly from the WLSQ (p < 0.001). The cross-correlations among residuals at different wavelengths were found to be significantly reduced by the EKF method compared to WLSQ in three physiologically relevant spectral bands 0.04 to 0.15 Hz, 0.15 to 0.4 Hz and 0.4 to 2.0 Hz (p < 0.001). This observed reduction in residual cross-correlation is consistent with reduced cross-talk error in the hemodynamic estimates from the proposed EKF method.

Quantifying spectroscopic concentration ratio by polarization subtraction technique

Nonlinear correlation between attenuation and absorption due to the presence of scattering is the main reason for inaccurate spectroscopic quantitative investigations. The polarization subtraction methods are applied to reduce the scattering in order to linearise attenuation to absorption. Monte Carlo simulation shows that the polarized light offers better performance than unpolarized light at giving the most accurate estimate of the concentration ratio of absorbers using the modified Lambert-Beer law. Our results demonstrate that spectrophotometry with polarized technique offers the potential to be a simple and costeffective system.

Concentration measurement of NO using self-absorption spectroscopy of the γband system in a pulsed corona discharge

Nitric oxide (NO) concentrations were measured using the γ band system spectrum based on the strong self-absorption effect of NO in pulsed corona discharges. The radiative transitional intensities of the NO γ band were simulated based on the theory of molecular spectroscopy. The intensities of some bands, especially γ(0,0) and γ(1,0), are weakened by the self-absorption. The correlations between the spectral self-absorption intensities and NO concentration were validated using a modified Beer-Lambert law with a combined factor K relating the branching ratio and the NO concentration, and a nonlinear index α that is applicable to the broadband system. Optical emissive spectra in pulsed corona discharges in NO and N2/He mixtures were used to evaluate the two parameters for various conditions. Good agreement between the experimental and theoretical results verifies the self-absorption behavior seen in the UV spectra of the NO γ bands.

Study of optical parameters of polystyrene spheres in dense aqueous suspensions

We investigated the dependence of the scattering and absorption coefficients of particles in dense suspensions by the low-coherence fiber optic dynamic light scattering (FODLS) technique. The estimated particle size was used to calculate the scattering coefficient of particles suspended in dense suspensions. The path-length resolved intensity distributions of light backscattered from absorbing dense suspensions were investigated experimentally. The absorption coefficient can be obtained by applying the measured path-length resolved intensity distributions to the modified Lambert-Beer law. As a result, the low-coherence FODLS technique can simultaneously measure the scattering and absorption coefficients of particles in absorbing dense suspensions, and the scattering and absorption coefficients are independent of each other in dense suspensions in the low-scattering regime of 2l(d) < 10ℓ*.

An ABC of near Infrared Photon Migration in Tissues: The Diffusive Regime of Propagation

In this paper, the theories commonly used for the study of photon migration through biological tissues and for biomedical applications are reviewed. The concepts of absorption and scattering are introduced with particular reference to biological tissues and to the near infrared wavelength range. In particular, the basic definitions of optical properties and their statistical meaning, the Beer–Lambert law, the modified Beer–Lambert law, the radiative transfer equation and the diffusion equation are examined and described. The main frame of the theories is provided in the time domain, in the continuous wave domain and in the frequency domain and the principal solutions of the radiative transfer equation and of the diffusion equation are reviewed. The propagation of photons through biological tissue can be accurately described with solutions of the radiative transfer equation, while solutions of the diffusion equation are subjected to intrinsic approximations that limit their range of validity. Whenever the solutions of the diffusion equation provide a sufficiently accurate description of photon migration, we have a diffusive regime of propagation and the media where this happens can be denoted as diffusive as well. A rule to identify the diffusive regime of propagation has been provided. For many biological tissues, the diffusive regime of propagation can be established, even near the source, provided the photons have travelled trajectories with lengths greater than four times the transport mean free path.

Multispectral reflectance imaging of brain activation in rodents: methodological study of the differential path length estimations and first in vivo recordings in the rat olfactory bulb

Dynamic maps of relative changes in blood volume and oxygenation following brain activation are obtained using multispectral reflectance imaging. The technique relies on optical absorption modifications linked to hemodynamic changes. The relative variation of hemodynamic parameters can be quantified using the modified Beer-Lambert Law if changes in reflected light intensities are recorded at two wavelengths or more and the differential path length (DP) is known. The DP is the mean path length in tissues of backscattered photons and varies with wavelength. It is usually estimated using Monte Carlo simulations in simplified semi-infinite homogeneous geometries. Here we consider the use of multilayered models of the somatosensory cortex (SsC) and olfactory bulb (OB), which are common physiological models of brain activation. Simulations demonstrate that specific DP estimation is required for SsC and OB, specifically for wavelengths above 600 nm. They validate the hypothesis of a constant path length during activation and show the need for specific DP if imaging is performed in a thinned-skull preparation. The first multispectral reflectance imaging data recorded in vivo during OB activation are presented, and the influence of DP on the hemodynamic parameters and the pattern of oxymetric changes in the activated OB are discussed.

Algorithm Establishment with Model Experiment for Continuous-Wave Functional Near-Infrared Spectroscopy

Although functional near-infrared spectroscopy (fNIRS) has been developing as a useful tool for monitoring functional brain activity since the early 1990s, the quantification of hemoglobin concentration changes is still controversial and there are few detailed reports especially for continuous-wave (CW) instruments. By means of a two-layer model experiment mimicking hemodynamic changes in brain and mathematical analysis based on the modified Beer-Lambert law, we established an algorithm for a CW functional near-infrared spectroscopy (CW-fNIRS). The accuracy of this algorithm was validated both in comparison with direct measurements on brain tissue model and in vivo measurement upon human valsalva maneuver. This described method can also be utilized for other CW-fNIRS instruments to establish measuring algorithm.

In-line absorption sensor based on coiled optical microfiber

We fabricated and tested an evanescent-wave absorption sensor consisting of an optical microfiber coil resonator embedded in fluidic channel walls. Low concentrations of flowing analyte show optical losses in agreement with a modified Beer–Lambert law. Higher concentration causes a limit value of the measured optical losses arising from adsorption mechanisms.

「最近の脳科学」光脳機能イメージングの進歩

Measurement of multichannel continuous-wave near-infrared spectroscopy (CW-NIRS) is dependent on the modified Beer-Lambert law, which includes optical path length (PL) as an essential parameter. PLs are known to differ across different head regions and between individuals, but the distribution of PLs for the whole head has not been evaluated so far. Thus, using time-resolved near-infrared spectroscopy (TR-NIRS), we measured the optical characteristics, including PL, scattering coefficients (μls), and absorption coefficients (μa) at three wavelengths (760, 800, and 830 nm). We then constructed maps of these parameters on the surface of the subject′s head. While the PLs in nearby channels are similar, they differ depending on the regions of the head. The PLs in the region above the Sylvian fissure tended to be shorter than those in the other regions at all of the wavelengths. The difference in the distribution of PLs may be attributed to differences in tissue absorption and scattering properties. The current study suggests the importance of considering PL differences in interpreting functional data obtained by CW-NIRS.

New closed-form approximation for skin chromophore mapping

The concentrations of blood and melanin in skin can be estimated based on the reflectance of light. Many models for this estimation have been built, such as Monte Carlo simulation, diffusion models, and the differential modified Beer-Lambert law. The optimization-based methods are too slow for chromophore mapping of high-resolution spectral images, and the differential modified Beer-Lambert is not often accurate enough. Optimal coefficients for the differential Beer-Lambert model are calculated by differentiating the diffusion model, optimized to the normal skin spectrum. The derivatives are then used in predicting the difference in chromophore concentrations from the difference in absorption spectra. The accuracy of the method is tested both computationally and experimentally using a Monte Carlo multilayer simulation model, and the data are measured from the palm of a hand during an Allen's test, which modulates the blood content of skin. The correlations of the given and predicted blood, melanin, and oxygen saturation levels are correspondingly r = 0.94, r = 0.99, and r = 0.73. The prediction of the concentrations for all pixels in a 1-megapixel image would take ∼ 20 min, which is orders of magnitude faster than the methods based on optimization during the prediction.

Hyperspectral Imaging in Diabetic Foot Wound Care

Diabetic foot ulceration is a major complication of diabetes and afflicts as many as 15 to 25% of type 1 and 2 diabetes patients during their lifetime. If untreated, diabetic foot ulcers may become infected and require total or partial amputation of the affected limb. Early identification of tissue at risk of ulcerating could enable proper preventive care, thereby reducing the incidence of foot ulceration. Furthermore, noninvasive assessment of tissue viability around already formed ulcers could inform the diabetes caregiver about the severity of the wound and help assess the need for amputation. This article reviews how hyperspectral imaging between 450 and 700 nm can be used to assess the risk of diabetic foot ulcer development and to predict the likelihood of healing noninvasively. Two methods are described to analyze the in vivo hyperspectral measurements. The first method is based on the modified Beer-Lambert law and produces a map of oxyhemoglobin and deoxyhemoglobin concentrations in the dermis of the foot. The second is based on a two-layer optical model of skin and can retrieve not only oxyhemoglobin and deoxyhemoglobin concentrations but also epidermal thickness and melanin concentration along with skin scattering properties. It can detect changes in the diabetic foot and help predict and understand ulceration mechanisms.

A diffuse reflectance spectroscopic study of UV-induced erythematous reaction across well-defined borders in human skin

The colour of tissue is often of clinical use in the diagnosis of tissue homeostasis and physiological responses to various stimuli. Determining tissue colour changes and borders, however, often poses an intricate problem and visual examination, constituting clinical praxis, does not allow them to be objectively characterized or quantified. Demands for increased inter- and intra-observer reproducibility have been incentives for the introduction of objective methods and techniques for tissue colour (e.g. erythema) evaluation. The aim of the present paper was to study the border zone of a UVB-provoked erythematous response of human skin in terms of blood volume and oxygenation measured by means of diffuse reflectance spectroscopy using a commercial probe. A provocation model, based on partial masking of irradiated skin areas, defines two erythema edges at every skin site responding to the UV irradiation. In every subject, five test sites were exposed with a constant UV light irradiance (14 mW/cm(2)), but with different exposure times (0, 3, 6, 9 and 12 s). An analysis of the spectral data measured across the two edges was performed for every scan line. The oxygenized and deoxygenized haemoglobin contents were estimated in every measurement point, using a modified Beer-Lambert model. The fit of the experimental data to the model derived by the modified Beer-Lambert law was excellent (R(2)>0.95). Analysing data for the chromophore content showed that the erythematous response in the provoked areas is dominated by the increase in oxyhaemoglobin. The widths for the left and right border zone were estimated to be 1.81+/-0.93 and 1.90+/-0.88 mm, respectively (mean+/-SD). The unprovoked area between the two edges was estimated to be 0.77+/-0.68 mm. While the chosen data analysis performed satisfactorily, the ability of the probe design to differentiate the spatial aspects of a reaction with abrupt borders was found to be suboptimal resulting in a probable overestimation of the erythematous edge slope. Probe modification or imaging techniques are possible solutions.

New cross-talk measure of near-infrared spectroscopy and its application to wavelength combination optimization

In near-infrared spectroscopy, concentration changes in oxygenated and deoxygenated hemoglobin are calculated from the changes in the attenuation of the measurement light. This is done by solving a linear equation based on the modified Lambert-Beer law. To solve this equation, we need to know the partial optical pathlengths in the activated region in the brain. Because they are difficult to know, a wavelength-independent constant or a wavelength-dependent total optical pathlength has been substituted for these values in actual measurements. This kind of substitution inevitably produces errors, called cross-talk, when calculating concentration changes. In this paper, we propose a new cross-talk measure for dual and triple wavelength measurements, and analyze it over various wavelength combinations. The results indicate that constant substitution is not inferior to total path-length substitution in dual wavelength measurements, and that total path-length substitution is very effective for triple wavelength measurements.

New method of estimating wavelength-dependent optical path length ratios for oxy- and deoxyhemoglobin measurement using near-infrared spectroscopy

In near-infrared spectroscopy (NIRS), concentration changes in oxy- and deoxyhemoglobin are calculated using an attenuation change of the measurement light and by solving a linear equation based on the modified Lambert-Beer law. While solving this equation, we need to know the wavelength-dependent mean optical path lengths of the measurement lights. However, it is very difficult to know these values by a continuous-wave-type (CW-type) system. We propose a new method of estimating wavelength-dependent optical path length ratios of the measurement lights based on the data obtained by a triple wavelength CW-type NIRS instrument. The proposed method does not give a path length itself, but it gives a path length ratio. Thus, it is possible to obtain the accurate hemoglobin concentration changes without cross talk, although the method cannot contribute to the quantification of the absolute magnitude of hemoglobin changes. The method is based on the principle that two possible estimations of hemoglobin concentration changes calculated using a triple-wavelength measurement system should be identical. The method was applied to the experimental data of human subjects' foreheads. The estimated path length ratios were very similar to literature values obtained by using picosecond laser pulses and a streak camera detector [M. Essenpreis et al., Appl. Opt. 32(4), 418-425 (1993)].

Regression-based model of skin diffuse reflectance for skin color analysis

A simple regression-based model of skin diffuse reflectance is developed based on reflectance samples calculated by Monte Carlo simulation of light transport in a two-layered skin model. This reflectance model includes the values of spectral reflectance in the visible spectra for Japanese women. The modified Lambert Beer law holds in the proposed model with a modified mean free path length in non-linear density space. The averaged RMS and maximum errors of the proposed model were 1.1 and 3.1%, respectively, in the above range.

Theoretical analysis of crosstalk between oxygenated and deoxygenated haemoglobin in focal brain-activation measurements by near-infrared topography

AbstractThe crosstalk between concentration changes in oxygenated haemoglobin and deoxygenated haemoglobin calculated by the modified Lambert-Beer law in near-infrared topography is theoretically investigated. The changes in intensity detected with probe pairs on the scalp caused by the concentration change in either oxygenated or deoxygenated haemoglobin induced by the focal brain activation is predicted by Monte Carlo simulation. The topographic images of the changes in oxygenated and deoxygenated haemoglobin are obtained from the changes in the intensity of light at two wavelengths detected by probe pairs to evaluate the crosstalk. The crosstalk slightly depends on the positional relationship between the probe arrangement and the focal brain activation and is minimised when the focal brain activation is located below a measurement point that is the midpoint between a probe pair. The 690-/830-nm wavelength pair is practically effective for reducing the crosstalk, especially the crosstalk from oxygenated haemoglobin to deoxygenated haemoglobin, in the NIR topography.