Modified Lambert Beer Research Articles

Simulated Annealing-Based Wavelength Selection for Robust Tissue Oxygenation Estimation Powered by the Extended Modified Lambert–Beer Law

In this paper, we present a set of algorithms to enable the development of inexpensive hyperspectral sensors capable of estimating tissue oxygenation for wound monitoring. Estimation is conducted using the extended modified Lambert–Beer law, which has previously been proven robust to differences in melanin concentration. We introduce a novel wavelength selection algorithm that enables the estimation to be performed with high accuracy using only a small number (5–10) of wavelengths. Validation performed with Monte Carlo simulation data resulted in prediction errors <1%, with no significant differences among various skin types, for as few as five wavelengths under conditions representing both high precision instrumentation and more cost-effective sensors designed with inexpensive LEDs and/or filters. Validation with in vivo data collected from an occlusion study with 13 Asian volunteers showed statistically significant separation between the estimates for the at-rest and arterial occlusion states. Additional stability testing proved the proposed algorithms to be robust to small changes in the selected wavelengths as may occur in a real LED due to manufacturing tolerances and temperature fluctuations. This work concluded that the development of an inexpensive hyperspectral device for wound monitoring in all skin types is feasible using just a small number of wavelengths.

Methods of tunable diode laser absorption saturation spectroscopy to gas sensing under optically thick conditions

AbstractThe absorption saturation under optically thick conditions will bring difficulties to laser spectroscopy gas sensing. We report the spectrum two wings reconstruction method and the transmitted laser intensity fitting method for tunable diode laser absorption saturation spectroscopy gas absolute measurements under optically thick conditions, and used the modified Lambert Beer's law to calculate methane concentration based on the incomplete spectrum of absorption saturation. The maximum deviation between the experimental measurement results and the standard methane concentration is about 4.7%, which verifies the feasibility of these new methods and also show that they have great potential for expanding the gas sensing range of a single absorption line.

Towards Skin Tissue Oxygen Monitoring: An Investigation of Optimal Visible Spectral Range and Minimal Spectral Resolution

This paper investigated the minimum spectral resolution and optimal spectra range for optical monitoring of skin blood oxygen saturation (StO2). For this purpose, this study recruited fourteen Asian volunteers for demonstration work. The performed measurements included reflectance information collected from the recruits during at rest and after a pressure of 140 mmHg was applied on their upper right arm. The prediction of the required value was via analysis of data of the considered visible ranges of 500 – 660 nm, 520 – 645 nm, 520 – 600 nm, and 530 – 570 nm, with sampling resolutions of 1 nm, 2 nm, 5 nm, and 10 nm. The offline data analysis using Extended Modified Lambert Beer model revealed that the StO2 value predicted using spectral data in the range 530 – 570 nm showed considerable similarity with that obtained from 520 – 645 nm range at spectral resolutions of up to 5 nm. The mean and standard deviation of the differences in the values obtained from these spectral ranges in the case of 5 nm sampling is given by 7 ± 8.6 % and 14 ± 3.2 % for at rest and blood occlusion experiment, respectively. The higher variability in the value predicted for the latter experiment is likely due to insufficiency of the employed technique to extricate the distinctive features in hemoglobin spectra using the corresponding resolution. The findings of this study may be useful as a guide to facilitate in the design of multispectral imaging system for optical monitoring of one’s StO2 with high speed.

Modified lambert beer for bilirubin concentration and blood oxygen saturation prediction

Noninvasive measurement of health parameters such as blood oxygen saturation and bilirubin concentration predicted via an appropriate light reflectance model based on the measured optical signals is of eminent interest in biomedical research. This is to replace the use of conventional invasive blood sampling approach. This study aims to investigate the feasibility of using Modified Lambert Beer model (MLB) in the prediction of one’s bilirubin concentration and blood oxygen saturation value, SO2. This quantification technique is based on a priori knowledge of extinction coefficients of bilirubin and hemoglobin derivatives in the wavelength range of 440 – 500 nm. The validity of the prediction was evaluated using light reflectance data from TracePro raytracing software for a single-layered skin model with varying bilirubin concentration. The results revealed some promising trends in the estimated bilirubin concentration with mean ± standard deviation (SD) error of 0.255 ± 0.025 g/l. Meanwhile, a remarkable low mean ± SD error of 9.11 ± 2.48 % was found for the predicted SO2 value. It was concluded that these errors are likely due to the insufficiency of the MLB at describing changes in the light attenuation with the underlying light absorption processes. In addition, this study also suggested the use of a linear regression model deduced from this work for an improved prediction of the required health parameter values.

Eliminating interferences due to the differences in optical parameters of flexible conveying tubes on on-line spectral analysis based on the method of multi-wavebands reference solution calibration

On-line spectral analysis technology can real-time monitor the key links in the process of liquid transportation, and provide real-time guidance for reliable and efficient delivery of liquids. In the process of on-line spectral analysis of any solution in the flexible conveying tube, accuracy of the spectral analysis is reduced due to the differences in optical parameters of the flexible conveying tubes. Therefore, this study investigates the impact of differences in flexible conveying tubes on on-line spectral analysis of liquids. A method of multi-wavebands reference solution calibration (MWRSC), based on the modified Lambert Beer’s law, is proposed to inhibit such spectral interference. The ultraviolet, visible, and near-infrared wavebands or the combination of the wavebands of the spectral data of the sample are respectively calibrated, and the calibrated spectral data are modeled by partial least squares regression (PLSR) to obtain eight calibration models. The inhibition effect of the eight models on the optical differences of the flexible conveying tubes was compared. The experimental results show that full-wavebands spectrum of the sample calibrated by the MWRSC method can effectively inhibit the impact caused by the differences in the flexible conveying tubes and improve the accuracy of the spectral analysis. This study lays the foundation for on-line spectral analysis of blood and other complex mixed solutions when transported using flexible conveying tubes.

A Handheld Technology for Optical Monitoring of Transcutaneous Blood Oxygen Saturation

This paper presents the use of a handheld technology for noninvasive prediction of one’s transcutaneous blood oxygen saturation, StO2, via an in-house developed skin oxygenation system. The quantification strategy involved the use of wavelength dependent Modified Lambert Beer law and is based on light signals of wavelengths 532 nm, 560 nm and 650 nm reflected from the selected skin site. This study performed at rest and arterial blood occlusion experiment on left palm of the hand of five healthy Asian volunteers to evaluate the performance of the system and to verify the validity of the predicted results. The preliminary results revealed a considerable decrease in the predicted mean percent StO2 value from 63.7 ± 13.2 % for at rest condition to 52.2 ± 11.4 % after a pressure of 140 mmHg was applied on upper left arm of these recruits for 120 seconds. This work concluded that the developed optical system is able to provide comprehensive information on spatially dependent StO2 and it has unlimited skin access, hence may be potentially used in field applications to assess the skin oxygen level of those in workforce whose job is at risk of exposure to poisonous gases.

Investigation of gender and prandial state as factors affecting skin bilirubin level

This paper demonstrates the use of the developed non-invasive optical system to measure differences in the mean concentration of skin bilirubin Cbil(m) among individuals of different gender and at different prandial state. This system employed the use of color filters to allow an illumination of the selected skin site using light beams of centre wavelength 420 nm, 440 nm and 460 nm. The prediction of the required skin bilirubin concentration value is via Modified Lambert Beer law. This study conducted experiments on the back of the hand of twelve recruits. The results revealed a higher mean Cbil(m) value of 0.25 ± 0.007 µmol/L for males as compared to 0.14 ± 0.0086 µmol/L measured for females. In addition, this work observed a decrease in the mean Cbil(m) value for the ten recruits of mixed gender from 0.23 ± 0.06 µmol/L at preprandial phase to 0.18 ± 0.04 µmol/L during the postprandial period. This study concluded that the developed system is able to detect changes in the skin bilirubin concentration level with one’s gender and prandial state as reported in literature. However, this system may be further improved for future clinical application on jaundiced patients.

Point Spectroscopy System for Noncontact and Noninvasive Prediction of Transcutaneous Bilirubin Concentration

This paper presents the use of a point spectroscopy system to determine one’s transcutaneous bilirubin level using Modified Lambert Beer model and the developed fitting routine. This technique required a priori knowledge of extinction coefficient of bilirubin and hemoglobin components in the wavelength range of 440-500 nm for the prediction of the required parameter value. This work was conducted on different skin sites of six healthy Asians namely on the thenar region of the palm of their hand, back of the hand, posterior and anterior forearm. The obtained results revealed the lowest mean transcutaneous bilirubin concentration of 0.44±0.3 g/l predicted for palm site while the highest bilirubin level of 0.98±0.2 g/l was estimated for posterior forearm. These values were also compared with that presented in the literature. This study found considerably good consistency in the value predicted for different subjects especially at the thenar region of the palm. This work concluded that the proposed system and technique may be suitably served as an alternative means to noncontact and noninvasive measurement of one’s transcutaneous bilirubin level at palm site.

Investigation of spatial resolution dependent variability in transcutaneous oxygen saturation using point spectroscopy system

This paper aims to investigate the variation in one’s percent mean transcutaneous oxygen saturation (StO2) with differences in spatial resolution of data. This work required the knowledge of extinction coefficient of hemoglobin derivatives in the wavelength range of 520 – 600 nm to solve for the StO2 value via an iterative fitting procedure. A pilot study was conducted on three healthy subjects with spectroscopic data collected from their right index finger at different arbitrarily selected distances. The StO2 value estimated by Extended Modified Lambert Beer (EMLB) model revealed a higher mean StO2 of 91.1 ± 1.3% at a proximity distance of 30 mm compared to 60.83 ± 2.8% at 200 mm. The results showed a high correlation between data spatial resolution and StO2 value, and revealed a decrease in StO2 value as the sampling distance increased. The preliminary findings from this study contribute to the knowledge of the appropriate distance range for consistent and high repeatability measurement of skin oxygenation.

Multispectral imaging of acute wound tissue oxygenation

This paper investigates the appropriate range of values for the transcutaneous blood oxygen saturation (StO2) of granulating tissues and the surrounding tissue that can ensure timely wound recovery. This work has used a multispectral imaging system to collect wound images at wavelengths ranging between 520[Formula: see text]nm and 600[Formula: see text]nm with a resolution of 10[Formula: see text]nm. As part of this research, a pilot study was conducted on three injured individuals with superficial wounds of different wound ages at different skin locations. The StO2 value predicted for the examined wounds using the Extended Modified Lambert–Beer model revealed a mean StO2 of [Formula: see text]% compared to [Formula: see text]% at the surrounding tissues, and [Formula: see text]% for control sites. These preliminary results contribute to the existing knowledge on the possible range and variation of wound bed StO2 that are to be used as indicators of the functioning of the vasomotion system and wound health. This study has concluded that a high StO2 of approximately 60% and a large fluctuation in this value should precede a good progression in wound healing.

MULTISPECTRAL IMAGING SYSTEM FOR QUANTITATIVE ASSESSMENT OF TRANSCUTANEOUS BLOOD OXYGEN SATURATION

This paper presents the use of Extended Modified Lambert Beer (EMLB) model for quantification of transcutaneous blood oxygen saturation (StO2) via a noninvasive approach. Continuous wave (CW) reflectance spectroscopy system is employed for measurement of intensity reflected from left index finger of an Asian nonsmoking volunteer at resting condition. Multispectral images captured in the wavelength range of 520 − 600 nm at an interval of 10 nm are mathematically analyzed and fitted using the developed fitting algorithm to give the best estimation of StO2. The result from this preliminary study revealed a mean StO2 value of 75 ± 5% for the participating individual, which value agreed considerably well with that presented in previous works. This work concluded that the developed spectroscopy system and quantification technique can potentially be used as an alternative means to clinical assessment of wound healing progress

IN SITU MONITORING OF MEAN BLOOD OXYGEN SATURATION USING EXTENDED MODIFIED LAMBERT BEER MODEL

We present the use of Extended Modified Lambert–Beer model for optical monitoring of mean blood oxygen saturation ( S m O 2) via a fitting procedure. This work focuses on the absorption characteristics of hemoglobin derivatives in the wavelength range of 520–600 nm to give the best estimates of S m O 2. The study of the feasibility of applying this analytic method to skin oximetry is via spectroscopy data collected from fingertips of four healthy volunteers both at rest and during arterial blood occlusion condition. The results revealed a decrease in the mean of mean and standard deviation of S m O 2 value of fingertips from 94.5 ± 2.19% when volunteers were at rest to 56.76 ± 5.8% during the arterial blood occlusion measurement. The larger variation in the value estimated for blood occlusion condition could be a result of differences in volunteers' physical fitness and hypertension status. These estimated S m O 2 values agreed reasonably well with the value reported in most of the previous studies. This work concluded that the proposed technique can potentially be used as a complementary technique to clinical assessment of skin grafts and burnt skin.

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.

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.

Measurement of optical constants for dense media by low-coherence dynamic light scattering

We perform the optical constants measurements for different absorption dense media by low-coherence dynamic light scattering (DLS) technique. The estimated particle size is used to calculate the scattering coefficient of particles suspended in dense media. The path-length resolved intensity distributions of light backscattered from the absorbing dense media are investigated experimentally by virtue of path-length resolved performance in low-coherence DLS measurements. The absorption coefficient can be obtained by applying the measured path-length resolved intensity distributions to the modified Lambert–Beer law. As a result, we proposed a new low-coherence DLS technique in simultaneous measurement of the scattering and absorption coefficients of absorbing dense media.

Rethinking satellite-based solar irradiance modelling: The SOLIS clear-sky module

Accurate solar irradiance data are not only of particular importance for the assessment of the radiative forcing of the climate system, but also absolutely necessary for efficient planning and operation of solar energy systems. Within the European project Heliosat-3, a new type of solar irradiance scheme is developed. This new type will be based on radiative transfer models (RTM) using atmospheric parameter information retrieved from the Meteosat Second Generation (MSG) satellite (clouds, ozone, water vapour) and the ERS-2/ENVISAT satellites (aerosols, ozone). This paper focuses on the description of the clear-sky module of the new scheme, especially on the integrated use of a radiative transfer model. The linkage of the clear-sky module with the cloud module is also briefly described in order to point out the benefits of the integrated RTM use for the all-sky situations. The integrated use of an RTM within the new Solar Irradiance Scheme SOLIS is applied by introducing a new fitting function called the modified Lambert–Beer (MLB) relation. Consequently, the modified Lambert–Beer relation and its role for an integrated RTM use are discussed. Comparisons of the calculated clear-sky irradiances with ground-based measurements and the current clear-sky module demonstrate the advantages and benefits of SOLIS. Since SOLIS can provide spectrally resolved irradiance data, it can be used for different applications. Beside improved information for the planning of solar energy systems, the calculation of photosynthetic active radiation, UV index, and illuminance is possible.

Optical measurements of absorption changes in two-layered diffusive media

We have used Monte Carlo simulations for a two-layered diffusive medium to investigate the effect of a superficial layer on the measurement of absorption variations from optical diffuse reflectance data processed by using: (a) a multidistance, frequency-domain method based on diffusion theory for a semi-infinite homogeneous medium; (b) a differential-pathlength-factor method based on a modified Lambert–Beer law for a homogeneous medium and (c) a two-distance, partial-pathlength method based on a modified Lambert–Beer law for a two-layered medium. Methods (a) and (b) lead to a single value for the absorption variation, whereas method (c) yields absorption variations for each layer. In the simulations, the optical coefficients of the medium were representative of those of biological tissue in the near-infrared. The thickness of the first layer was in the range 0.3–1.4 cm, and the source–detector distances were in the range 1–5 cm, which is typical of near-infrared diffuse reflectance measurements in tissue. The simulations have shown that (1) method (a) is mostly sensitive to absorption changes in the underlying layer, provided that the thickness of the superficial layer is ∼0.6 cm or less; (2) method (b) is significantly affected by absorption changes in the superficial layer and (3) method (c) yields the absorption changes for both layers with a relatively good accuracy of ∼4% for the superficial layer and ∼10% for the underlying layer (provided that the absorption changes are less than 20–30% of the baseline value). We have applied all three methods of data analysis to near-infrared data collected on the forehead of a human subject during electroconvulsive therapy. Our results suggest that the multidistance method (a) and the two-distance partial-pathlength method (c) may better decouple the contributions to the optical signals that originate in deeper tissue (brain) from those that originate in more superficial tissue layers.

Mapping of calf muscle oxygenation and haemoglobin content during dynamic plantar flexion exercise by multi-channel time-resolved near-infrared spectroscopy

A compact and fast multi-channel time-resolved near-infrared spectroscopy system for tissue oximetry was developed. It employs semiconductor laser and fibre optics for delivery of optical signals. Photons are collected by eight 1 mm fibres and detected by a multianode photomultiplier. A time-correlated single photon counting board is used for the parallel acquisition of time-resolved reflectance curves. Estimate of the reduced scattering coefficient is achieved by fitting with a standard model of diffusion theory, while the modified Lambert–Beer law is used to assess the absorption coefficient. In vivo measurements were performed on five healthy volunteers to monitor spatial changes in calf muscle (medial and lateral gastrocnemius; MG, LG) oxygen saturation (SmO2) and total haemoglobin concentration (tHb) during dynamic plantar flexion exercise performed at 50% of the maximal voluntary contraction. At rest SmO2 was 73.0 ± 0.9 and 70.5 ± 1.7% in MG and LG, respectively (P = 0.045). At the end of the exercise, SmO2 decreased (69.1 ± 1.8 and 63.8 ± 2.1% in MG and LG, respectively; P < 0.01). The LG desaturation was greater than the MG desaturation (P < 0.02). These results strengthen the role of time-resolved near-infrared spectroscopy as a powerful tool for investigating the spatial and temporal features of muscle SmO2 and tHb.

Modeling and Optimization of Solar‐Control Glasses

Computer‐assisted design of experiments based on the D‐optimal design methodology and multiple linear regression analysis has been applied to the control and optimization of solar‐control properties of a sulfate‐fined soda–lime–silicate glass (72.7% SiO2, 14.2% Na2O, 10.0% CaO, 2.5% MgO, 0.6% Al2O3) which has been modified with Fe2O3 (0.0 to 0.8 wt%), NiO (0.0 to 0.15 wt%), CoO (0.0 to 0.15 wt%), V2O5 (0.0 to 0.225 wt%), TiO2 (0.0 to 1.5 wt%), SnO (0.0 to 3.0 wt%), ZnS (0.0 to 0.09 wt%), ZnO (0.0 to 2.0 wt.), CaF2 (0.0 to 2.0 wt%), and P2O5 (0.0 to 2.0 wt%) additions. The experimental design consisted of 64 initial glass compositions which were fired as 500 g batches under ambient conditions in platinum crucibles at 1500°C for 3 h. The samples were then measured for total solar transmittance in accordance with the specifications of ASTM E903–96 (weighted ordinate method) using a Cary‐500 UV/vis/near‐IR spectrophotometer equipped with an integrating sphere. CIE‐LAB color and visible transmittance (illuminant‐A) was measured in accordance with the specification of ASTM E308. The total metal content, calculated as of V2O5, CoO, NiO, Fe2O3, FeO, P2O5, TiO2, SnO, ZnO, F, and SO3, was measured for each glass sample. A modified Lambert–Beer absorption law was utilized to correlate the apparent optical density at 210 discrete wavelengths necessary for the calculation of solar and visible transmittances to the glass batch composition. The developed model was then validated and was shown to exhibit excellent agreement with the measured optical transmission data. Innovative solar‐control glasses with exceptional performance characteristics have been realized in the current investigation by application of novel computer‐assisted design and multiple correlation methodologies.