Modified Beer-Lambert Law Research Articles

PV-MBLL algorithm for extraction of absolute tissue oxygenation information by diffuse optical spectroscopy

Background and objectiveTissue blood oxygenation contains critical information for biomedical studies and healthcare. The primary approach to extract the absolute value of tissue blood oxygenation (e.g., oxygen saturation) is spatial-resolved algorithm for near-infrared diffuse optical spectroscopy with continues-wave (CW) light, which require acquisition of the optical signals from multiple pairs of sources and detectors (S-D). This study reports the first attempt for absolute oxygenation measurement with single S-D pair of optical signals. MethodsA novel algorithm, namely, phantom-validation modified Beer-Lambert law (PV-MBLL), was created to fully utilize the optical signals from single S-D pair. This algorithm is combined with two-step phantom measurement to extract the absolute value of tissue oxygenation in CW system. The proposed PV-MBLL algorithm was compared with the conventional spatial-resolved algorithm on both step-varied liquid phantom and human experiment of cuff occlusion on arms. The one-way ANOVA analysis was performed to investigate the difference between the two algorithms. ResultsBy using the PV-MBLL algorithm, the reconstructed tissue absorption coefficient is highly accurate (not larger than 5.35% in error) over a wide range (0.02–0.20 cm−1). By contrast, the spatial-resolved algorithm leads to much larger errors (up to 37.57% in error). Moreover, the responses of oxygen saturation to cuff occlusion differ significantly (p < 0.005) with the two algorithms. ConclusionsThe proposed PV-MBLL algorithm has promising potential for accurate acquisition of oxygenation information. Additionally, the single S-D pair greatly reduces the size of optical probe and instrument cost, thus it is highly appropriate for the tissues with small size and large curvature.

Dual-Wavelength Diffuse Optical Tomographic System for Direct Concentration Measurement

This article presents a promising dual-wavelength continuous wave (CW) diffuse optical tomography (DOT) system for direct estimation of concentrations and hemodynamic parameters for potential application in detection of rheumatoid arthritis (RA). The generalized curved-beam reconstruction technique is modified for direct estimation of hemodynamic parameters. The Rosenbrock’s function is fit to estimate the photon path as curved one followed by majority photons that enabled the use of modified Beer–Lambert law (MBLL) in differential form with assumption that unknown absorption coefficient ( $\mu _{a}$ ) varies from one path to another. The $\mu _{a}$ values are calculated and back-projected along the photon paths for image reconstruction without solving the inverse problem. Thus, stability is not an issue in image reconstruction. Also, there is no need for baseline measurement and prior information on perturbation, unlike the iterative methods used for dynamic imaging. The reconstructed images of the distal interphalangeal (DIP) and proximal interphalangeal (PIP) joints of a healthy male volunteer showed good consistency and are used for direct optical estimation of the physiological parameters. A novel application of optical imaging beyond biomedical applications is demonstrated by imaging the gradual dispersion of viscous Indian ink and glycerin mixture in turbid water with encouraging results.

Effects of Processing Methods on fNIRS Signals Assessed During Active Walking Tasks in Older Adults.

Functional near infrared spectroscopy (fNIRS) is a noninvasive optics-based neuroimaging modality successfully applied to real-life settings. The technology uses light in the near infrared range (650-950nm) to track changes in oxygenated (HbO2) and deoxygenated hemoglobin (Hb) obtained from measured light intensity using light-tissue interaction principles. fNIRS data processing involves artifact removal and hemodynamic signal conversion using modified Beer-Lambert law (MBLL) to obtain Hb and HbO2, reliably. fNIRS signals can get contaminated by various noise sources of physiological and non-physiological origins. Various algorithms have been proposed for the elimination of artifacts from frequency selective filters to blind source separation methods. Hemodynamic signal extraction using raw intensity measurements at multiple wavelengths based on MBLL usually involves apriori knowledge of certain conversion parameters such as molar extinction coefficients ( ε ) and differential path length factor (DPF). Different sets of conversion parameters dependent upon wavelength, chromophores, and age have been reported. Variation in processing algorithms and parameters can cause differences in Hb and HbO2 extraction which can in turn change study outcomes. Using fNIRS, we have previously shown significant increases in oxygenation in the prefrontal cortex from Single-Task-Walking (STW) to Dual-task-Walking (DTW) conditions in older adults due to greater cognitive demands inherent in the latter condition. In the current study, we re-analyzed our data and determined that although using different conversion parameters i.e. ε and age dependent DPF and filter cut-off frequencies at 0.14 and 0.08Hz including those designed to remove confounding effects of Mayer waves had caused some linear increases or decreases on the extracted Hb and HbO2 signals, those effects were minimal in task related comparisons and hence, the overall study outcomes.

Characterizing the fluid-matrix affinity in an organogel from the growth dynamics of oil stains on blotting paper.

Grease, as used for lubrication of rolling bearings, is a two-phase organogel that slowly releases oil from its gelator matrix. Because the rate of release determines the operation time of the bearing, we study this release process by measuring the amount of extracted oil as a function of time, while we use absorbing paper to speed up the process. The oil concentration in the resulting stain is determined by measuring the attenuation of light transmitted through the paper, using a modified Lambert-Beer law. For grease, the timescale for paper imbibition is typically 2 orders of magnitude larger than for a bare drop of the same base oil. This difference results from the high affinity, i.e. wetting energy per unit volume, of the oil for the grease matrix. To quantify this affinity, we developed a Washburn-like model describing the oil flow from the porous grease into the paper pores. The stain radius versus time curves for greases at various levels of oil content collapse onto a single master curve, which allows us to extract a characteristic spreading time and the corresponding oil-matrix affinity. Lowering the oil content results in a small increase of the oil-matrix affinity yet also in a significant change in the spreading timescale. Even an affinity increase of a few per mill doubles the timescale.

Intraoperative quantitative functional brain mapping using an RGB camera.

.Intraoperative optical imaging is a localization technique for the functional areas of the human brain cortex during neurosurgical procedures. However, it still lacks robustness to be used as a clinical standard. In particular, new biomarkers of brain functionality with improved sensitivity and specificity are needed. We present a method for the computation of hemodynamics-based functional brain maps using an RGB camera and a white light source. We measure the quantitative oxy and deoxyhemoglobin concentration changes in the human brain cortex with the modified Beer–Lambert law and Monte Carlo simulations. A functional model has been implemented to evaluate the functional brain areas following neuronal activation by physiological stimuli. The results show a good correlation between the computed quantitative functional maps and the brain areas localized by electrical brain stimulation (EBS). We demonstrate that an RGB camera combined with a quantitative modeling of brain hemodynamics biomarkers can evaluate in a robust way the functional areas during neurosurgery and serve as a tool of choice to complement EBS.

Noise reduction from chromophore images and reliability improvement by successive minimization of intermixture in the modified Lambert-Beer law

We developed an optimization method of chromophore vectors for skin images in the modified Lambert-Beer law. In the proposed method, vectors are optimized to minimize intermixture between melanin, hemoglobin, and shading components. Using the proposed method, the vectors can be optimized appropriately and stably. The proposed method also optimizes shading images, which may contain useful information. The melanin component obtained using the proposed method has a good correlation with that obtained from the conventional method with a reflectance spectrum. The proposed method advances the capability of prompt action upon installation of new equipment and eliminates arbitrary judgment of acceptance or rejection of vectors for each test image, which improves objectivity.

Differential pathlength factor in continuous wave functional near-infrared spectroscopy: reducing hemoglobin's cross talk in high-density recordings.

Functional near-infrared spectroscopy (fNIRS) estimates the functional oscillations of oxyhemoglobin and deoxyhemoglobin in the cortex through scalp-located multiwavelength recordings. Hemoglobin oscillations are inferred through temporal changes in continuous-wave (CW) light attenuation. However, because of the diffusive multilayered head tissue structures, the photon path is longer than the source-detector separation, complicating hemoglobin evaluation. This aspect is incorporated in the modified Beer-Lambert law where the source-detector distance is multiplied by the differential pathlength factor (DPF). Since DPF estimation requires photons' time-of-flight information, DPF is assumed a priori in CW-fNIRS. Importantly, errors in the DPF spectrum induce hemoglobin cross talk, which is detrimental for fNIRS. We propose to estimate subject-specific DPF spectral dependence relying on multidistance high-density measurements. The procedure estimates the effective attenuation coefficient (EAC), which is proportional to the geometric mean of absorption and reduced scattering. Since DPF depends on the scattering-to-absorption ratio, EAC limits the spectral dependence assumption to scattering. This approach was compared to a standard frequency-domain multidistance procedure. A good association between the two methods ( ) was obtained. This approach could estimate low-resolution maps of the DPF spectral dependence through large field of view, high-density systems, reducing hemoglobin cross talk, and increasing fNIRS sensitivity and specificity to brain activity without instrumentation modification.

A simple but quantitative method for non-destructive monitoring of myoglobin redox forms inside the meat.

This study aims at exploring a simple and quantitative method for non-destructive monitoring of the myoglobin redox forms inside of beef. The modified Beer-Lambert law was employed to derive an equation that delineates a relationship between attenuance differences and oxy-, deoxy-, and met-myoglobin proportions. An experiment with forty-three well-bled muscle beef samples during 7days of storage was performed to validate the equation. Firstly, the reflection spectra were collected from the beef samples using a probe consisting of a light source and a light detector. Secondly, the attenuance differences, A630-615 and A578-567, were calculated from the measured spectra. Finally, these attenuance differences were placed into the derived equation to determine the proportions of the three myoglobin redox forms. Both the met-myoglobin proportion and meat oxygenation computed via the attenuance differences established a strong correlation with the ones estimated using the whole spectrum (R2 > 0.88). The experimental results suggest the potential of using the attenuance at five wavelengths (524, 567, 578, 615, and 630nm) to monitor oxy-, deoxy-, and met-myoglobin inside of beef in a simple and fast manner with little to no sample preparation.

MBLL with weighted partial path length for multi-distance probe configuration of fNIRS.

Functional near-infrared spectroscopy (fNIRS) has broad prospects in both clinical application and brain-computer interface. To improve the spatial resolution, modified Beer-Lambert law with weighted partial optical path length (wMBLL) is proposed for multi-distance probe configuration. Taking both surface tissue layers and deep tissue layers into consideration, the partial optical path length is estimated as a function of the distance between source and detector. Besides, a multi-distance, 15mm and 30mm, probe configuration is designed, which approximates a rectangle. Constructed with 9 sources and 14 detectors, 40 channels are produced, including 20 short short-separation channel and 20 long-separation channel. Also, experiment is implemented with left hand grip-stretch movement and involves five healthy subjects. The concentration of HbO is used to image the brain activation map. Results demonstrate that, compared with the conventional method, the proposed wMBLL method is effective to detect brain activity with higher spatial resolution.

Assessment and Classification of Mental Workload in the Prefrontal Cortex (PFC) Using Fixed-Value Modified Beer-Lambert Law

Optical-neuro-imaging based functional Near-Infrared Spectroscopy (fNIRS) has been in use for several years in the fields of brain research to measure the functional response of brain activity and apply it in fields such as Neuro-rehabilitation, Brain-Computer Interface (BCI) and Neuro-ergonomics. In this paper we have enhanced the classification accuracy of a Mental workload task using a novel Fixed-Value Modified Beer-Lambert law (FV-MBLL) method. The hemodynamic changes corresponding to mental workload are measured from the Prefrontal Cortex (PFC) using fNIRS. The concentration changes of oxygenated and deoxygenated hemoglobin (Δc HbO (t) and Δc HbR (t)) of 20 participants are recorded for mental workload and rest. The statistical analysis shows that data obtained from fNIRS is statistically significant with p 1.97 at confidence level of 0.95. The Support Vector Machine (SVM) classifier is used to discriminate mental math (coding) task from rest. Four features, namely mean, peak, slope and variance, are calculated on data processed through two different variants of Beer-lambert Law i.e., MBLL and FVMBLL for tissue blood flow. The optimal combination of the mean and peak values classified by SVM yielded the highest accuracy, 75%. This accuracy is further enhanced using the same feature combination, to 94% when those features are calculated using the novel algorithm FV-MBLL (with its optical density modelled form the first 4 sec stimulus data). The proposed technique can be effectively used with greater accuracies in the application of fNIRS for functional brain imaging and Brain-Machine Interface.

Near-Infrared Spectroscopy (NIRS)-based Digit Skin Tissue Blood Flow Measurement System

The tissue blood flow (BF) and vascular resistance are the important information for consult peripheral vascular system which related to cardiovascular disease. Unfortunately, most of the current BF monitors are costly, built in huge size and preferable use in hospital and clinic. In the present study, a portable digit skin tissue BF measurement system had been developed using Near-infrared spectroscopy (NIRS) method with simple circuitry and low cost that can be afforded by patients to monitor their cardiovascular information. This system consists of a self-developed NIRS probe; LED and a photodiode, and an Arduino Uno board with MATLAB software as the processing unit. The NIR LED transmits 810 nm light source through biological tissue then detected by the photodiode. The output signal from the NIRS probe is based on resistance changes in the photodiode and by applying the voltage divider law, the signal is further processed by the Arduino with the MATLAB software. Then, according to the modified Lambert-Beer Law in scattering medium, the change in total concentration of haemoglobin ( ) is plotted in order to get a quantitative BF reading which based on its maximum change during venous occlusion. To evaluate the proposed BF measurement system, BF measurement tests had been conducted on four healthy subjects during resting and after exercise. The study had shown that the results of BF after the exercise were in average of 1.5 time higher than the resting BF and this finding agrees with previous research works.

Computational study of photo-thermal ablation of large blood vessel embedded tumor using localized injection of gold nanoshells

Attaining a precise necrosis of tumor sparing normal tissue during carcinomas thermo-therapy via nominally invasive scheme like irradiation of laser is a recent challenge. In this study, a combined diffusion and convective energy equations were solved using COMSOL Multiphysics to predict the tissue thermal profile during laser assisted thermo-therapy with different tissue vascular networks. A comparative analysis between intratumoral and intravenous loading scheme of silica-gold nanoshells (AuNs) was also performed. AuNs cluster position and alignment was altered to achieve precise ablation of a large tumor with minimum damage to healthy tissue and improvement in necrosis in the vicinity of large blood vessels (LBV). A modified Beer-Lambert law and Arrhenius equation was applied to model laser heat propagation and to compute thermal damage respectively. Simulation results suggests the dominance of targeted nanostructure injection in cluster form over intravenous scheme in terms of precise control over spreading of necrotic zone due to selective laser dose delivery into the tumor. An effective tumor ablation, sparing normal tissue is best revealed for Type-A intratumoral scheme comparing Type-B and C as the reallocation of cluster position can help to achieve an irregular shaped necrotic zone. In addition a comparative analysis between dual-phase-lag (DPL) and classical Fourier approach within a tumor-blood inhomogeneous inner structure was made to access the effect of relaxation time onto biological thermal response. Numerical results show a difference in temperature profile between these two approaches during non-equilibrium condition i.e at the prior phases of laser heating and cooling whereas the results overlaps at higher instants. Since the DPL based bioheat conduction model can predict the inherent wave nature of the thermal front which is propagating at a finite speed. This study may improve the real clinical invasive schemes applied to ablate malignant tumor during hyperthermia treatment.

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.

Monitoring of Brain Oxygenation During and After Cardiopulmonary Resuscitation: A Prospective Porcine Study.

This study aimed to evaluate the usefulness of near-infrared time-resolved spectroscopy (TRS) for the monitoring of post-resuscitation encephalopathy. Cardiac arrest (CA) was induced in pigs by electrical stimuli; then, return of spontaneous circulation (ROSC) was achieved by direct current. The changes in cerebral oxygenation were analyzed by two methods: (1) the time-independent calculation based on the modified Beer-Lambert law (MBL), and (2) the curve-fitting method based on the photon diffusion theory (DT). The changes in reduced scattering coefficient (μs') in DT were also calculated. Post-resuscitation encephalopathy was evaluated by MRI findings. During CA, cerebral oxygen saturation (ScO2) decreased to the lowest level, and then gradually increased during the chest compression period. When ROSC was achieved, ScO2 (DT) increased further, but ScO2 (MBL) decreased transiently. This strange phenomenon disappeared when the scalp was peeled off and the probes were directly fixed to the cranial bone. In some cases, a sustained decrease in μs' was observed several hours after ROSC and, in such cases, MRI Diffusion Enhancement Image (DWI) showed findings suggestive of post-resuscitation encephalopathy. In conclusion, simultaneous monitoring of cerebral oxygenation with MBL and DT may provide more information about the vascular response of different layers. Also, the monitoring of μs' may help us to recognize the occurrence of post-resuscitation encephalopathy in real time.

FNIRS differentiates cognitive workload between concussed adolescents and healthy controls

fNIRS differentiates cognitive workload between concussed adolescents and healthy controls

Cognitive workload as the physiologic basis for symptom provocation with task performance in concussion: an fNIRS study of prefrontal brain activity

Cognitive workload as the physiologic basis for symptom provocation with task performance in concussion: an fNIRS study of prefrontal brain activity

The Influence of Game Demand on Distraction from Experimental Pain: A fNIRS Study

The Influence of Game Demand on Distraction from Experimental Pain: A fNIRS Study

Functional Near-Infrared Spectroscopy in Athletes Pre- and Post-Season Demonstrates Consistent Pattern of Frontal Cortical Activation with King-Devick Testing

Functional Near-Infrared Spectroscopy in Athletes Pre- and Post-Season Demonstrates Consistent Pattern of Frontal Cortical Activation with King-Devick Testing

Prefrontal Cortex Activity during Dual Task Performance: A Functional Neuroimaging Study

Prefrontal Cortex Activity during Dual Task Performance: A Functional Neuroimaging Study