Resolution and segmentation of hyperspectral biomedical images by multivariate curve resolution-alternating least squares

MCR-ALS is a resolution method that has been applied in many different fields, such as process analysis, environmental data and, recently, hyperspectral image analysis. In this context, the algorithm provides the distribution maps and the pure spectra of the image constituents from the sole information in the raw image measurement. Based on the distribution maps and spectra obtained, additional information can be easily derived, such as identification of constituents when libraries are available or quantitation within the image, expressed as constituent signal contribution. This work summarizes first the protocol followed for the resolution on two examples of kidney calculi, taken as representations of images with major and minor compounds, respectively. Image segmentation allows separating regions of images according to their pixel similarity and is also relevant in the biomedical field to differentiate healthy from non-healthy regions in tissues or to identify sample regions with distinct properties. Information on pixel similarity is enclosed not only in pixel spectra, but also in other smaller pixel representations, such as PCA scores. In this paper, we propose the use of MCR scores (concentration profiles) for segmentation purposes. K-means results obtained from different pixel representations of the data set are compared. The main advantages of the use of MCR scores are the interpretability of the class centroids and the compound-wise selection and preprocessing of the input information in the segmentation scheme.     

Quantification of analytes in overlapping peaks from capillary electrophoresis using multivariate curve resolution-alternating least squares methods

Application of multivariate curve resolution with alternating least squares (ALS) methods to second-order data from capillary electrophoresis diode array detector (CE-DAD) is shown. Second-order data are easily obtained by setting individual data matrix of CE run one in top of the other. Initial qualitative solutions obtained by evolving factor analysis can be further optimized by simultaneous analysis of multiple electrophoresis run data with ALS regression. Quantification is achieved by the comparison of the analyte peak areas with that of pure standards. During the ALS regression procedure, the following constraints were applied: (i) both concentrations and unit pure spectra of the resolved components must be positive; (ii) elution profiles have an unimodal shape; (iii) correspondence exists between common species in the different data matrices; (iv) the pure spectrum of each species is the same in all runs where it is present. The above methods were applied for the determination of dinitrotoluene (DNT) isomeric compounds in overlapping peaks from CE.     

Characterisation of hydrogen bond perturbations in aqueous systems using aquaphotomics and multivariate curve resolution-alternating least squares

Aquaphotomics is a new discipline that provides a framework for understanding changes in the structure of water caused by various perturbations, such as variations in temperature or the addition of solutes, using near infrared spectroscopy (NIRS). One of the main purposes of aquaphotomics is to identify water bands as main coordinates of future absorbance patterns to be used as biomarkers. These bands appear as consequence of perturbations in the NIR spectra. Curve resolution techniques may help to resolve and find new water bands or confirm already known bands. The aim of this study is to investigate the application of multivariate curve resolution-alternating least squares (MCR-ALS) to characterise the effects of various perturbations on the NIR spectra of water in terms of hydrogen bonding. For this purpose, the perturbations created by temperature change and the addition of four solutions of different ionic strength and Lewis acidity were studied (NaCl, KCl, MgCl₂ and AlCl₃, with concentrations ranging from 0.2 to 1 mol L⁻¹ in steps of 0.2 mol L⁻¹). Transmission spectra of all salt solutions and pure water were obtained at temperatures ranging from 28 to 45 °C. We have found that three distinct components with varying temperature dependence are present in water perturbed by temperature. The salt solutions studied exhibited similar trends with respect to the temperature perturbation, while the peak locations of their MCR-ALS pure components varied according to the ionic strength of the salt used.     

Kinetic approach for the enzymatic determination of levodopa and carbidopa assisted by multivariate curve resolution-alternating least squares

A combination of kinetic spectroscopic monitoring and multivariate curve resolution-alternating least squares (MCR-ALS) was proposed for the enzymatic determination of levodopa (LVD) and carbidopa (CBD) in pharmaceuticals. The enzymatic reaction process was carried out in a reverse stopped-flow injection system and monitored by UV-vis spectroscopy. The spectra (292-600 nm) were recorded throughout the reaction and were analyzed by multivariate curve resolution-alternating least squares. A small calibration matrix containing nine mixtures was used in the model construction. Additionally, to evaluate the prediction ability of the model, a set with six validation mixtures was used. The lack of fit obtained was 4.3%, the explained variance 99.8% and the overall prediction error 5.5%. Tablets of commercial samples were analyzed and the results were validated by pharmacopeia method (high performance liquid chromatography). No significant differences were found (α = 0.05) between the reference values and the ones obtained with the proposed method. It is important to note that a unique chemometric model made it possible to determine both analytes simultaneously.     

Application of multivariate curve resolution-alternating least squares for the determination of boron isotope ratios by inductively coupled plasma-optical emission spectrometry

Multivariate curve resolution-alternating least squares (MCR-ALS) was applied to atomic emission data obtained from inductively coupled plasma-optical emission spectrometry analysis of boron for the quantification of ¹⁰B/¹¹B ratios. The determination of isotopic composition of boron is based on the isotopic shift of ¹⁰B and ¹¹B in the emission line of 208.957 nm. After recording of the emission spectra in the range of 208.940–208.970 nm, evaluation of isotopic composition of boron containing samples was performed with MCR-ALS algorithm. MCR-ALS was able to resolve the emission spectra of ¹⁰B and ¹¹B mixtures. The performance of the proposed methods was tested by determination of ¹⁰B/¹¹B ratios in synthetic mixtures and also water samples.     

High contrast images of uterine tissue derived using Raman microspectroscopy with the empty modelling approach of multivariate curve resolution-alternating least squares

Approaches that allow one to rapidly understand tissue structure and functionality in situ remain to be developed. Such techniques are required in many instances, including where there is a need to remove with a high degree of confidence positive tumour margins during surgical excision. As biological tissue has little contrast, gold standard confirmation of surgical margins is conventionally undertaken by histopathological diagnosis of tissue architecture via optical microscopy. Vibrational spectroscopy techniques, when coupled to sophisticated computational analyses, are capable of constructing bio-molecular contrast images of unstained tissue. To assess the relative applicability of a range of candidate algorithms to distinguish the in situ bio-molecular structures of a complex tissue, the empty modelling approach of multivariate curve resolution-alternating least squares (MCR-ALS) was compared to hierarchical cluster analysis (HCA) or principal component analysis (PCA). Such chemometric analyses were applied to Raman images of benign (tumour-adjacent) endometrium, stage I and stage II endometrioid cancer. Re-constructed images from the in situ bio-molecular tissue architectures highlighted features associated with glandular epithelium, stroma, glandular lumen and myometrium. Of the tested chemometric analyses, MCR-ALS provided the best bio-molecular contrast images, superior to those derived following HCA or PCA, with clear and defined margins of histological features. Iteratively-resolved spectra identified wavenumbers responsible for the contrast image. Wavenumbers 1234 cm(-1) (Amide III), 1390 cm(-1) (CH(3) bend), 1675 cm(-1) (Amide I/lipid), 1275 cm(-1) (Amide III), 918 cm(-1) (proline) and 936 cm(-1) (proline, valine and proteins) were responsible for generating the majority of the contrast within MCR-ALS-generated images. Applications of sophisticated computational analyses coupled with vibrational spectroscopy techniques have the potential to lend novel functionality insights into bio-molecular structures in vivo.     

New strategy to identify radicals in a time evolving EPR data set by multivariate curve resolution-alternating least squares

Electron paramagnetic resonance (EPR) spectroscopy is a powerful technique that is able to characterize radicals formed in kinetic reactions. However, spectral characterization of individual chemical species is often limited or even unmanageable due to the severe kinetic and spectral overlap among species in kinetic processes. Therefore, we applied, for the first time, multivariate curve resolution-alternating least squares (MCR-ALS) method to EPR time evolving data sets to model and characterize the different constituents in a kinetic reaction. Here we demonstrate the advantage of multivariate analysis in the investigation of radicals formed along the kinetic process of hydroxycoumarin in alkaline medium. Multiset analysis of several EPR-monitored kinetic experiments performed in different conditions revealed the individual paramagnetic centres as well as their kinetic profiles. The results obtained by MCR-ALS method demonstrate its prominent potential in analysis of EPR time evolved spectra.     

Application of multivariate curve resolution-alternating least squares (MCR-ALS) for resolving pyrogallol autoxidation in weakly alkaline aqueous solutions

Multivariate curve resolution — alternating least squares (MCR-ALS) has been applied to data collected from UV/Vis spectrophotometric analysis of the autoxidation process of pyrogallol in weakly alkaline aqueous solutions. The MCR-ALS analysis was able to explain the autoxidation kinetics of pyrogallol at pH 7.4 and 8.0, allowing deduction of the pure spectra and concentration changes of different species present throughout the entire process. The autoxidation process at pH 7.4 was found to follow a first-order reaction model, with formation of purpurogallin as the sole and terminal product. Changing the pH to 8.0 not only accelerated autoxidation of pyrogallol to purpurogallin but also introduced a further autoxidation of purpurogallin. At pH 8.0 the process fits a model of two consecutive first-order reactions. The first step is formation of purpurogallin, which reacts in a further autoxidation to form a yellow colored substance, most probably purpurogallin polymer.      

Rank analysis and simultaneous determination of acetylsalicylic acid,paracetamol, and caffeine in pharmaceuticals using second-order data and multivariate curve resolution-alternating least squares (MCR-ALS)

Mixtures of acetylsalicylic acid (ASA), paracetamol (PAR), and caffeine (CAF) have been successfully analyzed by constrained multivariate curve resolution-alternating least squares (MCR-ALS). The MCR-ALS methodology adequately exploits the second-order advantage which enables quantitation of analyte in the presence of unknown and uncalibrated interferences. The procedure simultaneously takes into account the spectroscopic and pH-dependent properties of the compounds, which leads to a higher selectivity. Specially, for CAF determination fully protonated or deprotonated forms of CAF are not dominant in the pH range of data acquisition but spectral changes with pH were recorded and used for accurate determination of CAF. Furthermore, quantitative determination of an analyte in a complex mixture is performed using a synthetic solution as standard containing only the analyte of interest. Even in the presence of the rank deficiencies, in most cases accurate quantitation with relative errors in prediction lower than 5 % was obtained. The procedure was successfully applied to the analysis of real samples (pharmaceuticals) using synthetic external standards. Percent relative errors of 4.03, 3.26, and 5.85 were obtained for ASA, PAR, and CAF, respectively, in A.C.A tablets and 4.49 and 2.75 for PAR and CAF, respectively in Novafen capsules.     

Novel combination of non-aqueous capillary electrophoresis and multivariate curve resolution-alternating least squares to determine phenolic acids in virgin olive oil

This paper presents the development of a non-aqueous capillary electrophoresis method coupled to UV detection combined with multivariate curve resolution-alternating least-squares (MCR-ALS) to carry out the resolution and quantitation of a mixture of six phenolic acids in virgin olive oil samples. p-Coumaric, caffeic, ferulic, 3,4-dihydroxyphenylacetic, vanillic and 4-hydroxyphenilacetic acids have been the analytes under study. All of them present different absorption spectra and overlapped time profiles with the olive oil matrix interferences and between them. The modeling strategy involves the building of a single MCR-ALS model composed of matrices augmented in the temporal mode, namely spectra remain invariant while time profiles may change from sample to sample. So MCR-ALS was used to cope with the coeluting interferences, on accounting the second order advantage inherent to this algorithm which, in addition, is able to handle data sets deviating from trilinearity, like the data herein analyzed. The method was firstly applied to resolve standard mixtures of the analytes randomly prepared in 1-propanol and, secondly, in real virgin olive oil samples, getting recovery values near to 100% in all cases. The importance and novelty of this methodology relies on the combination of non-aqueous capillary electrophoresis second-order data and MCR-ALS algorithm which allows performing the resolution of these compounds simplifying the previous sample pretreatment stages.     

主成分-偏最小二乘动力学分光光度法同时测定农药两组分

对氨基甲酸酯杀虫剂残杀威（PRO）和异丙威（ISO）的速差动力学光度法同时测定进行了研究。残杀威和异丙威均能在碱性条件下发生水解，水解生成的酚盐，均可以与对氨基苯酚及高碘酸钾混合物发生反应生成兰色化合物，且这是一个反应速率适中的动力学反应。本实验在538nm-700nm采集多个时间点下多个波长的动力学－－吸收光谱数据，构成量测矩阵。采用主成分－偏最小二乘法（PC－PLS）对测定数据进行了解析。本文对环境水样中残杀威和异丙威的含量进行了测定。取得了较好的分析结果。从而提出了一种易于实现，准确度高的残杀威和异丙威的同时测定新方法。     

Simultaneous fluorimetric determination of acetylsalicylic acid metabolites in urine by partial least squares multivariate calibration

A method is described for the simultaneous determination of the main urinary acetylsalicylic acid (aspirin) metabolites, salicyclic, salicyluric and gentisic acids, based on their native fluorescence. The urine was extracted into diethyl ether in acid medium, and back-extracted with glycine/sodium hydroxide buffer solution at pH 9.4. A comparative study of the results found using the excitation, the emission and the combination of the excitation plus the emission spectral data, as analytical signals, was performed. The data set, composed of the excitation plus the emission spectra, was selected as the analytical signal. The optimum wavelengths to record the excitation (_em=444 nm) and the emission spectra (_ex=323 nm) were selected to maximize the contribution from gentisic acid, which is the minor urinary metabolite. Partial least squares (PLS-1) multivariate calibration was then applied for the determination. Recovery values from urine samples spiked with salicyclic, salicyluric and gentisic acids varied from 90.1 to 97.6% (mean 93.6%), from 90.0 to 110% (mean 97.9%) and from 89.9 to 104.7% (mean 98.5%), respectively.     

Simultaneous fluorimetric determination of acetylsalicylic acid metabolites in urine by partial least squares multivariate calibration

A method is described for the simultaneous determination of the main urinary acetylsalicylic acid (aspirin) metabolites, salicyclic, salicyluric and gentisic acids, based on their native fluorescence. The urine was extracted into diethyl ether in acid medium, and back-extracted with glycine/sodium hydroxide buffer solution at pH 9.4. A comparative study of the results found using the excitation, the emission and the combination of the excitation plus the emission spectral data, as analytical signals, was performed. The data set, composed of the excitation plus the emission spectra, was selected as the analytical signal. The optimum wavelengths to record the excitation (lambda(em)=444 nm) and the emission spectra (lambda(ex)=323 nm) were selected to maximize the contribution from gentisic acid, which is the minor urinary metabolite. Partial least squares (PLS-1) multivariate calibration was then applied for the determination. Recovery values from urine samples spiked with salicyclic, salicyluric and gentisic acids varied from 90.1 to 97.6% (mean 93.6%), from 90.0 to 110% (mean 97.9%) and from 89.9 to 104.7% (mean 98.5%), respectively.     

偏最小二乘-分光光度法同时测定福美锌和代森锰农药残留量

利用紫外可见分光光度法研究了农药福美锌和代森锰与苯基荧光酮的相互作用,发现反应后的产物分别在波长为551和554 nm处最大有吸收,但光谱严重重叠.实验采集了450～700 nm波长范围吸光度数据,并对该数据进行一阶求导后用偏最小二乘法处理,据此建立了偏最小二乘-分光光度法同时测定福美锌和代森锰两种农药的新方法.福美锌和代森锰的线性范围分别为0.3～6.0和0.2～3.5 μg/mL;检出限分别为0.22和0.13 μg/mL.混合样品分析无需分离,方法简单、快速.用于水果、大米和自来水等实际样品测定.     

Constraining shape smoothness in multivariate curve resolution–alternating least squares

The resolution of complex multicomponent hyperspectral images with multivariate curve resolution–alternating least squares is mainly performed by using a limited number of constraints on the pure constituent distribution maps, such as non‐negativity or local constraints. This work proposes a constraint that works with the spatial information of the whole image and has been given the name shape smoothness constraint. Contrary to local constraints, shape smoothness constraint imposes a global character on the distribution map pattern. It uses two‐dimensional P‐splines to enforce smoothness of the global spatial features of the distribution maps generated within the alternating least squares procedure. This allows revealing main pattern(s) in the spatial data leaving high‐frequency signals, corresponding to fine‐scale structures in the image. This approach has been successfully applied on several simulated examples where imposing shape smoothness resulted in the recovery of the correct pattern for the image objects, which in turn provided more accurate distribution maps and spectral profiles. It was also shown that when information about the smoothness of the pattern(s) of the image constituents holds, the constraint can be a flexible and robust alternative for the resolution of real hyperspectral imaging data. Copyright © 2015 John Wiley & Sons, Ltd.     

Simultaneous spectrophotometric determination of ethinylestradiol and levonorgestrel by partial least squares and principal component regression multivariate calibration

Two spectrophotometric methods for the determination of Ethinylestradiol (ETE) and Levonorgestrel (LEV) by using the multivariate calibration technique of partial least square (PLS) and principal component regression (PCR) are presented. In this study the PLS and PCR are successfully applied to quantify both hormones using the information contained in the absorption spectra of appropriate solutions. In order to do this, a calibration set of standard samples composed of different mixtures of both compounds has been designed. The results found by application of the PLS and PCR methods to the simultaneous determination of mixtures, containing 4–11 μg ml⁻¹ of ETE and 2–23 μg ml⁻¹ of LEV, are reported. Five different oral contraceptives were analyzed and the results were very similar to that obtained by a reference liquid Chromatographic method.     

Second-order advantage in determining Co (II) in real samples using kinetic-spectrophotometric data matrices and multivariate curve resolution-alternating least square approach

In the present study, multivariate curve resolution coupled to alternating least-squares (MCR-ALS) was used to analyze kinetic-spectroscopic second-order data. The purpose of the study was to achieve important second-order advantage under the conditions of extreme spectral overlapping among sample components. The obtained experimental data indicated that MCR-ALS, unlike other second-order multivariate calibration algorithms, can conveniently handle the investigated analytical problem provided that matrix augmentation is implemented in the spectral mode instead of the usual kinetic mode. In this work, row-wise augmentation was used to break rank deficiency under conditions of extreme spectral overlapping among sample components. The approach was applied to determine Cobalt (II) based on its oxidation reaction with Fe (III) and 1, 10-phenantroline in micellar media. The results indicated good analytical performance toward the analyte despite the intense spectral overlapping and the presence of unexpected constituents in the test samples. The maximum and minimum band boundaries of feasible solutions corresponding to the species profiles were estimated by multivariate curve resolution. The results of the study indicated that unique solution can be practically obtained using MCR-ALS under the selection of suitable constraints such as trilinearity.     

Dual amperometric biosensor device for analysis of binary mixtures of phenols by multivariate calibration using partial least squares

A simple and reliable method for rapid evaluation of mixtures of phenolic compounds (phenol/chlorophenol, cathecol/phenol, cresol/chlorocresol and phenol/cresol) using a dual amperometric device is described. This new approach is based on the difference between the sensitivity of laccase and tyrosinase for different phenolic compounds. A multichannel potentiostat was used to monitor simultaneously laccase- and tyrosinase-based biosensors, and the data were treated using the partial least squares (PLS) chemometric algorithm. This system showed an excellent efficiency for the resolution of the phenolic mixtures. For example, in the phenol/chlorophenol mixture it was studied the determination of individual species in a concentration range from 1.0×10⁻⁶ to 10.0×10⁻⁶ mol l⁻¹ obtaining relative standard deviations of 3.5 and 3.1% for phenol and chlorophenol, respectively. The excellent correlation between the estimated and the real concentrations can also be observed by the correlation coefficients (0.9958 and 0.9981 for phenol and chlorophenol, respectively). These results show that proposed methodology can be successfully employed to the simultaneous determination of phenolic compounds in mixtures, even in more diluted solutions.     

Extension and application of multivariate curve resolution-alternating least squares to four-way quadrilinear data-obtained in the investigation of pollution patterns on Yamuna River,India—A case study

This study focuses on the development and extension of Multivariate Curve Resolution-Alternating Least Squares (MCR-ALS) to the analysis of four-way datasets. The proposed extension of the MCR-ALS method with non-negativity and the newly developed quadrilinear constraints can be exploited to summarize and manage huge multidimensional datasets and resolve their four way component profiles. In this study, its application is demonstrated by analyzing a four-way data set obtained in a long term environmental monitoring study (15 sampling sites × 9 variables × 12 months × 7 years) belonging to the Yamuna River, one of the most polluted rivers of India and the largest tributary of the Ganges river. MCR-ALS resolved pollution profiles described appropriately the major observed changes on pH, organic pollution, bacteriological pollution and temperature, along with their spatial and temporal distribution patterns for the studied stretch of Yamuna River. Results obtained by MCR-ALS have also been compared with those obtained by another multi-way method, PARAFAC. The methodology used in this study is completely general and it can be applied to other multi-way datasets.     

偏最小二乘紫外分光光度法同时测定甲基苯甲醛三种同分异构体

将偏最小二乘法(PLS)用于紫外分光光度数据的解析,建立了同时测定甲基苯甲醛3种同分异构体的模型。在230～304 nm范围内,将测得的48个样品的吸光度值作为校正集,另18个样品的吸光度值作为预测集用于建模。所建立的邻、间、对甲基苯甲醛模型的平均回收率分别为101.2%、100.2%和98.9%;均方根误差(RMSE)分别为0.2667、0.3853和0.2118;预测浓度范围分别为4.6～16.2μg/mL、5.8～17.4μg/mL和6.5～20.6μg/mL。讨论了混合物中3种同分异构体浓度比例对测定结果的影响,并确定了最佳的浓度比例范围。对模拟样品进行加标回收率试验。并通过与顺、反丁烯二酸两种同分异构体测定结果的比较,得出了有意义的结论。