Mathematical algorithms applied to the multi-linear regression functions for the multicomponent determination of pharmaceutical dosage form containing three-component mixtures

In the presence of closely overlapping spectra, the quantitative multiresolution of ternary mixtures of three active compounds paracetamol (PAR), caffeine (CAF) and acetylsalycilic acid (ASP) in tablets, without using pretreatment such as separation step and graphical procedure of spectra was accomplished by the multivariate spectral calibration models, tri-linear regression calibration (TLRC), multi-linear regression calibration (MLRC) and Cramer's rule solution (CRS) of three linear equation functions in the matrix form. In the first two models, TLRC and MLRC are based on the use of the linear regression functions at selected wavelength sets in the spectral region of 210-300 nm. In the case of CRS model, A1(1) (1%, 1 cm) were used to obtain three linear equation functions and this linear equation system was resolved by the Cramer's rule for the prediction of PAR, CAF and ASP in samples. In the TLRC and CRS models, the selection of the appropriate wavelength set was performed by the Kaiser's technique. The algorithms of these mathematical calibration models were briefly described. The validation of TLRC, MLRC and CRS models was carried out by analyzing various synthetic ternary mixtures and by using the standard addition technique. These three calibration approaches were applied to the analysis of the real pharmaceutical tablets containing PAR, CAF and ASP. The obtained results were statistically compared with each other by using experimental and statistical tests. In the comparison of TLRC and MLRC models to the classical approach, CRS technique, the successful assay results were observed for the quantitative multiresolution of ternary mixture of the subject active compounds.     

Comparison of various chemometric evaluation approaches for on-line FT-NIR transmission and FT-MIR/ATR spectroscopic data of methyl methacrylate solution polymerization

For the evaluation of vibrational spectroscopic data acquired on-line to a chemical reaction a broad range of different chemometric algorithms is available. The present study reports the comparative results obtained by different chemometric techniques from the data acquired by light-fiber coupled Fourier-transform near infrared (FT-NIR) transmission spectroscopy and Fourier-transform mid-infrared (FT-MIR) spectroscopy in the attenuated total reflection (ATR) mode to monitor the solution polymerization of methyl methacrylate (MMA). We have found that the results obtained by the application of multivariate curve resolution (MCR) methods to the MIR spectral data acquired during the polymerization of MMA are quite comparable to the results derived by partial least-squares calibration. In the case of the NIR data univariate calibration yields somewhat poorer results than multivariate calibration and MCR, but still inside an acceptable range.     

Chemometrics: the issues of measurement and modelling

In this paper, two spectral data sets have been used to illustrate the importance of maintaining chemical information whilst generating predictive multivariate calibration models. The first data set is based on 26 duplicate UV/VIS spectra for four meal ions (Fe, Ni, Co, Cu) present at varying concentrations in aqueous solution. Spectra were collected across the range 180–800 nm at a resolution of 3.5 nm generating 211 data points for each sample. Calibration was carried out using multiple linear regression (MLR) and a K-matrix approach to demonstrate the advantages the latter method has in describing real spectral features. In addition, the limitation of MLR in accommodating noise and spectral overlap in the data is also illustrated. The second data set based on NIR spectroscopy, was generated using a four-level 2 factor Factorial design strategy and consisted of two additives present at a range of concentrations in an aqueous caustic system, with the spectra being collected over the range 10,000–3000 cm⁻¹. Whilst a conventional partial least squares (PLS) model was applied to the data, it was through the use of variable selection (VS) prior to PLS and the application of weighted ridge regression (WRR) techniques that the need to develop chemometric methodology which intuitively reflected chemical information has been demonstrated. The results will also illustrate how a poorly designed experimental design protocol and missing data can limit the performance of the calibration models generated. The aims of this paper are not to prescribe ideal calibration methodology but rather to demonstrate the relevance of selecting multivariate calibration methodology that relates more to the chem rather than just the metrics in chemometrics.     

Selectivity for glucose,glucose-6-phosphate,and pyruvate in ternary mixtures from the multivariate analysis of near-infrared spectra

Near-infrared spectroscopy offers the potential for direct in situ analysis in complex biological systems. Chemical selectivity is a critical issue for such measurements given the extent of spectral overlap of overtone and combination spectra. In this work, the chemical basis of selectivity is investigated for a set of multivariate calibration models designed to quantify glucose, glucose-6-phosphate, and pyruvate independently in ternary mixtures. Near-infrared spectra are collected over the combination region (4,000–5,000 cm⁻¹) for a set of 60 standard solutions maintained at 37 °C. These standard solutions are composed of randomized concentrations (0.5–30 mM) of glucose, glucose-6-phosphate, and pyruvate. Individual calibration models are constructed for each solute by using the partial least-squares (PLS) algorithm with optimized spectral range and number of latent variables. The resulting standard errors are 0.90, 0.72, and 0.32 mM for glucose, glucose-6-phosphate, and pyruvate, respectively. A pure component selectivity analysis (PCSA) demonstrates selectivity for each solute in these ternary samples. The concentration of each solute is also predicted for each sample by using a set of net analyte signal (NAS) calibration models. A comparison of the PLS and NAS calibration vectors demonstrates the chemical basis of selectivity for these multivariate methods. Selectivity of each PLS and NAS calibration model originates from the unique spectral features associated with the targeted analyte. Overall, selectivity is demonstrated for each solute with an order of sensitivity of pyruvate > glucose-6-phosphate > glucose. Figure Combination near-infrared spectroscopy allows selective analytical measurements for glucose, glucose-6-phosphate, and pyruvate in ternary mixtures owing to the uniqueness of the individual absorption spectra for each solute     

Near-infrared spectroscopy of newly developed PEGylated lipids

Near-infrared (NIR) spectroscopy has been used to analyze a suite of synthesized PEGylated lipids (1-3) trademarked as QuSomes. The three amphiphiles used in this study, differ in their hydrophobic chain length and contain various units of polyethylene glycol (PEG) head groups. Whilst the spectra of QuSomes show a common pattern, differences in the spectra are observed which enable the lipids to be distinguished. NIR absorption spectra of these new artificial lipids have been recorded in the spectral range of 4800-9000 cm(-1) (approximately 2100-1100 nm) by using a new miniaturized spectrometer based on micro-optical-electro-mechanical systems (MOEMS) technology. Three NIR spectral regions are identified, (a) the high wavenumber region between 6500 and 9000 cm(-1) attributed to the first overtone of the hydroxyl stretching and second overtone of the C-H stretching mode; (b) the 5350-5900 cm(-1) region attributed to first overtone of the C-H stretching mode; and (c) the 4800-5300 cm(-1) region attributed to the combination O-H stretching and second overtone of the C=O stretching mode. For each of these regions, the lipids show distinctive spectra which allow their identification and characterization. NIR spectroscopy is a less used technique which does have great potential for the study of lipids, particularly to examine the behaviour of nanovesicles (liposomes) formed from lipids in aqueous suspensions. The study of such lipids is important since they are used as membrane models and prominent candidate for substance and drug delivery systems.     

The investigation of water diffusion into teflon copolymer revealed by fiber-optic evanescent wave spectroscopy

Fiber-optic evanescent wave infrared spectroscopy was used for the study of water diffusion in Teflon and has provided valuable information about the structure of water in amorphous hydrophobic polymers. Time-dependent absorption measurements were carried out in two spectral ranges: 3000-3800 cm(-1), associated with the O-H stretching mode, and 1620-1670 cm(-1), associated with the H-O-H bending mode of water. The results indicate that the IR spectra could be expressed as a superposition of spectra due to two species of water molecules: strongly and weakly hydrogen-bonded. We suggest that water molecules form clusters with strongly hydrogen-bonded molecules at the cores and with weakly hydrogen-bonded molecules at the external parts of the clusters. A mathematical model, based on a linear diffusion equation with a moving boundary, gave a ratio of 3.5 between the total number of molecules in a cluster and the number of water molecules at the core of the cluster.     

Discrimination between coupling networks of glucopyranosides varying at a single stereocenter using two-dimensional vibrational correlation spectroscopy

A combination of two-dimensional infrared (2DIR) correlation spectroscopy, linear absorption spectroscopy, and density functional theory quantum calculations was used to identify characteristic spectral features of two anomers of acetylated 2-azido-2-deoxy-D-glucopyranose. While the linear absorption spectra for the α and β anomers were distinctive, a substantial difference between them was observed only in the spectral region below 1200 cm(-1). The infrared correlation spectra of the two anomers differed significantly, even in regions where their linear absorption spectra were similar. Very substantial differences were found for the N≡N/C=O stretch mode region of the 2DIR correlation spectrum, indicating differences in the anharmonic coupling of the N≡N stretching mode of the equatorially oriented N(3) group with the CO modes when the C(1) ester was either in the axial (α anomer) or equatorial (β anomer) orientation. In addition, the energy transport patterns originating from the excited N≡N stretching mode were found to be different for the two anomers; up to a 1.8-fold difference in the energy transport times was observed for the probed modes of the same type in the two anomers. The results demonstrate the capability of 2DIR and relaxation-assisted 2DIR (RA 2DIR) spectroscopies to provide unique spectroscopic data specific to sugar anomers that vary at a single stereochemical center. These methods identify unique coupling networks within individual sugar stereochemical units and demonstrate the potential to identify a number of stereochemical differences among them.     

Adaptive wavelet transform suppresses background and noise for quantitative analysis by Raman spectrometry

Discrete wavelet transform (DWT) provides a well-established means for spectral denoising and baseline elimination to enhance resolution and improve the performance of calibration and classification models. However, the limitation of a fixed filter bank can prevent the optimal application of conventional DWT for the multiresolution analysis of spectra of arbitrarily varying noise and background. This paper presents a novel methodology based on an improved, second-generation adaptive wavelet transform (AWT) algorithm. This AWT methodology uses a spectrally adapted lifting scheme to generate an infinite basis of wavelet filters from a single conventional wavelet, and then finds the optimal one. Such pretreatment combined with a multivariate calibration approach such as partial least squares can greatly enhance the utility of Raman spectroscopy for quantitative analysis. The present work demonstrates this methodology using two dispersive Raman spectral data sets, incorporating lactic acid and melamine in pure water and in milk solutions. The results indicate that AWT can separate spectral background and noise from signals of interest more efficiently than conventional DWT, thus improving the effectiveness of Raman spectroscopy for quantitative analysis and classification.     

Data fusion in multivariate calibration transfer

We report the use of stacked partial least-squares regression and stacked dual-domain regression analysis with four commonly used techniques for calibration transfer to improve predictive performance from transferred multivariate calibration models. The predictive performance from three conventional calibration transfer methods, piecewise direct standardization (PDS), orthogonal signal correction (OSC) and model updating (MUP), requiring standards measured on both instruments, was significantly improved from data fusion either by stacking of wavelet scales or by stacking of spectral intervals, as demonstrated by transfer of calibrations developed on near-infrared spectra of synthetic gasoline. Stacking did not produce as significant an improvement for calibration transfer using a finite impulse response (FIR) filter, but application of SPLS regression to FIR-transferred spectra improves predictive performance of the transferred model.     

Determination of water in lubricating oils by mid- and near-infrared spectroscopy

Mid-infrared (MIR) and near-infrared (NIR) spectroscopy were used to determine water in lubricating oils with high additive contents that introduce large errors in determinations by the Karl-Fischer and hydride methods. MIR spectra were obtained in the attenuated total reflectance (ATR) mode and exhibited water specific band absorption in the region 3100–3700cm^–1, which facilitated calibration. Multivariate (partial least-squares regression, PLSR) and univariate calibration (based on peak height and band area as independent variables) were tested. Both led to errors of prediction less than 5%. NIRS determinations rely on absorbance and first-derivative spectra, in addition to two different types of multivariate calibration,viz. inverse multiple linear regression (MLR) and partial least-squares regression (PLSR). Both approaches gave similar results, with errors of prediction less than 2%.For none of the proposed approaches any sample pretreatment for recording spectra is required.     

Least-squares support vector machines and near infrared spectroscopy for quantification of common adulterants in powdered milk

This paper proposes the use of the least-squares support vector machine (LS-SVM) as an alternative multivariate calibration method for the simultaneous quantification of some common adulterants (starch, whey or sucrose) found in powdered milk samples, using near-infrared spectroscopy with direct measurements by diffuse reflectance. Due to the spectral differences of the three adulterants a nonlinear behavior is present when all groups of adulterants are in the same data set, making the use of linear methods such as partial least squares regression (PLSR) difficult. Excellent models were built using LS-SVM, with low prediction errors and superior performance in relation to PLSR. These results show it possible to built robust models to quantify some common adulterants in powdered milk using near-infrared spectroscopy and LS-SVM as a nonlinear multivariate calibration procedure.     

近红外光谱快速测定红花逆流提取过程中羟基红花黄色素A的含量

采用近红外光谱(NIRS)透射法对红花罐组式逆流提取过程中羟基红花黄色素A(Hydroxysafflor yellow A,HSYA)的含量进行快速无损的测定.在红花逆流提取过程中,以高效液相色谱法(HPLC)为对照分析方法,测定提取液中羟基红花黄色素A的含量,运用偏最小二乘(PLS)法建立NIR光谱与羟基红花黄色素A的HPLC分析值之间多元校正模型,并对逆流提取过程的未知样本进行含量预测.校正模型相关系数达到0.982,预测相关系数达到0.965,RMSEC和RMSEP分别为0.053和0.075,RSEC和RSEP分别为3.96%和5.25%.结果表明,NIRS可以作为一种准确、快速、无损的检测方法用于检测中药逆流提取过程有效成分含量变化规律.     

A procedure for calibration transfer between near-infrared instruments--a worked example using a transmittance single tablet assay for piroxicam in intact tablets

A procedure was developed for different modes of calibration transfer in near-infrared (NIR) spectroscopy, which included a method for the selection of a subset of samples appropriate for transfer. As a worked example, these guidelines were applied to the transfer of a multivariate calibration model, representing a validated NIR single tablet assay for the active within an intact pharmaceutical product, between three equivalent dispersive NIR transmission instruments. Transfer was first evaluated between two instruments, representing the situation where both were available during calibration development. A spectral correction method alone, applied to the transfer instrument, was not sufficient to facilitate transfer, with further optimisation of the calibration model using a novel wavelength selection algorithm necessary to remove regions of the spectral range that resulted in skewed predictions on the second instrument. Through this approach, a single calibration model was found to be equally accurate and precise on the two instruments. A procedure, using the Kennard-Stone algorithm, is described for determining a reduced number of samples as a transfer set using only the spectral information from the original instrument. The purpose of the subset was to permit transfer to a new instrument where that instrument was not available until after calibration development or where it was undesirable to re-measure the full sample set (i.e. due to excessive reference chemistry). Utilising the transfer set, transfer to a third instrument was evaluated. The calibration model, optimised between the first two instruments, was not directly applicable for the third instrument, with further wavelength selection required to remove a small region of spectral data. On completion, using a full statistical evaluation, a single calibration model was found to be equally accurate and precise on all three instruments.     

Simultaneous determination of penicillin and ampicillin by spectral fibre-optical enzyme optodes and multivariate data analysis based on transient signals obtained by flow injection analysis

A multicomponent detection system using optical biosensors and flow injection analysis is described. The analysis of mixtures containing penicillin and ampicillin was realised by evaluating dynamic measurements of Phenol Red spectra in penicillinase optodes in combination with a diode array spectrometer. A variety of optodes has been produced by changing the composition of the receptor gel and the working pH. A set of characteristic quantities (describing dynamic and static features) could be obtained for each optode. These were used to compare the predictivity of classical multivariate calibration methods as well as of an artificial neural network. In addition, different algorithms were applied for the evaluation of the spectral data in order to select the most appropriate method for feature extraction. In consequence, the information obtained from the multivariate calibration models was used to set up an optimal sensor array consisting of four optodes with different types of penicillinase at different working pH.     

Spectroscopic characterization of chromite from the Moa-Baracoa Ophiolitic Massif, Cuba

The Cuban chromites with a spinel structure, FeCr2O4 have been studied using optical absorption and EPR spectroscopy. The spectral features in the electronic spectra are used to map the octahedral and tetrahedral co-ordinated cations. Bands due Cr3+ and Fe3+ ions could be distinguished from UV-vis spectrum. Chromite spectrum shows two spin allowed bands at 17,390 and 23,810 cm(-1) due to Cr3+ in octahedral field and they are assigned to 4A2g(F) --> 4T2g(F) and 4A2g(F) --> 4T1g(F) transitions. This is in conformity with the broad resonance of Cr3+ observed from EPR spectrum at g = 1.903 and a weak signal at g = 3.861 confirms Fe3+ impurity in the mineral. Bands of Fe3+ ion in the optical spectrum at 13,700, 18,870 and 28,570 cm(-1) are attributed to 6A1g(S) --> 4T1g(G), 6A1g(S) --> 4T2g(G) and 6A1g(S) --> 4T2g(P) transitions, respectively. Near-IR reflectance spectroscopy has been used effectively to show intense absorption bands caused by electronic spin allowed d-d transitions of Fe2+ in tetrahedral symmetry, in the region 5000-4000 cm(-1). The high frequency region (7500-6500 cm(-1)) is attributed to the overtones of hydroxyl stretching modes. Correlation between Raman spectral features and mineral chemistry are used to interpret the Raman data. The Raman spectrum of chromite shows three bands in the CrO stretching region at 730, 560 and 445 cm(-1). The most intense peak at 730 cm(-1) is identified as symmetric stretching vibrational mode, A1g(nu1) and the other two minor peaks at 560 and 445 cm(-1) are assigned to F2g(nu4) and E(g)(nu2) modes, respectively. Cation substitution in chromite results various changes both in Raman and IR spectra. In the low-wavenumber region of Raman spectrum a significant band at 250 cm(-1) with a component at 218 cm(-1) is attributed F2g(nu3) mode. The minor peaks at 195, 175, 160 cm(-1) might be due to E(g) and F2g symmetries. Broadening of the peak of A1g mode and shifting of the peak to higher wavenumber observed as a result of increasing the proportion of Al3+O6. The presence of water in the mineral shows bands in the IR spectrum at 3550, 3425, 3295, 1630 and 1455 cm(-1). The vibrational spectrum of chromite gives raise to four frequencies at 985, 770, 710 and 650 cm(-1). The first two frequencies nu1 and nu2 are related to the lattice vibrations of octahedral groups. Due to the influence of tetrahedral bivalent cation, vibrational interactions occur between nu3 and nu4 and hence the low frequency bands, nu3 and nu4 correspond to complex vibrations involving both octahedral and tetrahedral cations simultaneously. Cr3+ in Cuban natural chromites has highest CFSE (20,868 cm(-1)) when compared to other oxide minerals.     

Simultaneous Determination of Timolol Maleate and Pilocarpine Hydrochloride in Ophthalmic Solutions by First Derivative UV Spectrophotometry and PLS-1 Multivariate Calibration

ABSTRACT

The use of UV spectrophotometry (first-derivative/zero-crossing and zero-order spectra/multivariate calibration) is reported for the analysis of two miotic agents in ophthalmic solutions. The resolution of these mixtures has been accomplished without prior separation or derivatisation by using: 1) first-derivative measurements at two appropriate zero-crossing points: λ₁ = 222 nm, where the absorption corresponding to excipients is negligible, and λ₂ = 307 nm, where the contribution of pilocarpine and excipients to the overall absorption is negligible, and 2) partial least squares (PLS-1) regression analysis of zero-order spectral data. Although the components show an important degree of spectral overlap, they have been simultaneously determined with high accuracy, and with no interference from ophthalmic solution excipients.     

Assessment of cellulose structural variety from different origins using near infrared spectroscopy

Near infrared (NIR) spectroscopy was tested as a rapid monitor of cellulose features by analyzing structurally distinguishable cellulose from different organisms ranging from Monera to Plantae as well as Animalia. The optimal spectral region was first identified using intra-crystalline deuteration, and then statistically analyzed based on second derivative spectra by principal component analysis. The score plots clearly distributed the samples according to crystalline structure such as relative crystallinity and allomorphism. These characteristics and the corresponding loading factors provided key NIR absorption criteria for identifying structural properties, especially in bands at 6527 and 6383 cm^?1, which correspond to I_α and I_β, respectively. In addition, calibration models were created for relative cellulose crystallinity using partial least square regression and for allomorph ratios using simple absorption band shifts at 6476–6446 cm^?1. NIR spectra of cellulose from various organisms combined with multivariate analysis can be used as a database for simple and rapid assessment of unknown cellulose materials.     

Simultaneous fluorometric determination of nalidixic acid and 7-hydroxymethylnalidixic acid by partial least squares calibration

The resolution of binary mixtures of nalidixic acid (NA) and 7-hydroxymethylnalidixic acid (OH-NA) has been accomplished by partial least squares (PLS) and principal component regression (PCR) multivariate calibration. The method of determination is based on the fluorescence emission of these compounds in the presence of gamma-cyclodextrin (gamma-CD). The formation of the inclusion compounds gives rise to an increase of the fluorescence emission compared to aqueous solution. The total luminescence information of the compounds has been used to optimize the spectral data set to perform the calibration. A comparison between the predictive ability of three multivariate calibration methods, PLS-1, PLS-2 and PCR, on three spectral data sets, excitation, emission and synchronous spectra has been performed. The PLS-1 method, applied to the emission spectra, has been selected as optimum. The proposed method has been applied to the simultaneous determination of NA and OH-NA in urine. Recovery values from urine samples containing (NA) and (OH-NA) range from 91 to 103% (mean 97%), and from 92 to 105% (mean 99%), respectively.     

Temperature-dependent far-infrared spectra of single crystals of high explosives using terahertz time-domain spectroscopy

Survey spectra of single-crystal HMX (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine), RDX (hexahydro-1,3,5-trinitro-1,3,5-triazine), and PETN (pentaerythritol tetranitrate) were acquired in the region from 10 to 80 cm(-1) using terahertz time-domain spectroscopy. The spectra were taken at temperatures ranging from 8.4 to 300 K. Generally, the spectra show multiple absorption peaks in the range 50-80 cm(-1), with PETN (110) showing strong absorption features at room temperature. RDX (210) is the most notable in the region 10-40 cm(-1), showing multiple spectral features, while HMX (010) shows a very broad absorption at 47.8 cm(-1) with a fwhm of 37.3 cm(-1). Future plans include polarization-dependent investigations for multiple crystallographic orientations over an increased spectral range and higher-level theoretical calculations.     

Determination of molecular line parameters for acrolein (C(3)H(4)O) using infrared tunable diode laser absorption spectroscopy

Acrolein (C(3)H(4)O) molecular line parameters, including infrared (IR) absorption positions, strengths, and nitrogen broadened half-widths, must be determined since they are not included in the high resolution transmission (HITRAN) molecular absorption database of spectral lines. These parameters are required for developing a quantitative analytical method for measuring acrolein in a single puff of cigarette smoke using tunable diode laser absorption spectroscopy (TDLAS). The task is complex since acrolein has many highly overlapping infrared absorption lines in the room temperature spectrum and the cigarette smoke matrix contains thousands of compounds. This work describes the procedure for estimating the molecular line parameters for these overlapping absorption lines in the wavenumber range (958.7-958.9 cm(-1)) using quantitative reference spectra taken with the infrared lead-salt TDLAS instrument at different pressures and concentrations. The nitrogen broadened half-width for acrolein is 0.0937 cm(-1)atm(-1) and to our knowledge, is the first time it has been reported in the literature.