Interrelationships between generalized Tikhonov regularization,generalized net analyte signal,and generalized least squares for desensitizing a multivariate calibration to interferences

Orthogonal pre‐processing (orthogonal projection) of spectral data is a common approach to generate analyte‐specific information for use in multivariate calibration. The goal of this pre‐processing is to remove from each spectrum the respective sample interferent contributions (spectral interferences from overlap, scatter, noise, etc.). Two approaches to accomplish orthogonal pre‐processing are net analyte signal (NAS) and generalized least squares (GLS). Developed in this paper is the mathematical relationship between NAS and GLS. It is also realized that orthogonal NAS pre‐processing can remove too much analyte signal and that the degree of interferent correction can be regulated. Similar to GLS, the degree of correction is accomplished by using a regularization (tuning) parameter to form generalized NAS (GNAS). Also developed in this paper is an alternative to GNAS and GLS based on generalized Tikhonov regularization (GTR). The mathematical relationships between GTR, GNAS, and GLS are derived. A result is the ability to express the model vector as the sum of two contributions: the orthogonal NAS contribution and a non‐NAS contribution from the interferent components. Thus, rather than the usual situation of sequentially pre‐processing data by either GNAS or GLS followed by model building with the pre‐processed data, the methods of GTR, GNAS, and GLS are expressed as direct computations of model vectors allowing concurrent pre‐processing and model building to occur. Simultaneous pre‐processing and model forming are shown to be natural to the GTR process. Two near‐infrared spectroscopic data sets are studied to compare the theoretical relationships between GTR, GNAS, and GLS. One data set covers basic calibration, and the other data set is for calibration maintenance. Filter factor representation is key to developing the interprocess relationships. Copyright © 2013 John Wiley & Sons, Ltd.     

Two‐way and three‐way approaches to ultra high performance liquid chromatography–photodiode array dataset for the quantitative resolution of a two‐component mixture containing ciprofloxacin and ornidazole

Two‐way and three‐way calibration models were applied to ultra high performance liquid chromatography with photodiode array data with coeluted peaks in the same wavelength and time regions for the simultaneous quantitation of ciprofloxacin and ornidazole in tablets. The chromatographic data cube (tensor) was obtained by recording chromatographic spectra of the standard and sample solutions containing ciprofloxacin and ornidazole with sulfadiazine as an internal standard as a function of time and wavelength. Parallel factor analysis and trilinear partial least squares were used as three‐way calibrations for the decomposition of the tensor, whereas three‐way unfolded partial least squares was applied as a two‐way calibration to the unfolded dataset obtained from the data array of ultra high performance liquid chromatography with photodiode array detection. The validity and ability of two‐way and three‐way analysis methods were tested by analyzing validation samples: synthetic mixture, interday and intraday samples, and standard addition samples. Results obtained from two‐way and three‐way calibrations were compared to those provided by traditional ultra high performance liquid chromatography. The proposed methods, parallel factor analysis, trilinear partial least squares, unfolded partial least squares, and traditional ultra high performance liquid chromatography were successfully applied to the quantitative estimation of the solid dosage form containing ciprofloxacin and ornidazole.     

Application of the wavelet method for the simultaneous quantitative determination of benazepril and hydrochlorothiazide in their mixtures

The discrete and continuous wavelet transforms were applied to the overlapping signal analysis of the ratio data signal for simultaneous quantitative determination of the title subject compounds in samples. The ratio spectra data of the binary mixtures containing benazepril (BE) and hydrochlorothiazide (HCT) were transferred as data vectors into the wavelet domain. Signal compression, followed by a 1-dimension continuous wavelet transform (CWT), was used to obtain coincident transformed signals for pure BE and HCT and their mixtures. The coincident transformed amplitudes corresponding to both maximum and minimum points allowed construction of calibration graphs for each compound in the binary mixture. The validity of CWT calibrations was tested by analyzing synthetic mixtures of the investigated compounds, and successful results were obtained. All calculations were performed within EXCEL, C++, and MATLAB6.5 softwares. The obtained results indicated that our approach was flexible and applicable for the binary mixture analysis.     

近红外光谱分辨率对定量分析的影响

利用近红外光谱建立了多组分混合物中对乙酰氨基苯酚和乙水杨胺的定量分析模型。定量模型可以快速准确地测定混合物中对乙酰氨基苯酚和乙水杨胺的含量。研究发现,光谱分辨率对定量分析模型有重要影响。以光谱分辨率4cm-1获得的光谱数据建立的对乙酰氨基苯酚定量模型,其校正集回归系数达到0·9992;其标准偏差为0.2120;同时模型的验证集回归系数为0.9996,而标准偏差达到0.1848。以分辨率1cm-1和8cm-1收集的光谱为基础获得的定量模型,其预测能力呈现不同程度下降趋势。研究结果表明,针对具体样品的特定组分,需要选择合适的光谱分辨率,进而获得最佳的定量分析结果。     

Wavelet unfolded partial least squares for near-infrared spectral quantitative analysis of blood and tobacco powder samples

Continuous wavelet transform (CWT) has been shown to be a high-performance signal processing technique in multivariate calibration. However, the signal processed by CWT with a specific wavelet may account for only a part of the information. To effectively utilize more abundant information contained in analytical signals, a method, named as wavelet unfolded partial least squares (WUPLS), was proposed. In the approach, the measured dataset is firstly extended by CWT with different wavelets, and then partial least squares (PLS) is employed to develop the quantitative model between the extended dataset and the target values. In order to select the representative wavelets, principal component analysis (PCA) is used to investigate the distribution of the signals obtained by CWT with different wavelets. The performance of the method was tested with blood and tobacco powder samples. Compared with the results obtained by PLS methods, the WUPLS method combined with signal processing techniques is proven to be a promising tool for improving the near-infrared (NIR) spectral analysis of complex samples.     

Rapid Determination of Metabolites in Bio‐fluid Samples by Raman Spectroscopy and Optimum Combinations of Chemometric Methods

The application of Raman spectroscopic techniques combined with multivariate chemometrics signal processing promise new means for the rapid multidimensional analysis of metabolites non‐destructively, with little or no sample preparation and little sensitivity to water. However, Rayleigh scattering, fluorescence and uncontrolled variance present substantial challenges for the accurate quantitative analysis of metabolites at physiological levels in biologically varying samples. Effective strategies include the application of chemometrics pretreatments for reducing Raman spectral interference. However, the arbitrary application of individual or combined pretreatment procedures can significantly alter the outcome of a measurement, thereby complicating spectral analysis. This paper evaluates and compares six signal pretreatment methods for correcting the baseline variances, together with three variable selection methods for eliminating uninformative variables, all within the context of multivariate calibration models based on partial least squares (PLS) regression. Raman spectra of 90 artificial bio‐fluid samples with eight urine metabolites at near‐physiological concentrations were used to test these models. The combination of multiplicative scatter correction (MSC), continuous wavelet transform (CWT), randomization test (RT) and PLS modeling presented the best performance for all the metabolites. The correlation coefficient (R) between predicted and prepared concentration reached as high as 0.96.     

Multivariate standard addition method solved by net analyte signal calculation and rank annihilation factor analysis

This article describes the use of the net analyte signal (NAS) concept and rank annihilation factor analysis (RAFA) for building two different multivariate standard addition models called “SANAS” and “SARAF.” In the former, by the definition of a new subspace, the NAS vector of the analyte of interest in an unknown sample as well as the NAS vectors of samples spiked with various amounts of the standard solutions are calculated and then their Euclidean norms are plotted against the concentration of added standard. In this way, a simple linear standard addition graph similar to that in univariate calibration is obtained, from which the concentration of the analyte in the unknown sample and the analytical figures of merit are readily calculated. In the SARAF method, the concentration of the analyte in the unknown sample is varied iteratively until the contribution of the analyte in the response data matrix is completely annihilated. The proposed methods were evaluated by analyzing simulated absorbance data as well as by the analysis of two indicators in synthetic matrices as experimental data. The resultant predicted concentrations of unknown samples showed that the SANAS and SARAF methods both produced accurate results with relative errors of prediction lower than 5% in most cases.     

Effect of gold nanoparticle attached multi-walled carbon nanotube-layered indium tin oxide in monitoring the effect of paracetamol on the release of epinephrine

Raman spectroscopy and control charts based on the net analyte signal (NAS) were applied to polymorphic characterization of carbamazepine. Carbamazepine presents four polymorphic forms: I-IV (dihydrate). X-ray powder diffraction was used as a reference technique. The control charts were built generating three charts: the NAS chart that corresponds to the analyte of interest (form III in this case), the interference chart that corresponds to the contribution of other compounds in the sample and the residual chart that corresponds to nonsystematic variations. For each chart, statistical limits were developed using samples within the quality specifications. It was possible to identify the different polymorphic forms of carbamazepine present in pharmaceutical formulations. Thus, an alternative method for the quality monitoring of the carbamazepine polymorphic forms after the crystallization process is presented.     

Capability of detection and three-way data

Due to the possibility of making analytical determinations in the presence of non-modelled interferents and to identify the analyte of interest, calibrations based on scores of PARAFAC decomposition of three-way data are becoming increasingly important in routine analysis.Furthermore, the IUPAC and EU (European Decision 2002/657/EC) have accepted the definition given by the ISO 11843 for the capability of detection as the minimum net quantity detectable with a pre-set probability of false positive and false negative. What is more, recently our research group has generalised this definition of capability of detection, CCβ, to multivariate calibrations. In practice, CCβ is a good measure of the quality of the calibration because in its definition it brings together analytical sensitivity with precision in analytical determinations.This paper studies the effect of the pre-treatment of the sample, the signal/noise ratio and the second-order advantage on CCβ when using second-order signals modelled by PARAFAC. All of them are experimental factors which influence the quality of the calibration. Analytical pre-treatment is habitual in the analysis of real samples. Specifically, we analyse the effect of the extraction phase and the clean-up of milk samples on the determination of chlortetracycline by HPLC-DAD. It is shown that it is more efficient to do the joint PARAFAC decomposition of the pure standards with the milk samples.Secondly, the effect of asymmetry on CCβ, according to the path of the noise of the signals, is studied. Specifically, in the determination of naphthalene by excitation-emission spectroscopy, EEM, it is the emission spectrum which limits the capability of detection. It is shown that by eliminating the spectra with the poorest signal/noise ratio in this path, the capability of detection can be substantially improved.Thirdly, the impact on CCβ when the second-order advantage is used, that is when PARAFAC calibration is used over samples with an unknown interference not modelled in the calibration step. This is important to apply a PARAFAC calibration to routine analysis in the IUPAC and European Decision framework. Specifically, in the determination of enrofloxacine in poultry feeding water through excitation-emission fluorescence CCβ is evaluated when the PARAFAC is built only with calibration samples or with the calibration samples plus the test samples with uncalibrated and unknown interferent.     

Application of Multivariate Calibration Techniques to Simultaneous Spectrophotometric Determination of Copper and Iron Using 1‐(2‐Pyridylazo)‐2‐naphthol in AOT Micellar Solution

Multivariate calibration models (PCR and PLS) were developed for simultaneous determination of Fe(III) and Cu(II) with 1‐(2‐pyridylazo)‐2‐naphthol and AOT as chromogenic reagent and micellizing agent, respectively. In the presence of AOT the spectrum of Fe(III)‐PAN complex was shifted to higher wavelength and the overlapping with Cu‐PAN spectrum decreased. It seems that this anionic surfactant enters the structure of the Fe‐PAN complex to cause a shift in the absorption spectrum of it. The parameters controlling behavior of the systems were investigated and optimum conditions were selected. Sixteen ternary mixtures were selected as the calibration set. To select the number of factors in PCR and PLS algorithms, a cross validation method, leaving out one sample at a time, was employed. The calibration models were validated with 8 synthetic mixtures containing the metal ions in different proportions that were randomly designed. The best calibration model was obtained by using PLS regression. The method was successfully applied to simultaneous determination of copper and iron in biological samples.     

Simultaneous spectrophotometric determination of phenanthridine, phenanthridinone and phenanthridine N-oxide using multivariate calibration methods

The multivariate calibration methods, partial least squares (PLS) and principle component regression (PCR) have been used to determine phenanthridine, phenanthridinone and phenanthridine N-oxide in spiked human plasma samples. Resolution of binary and ternary mixtures of analytes with minimum sample pre-treatment and without analyte separation has been successfully achieved analyzing the UV spectral data. The net analyte signal (NAS) concept was also used to calculate multivariate analytical figures of merit such as limit of detection, selectivity and sensitivity. The simultaneous determination of three analytes was possible by PLS and PCR processing of sample absorbance in the 210–355 nm region. Good recoveries were obtained for both synthetic mixtures and spiked human plasma samples.     

Layer model approach to background correction in r.f.‐GDOES

Two methods are presented for dealing with variable background signals in radiofrequency glow discharge optical emission spectroscopy (r.f.‐GDOES). Their aim is to improve elemental analysis at trace levels, in bulk analysis or in compositional depth profiling, without having to measure background signals during the analysis. Each method uses background signals measured away from the analytical emission lines of interest during calibration only. The background signal is first determined during calibration for each material type of interest. During analysis in the first method the estimated background signal is varied according to the material type being analysed. In depth profiles this means identifying the various layers present as different material types, hence the name ‘layer model’. The second method is a more conventional approach, where part of the background signal is estimated as a spectral interference. Results are presented for the bulk analysis of a tool steel and for two depth profiles: TiO₂ coating on silicon and TiN‐coated tool steel. The two methods give similar results in the depth profiles, both significantly better than with a constant background. Copyright © 2004 John Wiley & Sons, Ltd.     

Quality control of pharmaceuticals with NIR: From lab to process line

This work describes a general framework for assessing the active pharmaceutical ingredient (API) and excipient concentrations simultaneously in pharmaceutical dosage forms based on laboratory-scale measurements. The work explores the comprehensive development of a near infrared (NIR) analytical protocol for the quantification of the API and excipients of a pharmaceutical formulation. The samples were based on a paracetamol (API) formulation with three excipients: microcrystalline cellulose, talc, and magnesium stearate. The developed method was based on laboratory-scale samples as calibration samples and pilot-scale samples (powders and tablets) as model test samples. Both types of samples were produced according to an experimental design. The samples were measured in reflectance mode in a Fourier-transform NIR spectrometer. Additionally, a new method for determining the minimum number of calibration samples was proposed. It was concluded that the use of laboratory-scale samples to construct the calibration set is an effective way to ensure the concentration variability in the development of calibration models for industrial applications. With this method, both API and excipients can be determined in high-throughput applications in the pharmaceutical industry.     

Influence of the procedure used to prepare the calibration sample set on the performance of near infrared spectroscopy in quantitative pharmaceutical analyses

Calibrating near infrared diffuse reflectance spectroscopy (NIRS) methods usually involves preparing a set of samples with a view to expanding the analyte concentration range spanned by production samples. In this work, the performances of the two procedures most frequently used for this purpose in near infrared pharmaceutical analysis, viz., synthetic samples obtained by weighing of the pure constituents of the pharmaceutical and doped samples made by under- or overdosing previously powdered production samples, were compared. Both procedures were found to provide similar results in the quantification of the active compound in the pharmaceutical, which was determined with a relative standard error of prediction (RSEP) of < 1.6%. However, the two types of sample preparation provide different spectra, which precludes the accurate quantification of synthetic samples from calibrations obtained with doped samples and vice versa. None of the mathematical pre-treatments tested with a view to reducing this different scattering (viz., second derivative, standard normal variate and orthogonal signal correction) could effectively solve this problem. This hinders accurate validation of the linearity of the procedure and makes it advisable to use doped samples which are markedly less different to production samples.     

Novel Approach to Two-Component Analysis Based on the Generalized Calibration Strategy

The generalized calibration strategy (GCS), developed and previously applied to chemical analysis, has been adapted to two-component (2C) analysis. According to the 2C-GCS procedure, a set of 10 calibration solutions containing a sample and standards of two analytes in well-defined composition was diluted. The measurements performed at a given dilution stage allow the concentration of both analytes in a sample to be evaluated with six apparent concentrations calculated with various mathematical approaches. As a result, the method allows the detection, examination, and elimination of nonlinear and interference effects with multiplicative and additive characteristics. To perform 2C-GCS automatically and effectively, a dedicated flow sequential injection system was designed to be fully controlled by a computer. Caffeine and paracetamol were determined in synthetic and pharmaceutical samples using this calibration approach. The analytes were determined with good precision and accuracy with low consumption of sample and standard solutions. On the basis of this experimental model, the influence of effects and tendencies in the examined analytical system was detected and evaluated.     

Naked‐Eye Readout of Analyte‐Induced NIR Fluorescence Responses by an Initiation–Input–Transduction Nanoplatform

Fluorescence visualization (FV) in the near‐infrared (NIR) window promises to break through the signal‐to‐background ratio (SBR) bottleneck of traditional visible‐light‐driven FV methods. However, straightforward NIR‐FV has not been realized, owing to the lack of methods to readily transduce NIR responses into instrument‐free, naked eye‐recognizable outputs. Now, an initiation–input–transduction platform comprising a well‐designed NIR fluorophore as the signal initiator and lanthanide‐doped nanocrystals as the transducer for facile NIR‐FV is presented. The analyte‐induced off–on NIR signal serves as a sensitizing switch of transducer visible luminescence for naked‐eye readout. The design is demonstrated for portable, quantitative detection of phosgene with significantly improved SBR and sensitivity. By further exploration of initiators, this strategy holds promise to create advanced NIR‐FV probes for broad sensing applications.     

Characterisation of a Platinum‐based Electrochemical Biosensor for Real‐time Neurochemical Analysis of Choline

A choline biosensor was characterised in detail to determine the effects of physiologically relevant parameters on the ability of the sensor to reliably detect neurochemical changes in choline. This first generation Pt‐based polymer enzyme composite sensor displayed excellent shelf‐life and biocompatibility with no significant decrease in choline sensitivity observed following 14 days of storage dry, or in ex‐vivo rodent brain tissue. However, subjecting the sensor to repeated calibrations and storage over the same period resulted in significant decreases (20–70 %) due to enzyme denaturation associated with the repeated calibration and storage cycles. Potential interference signals generated by the principal electroactive interferents present in the brain were minimal; typically <1 % of the choline current response at in vivo levels. Additionally, changing temperature over the physiologically relevant range of 34–40 °C had no effect on sensitivity, while increasing pH between 7.2 and 7.6 produced only a 5 % increase in signal. The limit of detection of the sensor was in the low μM range (0.11±0.02 μM), while the in vitro response time was determined to be less than the solution mixing time and within ca. 5 s, suggesting potential sub‐second in vivo response characteristics. Finally, the sensor was implanted in the striatum of freely moving rats and demonstrated reliable detection of physiological changes in choline in response to movement, and pharmacological manipulation by injection of choline chloride.     

Quantitative analysis of tea using ytterbium‐based internal standard near‐infrared spectroscopy coupled with boosting least‐squares support vector regression

The present study demonstrated the possibility of utilizing the ytterbium (Yb)‐based internal standard near‐infrared (NIR) spectroscopic measurement technique coupled with multivariate calibration for quantitative analysis of tea, including total free amino acids and total polyphenols in tea. Yb is a rare earth element aimed to compensate for the spectral variation induced by the alteration of sample quantity during the spectral measurement of the powdered samples. Boosting was invoked to be combined with least‐squares support vector regression (LS‐SVR), forming boosting least‐squares support vector regression (BLS‐SVR) for the multivariate calibration task. The results showed that the tea quality could be accurately and rapidly determined via the Yb‐based internal standard NIR spectroscopy combined with BLS‐SVR method. Moreover, the introduction of boosting drastically enhanced the performance of individual LS‐SVR, and BLS‐SVR compared favorably with partial least‐squares regression. Copyright © 2013 John Wiley & Sons, Ltd.     

NIR analysis of pharmaceutical samples without reference data: improving the calibration

Using an appropriate set of samples to construct the calibration set is crucial with a view to ensuring accurate multivariate calibration of NIR spectroscopic data. In this work, we developed and optimized a new methodology for incorporating physical variability in pharmaceutical production based on the NIR spectrum for the process. Such a spectrum contains the spectral changes caused by each treatment applied to the component mixture during the production process. The proposed methodology involves adding a set of process spectra (viz. difference spectra between those for production tablets and a laboratory mixture of identical nominal composition) to the set of laboratory samples, which span the wanted concentration range, in order to construct a calibration set incorporating all physical changes undergone by the samples in each step of the production process. The best calibration model among those tested was selected by establishing the influence of spectral pretreatments used to obtain the process spectrum and construct the calibration models, and also by determining the multiplying factor m to be applied to the process spectra in order to ensure incorporation of all variability sources into the calibration model. The specific samples to be included in the calibration set were selected by principal component analysis (PCA). To this end, the new methodology for constructing calibration sets for determining the Active Principle Ingredients (API) and excipients was applied to Irbesartan tablets and validated by application to the API and excipients of paracetamol tablets. The proposed methodology provides simple, robust calibration models for determining the different components of a pharmaceutical formulation.     

Real‐time homonuclear broadband and band‐selective decoupled pure‐shift ROESY

Unambiguous spectral assignments in ¹H solution‐state NMR are central, for accurate structural elucidation of complex molecules, which is often hampered by signal overlap, primarily because of scalar coupling multiplets, even at typical high magnetic fields. The recent advances in homodecoupling methods have shown powerful means of achieving high resolution pure‐shift ¹H spectra in 1D and also in 2D J‐correlated experiments, by effectively collapsing the multiplet structures. The present work extends these decoupling strategies to through‐space correlation experiments as well and describes two new pure‐shift ROESY pulse schemes with homodecoupling during acquisition, viz., homodecoupled broadband (HOBB)‐ROESY and homodecoupled band‐selective (HOBS)‐ROESY. Furthermore, the ROESY blocks suppress the undesired interferences of TOCSY cross peaks and other offsets. Despite the reduced signal sensitivity and prolonged experimental times, the HOBB‐ROESY is particularly useful for molecules that exhibit an extensive scalar coupling network spread over the entire ¹H chemical shift range, such as natural/synthetic organic molecules. On the other hand, the HOBS‐ROESY is useful for molecules that exhibit well‐separated chemical shift regions such as peptides (NH, Hα and side‐chain protons). The HOBS‐ROESY sensitivities are comparable with the conventional ROESY, thereby saves the experimental time significantly. The power of these pure‐shift ROESY sequences is demonstrated for two different organic molecules, wherein complex conventional ROE cross peaks are greatly simplified with high resolution and sensitivity. The enhanced resolution allows deriving possibly more numbers of ROEs with better accuracy, thereby facilitating superior means of structural characterization of medium‐size molecules. Copyright © 2014 John Wiley & Sons, Ltd.