A review on second- and third-order multivariate calibration applied to chromatographic data

The advantages behind the efforts of performing higher-order calibration methods - A case study

BACKGROUND

Across numerous investigations delved into second- and higher-order data, an undoubted finding emerges: models based on such data can effectively exploit the second-order advantage. However, whether further benefits can be achieved by modeling data of higher dimensions remains a subject of inquiry. In this regard, a prevailing question emerges in third-order data-based applications regarding the fundamental need to increase the data dimension and, hence, the data analysis complexity. This study aims to provide meaningful evidence to support the advantages inherent in employing third-order calibration methods despite the associated efforts, such as instrumentation and data analysis complexity.

RESULTS

This study compares the analytical performance achieved using a third-order calibration method with those obtained from most of the possible second-order calibration approaches derived from the same dataset. This work delves into the structural properties of the data, modeling limitations, and analytical characteristics associated with each model. Additionally, it includes a comprehensive statistical comparison of the models based on their recovery performance. First, the outcomes demonstrate the importance of capitalizing on all available chemical information and harnessing the full potential of data to maximize its benefits. Moreover, the results provide evidence that asserts the fact that third-order calibration methods bring the opportunity to increase the number of analytes that can be simultaneously determined, notwithstanding the need for more tedious experimental protocols, specialized instrumentation (sometimes), and quite complex data analysis.

SIGNIFICANCE

this research marks the first extensive comparison of third-order data calibration models with possible second-order calibration methods. Moreover, this work pioneers the incorporation of highly challenging non-multilinear data. The advancements detailed in this study emphasize the advantages of third-order data acquisition, notwithstanding the need for more tedious experimental protocols, specialized instrumentation (sometimes), and quite complex data analysis.

Quality assessment of traditional Chinese medicine based on data fusion combined with machine learning: A review

The authenticity and quality of traditional Chinese medicine (TCM) directly impact clinical efficacy and safety. Quality assessment of traditional Chinese medicine (QATCM) is a global concern due to increased demand and shortage of resources. Recently, modern analytical technologies have been extensively investigated and utilized to analyze the chemical composition of TCM. However, a single analytical technique has some limitations, and judging the quality of TCM only from the characteristics of the components is not enough to reflect the overall view of TCM. Thus, the development of multi-source information fusion technology and machine learning (ML) has further improved QATCM. Data information from different analytical instruments can better understand the connection between herbal samples from multiple aspects. This review focuses on the use of data fusion (DF) and ML in QATCM, including chromatography, spectroscopy, and other electronic sensors. The common data structures and DF strategies are introduced, followed by ML methods, including fast-growing deep learning. Finally, DF strategies combined with ML methods are discussed and illustrated for research on applications such as source identification, species identification, and content prediction in TCM. This review demonstrates the validity and accuracy of QATCM-based DF and ML strategies and provides a reference for developing and applying QATCM methods.

The Application of Chemometrics for Efficiency Enhancement and Toxicity Reduction in Cancer Treatment with Combined Therapy

Chemometrics is an important emerging discipline with unique charm formed by the intersection of mathematics, statistics, chemistry and computer science. The application of chemometrics in the field of pharmacy has injected fresh blood into the scientific research and clinical practice of medicine and has provided a sufficient scientific basis for drug analysis and content determination to solve the problem of cancer treatment with combined therapy in different ranges. This paper introduces the basic principles, advantages and disadvantages of several commonly used pattern recognition and multidimensional correction methods of chemometrics, reviews the application of chemometrics for efficiency enhancement and toxicity reduction in cancer treatment with combined therapy and summarizes its development and prospects in the future.

Multilinear Mathematical Separation in Chromatography

Chromatography is a powerful and generally applicable method for the analytical separation and quantification of the chemical constituents in complex mixtures because chromatographic separation can provide high selectivity by isolating all analytes from interferences. Multiway analysis based on the multilinear model is an increasingly widely used method for interference-free and fast determination of the chemical constituents also in complex mixtures because multilinear mathematical separation can provide high selectivity by extracting the pure signal of the analyte from the mixed signal of a real sample. By combining chromatographic separation with mathematical separation, multiway calibration method, multiway standard additions method, and multiway internal standard method can be established. Chromatography assisted by multiway analysis can reduce the requirements for complete chromatographic separation, save elution time, and decrease the consumption of the mobile phase, particularly when the peak coelution problem is difficult to solve. This review presents the fundamentals and analytical applications of multilinear mathematical separation in chromatography.

A down-to-earth analyst view of rotational ambiguity in second-order calibration with multivariate curve resolution - a tutorial

Rotational ambiguity is a phenomenon with the potential of generating an uncertainty in the estimation of analyte concentrations in protocols based on matrix instrumental data processed by multivariate curve resolution - alternating least-squares (MCR-ALS). This is particularly relevant when the second-order advantage is to be achieved, i.e., when selected analytes are determined in unknown samples having unexpected constituents, not considered in the calibration set of samples. It is therefore imperative that analytical chemists developing second-order multivariate calibration methods using MCR-ALS acknowledge the relevance of this issue, and more importantly, have access to the required tools to size the relative impact of this potential source of uncertainty on the estimated analyte concentrations. The purpose of this tutorial is to provide a down-to-earth view of rotational ambiguity, by studying in detail a synthetic example mimicking a typical chromatographic-spectral experiment, where a set of calibration samples is joined with an unknown sample having an uncalibrated interference. After explaining the background information needed to understand the origin of the phenomenon, the available tools for the estimation of the feasible MCR-ALS solutions and the derived uncertainty on analyte predictions will be discussed. A multi-component experimental system will also be discussed, stressing the fact that rotational ambiguity uncertainties, however small, should always be estimated and reported.

Antibodies purification from human plasma using fractionation, chromatography and gel electrophoresis assisted by multivariate analysis of complimentary absorption and fluorescence spectra

Employing simple precipitation (fractionation) using Cohn method and weak anion exchange chromatography with DEAE resin, antibodies such as Immunoglobulin G are purified from human plasma. Fractions are eluted from column in four different regions depending on washing NaCl concentrations. Absorbance and excitation-emission fluorescence spectral data are measured for separated chromatographic fractions and analyzed using Multivariate Curve Resolution- Alternating Least Squares (MCR-ALS) and Parallel Factor Analysis (PARAFAC) techniques. Resolved concentration and spectral profiles provided information about existing components in each fraction. Protein and non-protein components are distinguished considering their resolved pure spectra and information from the two applied spectroscopic techniques is complementary. A number of components displayed both fluorescence and absorbance signals. When concentration of component (protein or non-protein) in sample is low and no significant absorbance signal is observed, sensitive fluorescence is useful to recognize the component and for non-fluorescent components absorbance spectra are utilized. Electrophoresis is utilized for separation of proteins in each fraction and showed that one distinguished protein from fluorescence and/or absorbance data can be a group of proteins with similar pure spectra and retention volume. Results showed presence of two protein in the first region (IgM and IgA), a group of proteins in second region (IgM, α-globulin, and IgG), a pure protein in third region (IgG), and a group of β-globulin proteins in fifth region. It is well and clearly shown that multivariate analysis of different data sets with complementary information is necessary for better interpretation of such technically simple and biochemically complicated systems.

Simultaneous Determination of Medicinal Drugs with Overlapping Profiles Contained in Low Chromatographic Resolution Data using HPLC-DAD and Multivariate Curve Resolution

Background:

The increasing demand of effective pharmaceutical products directed to fight against malaria lead to the combination of at least two antimalarial drugs. This combination aims to minimize the Plasmodium falciparum resistance which is found when the most frequently used drugs are taken individually. Within this context, proguanil hydrochloride and chloroquine phosphate which have independent modes of action are taken together to prevent malaria. This paper aims to develop a fast and powerful analytical method for the simultaneous determination of proguanil hydrochloride and chloroquine phosphate in the commercial Paludrine/Avloclor dosage forms using a multi-way chromatographic calibration based on high-performance liquid chromatography with diode array detection (HPLC-DAD) and multivariate curve resolution – alternating leastsquares (MCR-ALS).

Methods:

A rapid and powerful analytical method based on HPLC-DAD and MCR-ALS was developed for the simultaneous quantification of proguanil hydrochloride and chloroquine phosphate in the commercial Paludrine/Avloclor antimalarial drugs. An isocratic mobile phase composed by 0.2 M ammonium acetate, acetonitrile, and methanol (40:25:35) and a flow rate of 1.2 mL min-1 were employed in the chromatographic runs with an elution time about 5 min.

Results:

This approach demonstrates that chromatographic analysis may become considerably simpler and economical in terms of time, cost, and organic solvent consumption when coupled to multiway calibration models such as MCR-ALS. In fact, this multi-way chromatographic calibration based on second-order HPLC-DAD data matrices (with extremely low chromatographic resolution) and MCR-ALS allows the development of greener analytical methods for complex samples. The proposed analytical method allowed the simultaneous quantification of two antimalarial APIs present in the commercial Paludrine/Avloclor drugs with low REP values below 8% for the simultaneous determination of proguanil hydrochloride and chloroquine phosphate.

Conclusion:

The proposed multi-way chromatographic strategy can be used for routine control of pharmaceutical dosage forms. It should be highlighted that MCR-ALS allowed to: (a) achieve the second- order advantage and the quantification of analytes in the presence of uncalibrated compounds such as coeluted profile measured in different magnitude of the signal in each successive chromatographic run and significant overlapping profiles and (b) separate the contribution of several components from chromatographic runs with extremely low separation of peaks through the deconvolution of the signal obtained, performing the so-called mathematical chromatography.

Multiblock modelling on the study of the kinetic degradation of rosuvastatin calcium in the presence of retention time shifts and rank deficiency

In pharmaceutical development, forced degradation studies are mandatory before the commercialization of any drug product. They aim at identifying the possible degradation routes and the potential products that may be formed during drug product shelf life. The most widely used techniques for monitoring this in the pharmaceutical industry are hyphenated techniques such as Liquid Chromatography coupled to ultraviolet diode array detector (LC-DAD). There are however some drawbacks, such as long analysis times required for the elution of all compounds and coelution, which is not easily detected since degradation products usually have spectra very similar to that of the drug. Chemometrics methods applied to LC-DAD data are capable of solving this issue, but the approaches described in the literature first require peak alignment to solve the rank deficiency problem, which is a delicate preprocessing method for high order data. The present work describes another approach where extra information - the kinetic degradation profiles - is included for the modelling, generating a third-order data set for each sample, resulting in a four-way array (sample x retention times x spectra x degradation profile). This approach has the advantage of using the information in the third mode to solve the peak co-elution problem without the need for peak alignment among samples. With the proposed approach, it was possible to study the degradation of calcium rosuvastatin, a modern cholesterol lowering drug, using a 2 min-run, despite all the challenges in the modelling of this data. The proposed strategy was compared to an approach based on augmenting the matrix in the spectral/kinetic modes (second order modelling strategy).

Simultaneous imaging of latent fingerprint and quantification of nicotine residue by NaYF4:Yb/Tm upconversion nanoparticles

Numerous investigations have been devoted to visualizing latent fingerprints (LFPs) for personal identification in forensic investigation and age estimation. While simultaneous detection of chemicals in fingerprint residues has yet to be explored. Herein, fluorescent NaYF₄:Yb/Tm up-conversion nanoparticles (UCNPs), which can emit blue fluorescence upon 980 nm near-infrared irradiation, have been employed in the imaging of LFPs with high contrast and high sensitivity. The furrows and ridges which provide detailed information of LFP have been displayed clearly by Tm-doped UCNPs. Meanwhile, the quantitation of nicotine residue in LFPs has been achieved based on the blue fluorescence absorbed by I₂-nicotine complex, and the data was analyzed by MATLAB with modified OPTA algorithm. It was proved that the established strategy was specific, sensitive, reliable and practical toward nicotine residue in LFPs with a detection limit of 0.05 μg.

Coupling of digital image processing and three-way calibration to assist a paper-based sensor for determination of nitrite in food samples

In this work, a novel and very interesting analytical methodology based on coupling of digital image processing and three-way calibration has been developed for determination of nitrite in food samples.

Four- and five-way excitation-emission luminescence-based data acquisition and modeling for analytical applications. A review

The latest advances in both theory and experimental procedures on third-order/four-way and fourth-order/five-way calibration methods are discussed. This report is focused on excitation-emission (fluorescence and phosphorescence) matrices generation, employing different variables as the third data mode (time retention in chromatography, pH gradient, fluorescence/phosphorescence lifetime, kinetics, or other chemical treatments). Fully capitalizing on the second-order advantage, it has been possible to develop appealing analytical applications in spite of the complexity of the data. Extraction of the significant chemical information about the system under study as well as the individual abundance of the contributing constituents after proper higher-order data decomposition has allowed to analytical researchers performing quantitative analysis of complex samples. The experimental works reported up to the present are introduced and discussed in order to illustrate concepts. Throughout this work, the analytical benefits achieved by modeling third- and fourth-order data are exposed, attempting to contribute to the ongoing debate in the chemometric community regarding the existence and the true nature of the third-order advantage.

Pharmacokinetic Analysis of Four Bioactive Iridoid and Secoiridoid Glycoside Components of Radix Gentianae Macrophyllae and Their Synergistic Excretion by HPLC-DAD Combined with Second-Order Calibration

An HPLC-DAD method combined with second-order calibration based on the alternating trilinear decomposition (ATLD) algorithm with the aid of region selection was developed to simultaneously and quantitatively characterize the synergistic relationships and cumulative excretion of the four bioactive ingredients of Radix Gentianae Macrophyllae in vivo. Although the analytes spectra substantially overlapped with that of the biological matrix, the overlapping profiles between analytes and co-eluting interferences can be successfully separated and accurately quantified by the ATLD method on the basis of the strength of region selection. The proposed approach not only determined the content change but also revealed the synergistic relationships and the cumulative excretion in vivo of the four ingredients in urine and feces samples collected at different excretion time intervals. In addition, several statistical parameters were employed to evaluate the accuracy and precision of the method. Quantitative results were confirmed by HPLC-mass spectrometry. Satisfactory results indicated that the proposed approach can be utilized to investigate the pharmacokinetics of Radix Gentianae Macrophyllae excretion in vivo.

A road map for multi-way calibration models

A road map is proposed for the selection of a multi-way calibration model according to the data properties.