chemometrics and pharmaceuticals

El-Gindy&Hadad: JournalofaoaCintErnationalVol.95,no.3,2012 609

Chemometrics in Pharmaceutical Analysis: An Introduction, Review, and Future PerspectivesAlAA El-Gindy and GhAdA M. hAdAdSuez Canal University, Pharmaceutical Analytical Chemistry Department, Faculty of Pharmacy, Ismailia 41522, Egypt

Guest edited as a special report on “Chemometrics in Pharmaceutical Analysis” by Łukasz Komsta.

Corresponding author’s e-mail: [email protected]: 10.5740/jaoacint.SGE_El-Gindy

SPECIAL GUEST EDITOR SECTION

Chemometrics is the application of statistical and mathematical methods to analytical data to permit maximum collection and extraction of useful information. The utility of chemometric techniques as tools enabling multidimensional calibration of selected spectroscopic, electrochemical, and chromatographic methods is demonstrated. Application of this approach mainly for interpretation of UV-Vis and near-IR (NIR) spectra, as well as for data obtained by other instrumental methods, makes identification and quantitative analysis of active substances in complex mixtures possible, especially in the analysis of pharmaceutical preparations present in the market. Such analytical work is carried out by the use of advanced chemical instruments and data processing, which has led to a need for advanced methods to design experiments, calibrate instruments, and analyze the resulting data. The purpose of this review is to describe various chemometric methods in combination with UV-Vis spectrophotometry, NIR spectroscopy, fluorescence spectroscopy, electroanalysis, chromatographic separation, and flow-injection analysis for the analysis of drugs in pharmaceutical preparations. Theoretical and practical aspects are described with pharmaceutical examples of chemometric applications. This review will concentrate on gaining an understanding of how chemometrics can be useful in the modern analytical laboratory. A selection of the most challenging problems faced in pharmaceutical analysis is presented, the potential for chemometrics is considered, and some consequent implications for utilization are discussed. The reader can refer to the citations wherever appropriate.

Advances in electronics and computing over the past 30 years have revolutionized the analytical laboratory. Technological developments have allowed instruments

to become smaller, faster, and cheaper, while continuing to increase accuracy, precision, and availability. Data analysis methods have also benefitted from advances in technical computing; commercially available mathematical programming packages allow scientists to perform complex calculations

with a few simple keystrokes. Furthermore, software sold with many commercial instruments contains automatic data-processing algorithms (e.g., Fourier transform analysis, data filtering, and peak recognition). The advances in computing allow researchers to obtain increasing amounts of chemically relevant information from their data; however, this is not always achieved using simple data-processing techniques. Svante Wold first coined the term ‘‘kemometri’’ (‘‘chemometrics’’ in English) in 1972 by combining the words kemo for chemistry and metri for measure (1). Presently, the journal Chemometrics and Intelligent Laboratory Systems defines chemometrics as ‘‘the chemical discipline that uses mathematical and statistical methods to design or select optimal procedures and experiments, and to provide maximum chemical information by analyzing chemical data’’ (2). The field of chemometrics has also benefitted from technological advances in the past 30 years, causing the number of researchers using chemometric methods to grow (3–5). Chemometrics has brought us a large number of valuable tools that allow us to resolve and display complex chemical information from often dynamic unstable systems (6–8). In general, the main areas of focus for these techniques have been multivariate calibration; pattern recognition, classification, and discriminatory analysis; and reactant and reaction process modeling and monitoring.

The purpose of this review is to describe various multivariate calibration chemometrics methods in combination with UV-Vis spectrophotometry, near-IR spectroscopy (NIRS), fluorescence spectroscopy, electroanalysis, chromatographic separation, and flow-injection analysis for the analysis of drugs in pharmaceutical preparations.

Multivariate Calibration Methods

Traditional concentration determinations are usually univariate, isolating one variable (e.g., peak current at one potential in an electrochemical measurement or the wavelength of maximum absorbance in a spectroscopic measurement). While intuitive and simple, this approach to data analysis is limited and wasteful. As an example, consider a UV-Vis spectrum of a particular analyte containing 500 data points. With only one data point being used for concentration determination (absorbance at one wavelength), after identification, 99.8% of the data will be discarded. Data collection can limit the throughput of an analytical methodology; it is not efficient to collect data that will not be used. In addition, a univariate measurement is extremely sensitive to interferents. It is often impossible to differentiate an analyte-specific signal from an interferent when looking at only one point of a data spectrum. Multivariate calibration methods involve the use of the multiple variables (e.g., the response at a range of potentials or wavelengths, or even over the entire

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range collected to calculate concentrations). This offers several advantages, often reducing noise and removing interferents (5). It can be easier to identify and to remove noise when looking at the entire data set, rather than one point. In addition, interferents can be taken into account, provided their measurement profile differs sufficiently from the analyte of interest (9). Multivariate methods are generally better than univariate methods. They increase the amount of possible information that can be obtained without loss; multivariate models can always be simplified to a univariate model (5). The advantages of multivariate methods come at a cost of computational power and complexity, but these drawbacks are easily handled with common mathematical software packages (e.g., Matlab).

Classical Least Squares (CLS)

CLS involves the application of multiple linear regression (MLR) to the classical expression of the Beer-Lambert law of spectroscopy:

A = KC (or dA/dλ = KC)

where the matrixes A and dA/dλ represent the zero-order absorbance and derivative absorbance matrixes, respectively; C is the concentration matrix; and K is the calibration coefficient matrix (10). The CLS technique can only be applied to systems where every constituent in the sample is known. If there is the possibility of contaminants in the (unknown) samples that were not present in the calibration mixtures, the model will not be able to predict the constituent concentrations accurately.

Inverse Least Squares (ILS)

ILS, sometimes known as P-matrix calibration, is called this because it originally involves the application of MLR to the inverse expression of the Beer-Lambert law of spectroscopy:

C = PA (or C = P × dA/dλ)

where the matrixes A and dA/dλ represent the zero-order absorbance and derivative absorbance matrixes, respectively; C is the concentration matrix; and P is the calibration coefficient matrix (10). Since it is not necessary to know the composition of the training mixtures beyond the constituents of interest, the ILS method is better suited to more complex types of analyses not handled by CLS. Disadvantages of the ILS method are that wavelength selection can be difficult and time-consuming, the number of wavelengths used in the model is limited by the number of calibration samples, and a large number of samples are required for accurate calibration.

Principal Component Regression (PCR) and Partial Least Squares Regression (PLS)

Among the different regression methods available for multivariate calibration, the factor analysis-based methods, including PLS and PCR, have received considerable attention in the chemometrics literature (11–18). PLS and PCR can be used directly for ill conditioned data by extracting the latent variables (factors). The number of latent variables is lower than the number of objects. These techniques are powerful multivariate

statistical tools that have been successfully and widely applied to the quantitative analysis of spectroscopic data because of their ability to overcome problems common to this data such as collinearity, band overlaps and interactions, and the ease of their implementation due to the availability of software. Here, only a brief introduction about PCR and PLS is given as the techniques are routinely used.

PCR is a widely used regression model for data having a large degree of covariance in the independent or predictor variables or where ill-conditioned matrixes are present. Instead of regressing the concentrations of a measurement system onto the original measured variables spectrum, PCR implements a principal component analysis (PCA) decomposition of the spectrum X data before regressing the concentrations information onto the principal component scores (19, 20). Some vectors having small magnitude are omitted to avoid the collinearity problem. PCR solves this by elimination of lower ranked principal components, which in turn reduces noise (error) present within the system.

PLS regression is related to both PCR and MLR. PCR aims to find the factors that capture most of the variance within the data before regression onto the concentration variables, whereas MLR seeks a single factor that correlates both the data and their concentrations. PLS attempts to maximize the covariance, thus capturing the variance and correlating the data together. As PLS searches for the factor space most congruent to both matrixes, its predictions are far superior to PCR (21). PCR and PLS techniques share many similarities, and the theoretical relationships between them has been covered extensively in the literature (11, 12, 13, 15, 18, 22, 23). PLS and PCR perform data decomposition into spectral loadings and scores prior to model building with the aid of these new variables. In PCR, the data decomposition is done using only spectral information, while PLS uses spectral and concentration data. Historically, PCR predates PLS. However, since its introduction, PLS appears, by most accounts, to have become the method of choice among chemists. On the other hand, the literature survey made by Wentzell and Vega-Montoto (24) surprisingly found that a few cases that indicated PLS gave better results than PCR, and a greater number of studies indicated no real difference in performance (22–24). In addition, by generic simulation of complex mixtures, Wentzell and Vega-Montoto concluded that in all of the simulations carried out, except when artificial constraints were placed on the number of latent variables retained, no significant differences were reported in the prediction errors reported by PCR and PLS (24). PLS almost always required fewer latent variables than PCR, but this did not appear to influence predictive ability. This statement has been also confirmed by the others (12, 17, 22, 23). However, global models, such as PLS, implicitly endeavor to include the variation due to external effects in the model, in much the same way as unknown chemical interferences can be included in an inverse calibration model. Provided the interfering variation is present in the calibration set, an inverse calibration model can, in the ideal case of additively and linearity, easily correct for the variation due to unknown interferences. It is assumed in global calibration models that the new sources of spectral variation can be modeled by including a limited number of additional PLS factors. Owing to increase in the calibration model’s dimensionality, it becomes necessary to measure a large number of samples under changing conditions in order to make a good estimation of the additional parameters. When


highly nonlinear effects are present in the spectra, many additional PLS (25) factors are necessary to model the spectral differences, and occasionally, it is not possible to model these spectral differences.

Artificial Neural Networks (ANNs)

The calibration problem is normally thought to be a linear one. However, Long et al. (26) found that the calibration becomes nonlinear when high levels of noise are present. In this case, an ANN approach can provide better prediction results. ANNs were originally designed to mimic the function of the human brain. They consist of a number of simple processing units (or neurons) linked by weighted modifiable interconnections. ANNs have been developed for quantitative analysis of samples during the last decade. Compared with MLR, ANN is a more flexible modeling methodology, since both linear and nonlinear functions can be used (or combined) in the processing units. This allows more complex relationships between a high-dimensional descriptor space and the given retention data, and may lead to better predictive power of the resulting ANN model compared with MLR. However, the major disadvantage of ANN is also directly related to the complex model infrastructure. Compared to MLR, it suffers from the perception of being a “black box” heuristic tool. ANN models generally are more difficult to interpret. Furthermore, to get robust calibrations by ANN, the number of samples must be higher than the number of weights to be estimated, which normally implies the use of a large number of calibration samples. Before building ANNs, methods for reducing the input dimensionality by mathematical preprocessing (fast Fourier transform, PCA, and variance analysis) are often used.

Locally Weighted Regression (LWR)

LWR applies PCR or PLS combined with a weighting scheme such that calibration samples closest to the sample to be predicted are given higher weight. Many variants are possible and the variant that probably should be preferred is one that has PLS for all samples with equal weights as the limiting case. In that case, when the data are linear and not clustered, the local method automatically becomes a global method. LWR was shown to perform well when clustered or nonlinear data were analyzed, but it has not been studied to the same extent as the preceding methods, so fewer diagnostics are available, and it is less well-known in which cases the method should be preferred or avoided. One disadvantage is that it is more time-consuming than other methods, because it requires that several sets of latent variables be determined. There also are indications that it is less robust towards wavelength shifts than other methods.

Radial Basis Functions (RBF) Combined with PLS

RBF-PLS is a local method. It seems to perform particularly well for difficult data structures. Too little is known, however, about its practical use. It is not clear yet in which exact circumstances it works well and what pitfalls may occur.

Other Multivariate Calibration Methods

Many other multivariate calibration methods were tried out, namely nonlinear variants of PLS, PCR, and MLR, nearest-neighbor methods, methods in which the regression is carried out on Fourier coefficients or wavelets. Some of these do not yield good results, several others perform equally well as (some of) the methods selected, but are less easy to understand or are less generally used. For this reason, they are not recommended for users who are not experienced in chemometrics.

Variable Selection Methods

One of the main features of multivariate regression techniques such as PLS or PCR is the generation of a model that will minimize the influence of variables that do not positively contribute to the model, while maximizing the contribution of variables that provide useful information. Selection of such variables is important (27–31) as the presence of a large number of unwanted variables in spectral data will contribute considerably to the error component and hence the predictive capability of the model. This situation is common with spectral data, where a large number of variables (i.e., wavelengths) exist, of which a large subset contains little or no real information (i.e., regions of no spectral response). In such circumstances, the application of a variable selection technique to identify information rich regions of the spectra can be extremely valuable for the selection of data appropriate for the construction of a more robust multivariate model. One possible approach to such a situation is to simply remove the variables that are information-poor (this would typically be the approach taken by the spectroscopist). However, manual deletion of variables suffers from two main flaws: there is no certainty that exactly the same section of the data will be removed every time; and removed sections may not be optimal from the point of view of the model (i.e., parts of a spectrum may not look to the eye to be information-rich, but for the model, they contain useful data). So when using this manual approach, there is a tendency to remove sections that contain either high noise or low detector response; however, such an approach can prove to be counter-productive in terms of robust model building (27–31). For example, information in the background noise can be extremely useful for establishing a robust calibration model, as noise-free spectra often have a large source of predictive error due to collinearity between neighboring wavelengths in a single peak (28, 29). The presence of a high degree of collinearity between variables in a model will tend to influence the matrix towards singularity, and this in turn will have a large influence on the coefficients generated. Furthermore, removing variables from a multivariate system can have a large impact on the corresponding coefficients, though this effect is more of a problem with methods such as MLR and PCR compared to PLS. Thus, the use of variable selection combined with PLS has considerable merit when applied to spectroscopic data in as much as it proactively enhances the robustness and predictive power of the PLS model.

Simulated Annealing (SA)

SA (32, 33) is a category of stochastic optimization algorithms first used by Kirkpatrick et al. (34) for the solution


of combinatorial optimization. It has been generalized by Bohachevsky et al. (35) for searching the global optimum on a continuous m-dimensional response surface. Thus, the search is based on an objective function defined for the problem. The search space for the SA algorithm can be constrained. The search space for the problem defines a high-dimensional surface. For a realistic number of sources and samples, the surface has numerous local minima in addition to the global minimum. SA is very attractive because of its mechanism for walking out of local optima. A typical SA step starting from a current point (Cc) generates a trial point (Ct) in its neighborhood. If the objective function value corresponding to this trial point, f(Ct), is less than that corresponding to the current point, f(Cc), then the Ct is accepted unconditionally, and the SA step is repeated. Otherwise, the Ct is accepted only with a given probability, which is dependent on a parameter, T, called the temperature. It controls the acceptance probability. The higher the value of T, the more likely that a trial solution with f(Ct) > f(Cc) is accepted. The merit of the algorithm comes from the acceptance of the detrimental state with a nonzero probability. It is this biased random walk that provides a chance to escape from any possible local minimum. The process of generating a Ct and making it the Cc if it is accepted is repeated until there is no change in the best objective function value obtained for a given number of successive steps, Ns. At this time, the process is considered to be at a steady state. When this steady state is reached, the temperature, T, is lowered by a factor Tf, 0 < Tf < 1. Again, the SA step is applied at the new temperature. The algorithm is stopped when the temperature is reduced to the size necessary for obtaining sufficient precision of the source contribution estimates in terms of the mixing fractions. The corresponding stopping criterion can be expressed by a predefined maximum number of steps for lowering the temperature, Nm. The detailed description of the algorithm is given by Song and Hopke (36). The performance of SA is influenced by the parameters T, Tf, Ns, and Nm. For different data sets, they may have different values in order to give satisfactory performance. SA has been applied to parameter estimation in linear and nonlinear models (37) and for feature selection (38).

Genetic Algorithm (GA)

GAs (39) were developed by Holland (40) as part of the study of adaptive processes. It is different from deterministic approaches in that the genetic algorithm tries to mimic the probabilistic evolutionary process in nature. The procedure builds a random population of strings, each of which represents one possible solution to the problem being investigated. In general, such a string can be a simple bit sequence, a vector of sequence numbers, or any other suitable linear representation of the parameters of the problem to be optimized. For each member of the population, a fitness value is calculated by transferring it to the function to be optimized. This fitness value determines the string’s relative position within all members of the population regarding their closeness to their optimum value. A new generation of values is then generated from copies of the strings of the old population, considering their relative fitness. Strings with fitness higher than the average are copied more times than strings with lower values. As an iterative application of this reproduction rule, it would only select the best string from the initial population. Two innovative features

are therefore introduced that change the values of arbitrarily chosen strings. A mutation event can randomly change one or more information unit of a string with a specific probability. A second change is made to some randomly chosen members of the population in which two strings are mixed by cutting them and recombining them crosswise providing that a considerable amount of information of each string remains intact. This new population then enters the next cycle and is exposed to the selective pressure; within each cycle, the string showing the highest fitness value is memorized. The process is repeated until a predefined end condition is met. It thus represents a versatile method for intelligent searching of the complex surface of solutions that may exist in the calibration problem (41–43). It has also been widely used for feature or variable selection in a variety of problems (44, 45). There have been several comparisons of the genetic algorithms with other feature selection methods (46–48). They can also be used in pattern recognition studies (49, 50). They tend to be computationally intensive, but the increasing computing power that is readily available make the GA more practical for many applications.

Other Variable Selection Methods

Several other wavelength selection methods have been used for selection of optimal set of spectral wavelength variables or regions for multivariate calibration such as single-term linear regression, multiterm regression, successive projections algorithm, and uninformative variable elimination. These algorithms work in different ways, and have been developed for different applications. It is therefore difficult to get an overview of which algorithm is best suited for a particular type of data. The user is required to select them in practice.

Applications

UV-Vis Spectrophotometry

UV-Vis spectrophotometry is a rapid, inexpensive analytical technique; therefore, it is highly suitable to control analysis of pharmaceutical preparations containing components that absorb in the UV region. However, the lack of specificity of UV-Vis absorption hinders application in the presence of overlap between bands of different components. The development of MLR and factor-based techniques have enabled the application of UV-Vis spectrophotometry to the analysis of complex mixtures without the need for a prior separation. In this overview, we illustrate the contributions of chemometrics to UV-Vis spectrophotometry, which have been successfully applied for pharmaceutical analysis (Table 1).

A good example for application of chemometry to UV spectra is the use of PLS-1 and PCR to resolve two multicomponent mixtures containing dextromethorphane hydrobromide, phenylephrine hydrochloride, chlorpheniramine maleate, methylparaben, and propylparaben, together with either sodium benzoate (Mix 1) or ephedrine hydrochloride and benzoic acid (Mix 2; 92). The absorbance data in the UV spectra were measured for the 76 or 71 wavelength points in the spectral region 210–240 or 210–224 nm considering the intervals of ∆λ = 0.4 or 0.2 nm for Mix 1 and Mix 2, respectively. Six latent variables for PLS-1 and six principal components for PCR (Mix 1), and seven latent variables for PLS-1 and seven principal components


Table 1. Application of chemometrics and UV-visible spectrophotometry for analysis of pharmaceuticals

Analyte Sample form Regression methoda Ref.

Telmisartan and hydrochlorothiazide Tablet PLS-1 and PCR 51

Ezetimibe and simvastatin Tablet CLS 52

Amoxicillin trihydrate and sodium diclofenac Tablet PLS-1 53

Caffeine, mepyramine, phenylpropanolamine, and pheniramine Tablet PCA and ANN 54

Diclofenac potassium and methocarbamol Tablet CLS, PCR, PLS, (RBF-ANN) 55

Losartan potassium, amlodipine besilate, and hydrochlorothiazide Tablet CLS, PCR, PLS, MLR 56

Triamterene and xipamide Tablet CLS, PCR, PLS 57

Tazarotene Gel PCR, PLS 58

Pyridoxine hydrochloride and isoniazid Tablet PCR, PLS 59

Dienogest and estradiol valerate Tablets PCR, PLS 60

Drotaverine hydrochloride, caffeine, and paracetamol Tablets PCR, PLS-1 61

Drotaverine hydrochloride, metronidazole, and diloxanide furoate Tablets PCR, PLS-1 61

Hydrochlorothiazide and spironolactone Tablets PLS, GA-PLS 62

Acetaminophen and ascorbic acid Pharmaceutical products, human serum, and urine

PCR, PLS 63

Metformin, pioglitazone, and pioglitazone acid degradate Tablets CLS, PCR, and PLS-2 64

Pyritinol dihydrochloride Tablets CLS, PCR, and PLS 65

Fat- and water-soluble vitamins in complex mixtures Multivitamin drugs, food addi-tives, and energy drinks

Component analysis algorithm (MILCA) 66

Oxybutynin hydrochloride Tablets and syrup PCR, PLS 67

Chlorpheniramine maleate enantiomers Enantiomers PLS 68

Nebivolol and hydrochlorothiazide Tablets PCR, PLS 69

Diflunisal and naproxen Tablets and suppositories CLS, PLS-1, and PCR 70, 71

Paracetamol, propiphenazone, caffeine, and thiamine Tablets PCR, PLS, and ANN 72

Rabeprazole Tablets CLS, PLS, and PCR 73

Clopidogrel bisulfate and aspirin Tablets ILS, CLS 74

Carbidopa, levodopa, and methyldopa Pharmaceutical samples and human serum

PLS, ANN 75

Paracetamol, ibuprofen, and caffeine Capsules PLS, GA-PLS, PC-ANN 76

Cilostazol Tablets CLS, PLS 77

Nifuroxazide and drotaverine hydrochloride Capsules CLS, PLS, and PCR 78

Atorvastatin calcium and fenofibrate Tablets CLS, ILS, PLS, and PCR 79

Norfloxacin and tinidazole erythromycin and trimethoprim. Tablets and oral suspension CLS and PCR 80

Bisacodyl in the presence of its degradation products Tablets and suppositories CLS, PLS, and PCR 81

Naproxen sodium and pseudoephedrine hydrochloride Tablets CLS, PLS, and PCR 82

Theophylline anhydrous, guaifenesin, diphenhydramine hydrochloride, methylparaben, propylparaben, and sodium benzoate

Syrup PCR and PLS-1 83

Caffeine, 8-chlorotheophylline, and chlorphenoxamine hydrochloride

Tablets and suppositories PLS and PCR 84

Mebeverine hydrochloride and sulpiride Tablets CLS 85

Theophylline Syrup PLS 86

Diprophylline, phenobarbitone, and papaverine hydrochloride Tablets PCR and PLS-1 87

Acetaminophen and diclofenac Tablets PLS-1 88

Chlorpheniramine maleate, phenylpropanolamine hydrochloride, ibuprofen, and caffeine

Tablets PCR and PLS-1 89

Chlorpheniramine maleate, phenylpropanolamine hydrochloride, and propyphenazone

Tablets and capsules PCR and PLS-1 89

Diprophylline, guaifenesin, methylparaben, and propylparaben Syrup PCR and PLS-1 90

Clobutinol, orciprenaline, saccharin sodium, and sodium benzoate Syrup PCR and PLS-1 90

Ambroxol and doxycycline Capsule CLS, PCR, and PLS-1 91


for PCR (Mix 2) were found to be optimum for resolving such spectral overlap and to determine each component.

NIRS

NIRS covers the transition from the visible spectral range to the mid-IR region. In the NIR region (800–2500 nm, or 12 821–4000 cm−1; 110), mainly vibrations of –CH, –OH, –SH, and –NH bonds are observed. All the absorption bands are the results of overtones or combinations of the fundamental mid-IR bands (111). NIRS is a fast and nondestructive analytical method. Associated with chemometrics, it becomes a powerful tool for the pharmaceutical industry. Indeed, NIRS is suitable for analysis of solid, liquid, and biotechnological pharmaceutical forms. Moreover, NIRS can be implemented during pharmaceutical development, in production for process monitoring, or in QC laboratories. NIRS is generally chosen for its speed, its low cost and its nondestructive characteristic towards the analyzed sample. NIR spectra are difficult to interpret. Therefore, the use of chemometrics is required.

A review of NIRS in pharmaceutical technologies classified

the pharmaceutical applications of NIRS and chemometrics into two classes: qualitative analyses and classifications, and quantitative applications (112).

(a) Qualitative analyses, identification, and classifications.—Qualitative analysis means classification of samples according to their NIR spectra. NIR spectral identifications are based on pattern recognition methods. Applications of pattern recognition methodologies within chemistry (113), biology (114), and food sciences (115) are important. The classification techniques can be divided into two categories: unsupervised and supervised. In the unsupervised classification, samples are classified without prior knowledge, except the spectra. Then the spectroscopist needs to explain these clusters. For supervised pattern recognition a prior knowledge, i.e., the category membership of samples, is required. Thus, the classification model is developed on a training set of samples with known categories (116). Then the model performance is evaluated by comparing the classification predictions to the true categories of the validation samples. The pharmaceutical applications in the field of qualitative analyses can be presented as follows:

(1) Analysis of starting materials.—The identification of

Table 1. (continued)


Dextromethorphane hydrobromide, phenylephrine hydrochloride, chlorpheniramine maleate, methylparaben, propylparaben, and sodium benzoate


Dextromethorphane hydrobromide, phenylephrine hydrochloride, chlorpheniramine maleate, methylparaben, propylparaben, ephedrine hydrochloride, and benzoic acid


Guiafenesin, dextromethorphane hydrobromide, phenylephrine hydrochloride, chlorpheniramine maleate, butylparaben, and sodium benzoate


Diphenhydramine, dextromethorphane hydrobromide, ephedrine hydrochloride, guiafenesin, and sodium benzoate


Atenolol, amiloride hydrochloride, and chlorthalidone Tablets PCR and PLS-1 94

Perphenazine, amitriptyline hydrochloride, and imipramine hydrochloride

Tablets PLS 95

Trimethoprim combined with sulfamethoxazole or sulfamethazine or sulfafurazole

Tablets PLS 96

Cyproheptadine hydrochloride, thiamine hydrochloride, riboflavin- 5-phosphate sodium dihydrate, nicotinamide, pyridoxine hydrochloride, and sorbic acid


Pseudoephedrine hydrochloride and ibuprofen Tablets CLS, ILS, PCR, and PLS-1 98

Amiloride hydrochloride, atenolol, hydrochlorothiazide, and timolol maleate

Tablets CLS, PCR, and PLS-1 99,100

Hydrochlorothiazide and spironolactone Tablets CLS, ILS, PCR, and PLS-1 101

Cyproterone acetate and estradiol valerate Tablets CLS, ILS 102

Cilazapril and hydrochlorothiazide Tablets CLS, ILS, PCR, and PLS-1 103

Mefenamic acid and paracetamol Tablets CLS, ILS, PCR 104

Chlorphenoxamine hydrochloride and caffeine Tablets CLS, ILS 105

Metamizol, acetaminophen, and caffeine Tablets ILS, PCA 106

Triamterene and hydrochlorothiazide Tablets PCR and PLS-1 107

Six amino acids Lab prepared mixture Linear neural network 108

Benazepril hydrochloride and hydrochlorothiazide Tablets PCR and PLS 109a ALS = Alternating least squares algorithm; BP-ANN = back propagation artificial neural network; GA-PLS = genetic algorithm partial least squares;

MILCA = mutual information least-dependent component analysis; RBF-ANN = radial basis function-artificial neural network.


incoming raw materials is now a common NIRS application (117) due to the minimal sample preparation. A lot of publications describe this kind of application because NIRS can be applied to control excipients, active pharmaceutical ingredients (APIs), and final products. Ulmschneider et al. (118–121) applied NIRS to identify different types of starches, sugars, celluloses, intermediates, and active ingredients with PCA and the cluster calibration module of Nircal® software (Büchi AG, Switzerland). NIRS was applied to differentiate between the different Avicel products (FMC BioPolymer, Philadelphia, PA; microcrystalline celluloses PH-101, 102, and 200; 122). The discrimination of celluloses (123) is statistically significant. Cellulose ethers were identified by NIRS. Different types of polyvinylpyrrolidones (povidones) are characterized by their viscosity measured in water. Kreft et al. (124) developed an NIRS method using soft independent modeling of class analogy for the determination of the povidone types. The identification of raw material can be performed directly upon reception in the warehouse or during the dispensing.

(2) Tablets.—A method was developed for the identification of illegal ecstasy tablets (125). The main identified substances were N-methyl-3,4-methylendioxyamphetamine, N-ethyl-3,4- methylendioxyamphetamine, and amphetamine. Discrimination of the substances in tablet matrixes was possible. Transmission NIRS combined with chemometric methods can also be applied for identity confirmation of clinical trial tablets (126). Tablet identification is commonly performed by NIRS in QC laboratories.

Polymorphism

The ability of a substance to occur in different crystalline forms is called polymorphism. The solid-state properties have an influence on the stability and dissolution properties of the pharmaceutical product. Moreover, fast analytical methods need to be implemented to help the galenical production. IR and Raman spectroscopies have been applied successfully to characterize API polymorphic forms. NIRS is also an analytical tool to solve this pharmaceutical issue (112). The processing of NIR spectra provides information concerning the crystalline form of miokamycin (127). NIR could increase the understanding of physical forms of theophylline (128). The characterization and the analysis of azithromicin, an antibiotic derived from erythromycin A, was studied by Blanco et al. (129).

Quantitative Analyses of Pharmaceutical Preparations

Many studies have been published during the last few years concerning determination of chemical compound content such as APIs, excipients, or moisture in pharmaceuticals. Many of the studies are presented here. Samples can be of various types, e.g., powders, granules, tablets, liquids, gels, films, or lyophilized vials (112). One original study has shown the determination of ethanol, propylene glycol and water directly through amber plastic bottles (130). NIRS is used for the quantitative determination of APIs, excipients, moisture, or coating thickness. Available literature about application of NIRS in the analysis of pharmaceutical compounds is presented in Table 2.

NIRS, in combination with PLS-1, was used for the simultaneous determination of the active principles

paracetamol, ascorbic acid, dextromethorphan hydrobromide, caffeine, and chlorpheniramine maleate in a pharmaceutical preparation (152). The method was applicable over a wide analyte concentration range (0.04–6.50%, w/w). The method required careful selection of the calibration set and thorough homogenization of the product.

Fluorescence Spectroscopy

Fluorescence spectroscopy is widely used in quantitative analysis because of its great sensitivity and selectivity as well as its relatively low cost. This technique has not, however, been widely applied to the simultaneous direct determination of several fluorescent components in mixtures, mainly because the fluorescence spectra of individual substances contain broad bands that often overlap. Several methods have been proposed to resolve such problems without manipulation of the samples or using time-consuming and highly expensive separation techniques (169). Due to the ability of chemometric methods to resolve the complex systems, they were developed for simultaneous determination of various mixtures. Table 3 summarizes the application of chemometrics and fluorescence spectroscopy for analysis of pharmaceuticals.

A good example for application of chemometry to emission fluorescence spectra is the use of PLS to determine flufenamic, mefenamic, and meclofenamic acids in mixtures (173). The emission fluorescence spectra between 370 and 550 nm with an excitation wavelength of 352 nm were recorded. The method applied PLS multivariate calibration to the resolution of this mixture using a set of wavelengths previously selected by Kohonen ANN.

Electroanalysis

Electroanalysis has long benefited from well-established techniques, such as potentiometric titrations, polarography, and voltammetry, and the more novel ones, such as electronic tongues and noses, which have enlarged the scope of applications. The electroanalytical methods have been improved with the application of chemometrics for simultaneous quantitative prediction of analytes or qualitative resolution of complex overlapping responses. Typical methods include PLS, ANNs, and multiple curve resolution methods.

Many electrochemical methods, especially voltammetric and polarographic techniques, have been described for application in analysis of pharmaceuticals and related materials. Pharmaceutical preparations are complex, often consisting of several drugs mixed in different benign matrixes; thus, the response profiles from voltammetric and polarographic measurements often consist of many overlapping signals. The use of chemometrics becomes essential in order to resolve the composite signals and facilitate the prediction of the component drugs in a preparation. In this overview, we illustrate the contributions of chemometrics to electroanalysis, which have been successfully applied for pharmaceuticals analysis (Table 4).

One example demonstrating the resolving power of chemometry in electroanalysis was the application of a PLS calibration method for the simultaneous voltammetric determination of indomethacin, acemethacin, piroxicam, and tenoxicam (192). It was possible to resolve complex mixtures


of analytes even when they had strongly overlapped signals. The method was applied to the electrochemical reduction region of four anti-inflammatory drugs and allowed the drugs to be quantified at concentrations between 0.52 and 4.09 μg/mL for acemethacin, 0.44 and 3.50 μg/mL for indomethacin, 0.43 and 3.40 μg/mL for piroxicam, and 0.42 and 3.30 μg/mL for tenoxicam with good results.

Chromatographic Separations

Most traditional chromatographic separation criteria or response functions are defined on chromatograms recorded by single channel detectors, e.g., a spectrometer measuring the absorbance at a single wavelength or a thermal conductivity detector. When the peaks are seriously overlapped, usually there is a lack of the information concerning the total number

Table 2. Application of chemometrics and NIRS for analysis of pharmaceuticals


Aspirin Suppository and tablets PLS-MCR-ALS 131, 132

Acetaminophen Syrup PLS 133

Acetaminophen and caffeine anhydrate Tablets PLS 134

Chlorogenic acid, caffeic acid, luteoloside, baicalin, ursodesoxycholic acid, and chenodeoxycholic acid

Injection PLS 135

Phenolic acids Radix Salvia Miltrorrhiza extract solutions PLS 136

Diphenhydramine hydrochloride Pharmaceutical wafers PLS-1 137

Rifampicin, isoniazide, and pyrazinamide Tablets PLS 138

Ampicillin Raw material O-PLS combined with ANN 139

Caffeine anhydrate Tablets PLS 140, 141

Ticlopidine hydrochloride Tablets PLS 142

Amoxicillin Raw material PLS-PCR-ANN 143

Aspirin and phenacetin Tablets PC-ANNs-RBF-ANN 144, 145

Erythromycin ethylsuccinate Raw material RBF-ANN 146

Cefoperazone sodium Raw material PLS 147

Econazole nitrate estradiol Human skin One-point net analyte signal multivariate calibration

148

Metronidazole Raw material ANNs 149

Econazole nitrate 4-cyanophenol Guinea pig skin PCR 150

Roxithromycin and erythromycin ethylsuccinate Tablets PLS-1 151

Paracetamol, ascorbic acid, dextrometorphan hydrobromide, caffeine, and chlorpheniramine maleate

Granules in single-dose bag PLS-1 152

Aminopyrine and phenacetin Tablets PC-ANNs 153

Acetaminophen and vitamin C Tablets PC-ANNs 154

Paracetamol and amantadine hydrochloride Tablets ANNs 155

Testosterone Thin-film composites PCR 156

Selamectin Topical formulations PLS 157

Vitamin C Food and pharmaceutical products PLS 158

Cineol Eucalyptus oil MLR 159

Oxytetracycline Oxytetracycline base PLS, PCR 160

Ketoprofen Translucent gel MLR, PLS 161

Clotrimazole Extruded film PLS 162

Metformin Tablets PLS 163

Steroid Tablets PLS 164

Gemfibrozil Tablets PLS 165

Ibuprofen Tablets PLS 166

Dexeketoprofen Hydrogel PLS 167

Mirtazapine Tablets PLS 168a MCR-ALS = Multivariate curve resolution-alternating least squares; O-PLS = orthogonal projection to latent structures; PC-ANNs = principal compo-

nent artificial neural networks; RBF-ANN = radial basis function-artificial neural network.


of chemical components, overlap degree of the peaks, and peak purity. Such information characterizes some crucial aspects of a separation process, and lack of it will lead to an inaccurate and misleading evaluation of separation quality as well as some computational ambiguity for many traditional response functions. In contrast, chromatography-(multichannel) spectroscopy instruments together with chemometric methods will largely increase the information content available in chromatographic detection. Chemometric processing of chromatographic data has been used to estimate the number of

chemical components, determinate the elution sequence, and assess peak purity.

Xu et al. (200) reviewed chemometric methods devoted to estimation of the number of chemical components, determination of elution sequence, and assessment of peak purity. Also, Goicoechea et al. (201) reviewed different chemometric strategies linked to chromatographic methodologies that have been used to cope with problems related to incomplete separation, the presence of unexpected components in the sample, matrix effects, and changes in the analytical signal due to sample pretreatment.

Table 3. Application of chemometrics and fluorescence spectroscopy for analysis of pharmaceuticals

Analytes Sample form Regression methoda Ref.

Levodopa and propranolol Tap water and urine samples PC-FFNNs 170

Pyridoxine and melatonin Tablets PCR and PLS 171

Propranolol, dipyridamole, and amiloride Tablets PARAFAC 172

Flufenamic, mefenamic, and meclofenamic acids PLS 173

Naproxen, salicylic acid, and acetylsalicylic acid Pharmaceuticals and human plasma PLS 174

Salicylic acid, codeine, and pyridoxine Tablets and capsules PLS 175

Nalidixic acid and 7-hydroxymethylnalidixic acid Urine samples PCR and PLS 176

Levofloxacin, garenoxacin, and grepafloxacin Urine samples PLS and ANNs 177

Acetylsalicylic acid, codeine, and ephedrine Urine samples PLS 178

Acetylsalicylic acid metabolites Urine samples PLS 179

Nafcillin and methicillin Synthetic mixtures PLS 180

Salicylic acid and diflunisal Human serum PLS 181

Leucovorin and irinotecan Urine samples N-PLS, BLLS 182

Norfloxacin, ofloxacin, and enoxacin Urine samples PLS 183

Furosemide and triamterene Urine samples PLS 184

Galantamine Artificial and natural water samples PARAFAC, U-PLS/RBL, N-PLS/RBL 185a ANN = Artificial neural network; N-PLS = multiway partial least-squares; BLLS = bilinear least-squares; N-PLS/RBL = multidimensional partial least-

squares coupled to residual bilinearization; PARAFAC = parallel factors analysis; PC-FFNNs = principal component analysis-feed forward neural networks; U-PLS/RBL = unfolded partial least-squares coupled to residual bilinearization.

Table 4. Application of chemometrics and electroanalysis for analysis of pharmaceuticals

Analytes Sample form Electroanalytical techniquea Regression methoda Ref.

Isoniazid and rifampicin Human serum DPP PLS 186

Nalidixic acid and its main metabolite 7-hydroxy-methylnalidixic acid

Urine samples SWAdSV CLS, PLS, and ANNs 187, 188

Epinephrine and norepinephrine Biological samples CV PCR 189

Dopamine and ascorbic acid Human serum LSV CLS, PCR, and PLS 190

Enrofloxacin and ciprofloxacin Urine and capsules DPAdSV PCR 191

Anti-inflammatory drugs Lab prepared mixture DPV PLS 192

Isoniazid and hydrazine Tablets LSV GA-PLS and PC-ANN 193

Ofloxacin, norfloxacin, and ciprofloxacin Bird feedstuffs LSSV PCR, PLS, and ANN 194

Paracetamol and phenobarbital Tablets DPSV PCR and PLS 195

Chlorpromazine and promethazine hydrochloride Rabbit blood DPSV PCR and PLS 196

Ascobic acid, 4-aminophenol, and paracetamol Lab prepared mixture LSV WNN 197

Vitamins B6 and B12 Injection SWV ANNs 198

Rabeprazole sodium Tablets DPP and DPAV CLS, PCR, and PLS 199a CV = Cyclic voltammetry; DPP = differential pulse polarography; DPAdSV = differential pulse adsorptive stripping voltammetry; DPSV = differential

pulse stripping voltammetry; DPAV = differential pulse anodic voltammetry; GA-PLS = genetic algorithm partial least squares; LSV = linear sweeping voltammetry; LSSV = linear sweep stripping voltammetry; PC-ANN = principal component-artificial neural networks; SWAdSV = square wave adsorp-tive stripping voltammetry; SWV = square wave voltammetry; WNN = wavelet neural network.


Chemometric processing of chromatographic data has been used for quantitative analysis of a binary mixture of trimethoprim and sulfamethoxazole in veterinary formulations (202), and a quaternary mixture of potassium guaiacolsulfonate, guaifenesin, diphenhydramine HCl, and carbetapentane citrate in syrup preparations (203). Also, the resolution and quantitation of pyrocatechol, ascorbic acid, and epinephrine coeluting mixtures were made using multivariate curve resolution with alternating least squares (MCR-ALS) method. The method was applicable for background correction and for resolution and quantitation of coeluted analyte mixtures in LC with voltammetric detection

(204). Chemometric methods were used to both optimize the separation of nonsteroidal anti-inflammatory drugs by isocratic RP-HPLC and develop retention predictive models (205). PCA has also been used in the determination of the chromatographic peak purity, allowing, for example, the analysis of synthetic binary mixtures of the local anesthetic drugs lidocaine and prilocaine (206). PCA was used for the similarity evaluation of different samples of Flos Lonicerae and Flos Lonicerae Japonicae through a simultaneous determination of multiple types of bioactive components (207). PCA has also been used for the modeling of nonlinear chromatography under overload

Table 5. Multicomponent drug determinations by FIA based on chemometric data analysis

Analytes Sample form FIA methoda Regression methoda Ref.

Vitamins B1, B2, and B6 Vitamin formulations FIA with fluorescence detection. Spectral discrimination

ANN 210

Cytosine, inosinate, and other nucleosides

Synthetic drug mixtures and pills

pH-gradient FIA with UV detection. Spectral and pH-based discrimination

MCR-ALS 211

Ascorbic acid, dopamine, epinephrine, and dipyrone

Synthetic drug mixtures and tablets

FIA with voltammetric detection. Voltammetric discrimination

MLR 212

Amoxicillin and clavulamic acid Powders pH-gradient SIA with UV detection. Spectral and pH-based discrimination

MCR-ALS 213–215

Levodopa and benserazide Tablets Stopped-flow FIA. Reagent: KIO4. Kinetic discrimination

Multiway PLS

PARAFAC

216

Zidovudine, zalcitabine, and nevirapine

Synthetic drug mixtures

pH-gradient FIA with UV detection. Spectral and pH-based discrimination

MCR-ALS 217

Levodopa and carbidopa Tablets Stopped-flow FIA with UV detection. Reagent: Polyphenol oxidase.

Spectral discrimination

PLS 218

Ofloxacin and ciprofloxacin

Ofloxacin and norfloxacin

Pills Stopped-flow continuous-flow system with chemiluminescence detection. Reagents: [Ru(bipy)2

3+] and Ce(IV). Kinetic discrimination

PLS 219

Ascorbic acid, uric acid, and paracetamol

Synthetic drug mixtures

SIA with linear sweep voltammetry. Voltammetric discrimination

ANN 220

Loratadine and pseudoephedrin Oral solutions pH-gradient FIA UV detection. Spectral and pH-based discrimination

PLS/RBL

MCR-ALS

ANN/RBL

221

Morphine and naloxone Synthetic drug mixtures

Stopped-flow continuous-flow system with chemiluminescence detection.

Reagents: [Ru(bipy)23+], MnO4

formaldehyde. Kinetic discrimination

PLS 222

Zidovudine Plasma pH-gradient FIA with UV detection. Spectral and pH-based discrimination

MCR-ALS 223

Levodopa and carbidopa Tablets Flow-batch systems with UV detection. Reagent: polyphenol oxidase.

Spectral discrimination

MLR, PLS 224

Levodopa and beserazide Tablets Multipumping flow system with chemilumines-cence detection. Reagent: luminol.

Kinetic discrimination

PLS, ANN 225

Codeine and noscapine Syrups Stopped-flow FIA with chemiluminescence detection.

Reagents: [Ru(bipy)23+], Ce(IV),H2SO4.

Acidity-based and kinetic discrimination

PLS, multiway

PLS

226

Ciprofloxacin, norfloxacin, and ofloxacin

Human urine pH-gradient FIA with fluorescence detection. Spectral and pH-based discrimination

Unfolded PLS multiway PLS PARAFAC MCR-ALS

227

a ANN = Artificial neural network; bipy = bipyridyl; MLR = multiple linear regression; MCR-ALS = multivariate curve resolution based on alternating least squares; PARAFAC = parallel factor analysis; RBL = residual bilinearization; SIMPLISMA = simple-to-use interactive self-modeling mixture analysis.


conditions of crude erythromycin samples on columns with different stationary-phase chemistries (208).

Flow-Injection Analysis

Flow-injection analysis (FIA) and related flow techniques in combination with chemometric methods can be used to perform multicomponent determinations of drugs. Although most of the FIA applications quantitate a single target, interest in flow methods in multicomponent analysis cannot be underestimated. Flow systems contribute to achieving high sample throughput, and minimize sample and reagent consumption in automated, simple, miniaturized procedures. Selectivity for each analyte of interest often relies on physicochemical approaches (e.g., specific reagents, multiparametric detection devices, and multichannel setup). Unfortunately, the performance of these strategies is limited, and interference problems may sometimes arise. In these circumstances, chemometric methods for data analysis can be exploited to attain selectivity. In this way, FIA methods can be extended to complex matrixes from pharmaceutical, clinical, and food fields. Table 5 summarizes combination of FIA and chemometric methods for analysis of multicomponent drug mixtures (209).

One example demonstrating the resolving power of chemometry in FIA was the successful flow injection amperometric quantitation of ascorbic acid, dopamine, epinephrine, and dipyrone in mixtures (in the µg/g range) by using an array of microelectrodes with units modified by the electrodeposition of different noble metals, together with multivariate calibration analysis (212). The four groups of microelectrodes utilized included a pure gold electrode and electrodes modified by electrodeposition of platinum, palladium, or a mixture of platinum + palladium. The array of microelectrodes was inserted in a flow cell, and the amperometric data acquisition was performed with a four-channel potentiostat. The analysis of the resulting signals was carried out by a multivariate calibration method using a group of 16 standard mixtures selected by a two-level factorial design.

Conclusions

Chemometrics has advanced in parallel with advancing analytical instrumentation and computational capability. It has expanded widely from its beginnings in curve fitting and QA into a variety of other areas, including multivariate calibration, pattern recognition, and mixture resolution. However, it can be seen that the field continues to develop and adapt to new challenges. One vision of the future is that chemometrics will be at the heart of the automated laboratory. As instruments acquire data more and more rapidly, there will be the need to optimize the instrumental and interpretative functions. This review highlights the application of chemometrics to pharmaceutical analysis in conjunction with different methods, such as UV-Vis spectroscopy, NIRS, fluorescence spectroscopy, electroanalysis, chromatographic separation, and FIA. The future looks very exciting indeed, and the next decade should see more growth and development of chemometrics.

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