Journal of Pharmaceutical and Biomedical Analysis 101 (2014) 123–140

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Review

Data processing of vibrational chemical imaging for pharmaceutical applications P.-Y. Sacré ∗ , C. De Bleye, P.-F. Chavez, L. Netchacovitch, Ph. Hubert, E. Ziemons University of Liege (ULg), Department of Pharmacy, CIRM, Laboratory of Analytical Chemistry, CHU, B36, 4000 Liege, Belgium

a r t i c l e

i n f o

Article history: Received 20 February 2014 Received in revised form 8 April 2014 Accepted 9 April 2014 Available online 19 April 2014 Keywords: Hyperspectral imaging Raman Near-infrared Infrared Chemometrics

a b s t r a c t Vibrational spectroscopy (MIR, NIR and Raman) based hyperspectral imaging is one of the most powerful tools to analyze pharmaceutical preparation. Indeed, it combines the advantages of vibrational spectroscopy to imaging techniques and allows therefore the visualization of distribution of compounds or crystallization processes. However, these techniques provide a huge amount of data that must be processed to extract the relevant information. This review presents fundamental concepts of hyperspectral imaging, the basic theory of the most used chemometric tools used to pre-process, process and post-process the generated data. The last part of the present paper focuses on pharmaceutical applications of hyperspectral imaging and highlights the data processing approaches to enable the reader making the best choice among the different tools available. © 2014 Elsevier B.V. All rights reserved.

Contents 1. 2.

3.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fundamental concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. Instrumentation for chemical imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1. Configurations for chemical images acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2. Sampling and spatial resolution consideration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1. Data pre-processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2. Data processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3. Data post-processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pharmaceutical applications (see Table 1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Homogeneity of distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Size determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

124 124 124 124 124 126 126 127 131 131 131 135

Abbreviations: ANN, artificial neural networks; API, active pharmaceutical ingredient; ATR-MIR, attenuated total reflectance mid-infrared; AUC, area under the curve; BTEM, band-target entropy minimization; CCD, charged coupled device; CLS, classical least squares; DHI, distributional homogeneity index; DPFT, dark point fixed transform; DR, depth resolution; EMSC, extended multiplicative scatter correction; FWHM, full width at half maximum; ICA, independent component analysis; k-NN, k-nearest neighbors; LDA, linear discriminant analysis; LIS, linear image signature; LIS-MVA, linear image signature multivariate data analysis; MCR-ALS, multivariate curve resolution-alternating least squares; MCT, mercury cadmium telluride; MIR, mid-infrared; MLR, multilinear regression; MSC, multiplicative scatter correction; MVA, multivariate data analysis; NIR, near-infrared; OSC, orthogonal signal correction; PARAFAC, parallel factor analysis; PAT, process analytical technology; PC, principal component; PCA, principal component analysis; PLS, partial least squares regression; PLS-DA, partial least squares discriminant analysis; PMF, positive matrix factorization; PSD, particle size distribution; RGB, redgreen-blue; RMSD, root mean square difference; RMSE, root mean square error; ROI, region of interest; RPD, ratio performance deviation; RSD, relative standard deviation; SDBP, standard deviation between pixels; SECV, standard error of cross-validation; SEDDS, self-emulsifying drug delivery system; SG, Savitzky-Golay; SIMCA, soft independent modeling of class analogy; SIMPLISMA, simple-to-use interactive self-modeling mixture analysis; SISAL, simplex identification via split augmented Lagrangian; SMF, spectral match filter; SMMA, self-modeling mixture analysis; SNR, signal-to-noise ratio; SNV, standard normal variate; SVD, singular value decomposition; SVM, support vector machines; TTFA, target transformation factor analysis; XRPD, X-ray powder diffraction. ∗ Corresponding author at: Laboratory of Analytical Chemistry, CIRM, University of Liege (ULg), 4000 Liege, Belgium. Tel.: +32 43664324; fax: +32 43664317. E-mail address: [email protected] (P.-Y. Sacré). http://dx.doi.org/10.1016/j.jpba.2014.04.012 0731-7085/© 2014 Elsevier B.V. All rights reserved.

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3.3. Polymorphic form investigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4. Content uniformity studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5. Dissolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6. Counterfeit drug detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7. Process understanding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1. Introduction First developed in the environmental and remote sensing fields, chemical imaging also called hyperspectral imaging is now commonly used in a variety of sectors such as material, food, biological and pharmaceutical analysis [1]. The main interest of chemical imaging is that it combines both spatial and spectral information. It is therefore possible to observe things invisible to the naked eye such as distribution of components based on their chemical properties (different compounds, polymorphic forms, salts). The advantage of these properties appears clearly in the frame of pharmaceutical forms development and analysis. Indeed, most of the compounds used in the pharmaceutical industry are white or nearly white powders and it is impossible with naked eyes to observe the distribution of a white powder in a white powder. Since the last decades, many initiatives have been set up in the pharmaceutical industries to get more understanding of processes with the objective of quality enhancement. To achieve this goal, a lot of research has been performed mainly with vibrational spectroscopic techniques such as Near-Infrared (NIR), Raman and Attenuated Total Reflectance-Mid-Infrared (ATR-MIR) [2–5]. Obviously, chemical imaging has its role to play within this frame and has been progressively more and more used for pharmaceutical dosage forms analysis [6]. Depending on the information sought, the appropriate spectroscopic technique and the appropriate data handling should be used. Indeed, each technique has its specificities, advantages and drawbacks that must be evaluated before starting any experiment. Once obtained, the collected data will encompass a specific pretreatment and analysis depending on the information that should be retrieved and interpreted. The objective of this review is to present the most used chemical imaging techniques for pharmaceutical products analysis. Theoretical background of the most used chemometric techniques will be provided. Finally, a review of the literature concerning pharmaceutical applications of vibrational spectroscopy-based chemical imaging techniques will be presented with a focus on the specific data handling performed for each application or technique. We wrote this review to provide the reader basic guidelines to help him performing state of the art chemical imaging analysis of pharmaceutical products.

2. Fundamental concepts 2.1. Instrumentation for chemical imaging NIR and Raman devices for chemical imaging are composed of a light source, optical parts (microscope objectives or lenses), a splitter (interferometer for Fourier-Transform devices, diffraction grating for dispersive devices or a tunable filter for global imaging devices) and a detector. MIR chemical imaging devices are mostly ATR devices with a germanium crystal and a mercury cadmium telluride (MCT) detector. All the spectroscopic parts of the device may be tuned for specific applications depending on the kind of sample studied and the sought information. More information about

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technical properties and tuning of devices may be found elsewhere [1,7,8]. 2.1.1. Configurations for chemical images acquisition Chemical imaging devices may be arranged in three configurations: point mapping, line scanning and global imaging [6,9,10]. These configurations may exist with both macroscopic and microscopic imaging devices [11,12]. a. Point mapping (Fig. 1a). This configuration is probably the most used for Raman chemical imaging. It consists of recording a spectrum at a specific spatial location, then the sample is moved, another spectrum is recorded at location adjacent to the previous one and so on until the whole mapping area is covered. The main advantage of this technique is the high spectral quality (resolution, full spectral range) achievable since all parameters of spectral acquisition may be optimized. However, the main drawback is the acquisition time limited by the acquisition time and the moving of the sample. Nevertheless, new Raman spectrometers allow ultra-fast acquisition modes with acquisition times around 1 ms with acceptable signal-to-noise ratio (SNR). b. Line scanning (Fig. 1b). Also known as the push-broom configuration, this technique is directly inspired from the remote sensing field. As with point mapping, spectra are recorded at defined spatial locations but with this configuration, the spectra of a whole line of the mapping area are simultaneously recorded. The advantages are the same as point mapping but the acquisition time is reduced. c. Global imaging (Fig. 1c). This configuration is probably the most used in NIR imaging devices. The sample is entirely illuminated with a high power light source and the whole mapping area is recorded simultaneously at a single wavelength. Then the tunable filter moves, selects another wavelength and so on until the whole spectral range is recorded. The main advantage of this configuration is the fast acquisition time allowing the acquisition of a whole map in seconds. However, the spatial resolution is limited by the size (pixels) of the detector and the spectral resolution is limited by the type of tunable filters used. Furthermore, the heat produced by the high power light source may be a limiting factor with some kind of samples as it may melt them down or degrade the compound of interest. As one can see, each configuration has its advantages and drawbacks. Unfortunately, these configurations are built-in and the analyst must choose a device that will meet its expectations based on a priori knowledge of the studied problem. 2.1.2. Sampling and spatial resolution consideration Spatial resolution may firstly be limited by the resolution power of the instrument (e.g. laser spot of ca. 100 ␮m for a macroscopic Raman system). But, when using microscopes, analysts want to have the highest possible spatial resolution. This resolution is, however, limited by the diffraction limit given by the equation: r = 0.61

 NA

(1)

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Fig. 1. (a) Three dimensional data cube acquired with the “point mapping” configuration. (b) Three dimensional data cube acquired with the “line scanning” configuration. (c) Three dimensional data cube acquired with the “global imaging” configuration.

where  is the wavelength of the irradiating sources (nm) and NA is the numerical aperture of the objective defined as

Another parameter must be considered when analyzing a sample with a confocal apparatus: the depth resolution (DR) [19] DR = 2.2

NA = n sin 

(2)

where n is the refractive index of the medium (1.0 for air) and  is half the angular aperture. Based on Eq. (1), one can see that Raman spectroscopy will provide smaller spatial resolution (ca. 0.5–1 ␮m) than NIR or MIR spectroscopy. However, with ATR-MIR, Chan and Kazarian achieved a spatial resolution of 4 ␮m with a wavelength of 3 ␮m [13]. NIR devices have a disadvantage that is the low absorptivity of overtones and combination bands. Therefore, to obtain satisfying SNR, the effective spatial resolution is much higher (hundreds of micrometers) than the diffraction-limited one (micrometers) [14]. To overcome the diffraction limit, authors have developed super-resolution algorithm [15–17]. The principle is to record several low resolution maps with a known spatial shift inferior to the pixel size and to mathematically combine them. The resulting images have a higher spatial resolution. Adar et al., has shown that for Raman imaging: “the use of the highest numerical aperture objective coupled with a step size 5–10 times smaller than the laser spot size will provide the highest quality chemical images” [18].

n (NA)2

(3)

where n is the refractive index of the material, NA is the numerical aperture and  is the laser wavelength (nm). For a material with n = 1.5, with a wavelength of 785 nm and with an objective of NA = 0.95, the DR would be of 914 nm. However, due to refraction differences of the sample, the effective DR is much higher. Tabaksblat et al. estimate that it is often five times higher than the theoretical value given by Eq. (3) leading to out of focus analysis and blurred mapping [20]. Another very important thing in chemical imaging is the representativity of the sample. Indeed, chemical imaging analyses only the surface of the sample. This surface is often a cross section and might not be representative of the whole population. Therefore, the spatial resolution and the number of samples to study must be suited to the studied problem to ensure that the information obtained is relevant. Furthermore, when performing micro scale analysis or Raman imaging analysis, the sample surface must be as flat as possible. As the Raman radiation has a very small penetration, any surface irregularity will provide a difference in spectral intensity that would lead to erroneous conclusion regarding compound concentration. Therefore, samples are most of the time microtomed or trimmed with high precision instruments [21].

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Fig. 2. Hyperspectral imaging data arranged as a hyperspectral cube. Spatial dimensions are named x and y and the spectral dimension is named ␭.

2.2. Data analysis Once acquired, hyperspectral data must be analyzed to extract the information sought. These data are presented as a threedimensional matrix (Fig. 2) with the two spatial dimensions (x, y) and the spectral dimension (). As most of the pre-processing and processing algorithms come from classical spectroscopy, an unfolding step is often necessary to transform the three dimensional data cube in a bi-dimensional matrix. To do so, the two spatial dimensions are concatenated in a single column with the second dimension remaining the spectral data. Hyperspectral data analysis may be divided in three main parts: pre-processing, processing and post-processing. Before undergoing pre-processing, NIR data must be background corrected to reflectance and conversed to absorbance (log10 (1/R)). Specific pretreatments of NIR hyperspectral images can be found elsewhere [22,23].

2.2.1. Data pre-processing This part, also known as pretreatment of data, aims at correcting the perturbations that occurred during the analysis (e.g. spikes) or limiting the effect of undesired phenomenon to facilitate the access to the desired information (e.g. scattering effects). Nonetheless, one has to know the goal of the analysis and to understand the spectroscopic phenomenon that occurred to determine which pre-processing technique to use. Indeed, scattering might be disruptive for compound identification or quantitation but it is very interesting to study the physical properties of the sample. The very first pre-processing that should be applied to our data is (when applicable) the selection of a region of interest (ROI). This might be very useful to remove undesired spectra from background or to select a specific part of the chemical image. Amigo et al., developed a useful toolbox in Matlab® for ROI selection [24,25]. ROI selection can be performed in two different ways: by manual selection or by the mean of principal component analysis (PCA) decomposition. Once performed, the first PC’s scores are displayed and the threshold is then selected manually by selecting the

lower limit and the upper limit in the score histogram. After being selected, the ROI spectra are refolded in a two-dimensional matrix. The pre-processing steps are the same as those employed in classical spectroscopy and mainly consist in the correction of spectral noise, baseline drifts (due to scattering in MIR and NIR spectroscopies and fluorescence in Raman spectroscopy) and spikes (or cosmic rays) in Raman spectroscopy. It is important to know and understand the chemistry and physic beside spectral measurements to choose correctly the pre-processing algorithms. Indeed, when used in an inappropriate way, pre-processing may introduce artifacts or causes a loss of information. Usually, different pre-processing should be tested and their results compared to ensure a correct data analysis and robust results.

2.2.1.1. Spikes and dead pixels correction. Raman spectra and more generally spectra acquired with a charge coupled device (CCD) detector are likely to be contaminated by cosmic rays. These highly energetic subatomic particles from space may hit a CCD pixel and saturate it providing a single unusually high intensity value (Fig. 3a). Dead pixels are anomalous pixels of the detector giving missing or zero values. The great majority of commercial software to acquire hyperspectral images includes real-time spikes correction based on multiple spectrum accumulation at the same location. As these perturbations are very unlikely to occur twice at the same location, the difference between the multiple spectra allows the detection and correction of spikes. However this implies an increase of analysis time and is therefore not always possible. This is the reason why it is sometimes necessary to correct the spikes afterwards. When very few spikes are present, a manual correction may be envisaged. Some algorithms have been developed if manual correction is not possible or if an automation of the correction is needed [26–29]. These algorithms are based on the fact that it is statistically impossible that two cosmic rays hit two neighboring pixels of the detector. Each spectrum is then compared to its neighbors and if an aberrant value is detected (the threshold is set manually),

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Other techniques (PCA, wavelets) are based on the decomposition of the data cube and the deletion of the noise related part of the signal [31–33]. 2.2.1.3. Baseline correction and normalization. When performing spectral analysis of a sample, drifts in the baseline may occur due to scattering or fluorescence (in Raman spectroscopy). Therefore, it is sometimes important to remove these perturbations to enhance and facilitate the access to the sought information. However, scattering information is sometimes important and need to be kept (see applications). The most used scattering correction algorithms include the standard normal variate (SNV) and the multiplicative scatter correction (MSC). These two pretreatments generally give similar results. However, due to their geometry, it is sometimes interesting to compare the obtained results since they may be different [34]. SNV is performed for each spectrum following the equation: xSNVi,j =

xi,j − x¯ j

(4)

Sj

where xSNVi,j is the corrected absorbance x at wavelength i for the spectrum j; xi,j is the absorbance x at wavelength i for the spectrum j, x¯ j is the mean absorbance of spectrum j and Sj is the standard deviation of spectrum j. SNV normalizes each spectrum returning a mean of 0 and a variance of 1 spectra dataset. MSC performs a linear regression of each spectrum on a reference spectrum (the mean or median spectrum). MSC aims at separating the chemical light absorption from the physical light scatter [35]. Regression parameters (intercept a and slope b) are computed as follows: a = x¯ i − bx¯¯

J

b=

j=1

(5)

(xi,J − x¯ i )(¯xj − x¯¯ )

J

j=1

(¯xj − x¯¯ )

2

(6)

where x¯¯ is the general mean or median reference absorbance value. SG first and second derivatives may also be employed for baseline correction purposes and to increase differences between spectra that could be useful for qualitative purposes (see applications). Raman spectra may also be baseline corrected using different approaches (such as Asymmetric Least Squares [36], mixture models [37], Weight Least squares and polynomial filter). These algorithms only correct baseline drifts and are mainly employed with Raman spectra to correct Fluorescence background (Fig. 3c).

Fig. 3. (a) Typical Raman spectrum with a baseline drift caused by fluorescence and affected by the presence of two spikes. (b) Raman spectrum of (a) after spikes correction. (c) Raman spectrum of (b) after baseline correction.

it is replaced by interpolation of the neighboring intensity values (Fig. 3b). 2.2.1.2. De-noising. Spectral noise may be corrected with a smoothing algorithm with the most used being Savitzky-Golay (SG) smoothing algorithm [30]. SG algorithm is based on a stepwise fitting of a polynomial to a subset of the spectral data. Two parameters may be tuned depending on the smoothing desired without losing too much information: the window width (width of the subset of the data) and the polynomial order. An increase of the window width and a decrease of the polynomial order will provide a higher smoothing.

2.2.2. Data processing 2.2.2.1. Univariate data analysis. When a specific peak corresponding to the studied compound without any interfering adjacent peak related to other compounds may be found, the easiest way to analyze the data is the extraction of the distribution map at the corresponding wavelength. Several information such as the Full Width at Half Maximum (FWHM), peak area or peak height may be extracted and mapped to follow specific compounds, diastereoisomers or polymorphs (see applications). This approach is hardly restricted to Raman and MIR spectra since they exhibit sharp peak patterns. However, it is sometimes difficult to find specific and well resolved peaks especially when the imaged sample has a complex matrix containing a lot of compounds. It is therefore necessary to use the multivariate data analysis approach. 2.2.2.2. Multivariate data analysis (MVA). MVA may be divided in three main categories: resolution, regression and classification

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Fig. 4. Unfolding of the hyperspectral datacube in the bi-dimensional matrix D. Bilinear decomposition of the matrix D into its constituents: C, concentration matrix; ST , spectra matrix; E, residual matrix.

techniques. Each category has its own specificities and will be used depending on the available information and the desired results. Most MVA algorithms are based on the fact that recorded spectra are the weighted sum of pure spectra of the components present. Based on this assumption, the unfolded data cube D may be decomposed in a concentration matrix C and a spectra matrix ST (see Fig. 4). D = C · ST + E

(7)

where E is the residual matrix. a. Resolution techniques: These techniques aim at decomposing the pre-processed data cube into the concentration and spectral matrices. Some of them may be called exploratory techniques since they can be performed easily without a priori knowledge. Among the exploratory techniques, Principal Component Analysis (PCA) is probably the most used [6,8,38]. PCA reduces the dimensionality of a problem making linear combinations of the original variables (manifest variables) returning new “latent” variables. Each manifest variable is weighted by a loading (p) representing the importance of the considered variable on the variance of the data. New dimensions called Principal Components (PC’s) express the variability of the data in a digressive way. The projection of a pixel onto the PC’s is called its score (t) and is given by the resolution of the PC equation: ti,n =

 j

pj,n × xi,j

(8)

where ti,n is the score of the ith object on the nth PC, pj,n is the loading of the jth manifest variable on the nth PC and xi,j is the value of the jth manifest variable of the ith pixel.

The result of PCA is the decomposition of the pre-processed D matrix in a T score matrix and a PT loading matrix. D = T · PT + E

(9)

The analogy with Eq. (7) is evident. Therefore, when refolding the score matrix, one has a semi quantitative representation of the spatial distribution of the compounds whose spectra may be seen in the loading matrix. The main advantage of PCA is its simplicity and straightforward application. However, the loadings may have positive or negative signs and so doesn’t always have a chemical sense. Moreover, they are often combinations of several compounds (see Fig. 5). To overcome these limitations and to obtain more meaningful results, other resolution techniques have been developed. Independent Component Analysis (ICA) has recently been successfully used to unmix Raman hyperspectral imaging data in a matrix S of independent sources signals (independent components, IC) and a matrix A of mixing coefficients [39]. Band Target Entropy Minimization (BTEM) [40] searches for the “simplest (irreducible) underlying patterns” in the spectroscopic data. The main advantage of BTEM over other curve resolution techniques is that it needs no estimation of the number of component present since it performs spectral resolution based on one spectrum at a time. Once all spectra are resolved, they are projected back on the pre-processed original data and the spatial distribution of each resolved constituent is generated. SIMPLe-to-use Interactive Self-Modeling Mixture Analysis is another technique that can be used to resolve spectra or concentration from pre-processed data (SIMPLISMA) [41]. Among the resolution techniques, the most used in hyperspectral imaging is the Multivariate Curve Resolution-Alternating Least Squares (MCR-ALS) [17,42–45]. MCR-ALS needs initial estimates of C or ST so the number of compounds to be resolved must be known. If one has no information, this can be estimated

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Fig. 5. First principal component (red line) obtained after analysis of a hyperspectral data cube and the corresponding pure spectra (compound A: green line, inversed spectrum of compound B: blue line, inversed spectrum of compound C: violet line). The first PC is correlated to the first compound and anti-correlated to compounds B and C). When refolding the associated score, the image will present high intensity values where compound A is present and low intensity values where compounds B and C indistinctively are present. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

by singular value decomposition (SVD). Then, estimates of C or ST can be obtained by SIMPLISMA. The algorithm starts with the estimate input and alternatively computes the C and ST matrices minimizing the residual matrix E at each turn until convergence is obtained. However, due to rotational ambiguities, an infinity of results may be obtained as shown in the following equation: D = CT · T−1 ST

(10)

where T may be an infinity of matrices. To restrain the number of solutions to Eq. (10), constraints are used such as non-negativity, correlation [46,47] or local-rank [48]. To overcome the low quality of resolution of minor compounds, an augmentation of the original data with pure spectra of the components [49] or multi-image analysis [50] may be performed. MCR-ALS is the technique of choice when dealing with samples of unknown composition or to quantify samples without calibration set (Fig. 6). b. Regression techniques: Even if quantitative or even semiquantitative information may be obtained with the resolution techniques without calibration, these are not very accurate. To obtain reliable quantitative information for every pixel, regression techniques are the best approach. The simplest regression algorithm is the Classical Least Squares (CLS) [51]. This technique needs the pure spectra of each compound and regress them against the pre-processed data cube following the Eq. (7): C = DS · (SST )

−1

(11)

However, this approach is very sensitive to any perturbation and will be biased if spectral perturbation occurs (degradation, polymorphism, physical state, noise, interaction between compounds such as hydrogen bonds. . .). Therefore, before applying CLS, one has to know the studied compounds, to obtain their

pure spectra and to be sure that the imaged sample spectra are the same as the reference ones. Beside these constraints, CLS returns reliable quantitative results. If one wants to quantify reliably complex or noisy hyperspectral data, the best choice will be the Partial Least Squares (PLS) algorithm [52]. This technique is based on the same principle as PCA since it diminishes the dimensionality of the problem by making linear combinations of the manifest variables. However, in this case, the loadings are computed in a way that they reflect the covariance between the describing variables (hyperspectral pre-processed data) and the response variables (concentration values) obtained with a reference technique (e.g. liquid chromatography). PLS is the most used regression technique in traditional spectroscopy and returns robust concentration predictions. However, the calibration step may be a limitation when working with unknown or samples of different composition. For this kind of samples, resolution algorithm will provide the best results. When regression algorithms are used, one has to test the performance of the developed model. This is generally performed evaluating the global error of the models by the means of Root Mean Squared Error (RMSE) during cross-validation (RMSECV) or with a test set (RMSEP). RMSE are computed with the following equation:

 RMSE =

n (Mi i=1

n

− Pi )2

(12)

where Mi is the measured (or reference) value, Pi is the predicted value and n is the population size. Beside the straightforward calculation of RMSE, this criterion is often computed with non-independent test sets [53]. Even when computed with an appropriate test set, the returned value only gives an idea of the global error of the model over the whole calibration range. This is clearly insufficient to declare

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Fig. 6. (a) Correlation coefficients between resolved spectra (loadings in abscissa) and reference spectra of a database after MCR-ALS analysis of an effervescent tablet. Red squares are associated to correlation coefficient values higher than 0.9. Salicylic acid (impurity of acetylsalicylic acid) was not found. (b) Concentration maps resolved by MCR-ALS analysis of an effervescent tablet. Hot colors are associated to high concentrations of the corresponding compound. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

a regression model as valid as stated by De Bleye et al. [54]. RMSE values may be of good help when developing a model but returned results should be handled with care when assessing the validity of the method.

c. Classification techniques: Beside the resolution and regression techniques that provide both qualitative and quantitative information, classification techniques only return qualitative information. Indeed, their goal is to assign each pixel to a class [55].

P.-Y. Sacré et al. / Journal of Pharmaceutical and Biomedical Analysis 101 (2014) 123–140

Among the clustering techniques, the most used is probably the K-means algorithm. This technique needs as input the number of classes to model. Then, each between-pixel distance is computed. The algorithm will group the pixels in n clusters so that the within cluster sum of square distance between each pixel and the mean value of the cluster (centroid) is minimal. This technique is said unsupervised since it classifies each pixel without any calibration set. Other techniques exist that need calibration set: k-nearest neighbor (k-NN), linear discriminant analysis (LDA), PLSdiscriminant analysis (PLS-DA), support vector machine (SVM), artificial neural networks (ANN). These techniques may have their utility but their main drawback is the fact that they classify each pixel to only one class. This is why they are called hard modeling techniques. However, in hyperspectral imaging, it is relatively rare that each pixel contains only one compound. Therefore, soft modeling techniques have been developed with the most used: fuzzy-C means clustering. This technique assigns to each pixel a degree of class membership. It allows the generation of more realistic images where a single pixel may be assigned to several classes [10]. Several studies have been performed and compared the usefulness of different chemometric tools in order to analyze and/or resolve Raman, NIR or ATR-MIR hyperspectral imaging data [43,44,56–64]. 2.2.3. Data post-processing Once the data have been processed, the post-processing step consists in extracting the relevant information from the results obtained. Most of the time, distribution maps are only visually inspected and spectra (if resolved by a resolution technique) are compared with reference spectra possibly by means of a correlation coefficient. Beside this straightforward but informative inspection, more objective analysis may be performed depending on the information sought. 3. Pharmaceutical applications (see Table 1) 3.1. Homogeneity of distribution Depending on the pharmaceutical form studied, the term “homogeneity” may cover different realities. Considering sample characteristics, different hyperspectral devices (e.g. whole tablets imaging, confocal microscopy of coating, etc.) and data analysis should be envisaged. To assess the homogeneity of distribution of a compound of interest, most authors use the statistics of the histogram of intensities. These values (mean, standard deviation, skewness and kurtosis) provide information on the homogeneity of concentration of the compound but the spatial information is not considered. As can be seen from Fig. 7, two distribution maps may have exactly the same histogram of intensities but totally different spatial distribution. This is why some authors developed algorithms to objectively characterize the homogeneity of distribution. Puchert et al. used the Linear Image Signature (LIS) to show the homogeneity of distribution of counterfeit samples [65]. To do this, they developed a PLS quantitative model and predicted the amount of API in the tablets. Then they concatenated the summed X and Y direction concentrations and performed the first derivative of the obtained result. They observed a clearly different distribution of API between genuine and counterfeit samples. Rosas et al. developed a homogeneity criterion based on the Poole index [66–69]. They obtained good results and were able

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to estimate the sample homogeneity. This technique is however complicated since it needs a long processing step (development of quantitative model, binarization, and determination of particle size). This approach is therefore hardly applicable during pharmaceutical dosage form development. Sacré et al. developed another criterion called Distributional Homogeneity Index (DHI) based on the homogeneity curves [70]. This approach computes the standard deviation between macropixels of increasing size for the studied map and the randomized studied map. The criterion is computed as the ratio between the areas under the curve (AUC) of both maps. The authors observed a linear relationship between DHI and the content uniformity values obtained by liquid chromatography assay. The main advantage of this technique is the easiness of use and the few processing steps since DHI may be computed on distribution map obtained by refolding the CLS or PCA score related to the compound of interest. To assess the homogeneity of distribution, one must keep in mind the representativity of sampling and consider the spatial resolution of each device. Several studies have been performed to assess the homogeneity of distribution among pharmaceutical dosage forms. Most of them concerned tablets and were realized with NIR chemical imagers in a global imaging configuration. As stated before, the main advantage of this configuration is the rapidity of image acquisition. Due to the nature of NIR spectral bands (overtones and combination bands), univariate analysis of NIR hyperspectral data is hard and advantageously replaced by multivariate analysis. The majority of the studies used resolution and exploration tools [60,61,71–75]. Regression tools have also been used. Among these, only CLS has been used during pharmaceutical development [76,77]. PLS regression was used to control or investigate well-established formulations because of the long and costly calibration model development [78]. The pretreatments used mostly consisted in SNV normalization and some authors used first or second SG derivatives to increase spectral differences between compounds. Post-processing of obtained distribution maps consisted mainly in visual inspection or histogram analysis even if these approaches are not reliable as explained previously. When regression models were used, the evaluation of the model was performed by RMSE values inspection. Raman chemical imaging has been used by Belu et al. to investigate the homogeneity of distribution of an API in the coating of a drug eluting stent during an elution study [79]. To achieve this goal, they performed optical cross-sections of 70 ␮m wide by 10 ␮m deep using a Raman confocal microscope. No pretreatment was applied and the data were analyzed by augmented-CLS. Hyperspectral images allowed the selection of the best drug/polymer ratio for the coating. Raman spectroscopy has also been used for homogeneity study of two different specific polymorphic forms of a single API [80], the characterization of semi-solid Self-Emulsifying Drug Delivery Systems (SEDDS) [81], the mapping of low dose drugs (