RESEARCH ARTICLE – Pharmaceutics, Drug Delivery and Pharmaceutical Technology

Study of the Homogeneity of Drug Loaded in Polymeric Films Using Near-Infrared Chemical Imaging and Split-Plot Design GUILHERME L. ALEXANDRINO, RONEI J. POPPI Institute of Chemistry, State University of Campinas – UNICAMP, Campinas, S˜ao Paulo 13084-971, Brazil Received 2 April 2014; revised 20 May 2014; accepted 21 May 2014 Published online in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/jps.24051 ABSTRACT: Split-plot design (SPD) and near-infrared chemical imaging were used to study the homogeneity of the drug paracetamol loaded in films and prepared from mixtures of the biocompatible polymers hydroxypropyl methylcellulose, polyvinylpyrrolidone, and polyethyleneglycol. The study was split into two parts: a partial least-squares (PLS) model was developed for a pixel-to-pixel quantification of the drug loaded into films. Afterwards, a SPD was developed to study the influence of the polymeric composition of films and the two process conditions related to their preparation (percentage of the drug in the formulations and curing temperature) on the homogeneity of the drug dispersed in the polymeric matrix. Chemical images of each formulation of the SPD were obtained by pixel-to-pixel predictions of the drug using the PLS model of the first part, and macropixel analyses were performed for each image to obtain the y-responses (homogeneity parameter). The design was modeled using PLS regression, allowing only the most relevant factors to remain in the final model. The interpretation of the SPD was enhanced by utilizing the orthogonal PLS algorithm, where the y-orthogonal variations in the C 2014 Wiley Periodicals, Inc. and the American Pharmacists Association J Pharm design were separated from the y-correlated variation.  Sci Keywords: imaging spectrosocopy; factorial design; macropixel analysis; multivariate analysis; near-infrared spectroscopy; polymers; partial least squares.

INTRODUCTION Chemical imaging (CI) coupled with vibrational spectroscopy [essentially Mid-infrared, near-infrared (NIR), and Raman] allows further analytical characterization of solid dosage forms of pharmaceuticals, and it has been encouraged by US FDA’s process analytical technology to ensure quality control over pharmaceutical processes.1,2 CI provides unique spectral information with spatial resolution (i.e., the sample region of interest is split in regular squares, denominated pixels, that possess their own spectra), and this analytical methodology has been exploited during numerous pharmaceutical process applications, such as the chemical distribution of the ingredients,3 blend homogeneity,4 coating,5 polymorphism,6 authentication,7 and dissolution.8 In NIR-CI, because of the overlap of the spectral bands in the pixels, multivariate methods are usually required to extract chemical information from the samples. During the quantitative analyses, partial least-squares (PLS) regression has been used to obtain the concentration of the constituents in the pixels. PLS models are developed from CI data because the bulk concentrations of the analyte in the entire samples are known. Although the concentration of the analyte cannot be distinguished between the pixels in a sample, its respective bulk concentration can be correlated with the mean spectrum of that sample. After developing a PLS model, it can be applied in the spectra of the pixels, generating concentration maps.6,9 Transdermal drug delivery systems are currently being developed for existing drugs because of the advantages of these

Correspondence to: Ronei J. Poppi (Telephone: +55-19-35213126; Fax: +5519-35213023; E-mail: [email protected]) Journal of Pharmaceutical Sciences  C 2014 Wiley Periodicals, Inc. and the American Pharmacists Association

matrices, including their noninvasive application, the avoidance of first-pass hepatic metabolism for drugs with poor oral bioavailability, sustained delivery to achieve a steady plasma profile, and patient-friendly flexibility (i.e., reduction of dose schedules and easy withdrawal if there is any inconvenience).10,11 Moreover, different associations and/or proportions among the polymers in films can be adjusted to achieve the desired drug release profile.12 The homogeneity of active pharmaceutical ingredient and excipients in pharmaceuticals is an important parameter to be monitored when developing pharmaceutical formulations to guarantee well-defined dissolution profiles and, consequently, satisfactory drug pharmacological properties in the organism.13 In CI, for images generated from the quantification methods, the distribution of the constituents in a sample can be analyzed using the frequency histograms plotted from their respective concentration values in the pixels.3,14,15 However, the resulting analysis will be subjective and must be followed by the respective images, whereas images with different levels of homogeneity can generate the same histogram.16 In this context, Hamad et al.17 developed the concept of macropixel analysis for chemical images to generate reasonable and quantitative analyses of image homogeneity. Macropixel analysis divides an image into equally sized blocks of pixels and calculates statistical parameters between the blocks. Further information regarding the different forms of macropixel analysis and the statistics between the macropixels used to quantify the homogeneity of the chemical images are described in the section Macropixel Analysis of Chemical Images. In this work, a new strategy for a quantitative evaluation of the homogeneity of a drug loaded in a polymeric film is presented using NIR-CI and experimental design. The pharmaceutical matrix model used for simulating polymeric films loaded with a drug for transdermal applications was composed Alexandrino and Poppi, JOURNAL OF PHARMACEUTICAL SCIENCES

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RESEARCH ARTICLE – Pharmaceutics, Drug Delivery and Pharmaceutical Technology

by blends of the biocompatible polymers hydroxypropilmetilcellulose (HPMC), polyvinylpyrrolidone (PVP), and polyethyleneglycol (PEG), loaded with paracetamol (PAR). In the first part of the study, a PLS model was developed for the pixel-to-pixel predictions of the drug in this type of film, so that the chemical images of the drug in future samples could be obtained. Next, a split-plot design (SPD) was elaborated to stress how the variability of different proportions of the polymers (mixture variables) and process conditions (process variables) can affect the homogeneity of the drug dispersed throughout films. The process variables chosen for this study were: (1) drug content in the formulations (DRUG) and (2) curing temperature (TEMP). The numerical values representing the drug homogeneity in the samples from the SPD (y-responses) were extracted for each sample through macropixel analysis of their respective chemical images obtained from the PLS model computed in the first part. The experimental design (containing main and interaction terms of process and mixture variables) was also modeled using PLS regression, and the importance of each term for the design matrix X for the y-explained variance was analyzed using the significance of the regression coefficients and by calculating the variable importance on projection (VIP) parameters. The robustness of the PLS regressions while excluding nonsignificant terms was evaluated using the evolution of the cross-validation error and visual inspection of the residues. When the design matrix contained only significant terms (Xsig), a multivariate regression was also performed using orthogonal projections to latent structures (OPLS) algorithm. This method has an advantage over PLS; the y-orthogonal variations in Xsig can be separated from the y-correlated variation, enriching the model interpretation.

THEORY

macropixels in binary images to study the homogeneity excipients in tablets via NIR-CI. Rosas and Blanco19,20 employed a macropixel analysis for the chemical images of colored sand samples and pharmaceutical solid dosage forms by adjusting known mixing indexes from the macropixel statistics to study the homogeneity of the constituents in these samples. Split-Plot Experimental Design with PLS Regression Split-plot designs are formed by blocked experiments that randomly vary easy-to-change factors within the blocks, whereas the hard-to-change factors are randomly varied only when moving from one block to another, resulting in two experimental units.21,22 The hard-to-change factors that define the blocks are the main plots, whereas the subsets of those are the subplots. The split-plot approach can be exploited in mixture designs submitted to different process conditions; the mixture and process variables are treated as subplots and main plots, respectively.23 For a design with two main plots and three subplots, the influence of these variables on an experimental response can be analyzed via multivariate regression according to a general mixed model equation presented in Eq. (1). Yijklm = μ + zi + zj + zij + xk + xl + xm + W + eij klm

(1)

where Yijklm is the model response; zi and zj are the main plot effects (process variables); zij is their interaction term; xk , xl , and xm are the subplot effects (mixture variables); W comprises all of the main subplot and subplot–subplot interaction terms; μ is the model intercept; and eijklm is the regression error. Blocking the experiments results in two error sources, the main plot error, which is the same for experiments within the blocks, and the subplot error, which is uncorrelated within and among the blocks.24 Equation (1) can also be rewritten in matrix notation, as shown in Eq. (2):

Macropixel Analysis of Chemical Images Macropixel analysis requires chemical images to be characterized using a defined score value for each pixel, including images built for quantification (e.g., concentration), exploratory data analysis (e.g., PCA, unsupervised clustering methods), and others. Macropixel analysis can be conducted using nonoverlapped macropixels (Discrete-Level Tiling method), or with all possible macropixel sizes, through the method designated Continuous-Level Moving Block (CLMB). In the first method, the macropixels must be equally sized so that they can be fitted adjacently throughout the image; in the CLMB method, one macropixel systematically scrolls through the entire image row-to-row and column-to-column, and this procedure is performed repeatedly until the macropixel has the same dimensions as the entire image. In both methods, the variance between the subregions of the images is minimized while varying the sizes of the macropixels; however, during the CLMB, all possible macropixel sizes can be analyzed. To comprehend how the CLMB method works, the reader is referred to Ref. 17. The macropixel statistics are usually calculated as the score average value of the included pixels, and the standard deviation of the averaged macropixels in an image can be used as a numeric parameter for homogeneity. Hamad et al.17 defined the specific concentration ranges of PAR in the macropixels using the chemical images of tablets and used a minimum macropixel size that included all of the macropixels in this range as a quantitative criterion of homogeneity. Wu et al.18 analyzed the Alexandrino and Poppi, JOURNAL OF PHARMACEUTICAL SCIENCES

y = bX + δ + ε

(2)

where X is the design matrix (composed by the main and interaction fixed effects), b is the regression coefficients vector, δ and ε are the main plot and subplot error vectors, respectively, and y is the responses vector. For balanced designs, b is usually calculated from Eq. (2) through the generalized leastsquares (GLS) regression: bGLS = (XT V−1 X)−1 XT V−1 y, where V is a diagonal matrix that accounts for the main plot and subplot error variances, σ 2 MP and σ 2 SP , respectively. An appropriate ANOVA can be used to calculate the variances of the errors in fully replicated SPD,25 but this method becomes impracticable if numerous experiments are necessary. Subsequently, nonfully replicated SPD have also been proposed,26 and the error variances of the main plot and subplot can be obtained using additional replicates only in the central point. Generalized least-squares is a suitable method for regression in which two independent error variances must be accounted during the uncertainty estimation of the regression coefficients; however, the covariance matrix must not be illconditioned, generating good estimations of the regression cox efficients. In mixture designs, the constraint (i) = 1 results in nonindependent and highly collinear variables that may lead to ill-conditioned covariance matrices. Afterward, projection methods, such as PLS regression, become more suitable for modeling mixture designs after they can handle DOI 10.1002/jps.24051

RESEARCH ARTICLE – Pharmaceutics, Drug Delivery and Pharmaceutical Technology

collinearity without needing to reparameterize the coefficients (as it occurs with the multiple linear regressions). In a model regression with PLS-based algorithms, no mathematical distinction is present between the process and mixture variables, facilitating the interpretation of the model.26 The design matrix X is generally autoscaled; the coefficients of the models represent the changes in the y-responses relative to the reference defined in the central levels of the process variables and the central point of the n-component mixture diagram. Crossvalidation is recommended when choosing the correct number of model components to avoid overfitting.27,28 For a PLS model with a single y-response vector, the SIMPLS algorithm calculates the regression coefficients of the model from the weights matrix R and the nonnormalized y-loadings Q: bPLS = RQT .29 The product (RRT ) is the approximate covariance matrix of the PLS regression coefficients; a straightforward approach from the ordinary least-squares (OLS) method is proposed for calculating the variances of the PLS coefficients,30 Eq. (3). var (bPLS ) =RRT σ 2

(3)

Note that Eq. (3) is an approximation based on a linear estimation of the regression coefficients, similar to the OLS and principal component regression methods. However, the PLS estimator of the regression coefficients (which comes from R) is nonlinear, resulting in a nonexact solution for Eq. (3).31 Other approximate results can be obtained from linearizing the PLS estimators using a Jacobian matrix or resampling-based methods, such as bootstrap and jack-knifing.32 In addition, Eq. (3) accounts for only a single error variance (σ 2 ) (as it occurs in OLS regression) that is usually defined by the root-mean-square error of the calibration/cross-validation (RMSEC/CV) for the PLS models without lack of fit.30 For SPD wherein the error variances were calculated from replications (this work), σ 2 can be taken as (σ 2 MP + σ 2 SP ) to equal σ 2 SP within the subplots. In the PLS regression, some undesirable systematic variations in X cannot be correlated to the y-responses; specifically, a portion of the variability in X may be orthogonal to y. Therefore, the OPLS algorithm was developed to filter X such that the y-uncorrelated (orthogonal) variability in X is separated from the y-correlated one. Although the PLS and OPLS methods provide the same y-predictions if the same amounts of components are employed in both models, once that removing the orthogonal components has no influence over the correlation between X and y; with OPLS, the y-correlated variation in X will be described in a separate model component, whereas the y-uncorrelated variation will be described using one or more orthogonal components.33 Consequently, for OPLS, the variables are analyzed in terms of the y-correlated and y-orthogonal loading vectors; only variables with a relevant loading in the ycorrelated component are important for the X–y modeling. For PLS, distinguishing the extent of the orthogonal part that can be presented in the loadings of the components is impossible; therefore, the interpretation of the variables in a PLS model can be misleading.

MATERIALS AND METHODS Materials The polymer films were produced as blends of hydroxypropyl methylcellulose 15 MPA (Sigma–Aldrich, St. Louis, MI), PVP DOI 10.1002/jps.24051

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(MW 40,000 gmol−1 ; Vetec, Duque de Caxias, Rio de Janeiro, ˜ Paulo, Brazil), and PEG (MW 400 gmol−1 ; Synth, Diadema, Sao Brazil). PAR (USP grade) was also obtained from Synth. Deionized water was obtained from a Milli-Q system (EMD Millipore Corporation, Billerica, Massachusetts). Preparation of Films Loaded with PAR Films were prepared using the solvent evaporation method: for each sample, polymers (total amount of 100 mg) and drug were initially dissolved in 5.0 mL of deionized water. Afterward, the casting solutions were transferred to glass Petri dishes and submitted to solvent evaporation in an oven at a constant temperature during the film-forming process. The fraction of each polymer and drug in films, as well as the curing temperature, were different, as specified in sections Preparation of Films Loaded with PAR for Pixel-to-Pixel quantification of the drug with PLS and Preparation of Films Loaded with PAR for the Split-Plot Experimental Design. Preparation of Films Loaded with PAR for Pixel-to-Pixel Quantification of the Drug with PLS The PLS models were developed using 17 film samples split into calibration (12 samples) and test (five samples) sets. Because the drug and polymer contents are not equal between the pixels of each sample, the calibration set must include samples with the widest possible ranges of the constituents (i.e., polymers and drug). Moreover, the samples prepared for the calibration and test sets must yield consistent films. Therefore, restricted weight ratio ranges of the polymers were used while preparing the calibration/test samples: 0.1 ≤ XHPMC ≤ 0.8, 0.1 ≤ XPVP ≤ 0.8, and 0.1 ≤ XPEG ≤ 0.6, considering that XHPMC + XPVP + XPEG = 1. Because of the limited aqueous solubility of PAR (15 mg/mL at 25◦ C), its weight in the samples ranged from 0 to 70 mg (0 ≤ %PAR ≤ 41). Because these weight ratios in the polymers generate in an irregular subspace in the threepolymer mixture diagram, D-optimal algorithm was employed to define the polymer contents in the samples. The final compositions of the samples (polymers + PAR) are listed in Ref. 34 Films were formed after curing at 60◦ C for 24 h. Preparation of Films Loaded with PAR for the Split-Plot Experimental Design In the SPD, the process and mixture variables were defined as the main plots and subplots, respectively. The main plots were coded in two levels: −1 (lower level) and +1 (upper level). The polymer contents of the films (subplots) were varied according to a restricted centroid design. The levels of the process variables and the boundaries imposed on the proportions of the polymers (mixture variables) used to prepare the films can be observed in Table 1. The film formulations were prepared according to four main plot combinations blocked with seven different subplot combinations of mixture variables (Fig. 1). Two additional subplot replicates were also added in each block to verify whether the subplot variances inside the blocks varied, and the σ 2 SP was estimated in the overall central point, generating 36 (9 × 4) experiments. The error variances were calculated separate from replications based on the procedure proposed by Kowalski et al.26 : in the whole-plot combination (DRUG = 1, TEMP = 0), three-subplot triplicates were performed in the centroid central point [0.37(hpmc), 0.37(pvp), and 0.26(peg)]. This procedure was repeated three times, resetting Alexandrino and Poppi, JOURNAL OF PHARMACEUTICAL SCIENCES

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RESEARCH ARTICLE – Pharmaceutics, Drug Delivery and Pharmaceutical Technology

Table 1. Experimental Conditions for the Preparation of Films in the Split-Plot Experimental Design Levels Process variables TEMP DRUG Mixture variables Hpmc Pvp Peg

−1 40◦ Ca 20%

+1 60◦ Cb 35%

0.70 0.45 0.40 0.37 0.20 0.70 0.45 0.40 0.37 0.20 0.60 0.40 0.26 0.10

Curing times: a 72 h and b 24 h.

Figure 2. Homogeneity curve for sample 10 (see Table 2); the gray region denotes the area above the curve that was utilized as the corresponding homogeneity parameter.

Figure 1. Scheme depicting the split-plot experimental design proposed to study the homogeneity of PAR in the three-component polymeric films.

the whole-plot and subplot variables each time and resulting in nine blocked replications in the overall central point. Hyperspectral Images Acquisition The spectra were obtained using a Spectrum 100N FT-NIR spectrometer coupled with a Spotlight 400N Imaging System equipped with a linear MCT detector array (PerkinElmer, Waltham,MA). The spectra were acquired under flowing N2 in transmittance mode directly from the Petri dishes in which films were formed from 4000 to 7800 cm−1 , at a resolution of 16 cm−1 while using air as a reference. The mapped area was 10,500 × 10,500 :m2 with a pixel resolution of 50 :m. Data Treatment Spectra Preprocessing The spectra were first converted to absorbance and smoothed using the Savitzky–Golay algorithm with the first derivative (window 11, polynomial order 2), followed by normalization to the unit vector length, correcting the scaling variations in the absorbance between the pixels (because of the slight variation of the film thickness in different regions of the samples). PLS Regression for Pixel-to-Pixel Predictions of PAR Initially, the baseline signals and noisy patterns were eliminated by excluding the 6083–7800 and 5276–5364 cm−1 ranges Alexandrino and Poppi, JOURNAL OF PHARMACEUTICAL SCIENCES

from the preprocessed spectra. Afterward, the mean spectrum was calculated for each sample: the ones from formulations 1–12 were gathered in the calibration matrix, whereas the remaining mean spectra (formulations 13–17) were selected for the test group (see Ref.34. The calibration/test matrices and the respective y-responses (bulk concentrations of PAR) were mean centered, and a PLS model was built using SIMPLS algorithm from PLS Toolbox 6.2 (Eigenvector Research Inc., Wenatchee, Washington). The pixel-to-pixel quantification of PAR was performed by applying the PLS model throughout the spectra of the entire images produced from the SPD. The calculations were performed in the Matlab R2009a software (MathWorks, Natick, Massachusetts). Macropixel Analysis of the PAR Images from the Split-Plot Experimental Design In this work, an in-house Matlab routine was developed for performing the macropixel analysis of the chemical images. The CLMB method was chosen because of the greater exploration of larger macropixels during the homogeneity analysis of the film formulations produced in the SPD. The homogeneity parameters were used to characterize the PAR distribution in films; therefore, their y-responses on the SPD were the area below the homogeneity curve (Fig. 2) of each film. This measurement represents all of the information regarding homogeneity included in the sample; therefore, the variations in the homogeneity between the samples could be better discriminated. PLS Regression of the Split-Plot Experimental Design The design matrix X employed for the PLS regression of the split-plot experimental design was built according to the general equation of the mixed model containing two process variables z(i); i = 1(DRUG) or 2 (TEMP) and three-mixture variables x(i); i = 1(hpmc), 2 (pvp), or 3 (peg), according to Eq. (4): DOI 10.1002/jps.24051

RESEARCH ARTICLE – Pharmaceutics, Drug Delivery and Pharmaceutical Technology

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Table 2. Design Matrix (Autoscaled) Containing the Process and Primary Mixture Factors of the Sample Alongside Their Respective Homogeneity Values (y-Responses) Sample

DRUG

TEMP

hpmc

pvp

peg

y

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1

−1 −1 −1 −1 −1 −1 −1 −1 −1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 −1 −1 −1 −1 −1 −1 −1 −1 −1

1 0 0 0.50 0.40 0 0.34 0.34 0.34 1 0 0 0.50 0.40 0 0.34 0.34 0.34 1 0 0 0.50 0.40 0 0.34 0.34 0.34 1 0 0 0.50 0.40 0 0.34 0.34 0.34

0 1 0 0.50 0 0.40 0.34 0.34 0.34 0 1 0 0.50 0 0.40 0.34 0.34 0.34 0 1 0 0.50 0 0.40 0.34 0.34 0.34 0 1 0 0.50 0 0.40 0.34 0.34 0.34

0 0 1 0 0.60 0.60 0.32 0.32 0.32 0 0 1 0 0.60 0.60 0.32 0.32 0.32 0 0 1 0 0.60 0.60 0.32 0.32 0.32 0 0 1 0 0.60 0.60 0.32 0.32 0.32

0.24 0.49 0.64 0.21 0.72 0.79 0.57 0.39 0.31 1.13 0.29 0.48 0.97 0.67 0.66 0.68 0.82 0.94 0.27 0.35 0.25 0.39 0.18 0.38 0.39 0.28 0.32 0.08 0.22 0.25 0.74 0.43 0.48 0.16 0.28 0.13

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

y=

2 i=1

α (i) .z (i) +

+β 123 .x1.x2.x3 + + +

3 

 i=j

2 i=1

3 i=1

3 i=1

β (i) .x (i) +

3 

 i=j

β (ij ) .x (i) .x (j )

γ (i) . (z1 + z2 + z1z2) .x (i)

r 2 FSP

=

i=1

 m  j =1 yij − yi. r (m − 1)

r 2 FMP

=

  yi. − y¯ r− 1

i=1

(5)

(6)

where yij is the jth value in the ith main plot, yi. is the mean value of the ith main plot, y¯ is the overall mean value, m is the number of subplot replicates in each main plot, and r is the total number of replicates. The PLS model of the SPD was also built using the PLS Toolbox 6.2 for Matlab, and the OPLS algorithm was com˚ puted using the Simca-P+ 12.0.1 software (Umetrics, Umea, Sweden).

PLS Calibration and Pixel-to-Pixel Prediction of PAR

(4)

where α(i) and β(i) are the regression coefficients for the process and mixture of main factors, respectively, whereas the remaining coefficients denote the interaction terms. The SPD (only with the main factors) with the respective y-responses is presented in Table 2. In the central point within each main plot, the averages of the respective triplicates were used for regression because their variances did not exceed σ 2 . A PLS regression model was computed with a latent variable number chosen while using the minimal leave-one-out RMSECV. The blocked replications in the overall central point were DOI 10.1002/jps.24051

not included in the model and were only used to calculate σ 2 SP and σ 2 MP (Eqs. (5) and (6). The variances in the model regression coefficients were calculated using Eq. (3), with σ 2 = σ 2 MP + σ 2 SP .

RESULTS AND DISCUSSION

γ (ij ) . (z1 + z2 + z1z2) .x (i) .x (j )

δ (i) .z (i) . (x1.x2.x3) + ε.z1.z2.x1.x2.x3

Figure 3. Predicted PAR concentrations in the calibration and test samples after the PLS regression.

The best PLS model with the mean spectra of the film formulations from the calibration set (i.e., formulations 1–12) was formed using three latent variables. This number was chosen based on a visual inspection of the residual formulations from the test set (formed by the formulations 13–17), once that overfitting must be avoided to obtain accurate pixel-to-pixel predictions later. In the plot of the predicted against the bulk PAR concentrations (Fig. 3), a good fit could be verified between the calibration and test samples (R2 Pred = 0.99), as well as a random distribution of the residues that showed no evidence of overfitting in the developed model. The RMSEC and root-mean-square errors of prediction (RMSEP) obtained from the model indicates that three components were sufficient to provide a satisfactory accuracy regarding the calibration and Alexandrino and Poppi, JOURNAL OF PHARMACEUTICAL SCIENCES

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RESEARCH ARTICLE – Pharmaceutics, Drug Delivery and Pharmaceutical Technology

Figure 4. Chemical images of the PAR concentration in the polymeric films prepared according to the split-plot experimental design (see Table 2). The main plots (i.e., MP1, MP2, MP3, and MP4) are designated by the levels of the process variables. The subplots were arranged according to MP1 by their polymeric compositions in the following order: HPMC, PVP, and PEG.

the future predictions of PAR concentrations in the pixels of the samples. Moreover, the similarity between RMSEC and RMSEP validates the robustness of the model and the avoidance of nonoverfitting. The PLS model was applied in the spectra of the pixels from the formulations prepared during the split-plot experimental design (see Table 2), and the PAR chemical distribution in the samples can be visualized as the concentration distribution maps shown in Figure 4. A pronounced tendency toward increasing the PAR heterogeneity exists in formulations with the same polymeric composition when modulating both DRUG and TEMP levels between −1 and 1 (see MP2 and MP4 in Fig. 4). Moreover, the DRUG factor has a stronger influence over the PAR homogeneity than TEMP because increases in the PAR heterogeneity because of DRUG can be observed in TEMP levels of −1 (see MP3 and MP4 in Fig. 4) and 1 (see MP1 and MP2 in Fig. 4); the same is only true for TEMP at DRUG level of 1 (see MP2 and MP3 in Fig. 4). The influence of the mixture variables on the PAR heterogeneity is limited because no conclusion can be drawn after only visually inspecting the formulations from MP1 and MP4 (DRUG level of −1). However, analyzing the remaining main plots reveals that PAR heterogeneity seems to be higher in formulations with equal quantities of HPMC and PVP; this parameter is lower when PEG is the major polymer in the film. Additional diagnostics regarding the significant factors and the magnitude of their effects on the PAR heterogeneity throughout the films include multivariate models developed based on the SPD and PLS regression. Alexandrino and Poppi, JOURNAL OF PHARMACEUTICAL SCIENCES

The Split-Plot Experimental Design The PLS regression for modeling the SPD was computed according to the complete mixed model in Eq. (4) (total amount of 30 terms). One latent variable was selected while using a crossvalidated model that explains approximately 64% of the data variance for the response (dependent variable). The blocked replications in the central point resulted in a variance of σ 2 = 0.036 that was employed alongside the PLS weights (R) in Eq. (3) to calculate the variances of the regression coefficients. The importance of the variables in the model was analyzed using the VIP value of each variable while inspecting its regression coefficient. The VIP is a sum of the squares of the PLS weights for a single variable in all the model components weighted by the explained variance of each component; therefore, the importance of a single variable for the PLS model was accumulated using their weights in every model component.35 Because the influences of each variable on models X (expressed by their PLS weights) and y are represented by the VIP values and regression coefficients, respectively, the importance of the variables in the PLS model are highlighted in the VIP and regression coefficients plots (Fig. 5). When analyzing the VIPs, the common threshold of VIP = 1 (that is the average of the VIP values of all variables) was employed to select the most important variables of X (i.e., the variables with VIP ≥ 1). In the VIP plot including all the variables from the PLS model (see Fig. 5), nine variables had VIP values higher than the threshold: DRUG, DOI 10.1002/jps.24051

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Figure 5. Variable importance on projections and regression coefficients for the PLS model calculated according to Eq. (4). The main and interaction terms (total amount of 30 variables) involving the process and mixture variables were accounted for in design matrix X to verify their influence on the model from the split-plot experimental design.

DRUG*hpmc, DRUG*peg, TEMP*hpmc, DRUG*hpmc*peg, DRUG*pvp*peg, DRUG*hpmc*pvp*peg, DRUG*TEMP*hpmc, and DRUG*TEMP*hpmc*pvp. The high magnitude of the VIP values for most of these variables compared with those of the remaining variables in the experimental design (i.e., the variables with VIP < 1) emphasizes the major importance of the above-mentioned terms regarding model X; therefore, the VIPsbased “greater than one rule” could be applied properly while selecting the most important variables in the experimental design. Moreover, the high correlation of these variables with the y-responses is also validated by their regression coefficients (see Fig. 5), reinforcing the maintenance of these terms during the PLS modeling of the experimental design. Therefore, analyzing the VIP and regression coefficient plots suggested the exclusion of the nonrelevant variables (total amount of 21 terms, see Fig. 5) from the design matrix X. A new PLS model was developed with only the nine most important variables (X2 ). This change improved the robustness of the model (lower RMSECV) and increased the explained variances for both X2 and y, demonstrating the advantages of excluding the nonrelevant variables (Table 3). DOI 10.1002/jps.24051

Table 3. The Variance in X (%var-X), y (%var-y), and RMSECV for the PLS Models Developed for the Split-Plot Experimental Design

%var-X %var-y RMSECV

Full PLS Model (30 Variables) 1 LV

Reduced PLS Model (Nine Variables) 2 LVs

11.06 63.89 0.23

48.32 74.15 0.18

The importance of the variables was reanalyzed in the reduced PLS model, once that a misleading interpretation of the results could occur if any variable that was not responsible for the y-explained variance was included in the final PLS model. Because the VIP values changed when the PLS model was computed from X2 , the direct exclusion of the variables herein based only on a user-defined threshold might lead to the erroneous elimination of important variables, generating an incomplete final PLS model. Therefore, the importance of the variables in X2 was verified by analyzing the evolution of the model Alexandrino and Poppi, JOURNAL OF PHARMACEUTICAL SCIENCES

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RESEARCH ARTICLE – Pharmaceutics, Drug Delivery and Pharmaceutical Technology

2. If all the regression coefficients are significant, the variable with the least VIP value was excluded from the last design matrix.

Figure 6. Evolution of the RMSECV and y-explained variance of the PLS models computed after excluding the nonrelevant terms from the experimental design. The values in brackets denote the X-explained variance of the corresponding models: 1 (split-plot reduced—2 LVs, nine terms), 2 (exclusion of DRUG*hpmc*pvp*peg— 2 LVs, eight terms), 3 (exclusion of DRUG*pvp*peg— 2 LVs, seven terms), 4 (exclusion of DRUG*hpmc*pvp— 2 LVs, six terms).

performance after excluding the least relevant variables (one variable at a time) from the design matrix. This procedure was performed repeatedly according to the following steps until the simplest model was generated, containing only the relevant terms for the experimental design: 1. Exclusion of the variables with nonsignificant regression coefficients from the corresponding design matrix.

After each step (1 or 2), a new PLS regression was computed, and the evolution of the model performance was confirmed using the stabilization/decline of the cross-validation error, as well as the increased percentage of the X-explained variance without a considerable reduction in the model fitness (i.e., the percentage of y-explained variance). The final PLS model with the best performance was computed using 2 LVs after the DRUG*hpmc*pvp*peg, DRUG*pvp*peg, and DRUG*hpmc*pvp variables were excluded from X2 . The performance of PLS models was computed after excluding each mentioned variable, confirming their lack of relevance when explaining the split-plot experimental design, as observed in Figure 6. The equation for the final PLS model Eq. (7) indicates that both process conditions (expressed by the variables DRUG and TEMP) exert a relevant influence on the y-responses, and the first one exerts a major effect. The increased drug heterogeneity in the films was predominantly dictated by interaction terms formed by the process and mixture variables; the HPMC content could be distinguished from the polymers in the final PLS model. The model quality could also be proven using the absence of outliers in the score plot; the samples are grouped according to their respective DRUG variable levels (Fig. 7a) and the nonsignificant changes in the residue distribution (Fig. 7b). y = 0.24 (±0.12) ∗ DRUG + 0.24 (±0.09) ∗ DRUG∗hpmc +0.22 (±0.09) ∗ DRUG ∗ peg + 0.37 (±0.17) ∗TEMP∗hpmc +0.31 (±0.10) ∗TEMP ∗ DRUG∗hpmc +0.29 (±0.10) ∗TEMP ∗ DRUG∗hpmc∗pvp

(7)

Figure 7. (a) Score plot for the final PLS model. The values in brackets denote the X-explained variance of the corresponding LV. Samples with DRUG levels = −1 (◦) and +1(•). (b) Residues of the PLS model computed according to Eq. (4) (full PLS model) and the model containing only the important variables (final PLS model). Alexandrino and Poppi, JOURNAL OF PHARMACEUTICAL SCIENCES

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RESEARCH ARTICLE – Pharmaceutics, Drug Delivery and Pharmaceutical Technology

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be extracted from the models, such as the explained variances in X and y, RMSECV, VIPs, and residues, was essential to interpret the experimental design in detail until a PLS model including only the key terms could be fitted successfully. The effects of each relevant variable on only the y-correlated variance of the experimental design were further elucidated using the OPLS regression that segregated the nonaffecting variation to enhance the interpretation of the model. Finally, this study revealed a new experimental design approach in which an important factor related to formulation development (i.e., the drug homogeneity) could be quantitatively evaluated through imaging spectroscopy and chemometrics, contributing as a new strategy for characterizing drug delivery systems.

ACKNOWLEDGMENTS Figure 8. Orthogonal projections to latent structure weights from the predictive (w[1]) and y-orthogonal (wo[1]) components, where only the important terms (six variables) were considered in the design matrix.

A further interpretation of the model expressed in Eq. (7) (with only the most relevant variables in the design matrix, Xsig) was obtained with an OPLS regression. The model was computed with only one y-orthogonal component, such that the total number of components (and consequently their ypredictions) in both PLS and OPLS models were the same. The percentages of the explained variances in the y-correlated and y-orthogonal components were 27.7% and 74.9%, respectively. The OPLS weights are shown in Figure 8, where w[1] denotes the weights in the predictive component, and wo[1] denotes those from the orthogonal component. When the plotted data are projected onto the w[1] axis, the importance of each variable for the y-correlated variation is expressed quantitatively. Therefore, the smallest effect of the TEMP*hpmc interaction term and the highest one for the DRUG process variable in the experimental design is revealed. This conclusion could not be based on the magnitude of the PLS regression coefficients; however, the major effect of DRUG in the experimental design was also highlighted by the sample groupings in the PLS scores plot (see Fig. 7a).

CONCLUSIONS Chemical images of the polymeric films loaded with PAR generated reliable evidence regarding the importance of the film composition and the external conditions related to their preparation, including the amount of drug loaded and curing temperature, in the context of the homogeneity of the drug dispersed in the matrix. Some general observations related to the influence of the main factors regarding the changes in the PAR homogeneity could be observed only after a visual inspection of the chemical images; however, when these qualitative descriptions of the PAR homogeneity in the films were transformed to quantitative parameters via macropixel analysis, an experimental design approach could be developed; several factors were analyzed simultaneously using a split-plot methodology involving blocked experiments. The analysis of PLS model parameters represented a successful approach to modeling split-plot experimental designs based on chemical images. The set of information that could DOI 10.1002/jps.24051

The authors are grateful to Brazil’s National Council of Scien˜ Paulo tific and Technological Development (CNPq) and the Sao Research Foundation (FAPESP) for financial support.

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DOI 10.1002/jps.24051