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Detection of nucleation during cooling crystallization through Moving Window PCA applied to in situ infrared data Alessandra Taris, Thomas B. Hansen, Ben-Guang Rong, Massimiliano Grosso, and Haiyan Qu Org. Process Res. Dev., Just Accepted Manuscript • DOI: 10.1021/acs.oprd.7b00076 • Publication Date (Web): 23 Jun 2017 Downloaded from http://pubs.acs.org on June 25, 2017

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Organic Process Research & Development

Detection of nucleation during cooling crystallization through Moving Window PCA applied to in situ infrared data Alessandra Taris†, Thomas B. Hansen‡, Ben-Guang Rong‡, Massimiliano Grosso†*, Haiyan Qu‡ †

Dipartimento Ingegneria Meccanica, Chimica e dei Materiali, Università degli Studi di Cagliari,

Via Marengo 2, Cagliari, 09123, Italy ‡

Department of Chemical Engineering, Biotechnology and Environmental Technology,

University of Southern Denmark, Campusvej 55, 5230 Odense, Denmark

ACS Paragon Plus Environment

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Abstract

The method here proposed based on the Moving Window Principal Component Analysis can be employed in time-varying processes tracked through in situ spectroscopy. In the case under investigation, it aimed to detect the nucleation during crystallization processes. For this purpose, statistical indexes were employed and contribution plot helped identifying the spectral variables that were changing due to nucleation. Isonicotinamide was here considered as model active pharmaceutical ingredient and its cooling crystallization was monitored by means of in situ Infrared spectroscopy. The procedure allowed to overcome issues that may be encountered with static Principal Component Analysis, since it could distinguish the slow-varying changes due to external perturbations (temperature) from abnormal events such as the sudden concentration decrease related to the crystallization. The proposed method demonstrated to correctly detect nucleation without any a priori knowledge of the peaks involved in the process, leading the false alarm rate from 77.38 % (obtained with the static Principal Component Analysis) to 6.9%.

Keywords: Moving Window Principal Component Analysis; crystallization monitoring; nucleation; contribution plots; control charts.


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1. Introduction One of the most important unit operations in pharmaceutical industry is crystallization, which is commonly used to separate and purify Active Pharmaceutical Ingredient (API). The key property attributes of a crystalline product include purity, crystal shape, crystal size distribution (CSD), mean crystal size and the polymorphic form. Formation of these key properties, especially the particulate properties and polymorphism, are strongly dependent on the operation parameters of the crystallization process in terms of temperature, concentration of the solute, presence of seeds or impurities. For these reasons, monitoring and control batch cooling crystallization processes play a key role in optimizing product quality and process performances. To this aim, the U.S. Food and Drug Administration (FDA) promotes the use of in situ analytical technologies, usually referred to as Process Analytical Technologies (PATs), and advanced control methodologies for process understanding, analysis, and control.1 During cooling crystallization, the API is firstly completely dissolved in the solvent at a temperature higher than the saturation temperature. When the solution is cooled down, the system reaches supersaturated conditions, and spontaneous primary nucleation is driven out by the supersaturation. Nucleation denotes the initiation of the new solid phase, and therefore plays a significant role in the formation of many key properties of the crystals, especially the particle size and polymorphism. The temperature at which primary nucleation occurs depends on different factors such as initial concentration, cooling rate, level of agitation and presence of impurities.2 Hence, due to the nondeterministic nature of the primary nucleation, its exact prediction beforehand is not always possible and values obtained at lab scale may not be exactly reproducible at industrial scale. From a monitoring point of view, this information is important for the control system to assess the exact timing for the proper implementation of the subsequent actions to be accomplished


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during manufacturing of pharmaceuticals. Moreover, in industrial crystallization processes, seeding is commonly used to induce secondary nucleation to control the particle size as well as the polymorphism.3 When seeding is applied, it is essential that seeds crystals are added to the supersaturated solution before the primary nucleation occurs, i.e., seed crystals have to be added before the supersaturation level reaches the metastable zone limit. Hence, systematic approaches that can accurately detect the primary nucleation will enable the detection of the metastable zone limit for a given system with a specific cooling rate, and thus will contribute to a successful design and development of seeded batch crystallization processes. The onset of nucleation usually manifests as a sudden change of the visual properties of the solution (such as e.g. turbidity) and can be experimentally detected by e.g., naked eyes observation or by optical density changes detected by light transmission. On the other hand, Attenuated Total Reflection Fourier Transform Infrared (ATR-FTIR) can represent a useful tool for in-line monitoring of crystallization. It was firstly proposed by Dunuwila et al.4 as a method to infer the solubility and the supersaturation of solutes in liquids and to measure supersaturation in real time during crystallization processes.5 Moreover, the ATR-FTIR has been successfully employed for feedback control of cooling and antisolvent crystallizations.6,7,8,9 It was proposed as well in a pilot plant setup to monitor paracetamol crystallization10 and batch cooling crystallization of β-L-glutamic acid.11 Different examples of nucleation detection during crystallization can be found in literature.12,13,14 Nevertheless, since real time analyzers like infrared spectroscopy provide highly informative data, methodologies able to interpret and gather information from these data are required. With this regard, Principal Component Analysis (PCA) is a well-known multivariate technique15 that can be employed to compress data. It has been extensively applied to spectroscopic data for e.g.,


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quality control,16,17 health monitoring18 and reaction monitoring.19 PCA based approaches are employed together with spectroscopic measurements to monitor crystallization as well.20,21,22 In order to detect abnormal process behaviour or test if new observations are consistent with the reference conditions, T2 and Q control charts are usually employed.23 Moreover, the contribution plot can be exploited to identify which variables are most contributing to T2 and Q statistics and then are deviating from the typical behavior.24,25 Although process monitoring based on PCA has been successfully applied for stationary processes, its use can be questionable when measurements are collected during a dynamic process that depends on an external variable t (e.g., time, temperature, pressure). This may occur since data violate the assumption of independence with respect to t. Indeed, during a transient process, variables can intrinsically change (increase or decrease), although this occurrence does not necessarily imply that the system is out-of-control. When static PCA model is employed, only specific conditions are considered as the reference ones. Thus, it may result as ineffective to represent the status of the entire process, since the training set remains static. As a consequence, false alarms may occur and new observations may be erroneously classified as deviation from the reference conditions. To improve the monitoring of transient processes and address the false alarm issue, different methodologies have been developed such as dynamic PCA for autocorrelated data,26,27 Recursive PCA28 and Moving Window PCA29,30 for non-stationary data. An interesting comparison of these three methods and works can be found in De Ketelaere et al.31 In addition, useful guidelines to choose the correct parameters in RPCA and MWPCA are provided by Schmitt et al.32 In detail, these latter methods involve updating the PCA model considering different datasets. Recursive PCA (RPCA) includes new observations and exponentially downweighs old ones to evaluate the mean and covariance matrices used in PCA. However, at


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some point older data may become unrepresentative of the varying process. Moving Window PCA (MWPCA) can overcome some of deficiencies of RPCA, building a suitable adaptive model. It basically consists in moving a window slide along the data such that the oldest observations are removed and the newest ones, that are more representative of the current process operation, are included. Among the methods applied to in situ spectroscopic data collected during cooling crystallization, dynamic PCA33,34 is implemented to infer when the system is approaching nucleation, however it is not able to predict the actual onset of crystallization, as static PCA, it does not take into account the dynamic information contained within spectral data. For example, temperature may affect the vibration intensity and frequency of molecular bonds, as investigated by Simone et al.,35 and solute concentration in the solution phase influences spectra due to the mass transfer from solution phase to solid phase. Indeed, methods that detect nucleation in real time and automatically could improve the reliability and the promptness of the control system. In this work, MWPCA was investigated and proposed to treat evolving spectral data. Although this procedure is well known and extensively applied in process monitoring,36,37 up to our knowledge, no works in literature have employed it for the analysis of in situ spectroscopic data along the perturbing variable t. To evaluate the performance of the method, cooling crystallization of isonicotinamide (INA) in methanol monitored through FTIR spectroscopy was considered. In a previous work,38 PCA was employed for a-posteriori detection of nucleation temperature of INA crystals in various solvents and it revealed useful. Nevertheless, during inline monitoring, methods for in real time detection as spectra are collected would be required. To this aim, MWPCA represents a valuable tool that also considered the change of spectra due to temperature variations occurring during cooling crystallization. Since an abnormal deviation of


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spectra collected after nucleation could be observed, the detection could be pursued resorting to control charts of T2 and Q statistics. Moreover, contribution plots helped identifying which spectral variables were mostly changing and might be affected by nucleation. In the following, firstly static PCA and statistical control indexes are reviewed, then the implementation of MWPCA on spectroscopic data is introduced. Eventually, results section shows the comparison between static PCA and MWPCA applied to infrared measurements. 2. Case study: cooling crystallization of isonicotinamide Isonicotinamide (INA) is a pyridine derivative with an amido group in γ-position and has antitubercular, anti-pyretic and anti-bacterial properties. It is a popular coformer that can be used as partner molecules with Active Pharmaceutical Ingredients in co-crystal preparation.39 Moreover, several metal complexes of isonicotinamide have been used as drugs in medicinal processes since some coordination compounds of this relevant biological ligand are more effective than the free isonicotinamide molecule.40 Since its use in drug industry is becoming relevant, proper tools are required to in-line monitor crystallization of INA. 3. Materials INA and methanol (99.9% analytical grade solvents) were purchased from Sigma-Aldrich. 3.1. Experimental setup In-line IR spectra were collected from the INA solutions during cooling crystallization with a Mettler Toledo ATR FTIR ReactIR 15 equipped with a DiComp Diamond probe. Each spectrum was recorded every 30 seconds covering a spectral range 648.9 ‒ 2998 cm-1 with a resolution of 3.73 cm-1. 3.2. Cooling crystallization


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Experiment was performed according to Hansen et al.38 Cooling crystallization was carried out using an Easymax 102 synthesis workstation from Mettler Toledo with two 100 mL reactors. Mixing in the reactors was provided with crossbar stirring at 300 rpm and a condenser was mounted on each reactor to recover the evaporated solvent during crystallization. The Easymax 102 synthesis workstation was equipped with a built-in solid state thermostat, which ensured controlled cooling down to -25°C while still maintaining constant cooling rate. Cooling crystallization of INA has been conducted with solution saturated at 10°C. Before the cooling started, the solution was heated to 15°C above the saturation temperature for 1 hour to ensure complete dissolution of INA. The cooling rate was fixed at 0.5°C/min. The change of turbidity was visually observed and the corresponding temperature was stated as the nucleation point. The cooling was continued until a sufficient amount of crystals nucleated out of solution. IR spectra were collected using the in-line ATR FTIR probe that was inserted into the crystallizer. The experimental set-up is shown in Figure 1.


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Figure 1. Experimental set-up used for cooling crystallization of INA. 3.3. Infrared spectra Figure 2 depicts the IR spectra of methanol and INA in methanol saturated at room temperature. The main INA peaks (indicated as arrows) were located at 764, 850, 1219, 1413, 1555, 1604, 1630 and 1689 cm-1. While the peaks related to methanol bonds were located at 1022, 1115, 1413 and 1451 cm-1. It should be noted that the INA bond at 1413 cm-1 overlapped with the methanol one.


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Figure 2. Infrared spectra of methanol (black line) compared with the spectrum of the INA solution collected at room temperature (grey line). INA peaks were indicated with arrows. For the implementation of the algorithms, the data considered included spectra collected from the beginning of cooling (T= 24.9 °C) to the end of experiment (T= -9.8 °C) depicted in Figure 3. The spectral range considered was 648.9‒2002 cm-1 in order to exclude contributions not informative for INA crystallization. Hence, collected spectra were arranged in a matrix X(N×J), where N is the number of spectra (equal to 139) collected along the sampled temperatures (every 30 s) and J (=364) the wavenumbers.

Figure 3. Infrared spectra collected during cooling crystallization of isonicotinamide in methanol.


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4. Methods 4.1. Static Principal Component Analysis The Principal Component Analysis (PCA) is a well-known multivariate technique15 used to compress data and extract relevant information from experimental data. It is based on the decomposition of the generic data matrix X(N×J), as reported in eq (1).

(×)

=

∙ = ∙ +

(×) (×)

(× ) ( ×)

(×)

+ = (×)

(×)

(1)

where N is the number of observations and J the spectral variables (e.g. wavenumbers). The score matrix TA accounts for the first A projections of the spectral variables onto the new subspace identified by the principal components, the columns ta of the matrix (a=1, 2,.., A) are orthogonal. The loading matrix =

describes the relationship between the spectral

variables and the principal components, where corresponds to the first A columns of P and

is the prediction matrix obtained by retaining the first A is the residual loading matrix. principal components (PCs) and E is the residual matrix. Variables are in general pre-processed before PCA implementation, i.e. they are mean centred and scaled to unity variance. Therefore, PCA consists in two steps: (i)

calibration, the model is built based on the training set, (×) , therefore it should be chosen such that it is a quite fair representation of the normal operating condition (NOC). Subsequently, samples mean, covariance matrix and loading matrix P are computed. Then, the number of principal components is usually selected based on the cumulative variance explained;15

(ii)

prediction, new observations are projected onto the PCA model to evaluate whether they are consistent with it and they behave according to the training set. The new


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multivariate observation xk is projected onto the space spanned by the first A principal components through the relationship (2).

t k = xk ⋅ PA

(2)

4.2. On-line process monitoring 4.2.1. Indexes for statistical process control In order to detect abnormal process behaviour or classify a new observation as belonging to the training set, T2 and Q statistics are employed. For a new observation xk, they are evaluated through eqs (3) and (4). = ∙ !"# ∙

(3)

* = ( − ∙ + $ = % ∙ % , % = ( − (

(4)

* is the k-th observation where, in eq (3), Λ is the covariance matrix of the tk scores and ( predicted through the PCA model. In practice, the T2 statistic represents an overall measure of the distance of tk from the origin of the PCA subspace, whilst the Q statistic41 describes how well the PCA model predicts the xk vector. Statistical confidence limit for T2 statistic42 is calculated by means of eq (5) where Fα is the limiting value computed for a Fisher distribution with (A, NA) degrees of freedom. ,-. =

∙/ 0 "#1

2 (4, 5 ∙(" ) 3

− 4)

(5)

While, the upper control limit for Q is defined as:43 $678 = 9# :1 + 9 ℎ= >

?@ "# AB0

C+

DE ?@ F(A0 ) AB

G

#H ?@

(6)

where: 9- = ∑KL M# JK-

i=1, 2, 3


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ℎ= = 1 −

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29# 9O 39

cα is the α-th upper percentile of a normal distributed variable with zero mean and unity variance. 4.2.2. T2 and Q contribution plots Contribution plots demonstrate useful to identify which variables are mostly contributing to T2 and Q statistics and then are deviating from the typical behavior.24,44 The contribution index QR of the Q statistic can be evaluated for the k-th observation through eq (7). Each element of the vector corresponds to the ratio between the contribution of each variable to Q statistic and its expected value.24 T0

U SR = V-WX(Y

(7)

[) Z Z

\ is the loading matrix in the residual space. where S is the covariance matrix and

0

Similar definition for the contribution vector S of T2 is given in eq (8), where Λ is the eigenvalues matrix. 0

[ 1 / !]@._ Z à

Z S = V-WX(Y

Z!

0

(8)

]B [ ) Z 0

24 The limit value for the contributions Sbc and Sbd is generally given by a e#,3 . Nevertheless,

when the multiple statistical test is carried out on a multivariate sample, the probability of running into false alarm values increases with J variables. To avoid excessive false alarms and then reduce the chance of type I error, the Bonferroni correction can be employed.45,46 4.2.3. On-line process monitoring procedure On-line process monitoring is implemented following the subsequent steps: first, a PCA model, based on the reference data of the process, (×) , has to be identified. Therefore, the


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loading matrix P, is computed and the number A of principal components is selected. In addition, T2 and Q limits are evaluated according to eqs (5) and (6). For on-line monitoring, the new data points xk are projected onto the model space defined by the PCA model, spanned by the retained A loading vectors as reported in eq (2). Then, the associated values of the T2 and Q statistics are calculated by means of eqs (3) and (4) and usually reported in control charts. The occurrence Qk>Qlim and/or T2k>T2lim may be indicative of abnormal process behavior or that the observation is not consistent with the reference ones42,23 and alarm triggers. The performance of these two classifiers can be evaluated through two indicators: the false alarm rate (FAR) percentage that estimates the probability of type I error, as expressed in eq (9) and the missing detection rate (MDR) percentage that estimates the probability of type II error, as expressed in eq (10). 24f =

g,h

klf =

g

× 100%

h,g h

(9)

× 100%

(10)

Where NN is the number of observations belonging to the normal operating condition and NN,F is the number of observations belonging to the NOC but identified as out-of-control. NF is the number of faulty observations and NN,F represents the number of faulty observations detected as normal. These indicators should be as low as possible to ensure a robust monitoring and control system. Once the out-of-control observations are detected, contribution plots are usually employed, in order to identify which variables are deviating from the reference behavior and are contributing to T2 and Q statistics. 4.3. Moving Window Principal Component Analysis


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Although static PCA and indexes for statistical control can be still employed to reveal and isolate disturbances, the correct detection of faults cannot be always guaranteed when data contain dynamic information, and depend on external variable t (time, temperature, pressure, etc.). Indeed, in presence of slow-varying changes, false alarms may occur and reduce the reliability of the monitoring system. On the other hand, Moving Window Principal Component Analysis (MWPCA) is able to capture the process dynamics, correctly classify observations and detect faults,29 decreasing the number of false alarms. This method consists of performing PCA on a training set that is not static but it is continuously updated by removing the oldest observations and adding the newest ones as long as the window moves. Since a fixed size window is moved along the data, the size of the moving window, L, is a key parameter to choose. It depends on the rate at which the parameters (mean and covariance) change. There are different criteria for the selection of L, nevertheless, when the number of observations available is limited, the minimization of the sum of squared prediction errors (SSPE) of the validation set no (m×) (belonging to the NOC, where V is the size of the validation set) is employed32,47 as reported in eq (11). v *vt,l t ppqr(s) = ∑,Mu vL,M#txt − (

(11)

*v,6 is the observation of the validation set collected at t (with t=l+1, l+2, …, l+V) In eq (11) ( predicted through a PCA model built considering a training set whose observations are collected between t=T0 and t=l (where l=Lmin, Lmin+1, …, Lmax). After choosing the proper size window, a training set (w×) is selected to build a PCA model, new data are projected on the PCA subspace and if the control charts establish that they belong to NOC region, they are included in the new training set and the oldest observations are removed. The window is moved until a fault is detected.


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4.3.1. MWPCA applied to spectroscopic data for nucleation detection In this work, IR spectra collected during crystallization represented an example of transient data where temperature was the perturbing variable and affected spectra. MWPCA based approach was here proposed to infer nucleation point particularly in presence of slow-varying changes induced by temperature. Indeed, since nucleation denoted an abnormal deviation of spectra from those collected before that turning point, it could be considered as an out-of-control state of the system to indicate the onset of crystallization. The method here implemented, as other multivariate techniques, does not require any a-priori knowledge of the peaks or spectral regions evolving after nucleation and could be in principle applied also in case of partial overlapping peaks. It is shown in detail in Figure 4a: after selecting the window size, L spectra were considered for the training set (w×) and a PCA model was built, that involved determining the loading matrix P, mean and standard deviation of the j-th spectral variables, number of principal components, T2 and Q limits according to eqs (5) and (6). Then, the two subsequently collected spectra were projected onto the PCA model and T2 and Q were estimated according to eqs (3) and (4). The criterion adopted for the moving of the window was the following: if both observations were under the control limits, the new window was moved forward including these two observations and removing the oldest two ones. When the statistics evaluated for three consecutive future observations exceeded the limits, the system was defined as out-of-control, then onset of crystallization was detected and the window was not moved forward anymore. In this case, the contribution plot was analyzed to assess which spectral variables were mostly contributing to the abnormal statistic values, allowing the identification of the spectral regions that significantly changed due to nucleation. An illustrative example is


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reported in Figure 4b, where the grey and dashed rectangles represent spectra considered for training set and for the prediction set, respectively. The analysis was carried out with in-house procedures written in Matlab®R2015 environment equipped with the Statistics toolbox.

Figure 4. (a) Moving Window PCA algorithm to detect nucleation in crystallization processes. (b) Illustrative example of the MWPCA procedure. 5. Results and discussion 5.1. Static PCA The static PCA was firstly implemented to assess its ability to detect faults. Hence, spectra were baseline corrected and pre-processed through mean-centering and standardization. The static PCA was built considering a training set of spectra collected at T = [24.9 - 13.6] °C. The prediction set consisted of 94 observations collected at temperature from 13.6 °C to -9.8 °C. The first component explained 75.75% of the variance, the second 8.69% and the third 3.19%,


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while each of the subsequent components added maximum 1%. Therefore, three principal components were believed to describe most of the variance present in the evolving system. T2 and Q statistics were estimated for both training and prediction sets (depicted as open squares and grey circles, respectively) and represented in Figure 5. As it was expected, the values of the statistics calculated for the training set fell inside the normal operating region, only the Q statistic values pertaining two observations were slightly higher than the limit and therefore they could be classified as false alarms. Nonetheless, it should be noted that the false alarm rate in the training set was acceptable (3% of the total observations) and it was comparable to the significance level chosen for the limit value of the statistic (α=5%). Concerning the prediction set, as reported also in Pöllänen et al.,33 if more than three observations exceed the limit, the system can be considered as approaching the nucleation. However, it can be observed that the values of the two statistical indexes were clearly non-stationary (as also reported in Ku et al.26) and they increased with temperature. This feature was due to the fact that static PCA was not able to describe temperature-dependent data. Since in a previous work,38 we found out that naked eyes inspection of the change of turbidity provided the same results of ATR-FTIR coupled with PCA for off-line nucleation detection, visual observation was considered as a reference to assess and compare the accuracy of the methods. Hence, the control charts showed that the data collected at temperature below 7.1 °C resulted classified as out-of-control, but since the visually observed nucleation point occurred later at TNUCL

≈

-7.4 °C circa, they were defined as nucleation false alarms.

Therefore, the Q statistic correctly classified 30.85% of the prediction set and the false alarm rate was 77.38% (65 false alarms out of 84 observations collected before the nucleation). On the base of the T2 chart, 37.2% of spectra were correctly classified and the false alarm rate was 70.23% (59 false alarms out of 84 observations collected before the nucleation). Moreover, the alarm


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triggered at temperature T= 6.6 °C for T2 and T=7.4 °C according to Q chart, that was about 14 °C or, alternatively 30 min, earlier than the actual onset of the crystallization. These results demonstrated that static PCA led to questionable outcomes when used to monitor dynamic systems. Indeed, it considered systematic slow-varying changes as inconsistent with the training set behaviour instead as characteristic of the process. This occurred because it did not take into account that mean and covariance of new spectra changed with temperature. As it can be observed, the change of slope of the statistical indexes values could give an indication of the actual beginning of the nucleation, as reported also by Pöllänen et al.33 Nevertheless, from a monitoring point of view, a threshold that assesses automatically the beginning of crystallization and avoids false alarms would be more practical and reliable to the plant operator than a change of slope.


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Figure 5. Statistical monitoring using static PCA applied to Infrared data of INA in methanol. (a) Q statistic; (b) T2 statistic. Spectra were classified out-of-control at temperature below 6.6 °C and 7.4 °C, according to Q and T2 charts, respectively. Since the visually observed nucleation temperature was -7.4 °C circa, the false alarm rate was estimated as 77.38 % and 70.23 % for Q and T2, respectively. Another important aspect to take into account when a dynamic process is modeled through static PCA, is the selection of the proper training set size. Indeed, the effectiveness of the procedure may depend on the size of the window, which is the number of the observations included in the training set. In order to test the influence of the window size on the detection of nucleation, static PCA was implemented considering a training set whose size was increased from 20 observations in the temperature range T= 24.9-19.9 °C, to 40 observations collected in the temperature range T= 24.9 to 13.6 °C (value near the saturation temperature). Three latent variables were chosen since explained an average cumulative variance of 85.4%. Concerning the prediction set, it consisted of the observations collected at temperature T= Ttrain to the end of the experiment. Figure 6a shows that, when the size of the training set was increased from 20 to 40 observations, the threshold temperature denoting the approach nucleation decreased from about 17 to 7 °C. This means that, if the training set size is too low and the conditions (temperature) at which the observations were collected are quite far from the actual nucleation temperature, the alarm could trigger too early. In fact, comparing this results with the visually observed nucleation point (TNUCL ≈ -7.4 °C), the alarm started before the nucleation occurrence, that it could be from 24 °C to 14 °C earlier, depending on the window size. Figure 6b depicts the false alarm rate detected from the T2 and Q control charts with different size of the training set. One


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should notice that the ratio was quite high and did not decrease significantly by considering even wider window sizes (from 92% to 77.38%).

Figure 6. Results after implementation of static PCA increasing the training set from a size equal to 20 (T= 24.9 to 19.9°C) to 45 observations (T= 24.9 to 13.6 °C). (a) The temperature at which the alarm should trigger to indicate the approach nucleation was detected from the T2 and Q control charts: when the size increased, the temperature of the detected nucleation decreased. (b) the false alarm rate calculated for T2 and Q, decreased as the size increases, but it was still high. 5.2. Moving Window PCA According to the procedures illustrated in section 4.3, spectra pre-processing through meancentering and Unity Variance standardization was performed each time the window was moved.


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To choose the window size L through the SSPE criterion,32 the following parameters were taken into account: the minimum number of observations collected in the experimental window was Lmin= 20, therefore the dataset for the first window included the first 20 spectra collected between T= 24.9 and 19.9 °C; whereas regarding the maximum size Lmax=45, the dataset for the last window included 45 spectra collected from T= 24.9 up to T= 13.6 °C. This latter temperature value was chosen lower than the saturation one. The PCA model was developed with three principal components that explained between 81.89 and 88.90% of cumulative variance (depending on the window size). While, for the validation set, three subsequent spectra (V=l+1, l+2, l+3) were considered. The SSPE calculated through eq (11) is shown in Figure 7, as it can be seen, the optimal size of the moving window was estimated as equal to 43 spectra, corresponding to ∆T=10.8 °C and it was used hereafter for the MWPCA implementation.

Figure 7. SSPE calculated varying the window size. The minimum value was observed for L=43. MWPCA was then implemented according to the procedure shown in Figure 4: the PCA model was built selecting three latent variables explaining an average cumulative variance of


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86.66%. The results of the on-line monitoring procedure achieved for the most representative windows are depicted in Figure 8 to Figure 10. T2 and Q control charts are represented as figure (a) and (b), whereas figure (c) shows the contribution plot reporting the contribution of each wavenumber to Q statistic. This latter representation allowed the detection of the spectral regions significantly changing due to nucleation without any a-priori knowledge of the peaks involved in the crystallization process. Figure 8 depicts the results obtained from MWPCA built considering a training set where observations collected at T = 24.9‒13.6 °C were included. In more detail, Figure 8a and 7b, show the values of T2 and Q, open squares indicated the training set and grey circles the prediction set, the control limits were evaluated as in eqs (5) and (6) at 95% confidence level. Figure 8c shows the contribution plot, reporting the standardized residuals with respect to the corresponding wavenumbers according to eq (7). In addition, the main INA peaks are reported as open triangles for sake of comparison. The threshold value for the contribution cQ, reported with the dotted line, was computed with a 5% significance level and modified according to Bonferroni adjustment. As it can be observed in Figure 8a, the prediction set, reported as grey circles, could be classified as in-control, and the contribution of each spectral variable did not exceed the control limit. Concerning the results achieved for the window between T=2.9 and -7.6 °C (Figure 9), the Q statistic values for the prediction set were greater than the limit value (Figure 9b) and the onset of the crystallization could be detected at T= -7.9 °C, value quite near to the visually observed one (T ≈ -7.4 °C). Indeed, it can be inferred from the contribution plot that peaks related to INA located at 1689 and 1451 cm-1 were increasing with temperature and exceeded the threshold value. Since three observations were greater than the Q threshold, the window was not moved anymore and new observations were added to the prediction set. Figure 10a clearly shows that


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the values of Q statistic for the prediction set were greater than the threshold and considerably heightened; moreover, it can be inferred from the contribution plot that the contributions corresponding to the INA peaks dramatically increased, while the solvent ones did not change as expected. It is remarkable that the onset of the nucleation was detected by the Q statistic. On the other hand, according to the T2 chart, nucleation was detected at T = -8.7 °C, this delay could be due to the fact that in general T2 is less sensitive to deviations than Q.48

Figure 8. Nucleation detection during cooling crystallization of INA in methanol through Moving Window PCA. The model was built considering a training set (open squares) of observations collected at T=24.9‒13.6 °C. T2, Q and cQ control charts are reported, dash-dotted lines represent the control limits. The prediction set (grey circles) was classified as in-control, then nucleation did not occurred yet.


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Figure 9. Nucleation detection during cooling crystallization of INA in methanol through Moving Window PCA. The model was built considering a training set (open circles) of observations collected at T=2.9 ‒ -7.6 °C. T2, Q and cQ control charts are reported, dash-dotted lines represent the control limits. The prediction set (grey diamonds) was classified as out-ofcontrol according to Q control chart, then the onset of the crystallization was detected at T= -7.86 °C.


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Figure 10. Nucleation detection during cooling crystallization of INA in methanol through Moving Window PCA. The model was built considering a training set (open circles) of observations collected at T= 2.9 ‒ -7.6 °C. T2, Q and cQ control charts are reported, dash-dotted lines represent the control limits. It can be noted that the future observations (diamonds) strongly deviated from the NOC and the increasing values indicated that the crystallization was continuing. The contribution plot depicted in Figure 10c for the observations collected after the nucleation was magnified in Figure 11. At the beginning the extent of the contribution was limited, while it heightened as the crystallization progressed. The degree of the contribution changed from about 10 (before the nucleation, see Figure 10a) to 104 (after the nucleation). During the implementation of the MWPCA, Q statistic globally detected only six false alarms out of 86 global observations collected before nucleation, therefore the global false alarm rate was 6.97%. The missing detection rate was zero.


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Regarding T2, seven false alarms out of 86 global observations collected before nucleation were observed and the global false alarm rate was 8.14%. It should be noted that also four missing alarms were present, leading global missing detection rate to 30.7%. Therefore, Q statistic demonstrated more able to detect the nucleation when compared to the T2. Indeed, the latter statistic can discriminate out-of-control observations only when spectra largely deviate from the ones belonging to the training set.48 Therefore, it was more likely that Q gave the alarm earlier than T2. Note that MWPCA demonstrated revealed as a suitable method to treat data coming from transient processes like crystallization, since the moving window allowed of detecting only abnormal events, whereas systematic slow-varying changes caused by cooling were considered as intrinsically belonging to the process. It detected nucleation more accurately than static PCA, indeed, the false alarm rate noticeably decreased from 77.38% (static PCA) to 6.9% (MWPCA), that could improve the reliability of the control system.

Figure 11. Contribution plot of the observations detected as out-of-control. Contributions related to INA peaks increased as the crystallization proceeded, while the solvent ones did not vary. Since the nucleation occurred the INA peaks were supposed to change. 6. Conclusions


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In this paper, Moving Window PCA was proposed to monitor and model transient processes like crystallization. Indeed, when dynamic data were analyzed, process variables could intrinsically change and may influence parameters like mean and covariance. Hence, this method adapted PCA model to track the process dynamics and took into account the occurrence of notstationary data. Infrared spectroscopic data gathered during INA cooling crystallization in methanol were considered to apply and test the methodology. MWPCA demonstrated to be able to correctly identify the out-of-control status (in this case, nucleation), otherwise not achievable through static PCA. Indeed, T2 and Q control charts based on MWPCA detected the onset of crystallization at T= -7.9 °C, that was quite close to the temperature at which the change of turbidity was visually observed (T ≈ -7.4 °C). The main advantage is that it did not require any a priori information about the peaks involved in the crystallization or the metastable zone width. Finally, contribution plots identified the INA peaks as the mostly contributing variables to the out-of-control status. Moreover, it is worth noting that it could improve the control system reliability since the false alarm rate noticeably decreased from 77.38% (static PCA) to 6.9% (MWPCA). The obtained results can be used to develop advanced PAT-based process control strategies for the crystallization of active pharmaceutical ingredients. AUTHOR INFORMATION Corresponding Author * Massimiliano Grosso: [email protected] Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.


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ACKNOWLEDGMENTS The authors would like to thank Nete Sloth Bækgaard and Katrine Englund Christensen for all of their experimental work and immaculate laboratory notes for all experiments throughout their bachelor thesis at the Department of Chemical Engineering, Biotechnology and Environmental Technology, University of Southern Denmark. ABBREVIATIONS API, Active Pharmaceutical Ingredient; ATR-FTIR, Attenuated Total Reflection Fourier Transform Infrared; CSD, crystal size distribution, FDA, Food and Drug Administration; INA, isonicotinamide; MWPCA, Moving Window Principal Component Analysis; NOC, Normal Operating Condition; PAT, Process Analytical Technologies; PCA, Principal Component Analysis; SSPE, sum of squared prediction errors. References (1) Guidance for Industry, PAT—a framework for innovative pharmaceutical manufacturing and quality assurance, U.S. Food and Drug Administration (FDA), Rockville MD, USA, 2004. http://www.fda.gov/downloads/drugs/guidances/ucm070305.pdf (accessed on 20/01/2017). (2) Nývlt, J. The Kinetics of Industrial Crystallization. Elsevier: New York, 1985. (3) Hansen, T. B.; Qu H. Cryst. Growth Des. 2015, 15, 4694–4700. (4) Dunuwila, D. D.; Carroll, L. B.; Berglund, K. A. J. Cryst. Growth 1994, 137, 561–568. (5) Dunuwila, D. D.; Carroll, L. B.; Berglund, K. A. J. Cryst. Growth 1997, 179, 185–193.


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Table of Contents 44x23mm (300 x 300 DPI)


Detection of Nucleation during Cooling ... - ACS Publications

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