Mixture Component Prediction Using Iterative Optimization Technology

Article pubs.acs.org/IECR

Mixture Component Prediction Using Iterative Optimization Technology (Calibration-Free/Minimum Approach) Koji Muteki,* Daniel O. Blackwood, Brent Maranzano, Yong Zhou, Yang A. Liu, Kyle R. Leeman, and George L. Reid Pfizer Worldwide Research & Development, Eastern Point Rd, Groton, Connecticut 06340, United States ABSTRACT: Process analytical technology (PAT) plays an important role in the pharmaceutical industry. PAT is used extensively in process development, process understanding, and process control. Often, quantitative measurements are desired/ required and a calibrated model will have to be developed and implemented. The development, implementation, and maintenance of these quantitative models are both resource and time intensive. This paper describes a calibration-free/minimum approach, iterative optimization technology (IOT), which is used to predict (without calibration standards) the composition of a mixture while maintaining a similar predictability to calibration standard models. It typically involves using only pure standard spectra (collected prior to the analysis) and sample spectra collected during the analysis. This technology is applicable for predicting compositions during development of pharmaceutical products (where the synthetic route, formulation, or process is not set) and is not intended for use in good manufacturing practice (GMP) manufacture where quantitative measurements are made using validated models. For ideal mixture cases, the mixture composition is iteratively computed at every sample time point to minimize an excess absorption subject to constraints (e.g., mixture constraints, upper/lower limits). Linear IOT is used to describe these ideal mixture cases. For nonideal mixture cases, the excess absorption, including the nonlinear characteristic, is first represented by a Box-Cox transformation. A limited number of training/calibration samples is required for these nonlinear examples. The mixture composition is then iteratively obtained in a similar optimization framework as linear IOT. Nonlinear IOT is used to describe these nonideal mixture cases. Linear and nonlinear IOT have provided comparable prediction accuracy on binary and ternary mixtures as compared to a calibrated partial least squares (PLS) model. IOT enhanced the understanding of dosage form blending processes by determining the composition/ratio of all (spectrally discriminated) components in the blend in real time. As composition is predicted each revolution, determination of the blending end point (does each component trend meet the known target mixture ratio) can be easily determined. Linear and nonlinear IOT can also be used to aid process understanding via detecting/representing molecular interaction effects utilizing the excess absorption calculation. The effectiveness of the linear and nonlinear IOT is demonstrated through four online and offline pharmaceutical process examples (bin-blending process, rotary tablet press feed frame process, and two different solvent mixtures).

1. INTRODUCTION Process analytical technology (PAT) plays an important role in the pharmaceutical industry. PAT is used extensively in process development, process understanding, and process control.1 Spectroscopic techniques such as mid-infrared (MIR), nearinfrared (NIR), Raman, and ultraviolet (UV) are commonly used to monitor pharmaceutical processes (e.g., chemical reactions, blending, continuous mixing) online and in real time. These activities have been buoyed via regulatory guidance, including PATA Framework for Innovative Pharmaceutical Development, Manufacturing, and Quality Assurance.2 The aim of this PAT guidance is to increase process understanding and control and at the same time reduce the uncertainty and variation in the quality of the end product. IOT is applied to enhance process development and process understanding. Online quantitative measurements are often desired during process development and understanding. The traditional approach is to apply a calibrated model. The development, implementation, and maintenance of these quantitative models are both resource and time intensive. Generally, calibration standards are made by adding in anticipated variance into the standards, such as different ratios of components, lots of © 2013 American Chemical Society

materials, particles sizes, hardness, and water content. The standards can be made and analyzed in offline/online operations and may also be analyzed by a primary reference method such as chromatography. Calibration models such as partial least squares (PLS)3−9 are then made between mixture component spectra and mixture concentrations.10 These calibration models are typically employed in good manufacturing practice (GMP) environments, are fully validated, contain an appropriate number of representative samples, and will have to be periodically maintained. The resources required to develop and implement a quantitative model during development (when the synthetic route, formulation, and process are not set) is a barrier to using spectroscopic PAT tools for these analyses. Several examples come to mind. (1) A number of solvent mixtures and combinations are investigated for reaction completion and impurity profiles during active pharmaceutical ingredient (API) Special Issue: John MacGregor Festschrift Received: Revised: Accepted: Published: 12258

December 14, 2012 February 28, 2013 February 28, 2013 February 28, 2013 dx.doi.org/10.1021/ie3034587 | Ind. Eng. Chem. Res. 2013, 52, 12258−12268

Industrial & Engineering Chemistry Research

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(potency) to interpolate other potency values. This approach did not include typical sources of variance in the PCA model (e.g., lots, water content, hardness), and the approach was limited for use within a single experiment. As this approach utilizes reference data in operation, the potency results have good accuracy and are applicable to off-line analyses. Traditional chemometrics approaches are appropriate and accurate for many simple mixtures; however, they do not account for mixture constraints (∑i=I i=1 = 1, 0 ≤ ri ≤ 1, where ri is a mixture component ratio scalar; I is the total number of pure components) which must be physically satisfied. Without a mixture constraint, the sum of mixture component ratios would not necessarily be equal to 100%. As a consequence, the accuracy of predicted ratios, especially of very small or large component concentrations may be less than ideal (e.g., negative percentage or greater than 100%). This mixture constraint is critical when quantitatively monitoring multiple components in a mixture. An approach related to the calibration-free methods is self modeling curve resolution (SMCR).23,24 The goal of SMCR is to decompose spectral data from additive mixtures into pure component spectra and associated concentrations. To increase the uniqueness of the solution, multivariate curve resolution alternating least square (MCR-ALS) allows users to define unique feature regions.25 These SMCR and MCR-ALS methods are model-free in the sense that they do not in general require any prior knowledge or assumptions regarding the shape of the signal arising from individual components in a mixture. These would be useful especially when investigating “unknown” pure components as in trouble-shooting situations. However, this approach will utilize prior knowledge (e.g., the number of components, concentration of the components, spectral specificity, unimodality) to narrow down the possible solutions, and thus, the results depend on these constraints. Another concern for practical implementation of model-free methods is how to detect and account for molecular interaction effects (e.g., hydrogen bonding) which can occur in nonideal complex mixtures. This limitation in current approaches must be accounted for in order to ensure good prediction for mixtures with multiple components. Li et al.26 and Koga et al.27 proposed a new concept of excess absorption spectroscopy. Excess absorption is defined as the spectral difference between the sample and corresponding predicted solution (e.g., does the solution deviate from Beers−Lambert law). This approach can be used to assess the nonideality of mixtures, estimate selective molecular interactions, and to derive information about molecular interactions under nonideal mixture conditions. To understand nonlinear characteristics occurring due to molecular interaction, Koga et al.27 calculates the nonideality by taking the derivative of excess molar absorption with respect to the concentration. The differential calculation between one concentration and another is implemented. This calculation is useful for investigating the source of molecular interactions (offline); however, it may be difficult to predict the mixture composition quantitatively under nonideal mixture conditions online as the composition of the new mixtures will be unknown. Kriesten28,29 presented an indirect hard modeling approach based on the Voigt function consisting of a convolution of Gaussian and Lorentzian functions for nonlinear characterization. It involves using peak function parameters (width, height, position, shift, baseline, Gauss−Lorentz weight, etc). This approach may work well for simple nonideal mixture cases; however, due to the many fitting parameters, prior

development. Additionally, during solvent swaps, the composition of the solvents and temperature in the reactor can change considerably. Understanding of the composition in real time would be very beneficial as compared to developing a calibrated model covering the range of the individual combinations of solvent mixtures. (2) The primary reference method (e.g., HPLC, GC) data is not easily obtained. Cases where the material is highly reactive, real time data is required or to limit worker exposure when sampling are typical examples. Consequently, a calibration-free/minimum approach would be a useful and practical advancement to further and more routinely apply PAT tools during pharmaceutical development, especially for quantitative type analyses. Calibration-free methods/approaches have been previously disclosed. The use of standard deviation (SD) of a moving block of spectra collected over time has been proposed for blend uniformity monitoring.11−16 In these cases, blend homogeneity is assumed when the SD (of compound specific wavelengths or principal component analysis (PCA) scores) approaches zero. These approaches work well for blend uniformity monitoring of materials in a bin (static mixing, in which all components are added and subsequently mixed in one unit operation). In practice, these calibration-free methods measure differences between spectra from a single blending operation and a potency determination of the final blend is still typically performed.11 Additionally, choosing an SD value that is appropriate (considering the subsequent unit operations, percentage of API, or other excipients) for the blend, along with the trending of such data to produce meaningful information may not be straightforward. Although any component in the blend may be trended if there is spectral specificity and sensitivity, generally only the API is monitored (though looking at differences spectrum to spectrum will provide an overall blend “homogeneity” understanding). To ensure desired physical tablet properties such as hardness and dissolution as well as the content uniformity, it would be useful and informative to simultaneously predict the concentration of all mixture components during the blending operation.17 Calibration-free approaches for quantitatively predicting mixture components have been previously disclosed in the (chemometrics) literature. The main approach is to use the Beers−Lambert law, which assumes the spectral intensity is linearly related to the concentration of a component. Martens et al.18 presented a classical least squares (CLS) approach which represents the mixture spectra as a weighted sum of pure component spectra. Keller and Massart,19 Maeder and Zilian,20 and Gampp et al.21 reported an evolving factor analysis (EFA) which first decomposes the mixture component spectra with singular value decomposition (SVD) and then applies CLS to predict mixture concentration. This methodology requires spectra of mixture samples to extract latent variables for the SVD calculation. This results in an approach that is applicable to offline analyses. A similar approach is to use partial least squares (PLS) to represent the relationship between pure component spectra and 100% ratio matrix (e.g., for 3 components, [1 0 0; 0 1 0; 0 0 1]) and, then, predict the mixture composition by inputting the sample spectra into the PLS model.5 PLS can effectively deal with multicollinear relationships among multiple bands and provide a robust prediction. Liu22 presented a model-free approach using nearinfrared spectroscopy to predict tablet potency data. It involved using principal component analysis (PCA) and limited sample reference data (LC) at low, mid, and high spectral responses 12259

dx.doi.org/10.1021/ie3034587 | Ind. Eng. Chem. Res. 2013, 52, 12258−12268


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technology (nonlinear IOT) for nonideal mixing cases are proposed in sections 2.1 and 2,2, respectively. The mathematical algorithm demonstrating the difference between PLS (common calibration method) and IOT is discussed in section 2.3. 2.1. Linear Iterative Optimization Technology. The absorbance of a representative band of pure components and mixture components can be represented in the form of the Beers−Lambert law as30

knowledge to determine some peak function parameters is required. This paper describes a calibration-free/minimum approach, iterative optimization technology (IOT), which is used to predict (without calibration standards) the composition of a mixture while maintaining a similar predictability to calibration standard models. It typically involves using only pure standard spectra (collected prior to the analysis) and sample spectra collected during the analysis. This technology is applicable for predicting compositions during development of pharmaceutical products (where the synthetic route, formulation, or process is not set) and is not intended for use in GMP manufacture where quantitative measurements are made using validated models. For ideal mixture cases, the mixture composition is iteratively computed at every sample time point to minimize an excess absorption subject to constraints (e.g., mixture constraints, upper/lower limits). Linear IOT is used to describe these ideal mixture cases. For nonideal mixture cases where molecular interactions such as hydrogen bonding occur, the excess absorption, including the nonlinear characteristic, is first represented by a Box-Cox transformation. A limited number of training/calibration samples is required for these nonlinear examples and still represent a significant time/labor savings as compared to developing a fully calibrated model. The mixture composition is then iteratively obtained in a similar optimization framework as linear IOT. Nonlinear IOT is used to describe these nonideal mixture cases. Linear and nonlinear IOT have provided comparable prediction accuracy on binary and ternary mixtures as compared to a calibrated partial least squares (PLS) model. IOT can enhance the understanding of dosage form blending processes by determining the composition/ratio of all (spectrally discriminated) components in the blend in real time. This understanding of the time/energy/revolutions required to completely blend a mixture is important in the development and implementation of robust manufacturing processes. As composition is predicted each revolution, determination of the blending end point (does each component trend meet the known target mixture ratio) can be easily determined. The IOT approach to blending studies may lead to reduced/eliminated sampling and off-line testing for end point determination. Linear and nonlinear IOT can also be used to aid process understanding via detecting/representing molecular interaction effects (e.g., hydrogen bonding) utilizing the excess absorption calculation. The effectiveness of the linear and nonlinear IOT will be demonstrated through four online and offline pharmaceutical process examples (bin-blending process, rotary tablet press feed frame process, and two different solvent mixtures). To our knowledge, this is the first published calibration-free approach that provides good predictions on the composition of multiple components in a mixture for either “online” or offline analysis in the pharmaceutical industry. In section 2, the methodology including the linear and nonlinear IOT algorithms and how this differs with a common PLS calibration approach is presented. In section 3, the experimental information regarding material and equipment and the samples are described. In section 4, the results for the four examples are discussed. In section 5, the custom built IOT user interface for online implementation is shown.

xpure, i = εpure, ilpureCpure, i

(1)

xmix = εmix lmixCmix

(2)

where i is the number of pure components, xpure,i and xmix are the absorbance of pure and mixture components, εpure,i and εmix are the molar absorption coefficients of pure and mixture components, lpure and lmix are the optical path length of pure and mixture components, and Cpure,i and Cmix are the molar concentration of pure and mixture components, respectively. The ideal molar absorption coefficients of mixture components εideal can be represented using the mole fractions r instead of the molar concentration of compounds (Cpure,i, Cmix) as i=I

εideal =

∑ εpure,iri

(3)

i=1

where I is the total number of pure components and ri is a mole fraction of mixture components. The excess absorbance is expressed as ε E = εmix − εideal i=I

= εmix −

∑ εpure,iri (4)

i=1

εE is the excess molar absorption proposed by Li et al. and Koga et al.;27 in other words, it can be recognized as a deviation from Beers−Lambert law. The excess absorbance e can then be rewritten as 26

i=I

e = xmix −

∑ xpure,iri i=1

(5)

eq 5 can be extended to the absorbance of “multiple” wavelengths (N) as i=I

E lin = X mix −

∑ rX i pure, i i=1

(6)

where Xmix is the absorption of mixture components with the number of N wavelengths and Xpure,i is the absorption of pure components with the number of N bands. Elin corresponds to the excess absorbance, which quantifies the deviation of the mixture absorbance from the linear superposition of absorption of the individual components. For liquids, the deviation is due to chemical interactions, such as molecular association, disassociation, hydrogen bonding, etc. For solids the difference may also include changes in the optical path length due changes in the photon scattering, which is related to powder density, particle size, particle porosity, etc. Investigating the excess absorbance Elin may unveil new information on hydrogen bonding.26 Without a priori knowledge of the excess absorption, we propose that a reasonable estimate of the

2. METHOD The linear iterative optimization technology (linear IOT) for ideal mixing cases and nonlinear iterative optimization 12260



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For nonideal mixture cases, the linear excess absorbance Elin described in eq 6 may provide useful information about molecular interactions (e.g., hydrogen bonding), through the investigation of the spectral regions which have larger excess absorbance Elin (Li et al.26 and Koga et al.27). In order to accurately predict mixture component ratios even under nonideal mixtures, the excess absorbance can be rewritten by Box-Cox transformation equation as

mixture composition is obtained by minimizing the excess absorption. The mixture component ratio scalar ri is iteratively computed at every mixture sampling (typically as a function of time) so as to minimize the excess absorbance Elin described in eq 6 subject to some constraints such as mixture constraints and upper/ lower limits as N

min ∑ (X mix − ri

n=1

i=I

i=I

2 ∑ rX i pure, i)

Enonlin = X mix − fn (∑ rX i pure, i), where

i=1

i=1

s.t. 0 ≤ ri ≤ 1,

i=I

i=I

I

fn (∑ rX i pure, i) =

∑ ri = 1

λn ((∑i = 1 rX i pure, i) − 1)

λn

i=1

i=1

α ≤ ri ≤ β

(λ ≠ 0)

i=I

(7)

= ln(∑ rX i pure, i)

∑Ii=1

The mixture constraints (0 ≤ ri ≤ 1, ri = 1) should be satisfied for any mixture cases.31 The upper/lower limits should be reasonably set to avoid the complexity of optimization. If some other reasonable constraints may be available, they can be added into eq 7. For the ideal mixture cases, if the mixture component ratio vector r is suitably obtained, the excess absorbance Elin will theoretically include only spectral noise. Since the sum of the excess absorption Elin over N bands is minimized in eq 7, the optimization result may be affected by the selection of bands. Selecting appropriate compound specific spectral regions in IOT will impact the accuracy of the prediction results compared to calibration modeling as the calibration method modifies the weight of model coefficients depending on the contribution of spectral regions so as to minimize the prediction error of training samples. IOT (eq 7) equally weights the contribution of each spectral region. There are two assumptions and limitations for IOT. One is that the analysis conditions for the pure standards should be very similar to the analysis conditions of the samples. In most cases, the standard spectra will be collected offline (without any process disturbances), while the sample spectra will be collected during a process and will include some process contributions (e.g., agitation, temperature changes). Thus, some background effects may differ between standards and samples analyses. To minimize these effects, common spectroscopic preprocessing methods (e.g., standard normal variate (SNV) and derivative) are used. The target rotation method32 can also help minimize known spectral disturbances such as contributions from temperature and particle size. The second assumption is that the standard spectra are relatively independent to each other. Otherwise, the multicolinearity problem may occur during the optimization computation. The component ratios of structurally (and spectrally) similar materials will never theoretically be able to be predicted. It is important to select the suitable absorption bands while accounting for the independency of pure component spectra. Solutions to the optimization problems33,34 were obtained using Matlab35 and GAMS.36 The IOT user interface will be described in section 5. The above discussion can be applied to the following nonlinear IOT. 2.2. Nonlinear IOT. The nonlinear IOT consists of two steps: (1) representing nonlinear characteristics by “Box-Cox” transformation37 and (2) predicting the mixture component ratio as described in eq 7.

i=1

(λ = 0) (8)

where λn is a Box-Cox transformation parameter, and the Boxcox transformation is applied to the individual band n. Box-cox is well-known as a nonlinear transformation approach that does not assume the model structure in advance with only a simple transformation parameter λn.37 Enonlin is an excess absorbance after applying a Box-Cox transformation. Note, only one model parameter per region (Box-cox parameter λn) is required to represent the nonlinear relationship, thus overfitting problems are avoided. The Box-Cox transformation λn is computed so as to minimize the excess absorbance Enonlin (shown in eq 8) over the band N as i=I

min(X mixtrain − fn (∑ rtrain, iX pure, i))2 λn

i=1

(9)

where Xmixtrain is the spectra of “training” mixture samples and rtrain,i is the known mixture composition of these training samples. The number of training samples required can depend on the complexity of nonlinear characteristics. Most nonlinear characteristics are not very complicated (described via a highorder polynomial equation) but are simple curves (e.g., slow parabolic or log). A limited number of training samples are necessary to characterize the nonlinearity in most cases. Once the Box-Cox transformation λn is identified by eq 9, it does not require additional calibration standards to predict mixture component ratios for real samples. The mixture component ratio of new materials is iteratively computed in a similar optimization framework as that used in linear IOT (eq 7) as N

i=I

2 min ∑ (X mix − fn (∑ rX i pure, i)) ri

n=1

i=1

s.t. I

0 ≤ ri ≤ 1,

∑ ri = 1 i=1

α ≤ ri ≤ β

(10)

The assumption and limitation of the methodology and solutions for nonlinear IOT are the same as those described for linear IOT in section 2.1. 2.3. Comparison between PLS and IOT. The mathematical modeling differences between PLS and IOT are 12261



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Figure 1. Spectra of heptanes and IPA and mixture component spectra of 75.5% heptanes:24.5% iso-propanol (observed, predicted).

collected (five replicate measurements) and each averaged spectra was used for the subsequent analyses. A total of 85 spectra (17 mixtures and 5 replicate measurements) was collected for the comparison between a calibrated PLS model and linear IOT. 3.2. Bin-Blending Process Operation. A ternary powder mixture consisting of Microcrystalline Cellulose (MCC) (Avicel PH101, FMC Corporation, Philadelphia, PA), Fast Flo Lactose 316 (FFL) (Foremost Farms, Baraboo, WI), and an Active Pharmaceutical Ingredient (API) were blended in a 50 L bin-blender at 12 rpm (RPM). A 4.5 kg portion of MCC, 4.5 kg FFL, and 1 kg API (10 kg total weight) were added to the bin-blender. The ePAT 601 NIR (EXPO Technologies, LLC) was mounted at the bottom of the bin-blender. An optical shaft encoder reported the position of the blender to a custom built NIR-PC interface, and spectral acquisition was triggered when the blend was presented to the sample window once per revolution. The NIR spectral region collected was 942−1702 nm with a 6 nm spectral resolution. The order of material addition (charging) was MCC (first), API (second), and FFL (last). Consequently, the NIR spectrum from the first several blender rotations resembled MCC (prior to adequate mixing occurring). The spectra of each pure material (MCC, FFL, API) was collected before the experiment, and the sample spectra were collected during the mixing process every 5 s. 3.3. Rotary Tablet Press Feed Frame. A ternary powder mixture consisting of MCC (Avicel PH102, FMC Corporation, Philadelphia,PA), FFL (see previous page), and magnesium stearate (MgSt) (Mallinckrodt, Hazelwood, MO) was analyzed. Three gravimetric feeders and an inline powder mixing device fed blended powder streams into the inlet of a nine station rotary tablet press.38−40 The feed frame paddle wheel had 16 fingers each 3.8 mm wide. The tablet press feed frame was modified to incorporate an NIR probe to directly measure the blend composition circulating within the feed frame just prior to tableting. An ePAT 611 NIR was mounted to the feed frame from the top of paddle wheel.41 The NIR spectral region collected was 1100−2075 nm with a 4 nm spectral resolution. The NIR spectra were measured every 25 ms, and the average of 20 spectra were used in the analyses. Thus, spectra were collected every 0.7 s including processing time. A step test was conducted (changing the set point of mass feeders’ flow to change the composition of the mixture) to

described in this section. Section 4 describes the quantitative results between these approaches. A couple of common approaches using PLS models are used to predict mixture compositions. In the first method, a model is built between the mixture component spectra Xmix and mixture concentration r. The resultant model is used to predict the mixture component ratios after inputting the sample spectra. In another approach, a PLS model can be built between the pure component spectra Xpure and 100% ratio matrix (for example, for 3 components, [1 0 0; 0 1 0; 0 0 1]), as well. In these PLS models, a loading vector w of X side which is a key latent variable is computed so as to maximize a covariance matrix at the individual number of latent variables (for the above former case, wTXTmixrrTXmixw; for the latter case, wTXTpurerrTXpurew), subject to the normalized loading vector |w| = 1.3,4 The other latent variables such as scores, loading, and PLS coefficients (model parameters) are then calculated based on the loading vector w. Two major differences between PLS and IOT are highlighted below. The first is IOT and PLS are different in terms of the objective function form used to determine key model parameters or used to predict mixture component ratios. The objective function of IOT follows the Beers−Lambert law, while PLS does not necessarily do so. A second difference is that IOT takes into account the mixture constraints (0 ≤ r ≤ 1, ∑Ii=1 r = 1) during the prediction, but PLS does not include in the optimization framework. PLS was not developed specifically for spectral analysis. This general regression method provides robust predictions while effectively dealing with multicollinear relationships among X and Y variables. IOT and PLS will be quantitatively compared and discussed in section 4.

3. EXPERIMENT AND DATA Four pharmaceutical experiments are used to demonstrate the effectiveness of the IOT approach. The examples include an ideal binary solvent mixture, bin-blending process, rotary tablet press feed frame process, and nonideal binary solvent mixture. 3.1. Ideal Binary Solvent Mixtures. The ideal binary solvent mixtures consisting of heptanes and isopropanol (IPA) (obtained from Brenntag Northeast Inc., New Brunswick, NJ) were prepared and measured using an NIR XDS Process Analytics (Foss NIRsystems Inc.). The NIR spectral region collected was 1100−2200 nm with a 0.5 nm spectral resolution. The spectra of heptanes and isopropanol were individually 12262



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investigate the predictability of each component. The mixture component predictions were monitored by an custom built software described in section 5. 3.4. Nonideal Binary Solvent Mixture. Nonideal binary solvent mixtures consisting of water and IPA (Thermo Fisher Scientific Inc., Waltham, MA) were prepared and analyzed by mid-IR (MIR) (IC-10, Mettler-Toledo LLC, Columbus, OH). The MIR spectral region collected was 700 to 2700 cm−1 with a 1.8 cm−1 spectral resolution. The spectra of water and IPA (four replicate measurements) were collected before starting the experiment. Spectra from eight different mixtures ranging from 0.2% to 9.1% water (water levels of 0.2%, 0.4%, 0.6%, 0.8%, 1.0%, 2.0%, 5.7%, and 9.1%) were subsequently collected. These spectra are used for the comparative study between linear IOT and nonlinear IOT.

4. RESULT An (ideal binary solvent) mixture study consisting of Heptanes and IPA is described in section 4.1 to show how linear IOT compares to a PLS model built using all the mixture samples as training data. A bin-blending study using a ternary mixture (API, MCC, FFL) is presented in section 4.2 and is an example of how linear IOT can enhance blend monitoring understanding/capability. A rotary tablet press feed frame study consisting of a ternary mixture (MCC, FFL, MgSt) is described in section 4.3 and is an example of how linear IOT compares to a PLS model built using pure component spectra and 100% mixture concentration matrix ([1 0 0; 0 1 0; 0 0 1]). These comparisons utilize the same spectra for predicting the mixture component ratios. Finally, a nonideal binary solvent mixture study consisting of water and IPA is described in section 4.4 to show how linear/nonlinear IOT can be applied for nonideal mixtures while also providing useful information about potential inter/intra molecular interactions. 4.1. Binary Solvent Mixtures Results. The spectra of Heptanes (blue line) and IPA (green line) is shown in Figure 1. The spectrum of a solvent mixture (75.5% heptanes and 24.5% IPA, Xmix) is also shown in Figure 1 (pink line). The mixture component ratio of samples are calculated using the spectra of the pure components, sample spectra, and linear IOT (eq 7). The spectral regions of 1100−1500 nm (both heptane and IPA region), 1620−1820 nm (heptane region), and 2040−2200 nm (IPA region) was used for the analysis. These regions were selected so as to maximize the spectral distinction (independency) of pure components (heptanes and iso-propanol) to provide good prediction on individual mixture components. The predicted values of heptanes and IPA were 75.75% and 24.25%, respectively. These predicted values are very close to the actual values. The weighted sum of pure component spectra calculated with the predicted mixture component ratio (∑i=I i=1 rXpure,i) is shown in Figure 1 (red dotted line). There are minimal excess absorbances (Xmix − ∑i=I i=1 rXpure,i) over the spectral regions indicating an ideal mixture. All other mixture component ratios are calculated in the same manner. A PLS model was constructed using all 85 mixture sample spectra for “training”, and the model has one PLS component. The same spectral regions used for IOT were selected for the PLS model. The observed vs predicted result of linear IOT and PLS model is shown in Figure 2, and the R2 (%) and root mean squared error estimation (RMSEE) result of linear IOT and PLS model is listed in Table 1. The linear IOT approach provided similar prediction results as compared to the calibrated PLS model without building or utilizing calibration

Figure 2. Observed vs predicted results of linear IOT and PLS models.

Table 1. R2 (%) and RMSEE (Root Mean Squared Error Estimation) Result of Linear Iot and Full PLS Calibration full PLS calibration linear IOT

R2 (%)

RMSEE

99.7 99.6

0.33 0.74

standards. Thus, the linear IOT approach was an effective calibration-free method. 4.2. Bin-Blending Process Results. The ingoing component spectra (API, MCC, FFL) and the mixture sample spectra (collected every 5 s) are shown in Figure 3. The mixture

Figure 3. Spectra of API, MCC, FFL, and the mixture sample spectra collected during the process.

component ratio vector r was iteratively computed every 5 s using eq 7. The spectral region selected was 1424−1541 nm, and spectra were preprocessed with standard normal variate (SNV). The results of the individual component ratios predicted during the process is shown in Figure 4. As expected, during the first several rotations a large percentage of MCC is predicted as MCC is the bottom layer, and spectra were collected at the bottom of the blender. Linear IOT is used to provide insights on blender dynamics and the uniformity and composition at each blender rotation in real time. Conventional blend monitoring (calibration-free approaches) typically 12263



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Figure 4. Trend ratios predicted for each component (MCC, FFL, MgSt) during the blending process.

Figure 5. Trend ratios predicted for each component (MCC, FFL, MgSt) during step testing on a continuous mixing process.

calculate the standard deviation of a moving block of compound specific wavelengths or PCA scores.11−16 Applying IOT to understand blending would be useful as the blending dynamics can vary with blender type, blender rotation speed, variability of material properties (e.g., particle size), scale, and order of material addition.42,43 Note, as the composition of the blend is calculated using IOT (and as the actual in-going percentage of each component is known), a thorough investigation of the blending end point (homogeneous mixture) can be facilely performed with minimal (or no) sampling and off-line testing (thereby eliminating biases associated with sampling blends). 4.3. Rotary Tablet Press Feed Frame Process Operation Results. The ingoing component spectra (MCC, FFL, MgSt) of each material lot used in the experiment is collected. The sample spectra were collected every 0.7 s during the run. The mixture component ratios were iteratively calculated for each spectra using eq 7. The spectral region selected was 1893−1940 nm, and spectra were preprocessed with SNV and second derivative (window size = 7, polynomial

order = 2). The data pretreatment of SNV and second derivative (also preprocessing parameters) were applied to minimize the baseline shift which would be caused by some physical effects (e.g., particle size distribution, density) and to enhance the sensitivity for the model prediction. And, the wavelength region (1893−1940 nm) was selected to maximize the spectral distinct (independency) of pure components (MCC, FFL, MgSt). An additional inequality constraint of MgSt content less than 2% was added into eq 7 in order to optimize the calculations and increase the MgSt predictability (present at 1% in the blend). The linear IOT result of the step test is shown in Figure 5. The red dotted line shows the set point of the feeder which corresponds to the theoretical target value, and the blue line shows the predicted individual mixture component ratios. Prediction errors on MCC and FFL percentages are observed around 5 min. This is due to the process not yet being in steady state. The time delay between mass feeder change and steady state is a function of the amount of hold-up in the blender and the rate at which the blender is employed. The predicted mixture component ratios using linear 12264



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Figure 6. Comparison of linear IOT and PLS trend ratios predicted for each component (MCC, FFL, MgSt) during step tests on a continuous mixing process.

Figure 7. Spectra of water, IPA, and mixture samples.

IOT at the steady state condition (∼25 min) were in agreement with the theoretical component ratio values. The prediction errors for each component, including MgSt, was within 2%. A PLS model was constructed using the pure component spectra and 100% mixture concentration matrix (= [1 0 0; 0 1 0; 0 0 1]). The same spectral regions and preprocess conditions used for linear IOT was applied. Note, these two approaches (PLS and IOT) use exactly the same data to predict the mixture component ratios. The results for both methods are shown in Figure 6. The PLS model gave some prediction errors for the levels of MCC and MgSt; whereas the linear IOT gave good prediction for all the three components. The PLS model predicted some “negative” values and larger prediction variability for the MgSt. These are due to not accounting for the mixture constraints in the PLS algorithm. Thus, the linear IOT provided a more robust and accurate prediction on the ternary mixtures as compared to the PLS model constructed using only pure component spectra. This IOT prediction was performed online and in real time. The prediction trend was monitored by a custom built software which will be described in section 5. Future developments will investigate the use of the predicted mixture component ratios as control variables in

advanced process control systems (e.g., model predictive control, adaptive control). 4.4. Result of Nonideal Solvent Mixture Case. The MIR spectra for water (red line), IPA (pink line), and several sample mixtures (blue lines) are shown in Figure 7. For liquid water, 1640 cm−1 is a characteristic vibrational absorbance (OHbending) band.44 Noted in Figure 7 are strong nonlinear characteristics (absorption/band shifts in this region as the water concentration changes). This is caused by hydrogen bonding. No strong nonlinear characteristics are observed in the vibrational absorbance region associated with IPA (around 1140 cm−1). The mixture component ratios were computed by both linear IOT (eq 7) and nonlinear IOT (eqs 9 and 10). For the nonlinear IOT, only two training samples (at water = 1.0% and 9.1%) were used for the Box-Cox nonlinear transformation computation shown in eqs 8 and 9 to characterize the nonlinear relationship, and the remaining six mixture samples (water = 0.2%, 0.4%, 0.6%, 0.8%, 2.0%, and 5.7%) were used as a validation set. The results for linear IOT and nonlinear IOT prediction of water and IPA content using the two training mixture standards and six validation mixture samples are shown in Figure 8. Linear IOT gave some prediction error on higher 12265



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Figure 8. Comparison of linear IOT and nonlinear IOT for prediction of water and IPA composition.

Figure 9. Results of excess absorbance calculation for linear IOT and nonlinear IOT.

remains) indicating that there was a small error in the Box-Cox transformation. This is not expected to be of concern in predicting mixture component ratios as demonstrated in Figure. 8.

water content samples (due to nonlinear characteristics), although this error was not too high due to mixture constraints included in the optimization framework. Nonlinear IOT provided very accurate prediction on not only the two training mixture standards but also the six validation mixture samples. Thus, nonlinear IOT works well with only a limited number of training data to provide good prediction on mixture compositions for systems that do not follow the Beers− Lambert law. The effectiveness of these linear and nonlinear IOT methodologies can be probed by investigating the excess absorbance. The result of excess absorbance of the linear IOT and nonlinear IOT (eqs 6 and 8) is shown in Figure 9. The excess absorbance of the linear IOT largely appears in a region around 1640 cm−1 associated with water, and not as significantly in the IPA region around 1140 cm−1. Thus, water is exhibiting nonlinear absorption (primarily due to hydrogen bonding). Note, this excess absorbance information allows user to detect and investigate molecular interactions that may be occurring (can determine the interaction using the absorption band). The excess absorbance for linear IOT was significantly reduced by using nonlinear IOT, thus the nonlinear characteristic was well-desribed by the Box-Cox transformation. Nonlinear IOT did not completely eliminate the nonlinear characteristics (slight excess absorbance still

5. CUSTOM BUILT IOT USER INTERFACE To monitor individual mixture components online, a custom built user interface was developed using MATLAB. The program inputs a spectrum every 0.5−1.0 s during a process and computes the mixture component ratio based on the IOT algorithms. A screen shot of the IOT user interface process simulator is shown in Figure. 10. Sample spectra are monitored on the left side of the screen. The mixture component ratios time series trend are monitored on the right side of the screen. Each optimization computation was completed in approximately 0.5 s. 6. CONCLUSION Linear/nonlinear IOT has been successfully demonstrated in online and offline pharmaceutical processes. The effectiveness of the approaches was demonstrated through four examples (bin-blending process, rotary tablet press feed frame process, and two different solvent mixtures). For the ideal binary solvent mixture study (heptanes and IPA), linear IOT provided a similar prediction compared to a PLS model (linear IOT is an 12266



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Figure 10. IOT process simulator user interface.

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effective calibration-free approach). For the bin-blending process with the three components, linear IOT provided information on the composition and uniformity of the mixture at each sampling time point (rotation). As composition is predicted each revolution, determination of the blending end point (does each component trend meet the known target mixture ratio) can be easily determined. The IOT approach to blending studies may lead to reduced/eliminated sampling and off-line testing for end point determination. For the rotary tablet press feed frame with the three components, linear IOT provided more robust and accurate predictions as compared to the PLS model constructed (also) using pure component spectra. For the nonideal binary solvent mixtures, nonlinear IOT provided very accurate prediction on both the two training samples but also the six validation samples (the nonlinear characteristic was well represented by the Box-Cox transformation). Linear and nonlinear IOT can also be used to aid process understanding via detecting/representing molecular interaction effects (e.g., hydrogen bonding) utilizing the excess absorption calculation. It is hoped that IOT will enhance the use of spectroscopy (PAT) as routine analytical tools in pharmaceutical analyses. With the capability to more confidently predict composition without constructing/maintaining calibrated models, additional information and value can be extracted during use. We see these tools especially aiding process development, process understanding, and other development activities that occur prior to the synthetic route, formulation, or processing being set. Additional work will continue to expand the list applications for which IOT is appropriate, comparing IOT with fully validated models, and investigating if IOT can provide good predictions on mixtures containing greater than three components.

AUTHOR INFORMATION

Corresponding Author

*Tel.: (860) 686-2748. Fax: (860) 441-5423. E-mail: koji. muteki@pfizer.com. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors wish to thank Sonja Sekulic, Mike Pelletier, Benjamin J. Hritzko, Salvador Garcia-Munoz, Loren Wrisley, Bruno Hancock, William R. Ketterhagen, Paul Gerst, Howard W. Ward, Andreas Muehlenfeld, Matthias Danner, Mojgan Moshgbar, and Jun Huang at Pfizer Inc. for useful discussions.

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Mixture Component Prediction Using Iterative Optimization Technology

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