Design Space Approach for Pharmaceutical Tablet Development

Article pubs.acs.org/IECR

Design Space Approach for Pharmaceutical Tablet Development Kalliopi A. Chatzizacharia and Dimitris T. Hatziavramidis* School of Chemical Engineering, National Technical University of Athens, Heroon Polytechniou 9, Zografou, 15780 Athens Greece S Supporting Information *

ABSTRACT: Methodologies to determine the Design Space of a pharmaceutical product, within which continuous improvement can be implemented and postapproval changes in material attributes and process parameters can be introduced without prior approval, are presented. The type of methodology used depends on the type of experimental data obtained for the purpose of determining the Design Space. However, when one is unsure about the data collected to determine the Design Space, one can determine the quality of the data from successive application of the various methods and evaluation of the desirability measure for each method. The Design Spaces for a two- and three-process tablet manufacturing are determined by Response Surface Method (RSM), Bayesian Post Predictive Approach (BPPA), and Artificial Neural Networks (ANN), based on local or global specification limits of the response variables provided by multiresponse optimization and overlapping responses, respectively. The Response Surface Method is the most effective of these methods in determining the Design Spaces for the aforementioned data sets, confirming that the particular data are complete and lack uncertainty or structure, the specific features that the Bayesian Post Predictive Approach and Artificial Neural Networks methods are suited to address, respectively.

1. INTRODUCTION The aim of pharmaceutical development is to design a product and a series of processes to manufacture the product and consistently deliver performance to ensure product efficacy, safety and quality. Knowledge gained from pharmaceutical development and manufacturing experience facilitates identification of critical quality attributes (CQA) and critical material attributes (CMA) and process parameters (CPP) and supports the establishment of relations and mechanistic product-process design models between the CQAs, as output variables, and CMAs and CPPs, as input variables and parameters. CMAs and CPPs are identified through an assessment of the impact their variation can have on CQAs and their variation. Product and process requirements, attributes performance specifications, along with multivariate models based on chemistry and engineering fundamentals, help to define the feasible region for the subsequently formulated optimization problem. Solution of the multiobjective optimization problem yields an optimal product design.1,2 In the combined granulation−compression process of making the tablet dosage form, CQAs include, but are not limited to, granule size, powder and granule flowability and tablet weight and its variation, crushing strength, friability, disintegration time and dissolution, while CMA and CPP can be type and amount of binders, disintegrants, diluents, lubricants, and inlet air temperature, atomizing air pressure and other process variables, respectively. The regulatory framework regarding the manufacture of pharmaceutical products ensures patient safety through the use of well-defined processes with specified parameter ranges governed by a control plan which is the responsibility of the pharmaceutical industry. According to this framework any type of change in formulation or process conditions, however small, requires regulatory approval. Under the new Quality by Design (QbD) initiative, however, it will be possible to use knowledge from development studies to create a Design Space (DS) within which © 2014 American Chemical Society

changes in formulation and manufacturing processes promoting continuous improvement of process capability and product quality can be implemented without the need for further regulatory approval.3,4 According to ICH Q8, a Design Space is defined as “the multidimensional combination and interaction of input variables (e.g., material attributes) and process parameters that have been demonstrated to provide assurance of quality”. It is proposed by the applicant and is subject to regulatory assessment and approval. Once approved, it sets the boundaries within which changes in the input variables and process parameters can be made without further regulatory approval. Changes that result in input variable and process parameters values outside the Design Space initiate a regulatory post-approval change process.5 If the Design Space is intended to span multiple operational scales (lab, pilot plant, plant), normalized (coded) variables in the interval [−1, 1] may be used.6 The Design Space is a dynamic entity (e.g., temperature and pressure of the lyophilization cycle are functions of time), begins at drug conceptualization and continues to evolve over the entire life cycle of the product. During the life cycle of any pharmaceutical product, many factors can become drivers for changes to a manufacturing process or its unit operations, as more knowledge and understanding of formulation, processes, specifications, and drug market is gained, changes to raw materials, changes in the regulatory environment, and identification of new process technologies occur. While process changes may result in improved safety, quality, consistency, yield, throughput, and cost, the basic enablers for these changes are a well-characterized Design Space around processing parameter ranges, and a Received: Revised: Accepted: Published: 12003

February 10, 2014 July 1, 2014 July 10, 2014 July 10, 2014 dx.doi.org/10.1021/ie5005652 | Ind. Eng. Chem. Res. 2014, 53, 12003−12009

Industrial & Engineering Chemistry Research

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univariate models does not constitute a Design Space. Design Space (DS) is a combination of variables whose acceptable ranges are determined by multivariate models, e.g., Partial Least Squares (PLS), Partial Component Analysis (PCA) and Response Surface (RS).8,11 In mathematical terms, if x and y, vectors with n and m components, respectively, representing the input (critical material variables and process parameters) and output (critical quality characteristics) variables, respectively, and X the experimental or knowledge domain, respectively, the Design Space is defined as

thorough understanding of the impact of process parameter variation on the product’s CMAs, CQAs, and CPPs. From the engineering point of view, Design Space together with an appropriate Control Strategy can reduce and focus end-product testing, while increasing process performance and robustness. Development resources may be required to achieve a knowledgerich understanding of the process, but this investment can be offset by certitude of scale-up, more consistent manufacturing, and potential regulatory flexibility.7,8 Our literature review has shown that determination of the DS in QbD of pharmaceutical products was done using various methods with little or no regard for the type of experimental data obtained to this end. The present paper in which the DS approach was implemented in pharmaceutical tablet development examples shows the importance of the type of experimental data on deciding the type of the method used to determine the DS.

DS = {x̃ε X|E[yj |x] = yj|̂ x ε Lj ∀ j = 1, .., m ∧ yl̂|x ε L1U...Uym̂ |x ε Lm = L}

(1)

where L is the set of specifications for the responses yj. Design of Experiments (DOE) is a tool to obtain maximum information about the model that relates mean responses, which constitute the output, and the factors, which constitute the input, in the form

2. MATERIALS AND METHODS Two sets of experimental data for tablet manufacturing, the first from a study by Merkku et al.9 and the second from a study by Westerhuis et al.,10 were utilized in the present study. In the study of Merkku et al.,9 tablet manufacturing involves two important processes, powder granulation and compression. Granules were made in a fluidized bed granulator out of lactose α-monohydrate, 20% water dispersion of polyvinylpyrrolidone, and 2% of anhydrous theophylline. The granules were mixed with 0.5% of magnesium stearate before they were sent to the tablet press. The experimental data of Merkku et al.9 followed a 33 factorial experimental design in which, the response variables were granule flow rate (FL), angle of repose, lower and upper compression forces in the tablet press and their ratio (RCF), and tablet properties, such as mean weight (MW), crushing strength (CS), friability (FR), disintegration time (DT), as well as the standard deviations (SD) of the previous quantities factors that were the inlet air temperature (T), atomizing air pressure (p), and binder amount (m). In the study of Westerhuis et al.,10 tablet manufacturing involves three processes, wet granulation, drying and compression. Granules were made in a wet granulator out of microcrystalline cellulose (MCC), mannitol and HPC solution. The granules were dried, sieved, and mixed with 1.5% colloidal silicon solution and 0.5% of magnesium stearate before they were sent to the tablet press. The experimental data of Westerhuis et al.10 followed a Box− Behnken design, in which the response variables were crushing strength (CS), disintegration time (DT) and ejection force (EF) for the tablets; factors were the amount of water for wet granulation (Water), granulation time (Time), moisture of granules (Moisture), compression force (CompF.), and two composition variables, HPC and MCC. It should be noted that, according to ref 10, CS and DT of the tablets were logarithmically transformed because of the funnel-shaped heteroscedastic variance structure. In addition, four extremely large values of EF were considered as outliers. 2.1. Methods of Determining the Design Space. In order to explain the practice of Quality-by-Design (QbD), ICH guidelines define the Design Space (DS) as “the multidimensional combination of input variables (e.g., material attributes) and process parameters that have been demonstrated to provide assurance of quality”. A combination of proven acceptable ranges of input variables and process parameters, determined by

yj |x = f j (x ; θĵ) + εj ∀ j = 1, ..., m ∧ ∀ xε X

(2)

where θĵ is the vector of parameters and the error follows a normal distribution, i.e., εj ≈ N(0, σj2) ∀j = 1,..,m. The surface defined by the relation yj|̂ x = E[yj |x] = f j (x) ∀ j = 1, ..., m ∧ ∀ xε X

(3)

is called a Response Surface (RS). There are two methods of determining the DS, (a) mean overlapping responses,12,13 and (b) optimized responses. In the method of overlapping responses, one can take the projection of the RS on the various (xi, xj), ∀i, j = 1,...,n and i ≠ j, planes. In the method of optimized responses, the DS is defined from DS = {x1̃ *U...Ux̃ m*|x̃ j* = argmax E[yj |x̃] = argmax f j (x, θĵ) ∀ j = 1, .., m} (4)

Another way of determining the DS is from the solution of eq 3 in the form: SL Ŷ = f(X)

(5)

where Ŷ

SL

⎡ ŷ ⎤T ...y ̂ ⎡ x ...x ⎤T 1,LSL m ,LSL ⎢ ⎥ , X = ⎢ 1,L n ,L ⎥ = ⎢ ŷ ⎥ ⎣ x1,U...xn ,U ⎦ ⎣ 1,USL ...ym̂ ,USL ⎦

and LSL and USL are the lower and upper specification limits, respectively. If f(x) is nonlinear, the solution of eq 5 is obtained by iterative techniques X (r + 1) = X (r) − J−L 1 (X (r))F(X (r))

(6)

̂ SL

where F = f − Y , ⎡ ∂F ∂F ⎤ J−L 1 (X (r)) = (JT J)−1JT (X (r)), J(X (r)) = ⎢ ... ⎥ ⎣ ∂x1 ∂xn ⎦

with J the Jacobian matrix and r the iteration number. In practice, eq 5 is solved for X using Broyden’s method. 12004

dx.doi.org/10.1021/ie5005652 | Ind. Eng. Chem. Res. 2014, 53, 12003−12009


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ability to accommodate more data and retrain, and the ability to generate understandable rules.17 However, some drawbacks are the trial and error procedure of best node number choice for training, that the problem must be numeric in nature; reasonable quantities of data should be available to train an adequate model. The greatest benefits are achieved for multidimensional problems where it is difficult to express any analytic model and difficult to abstract the rules by any other mechanism than neural computing. In determining the optimum conditions on input variables and process parameters of a multiresponse problem, a popular strategy is to reduce the dimensionality of the problem. This strategy converts a multiresponse problem into a problem with a single aggregate measure and solves it as a single response optimization problem. The single aggregate measure is often defined as a desirability function12 or a loss function.18 The most popular form of a desirability function19 is

If f(x) is linear, i.e., SL Ŷ = AX

(7)

where ⎡ a1,1 .......... an ,1 ⎤ ⎢ .... .......... .... ⎥ A = ⎢ .... .......... .... ⎥ ⎢ .... .......... .... ⎥ ⎢ a .......... a ⎥ ⎣ 1, m n,m ⎦

the DS can be determined from X = (AT A)−1AT Y SL = AL−1 Y SL

(8)

The objective of ICH Q8 is to gain knowledge about the system and define a robust DS which guarantees that quality specifications are met. This objective cannot be attained when dealing with mean responses, if uncertainties or correlation structures are present. In such a case, the definitions of DS and eqs 1 and 4, are replaced by DS = {x̃ ∈ X |P(Yj ∈ Sj|x̃ , θ)̂ ≥ aj , j = 1, ..., m}

dμi

(9)

⎡ y ̂ − y max ⎤ β μi μi ⎥ =⎢ Tμi ≤ yμ̂ i ≤ yμmax i ⎢⎣ Tμi − yμmax ⎥ i ⎦

and ̂ DS = {x1̃ *U...Ux̃ m*|x̃ j* = argmax P(Yj > a)|x , θ)}

(10)

= 0yμ̂ i < yμmin oryμ̂ i > yμmax i i

respectively, where P(Yj) is the cumulative probability density function. A Bayesian posterior Predictive Approach (BPPA) which takes into account the correlation structure of the data, and the model parameter uncertainty was suggested by Peterson.14,15 The basis for the Bayesian approach is the following. If p(y|θ) is the conditional probability density function and p(θ) the probability density function of the parameter vector θ from prior times, the posterior probability p(θ| y) is p(y|θ)p(θ) p(y|θ)p(θ) p(θ|y) = = p(y) ∫θ p(y|θ)p(θ)dθ

⎡ y ̂ − y min ⎤α μi μi ⎥ min =⎢ y ≤ yμ̂ i ≤ Tμi ⎢⎣ Tμi − y min ⎥⎦ μi μi

(12)

max where ŷμi, ymin μi , yμi , Tμi denote the estimated mean response, minimum and maximum desired limits and target for ŷμi, respectively, and α, β are input parameters that determine the shape of the reliability function. The aggregate measure, D, called composite desirability, is the geometric mean of individual desirabilities, dμi:

D = (dμ1dμ2...dμp)1/ p

(13)

The conventional desirability approach outlined above does not consider the dispersion effects of the responses; i.e., it assumes that the random errors, εi, have constant variance, σεi2. If dispersion effects were taken into account, eq 13 would have been revised as

(11)

where p(y|θ) = L(θ,y) is the so-called likelihood of θ for fixed (observed) data y. When the data are incomplete or imprecise, neural networks (ANN), a technique which mimics the processing of the human brain, can be used to generate input−output relationships.16 This technique, which can be complemented with fuzzy logic and evolutionary computing, is particularly valuable when the data are of high uncertainty or conflicting CQAs are desired, e.g., hard tablets that disintegrate quickly. A neural network composed of an input and output layer with one hidden layer, i.e., a three-layer back-propagation network was chosen for the purposes of this study. A sigmoidal function (logsig) was used as the transfer function for the hidden layer and back-propagation of errors, while a linear transfer function (purelin) was used for the output layer. The Mean Squared Error (MSE) was used as the performance function of a different number of nodes in the hidden layer, and the optimal ANN structure was used for each data set. The efficiency of the network is dependent on the number of nodes, as if the number of nodes is below the optimal number or increased above it, there is a decrease in the efficiency of the network due to under- or overtraining of the network. It has been demonstrated that ANN is as effective and sometimes superior to polynomial equations in predicting quantitative nonlinear relationships between variables and responses, with benefits like effective use of incomplete data sets, rapid analysis of data, the

D = (dμ1dμ2...dμpdσ1dσ 2...dσp)1/2p

(14)

3. RESULTS Multiresponse optimization plots, based on Response Surface Method (RSM), for the data of Merkku et al.9 and Westerhuis et al.10 are shown in Figures 1 and 3, respectively. These plots, in addition to optimum conditions, m = 450 g (1, coded) and p = 1.086 bar (−0.824, coded) for the data of Merkku et al.,9 MCC = 67.01%, HPC = 2.00%, Water = 400 mL, Time = 3 min, Moisture = 5.18%, CompF = 28.46 kN for the data of Westerhuis et al.,10 show two sets of values of the input variables one of which corresponds to lower (subscripted l) the other to upper (subscripted u) specification limits for all the response variables in the neighborhood of optimum conditions. These two sets of values of the input variables constitute the bounds of the Design Space (DS). Table 1 shows, in addition to the bounds of DS determined by RSM, bounds of DS determined by ANN, BPPA, as well as by Broyden’s method, an inversion of RSM for solving eq 3. The bounds of the DS for the two sets of data9,10 are also determined with the method of “overlapping 12005



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inlet air temperature (T) with high statistical significance (p < 0.05). RSM generates the following model: FL = 11.856 − 0.3083p + 0.2139m + 0.2750p2 − 0.1708pm + 0.2083T 2

eq 15, in which the variables p, m, and T are in coded values, is very similar to eq 2 of ref 9. The output variable in the first process, granular flow rate, becomes an input variable in the second process of the two-process tablet manufacturing. In the second process, the binder amount and the lower-to-upper compression force ratio are also input variables. Analysis of variance for the response variables of the second of the two-process tablet manufacture shows that all response variables are functions of the granule flow rate (FL) and lower-to-upper compression force ratio (RCF), with low significance (p > 0.1). Here, it should be noted that the granule flow rate correlates highly with the standard deviation of the mean weight (MWSD) and quite highly with the lower-to-upper compression force ratio (RCF), as no granular flow results in variation in mean weight and, certainly, in compression forces. Because of the difficulty in correlating the response variables with the granular flow rate (FL) and the compressible forces ratio (CFR), the response variables of the twoprocess tablet manufacture were analyzed in terms of the input variables of the first step, T, p, and m. Analysis of variance shows that the response variables, MWSD, CS, FR, DT do not correlate with inlet air temperature, T, as neither does the granule flow rate, FL. These variables are functions of m and p with high significance. RSM generates the following models:

Figure 1. Optimization plot for data by Merkku et al. (ref 9.).

Table 1. Bounds of DS a. Data by Merkku et al. in ref 9

RSM m - optimum p - optimum ml pl mu pu

Broyden’s Method

Bayesian approach (BPPA)

neural networksa (ANN) (nod a = 20)

450.00 449.90 − 1.09 1.57 − 415.10 242.40 300.00 1.33 2.16 1.50 450.00 439.10 450.00 1.00 1.50 1.50 b. Data by Westerhuis et al. in ref 10

MCC - optimum HPC - optimum Water - optimum Time - optimum Moisture - optimum CompF - optimum MCCl HPCl Waterl Timel Moisturel CompFl MCCu HPCu Wateru Timeu Moistureu CompFu

369.10 1.27 316.00 2.60 548.00 0.46

RSM

Broyden’s Method

Bayesian approach (BPPA)

neural networksa (ANN) (nod b = 20)

68.51 2.00 414.24 3.28 4.98 10.00 77.94 5.00 650.00 3.00 2.80 15.15 69.28 2.00 400.00 3.00 5.20 30.00

68.52 1.89 414.23 3.24 5.00 30.06 77.98 5.25 650.00 2.87 2.73 15.07 65.96 0.90 399.93 2.48 5.35 30.57

− − − − − − 75.00 5.00 400.00 5.00 3.10 30.00 65.00 3.00 450.00 3.00 4.20 30.00

66.66 4.04 470.88 4.31 3.38 31.49 67.17 2.25 485.50 4.50 3.67 15.10 77.34 5.03 644.35 3.13 3.81 22.14

(15)

MWSD = 1.3657 − 0.3694p + 0.4194m CS = 43.5926 + 4.5833m FR = 3.1741 − 0.2056p − 0.4444m DT = 9.1296 + 0.8611p + 2.4722m

(16)

eq 16, in which the variables m and p are in coded values, are very similar to eqs 3 and 4 of ref9. We consider next the data of Westerhuis et al.10 of the threeprocess tablet manufacture. Two multivariate models can be utilized to describe tablet manufacturing, consisting of wet granulation, drying of the powder mixture, and compression of granules into tablets. The first model relates crushing strength (CS), disintegration time (DT), and ejection force (EF) with process variables from both the wet granulation and tableting processes and the composition variables of the powder mixture. The second model, in addition to the process and composition variables of granulation, uses physical properties of the granules as input variables. The authors claim that the addition of the physical properties of the granules to the input variables improves the predictive capabilities of the first model. Analysis of variance for the response variables shows that crushing strength (CS) is a strong function of MCC, CompF, Moisture, and Water in its square form and in its interaction with MCC, with high statistical significance (p < 0.001). Also, disintegration time (DT) is a strong function of MCC, HPC, CompF, Moisture and Water. The ejection force (EF) shows no significant terms. RSM generates the models:

a a,b nod: the number of nodes in the hidden layer of ANN resulting in highest correlation coefficient, R2.

responses” as described by eq 3 and implemented graphically by plotting this equation. We consider first the data of Merkku et al.9 Analysis of variance for the response variable of the first of the two processes in tablet manufacturing shows that granular flow rate (FL) is a strong function of binder amount (m), atomizing air pressure (p) and

log CS = 0.215*MCC + 0.006*Water + 0.219*Moisture + 0.102*CompF + (2.834 × 10−5)*(Water)2 − 0.001*(CompF)2 − (4.619 × 10−4)*MCC *Water − 0.008*Moisture*CompF − 8.9 12006

(17a)



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log DT = 0.190*MCC + 0.095*HPC + 0.004*Water − 1.280*Moisture + 0.074*CompF + (3.070 × 10−5)*(Water)2 + 0.184 *(Moisture)2 − (4.442 × 10−4)*MCC*Water − 5.4

(17b)

in which the variables are in uncoded or physical values and which are very similar to those of ref10. Equations17a−17b show that principal factors for CS and DT are MCC, Moisture and ComF. The plots of the “overlapping responses” method for the data by Merkku et al.9 and Westerhuis et al.10 are shown in Figures 2 and 4, respectively.

Figure 2. Design Space for data by Merkku et al. (ref 9.).

Figure 4. Design Space for data by Westerhuis et al. (ref 10); (a) contours on MCC−CompF plane; (b) contours on MCC−Moisture plane; (c) contours on Moisture−Compf plane. Figure 3. Optimization plot for data by Westerhuis et al. (ref 10).

4. DISCUSSION Figures 1 and 3 show the neighborhood of optimum conditions with a target, a minimum and a maximum of the responses for the data by Merkku et al.9 and Westerhuis et al.,10 respectively. On the basis of Figures 1 and 2, the bounds of the Design Space (DS) for both data sets, one of two-process tablet manufacturing by Merkku et al.9 and another of three-process tablet manufacturing by Westerhuis et al.,10 were estimated by the Response Surface Method (RSM), the Bayesian Post Predictive Approach (BPPA),

Estimated mean and specification limits of the responses and composite desirability for the various methods, RSM, ANN, and BPPA, are shown in Table 2. For the data sets by Merkku et al.9 and Westerhuis et al.,10 targets for the response variables are defined as the influential points determined by Partial Least Squares (PLS). For the same data sets, specification limits are defined as target ± standard deviation. 12007



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which, in turn, are slightly different than those estimated by Broyden’s method. Figures 2 and 4 show plots of eq 2, with the global LSL and USL of the responses, and the DS determined by “overlapping responses” for the data by Merkku et al.9 and Westerhuis et al.,10 respectively. The white area represents the DS, the gray area, the points that lay out of its limits, and the lines, the upper and lower specification limits of the corresponding response variable. With these graphical representations of the DS, each combination of the design variables that lie within the “knowledge” space can be easily checked whether it belongs in the DS without the need of any further calculations. The DS determined by “overlapping responses” is far more extended than the DS determined by multiple-response optimization, since in the former case the DS is determined from the global specification limits, while in the latter case, the DS is determined from local minima and maxima in the neighborhood of optimum conditions. The composite desirability of the various methods, RSM, BPPA, ANN as well as Broyden’s, is shown in Table 2. It can be seen that RSM has the highest composite desirability from all other methods including the inverse RSM (Broyden’s method) for both data sets of tablet manufacturing. The superiority of the direct over the inverse approximation (Broyden’s method) of RSM can be easily understood. Regarding the superiority of RSM over the BPPA and ANN and methods, it can be explained by the fact that both data sets are complete and lack the special features that make other methods such as BPPA and ANN more suitable. To this end, ANN is more suitable for fuzzy, or incomplete, complex data with contradicting Critical Quality Attributes (CQAs) and BPPA, as formulated by Peterson,14 is more suitable for data with high variability and high model parameter uncertainty, which can be approximated as multinormal. When applied to the data of Merkku et al.,9 BPPA and ANN are shown to be equally effective, with composite desirabilities 0.59 and 0.58, respectively. Broyden’s method for the same data, with composite desirability 0.67, is more effective than both ANN and BPPA. When applied to the data of Westerhuis et al.,10 the composite desirabilities of ANN and BPPA become 0.61 and 0.74, respectively. The latter shows that the effectiveness of BPPA, which has data multinormality as a prerequisite, substantially increases with the size of the data set (data of Merkku et al.9 consist of 27 trials with replications; data of Westerhuis et al.10 consist of 55 trials). The inverse RSM (Broyden’s method) for the data of Westerhuis et al.,10 with composite desirability 0.64, is more effective than ANN.

Table 2. Composite Desirability a. data by Merkku et al. in ref 9

specifications target = PLS influential points yl = target − standard deviation yu = target + standard deviation y is calculated from RSM target yl yu y is calculated from Broyden’s target yl yu y is calculated from BPPA yl yu y is calculated from ANN target yl yu

MWSD

Method’s Composite Desirability

CS

FR

DT

2.25

48.00

2.90

12.00

1.52

41.60

2.33

9.48

2.97

54.40

3.47

14.00

MWSD

CS

FR

DT

0.87

2.09 1.81 2.15 MWSD

48.18 47.12 48.18 CS

2.90 2.90 2.94 FR

10.89 10.70 10.74 DT

0.67

1.73 0.72 1.76 MWSD

48.17 41.83 47.86 CS

2.70 3.07 2.76 FR

11.73 9.32 11.42 DT

0.58

1.91 2.62 MWSD

44.00 55.85 CS

2.69 3.14 FR

11.60 14 DT

0.59

1.80 46.70 2.95 11.29 0.76 43.06 2.75 10.32 2.11 46.85 3.17 12.41 b. data by Westerhuis et al. in ref 10 Method’s Composite Desirability

specifications

CS

DT

EF

target = PLS influential points yl = target − standard deviation yu = target + standard deviation y is calculated from RSM target yl yu y is calculated from Broyden’s target yl yu y is calculated from BPPA yl yu y is calculated from ANN target yl yu

66.07

316.23

274.00

30.90

69.18

218.55

75.86

416.87

329.45

CS

DT

EF

0.85

66.07 41.69 75.86 CS

288.40 69.18 416.87 DT

273.93 218.55 293.19 EF

0.64

66.07 40.73 59.01 CS

288.40 74.82 417.45 DT

273.93 218.73 329.80 EF

0.74

57.54 72.44 CS

234.42 416.87 DT

269.15 281.84 EF

0. 61

61.40 37.646 60.79

287.08 70.21 419.33

270.99 237.21 309.70

5. CONCLUSIONS Determination of the Design Space (DS) is part of the Quality by Design (QbD) methodology and allows changes to the critical process and material parameters, CPP and CMP, respectively, to be made without previous regulatory approval. This can be done by various methods, Response Surface Method (RSM), Bayesian Post Predictive Approach (BPPA), and Artificial Neural Networks (ANN), depending on the type of experimental data obtained for the purpose of determining the DS. If the data are complete and there is little uncertainty, the proper method of determining the DS is the RSM. If the data involve high uncertainty and correlation structures, the proper method of determining DS is the BPPA. Finally, if data are missing or fuzzy, the proper method of determining DS is ANN. The DS was determined for a two-process tablet manufacturing9 and three-process tablet manufacturing10 by RSM, BPPA,

and the Artificial Neural Networks (ANN), and are shown in Table 1. In the same table, bounds of DS were also estimated by inverting RSM, i.e, solving eq 1 for known responses, yi, by Broyden’s method. In most cases, the bounds of DS estimated by ANN are much farther apart than those in the case of RSM, 12008



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(6) Boukouvala, F.; Muzzio, F. J.; Ierapetritou, M. G. Design Space of Pharmaceutical Processes Using Data-Driven-Based Methods. J. Pharm. Innov. 2010, 5, 119. (7) Mitchell, J. D.; Abhinava, K.; Griffiths, K. L.; McGarvey, B.; Seibert, K. D.; Sethuraman, S. Unit Operations Characterization Using Historical Manufacturing Performance. Ind. Eng. Chem. Res. 2008, 47, 6612. (8) Lepore, J.; Spavins, J. PQLI Design Space. J. Pharm. Innov. 2008, 3, 79. (9) Merkku, P.; Lindqvist, A.-S.; Leiviska, K.; Yliruusi, J. Influence of Granulation and Compression Process Variables on Flow Rate of Granules and on Tablet Properties, with Special Reference to Weight Variation. Int. J. Pharm. 1994, 102, 117. (10) Westerhuis, J. A.; Coenegracht, P. M. J.; Lerk, C. F. Multivariate Modelling of the Tablet Manufacturing Process with Wet Granulation for Tablet Optimization and in-Process Control. Int. J. Pharm. 1997, 156, 109. (11) Solvason, C. C.; Chemmangattuvalappil, N. G.; Eljack, F. T.; Eden, M. R. Efficient Visual Mixture Design of Experiments Using Property Clustering Techniques. Ind. Eng. Chem. Res. 2009, 48, 2245. (12) Harrington, E. . The Desirability Function. Ind. Qual. Control 1965, 121, 494. (13) Xu, K.; Lin, D. K. J.; Tang, L. C.; Xie, M. Multiresponse Systems Optimization Using a Goal Attainment Approach. IIE Trans. 2004, 36, 433. (14) Peterson, J. J. A Posterior Predictive Approach to Multiple Response Surface Optimization. J. Qual. Technol. 2004, 36. (15) Hayashi, Y.; Kikuchi, S.; Onuki, Y.; Takayama, K. Reliability Evaluation of Nonlinear Design Space in Pharmaceutical Product Development. J. Pharm. Sci. 2012, 101, 2. (16) Ibric, S.; Djuric, Z.; Parojcic, J.; Petrovic, J. Artificial Intelligence in Pharmaceutical Product Formulation: Neural Computing. Chem. Ind. Chem. Eng. Q. 2009, 15, 227. (17) Landín, M.; Rowe, R. C.; York, P. Advantages of Neurofuzzy Logic against Conventional Experimental Design and Statistical Analysis in Studying and Developing Direct Compression Formulations. Eur. J. Pharm. Sci. 2009, 38, 325. (18) Vining, G.; Myers, R. Combining Taguchi and Response Surface Philosophies: A Dual Response Approach. J. Qual. Technol. 1990, 38. (19) Lee, M.; Kim, K. Expected Desirability Function: Consideration of Both Location and Dispersion Effects in Desirability Function Approach. Qual. Technol. Quant. Manag. 2007, 4, 365.

and ANN, in two ways: (a) multiresponse optimization and (b) overlapping responses. Multiresponse optimization determines targets and maxima and minima of the responses and leads to a DS with bounds in the neighborhood of optimum conditions. The method of “overlapping responses” leads to a DS with bounds determined from the global lower and upper specification limits of the response variables. The effectiveness of the various methods, RSM, BPPA, and ANN, in determining the DS is measured by the composite desirability which, for the two data sets of tablet manufacturing, is higher for RSM. This is because the data in question are complete and lack the specific features that the ANN and BPPA methods are suited to address.

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ASSOCIATED CONTENT

* Supporting Information S

The levels of the factors for data sets by Merkku et al.9 and by Westerhuis et al.10 This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +30-210-7723125. Fax: +30-210-7723163. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge the financial support to Ms. Kalliopi Chatzizacharia, PhD Candidate in Chemical Engineering, in the form of a scholarship from the National Technical University of Athens.

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ABBREVIATIONS QbD = Quality by Design CQA = Critical Quality Attributes CMA = Critical Material Attributes CPP = Critical Process Parameters RSM = Response Surface Method ANN = Artificial Neural Networks BPPA = Bayesian Post Predictive Approach MCC = Microcrystalline cellulose CS = Crushing Strength EF = Ejection Force DT = Disintegration Time

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NOTE ADDED AFTER ASAP PUBLICATION This paper was original published ASAP on July 17, 2014, with errors in the table citations of the Results section. The corrected version was reposted on July 21, 2014.

REFERENCES

(1) Garcia, T.; Cook, G.; Nosal, R. PQLI Key Topics - Criticality, Design Space, and Control Strategy. J. Pharm. Innov. 2008, 3, 60. (2) Smith, B. V.; Ierapepritou, M. Framework for ConsumerIntegrated Optimal Product Design. Ind. Eng. Chem. Res. 2009, 48, 8566. (3) Zomer, S.; Gupta, M.; Scott, A. Application of Multivariate Tools in Pharmaceutical Product Development to Bridge Risk Assessment to Continuous Verification in a Quality by Design Environment. J. Pharm. Innov. 2010, 5, 109. (4) Huang, J.; Kaul, G.; Cai, C.; Chatlapalli, R.; Hernandez-Abad, P.; Ghosh, K.; Nagi, A. Quality by Design Case Study: An Integrated Multivariate Approach to Drug Product and Process Development. Int. J. Pharm. 2009, 382, 23. (5) International Conference on Harmonisation (ICH). Guideline Q8 (R2): Note For Guidance On Pharmaceutical Development, 2009. 12009


Design Space Approach for Pharmaceutical Tablet Development

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