2021 Volume 69 Issue 7 Pages 674-680
Quality by design (QbD) is an essential concept for modern manufacturing processes of pharmaceutical products. Understanding the science behind manufacturing processes is crucial; however, the complexity of the manufacturing processes makes implementing QbD challenging. In this study, structural equation modeling (SEM) was applied to understand the causal relationships between variables such as process parameters, material attributes, and quality attributes. Based on SEM analysis, we identified a model composed of the above-mentioned variables and their latent factors without including observational data. Difficulties in fitting the observed data to the proposed model are often encountered in SEM analysis. To address this issue, we adopted Bayesian estimation with Markov chain Monte Carlo simulation. The tableting process involving the wet-granulation process for acetaminophen was employed as a model case for the manufacturing process. The results indicate that SEM analysis could be useful for implementing QbD for the manufacturing processes of pharmaceutical products.
Compression of granules manufactured by wet-granulation process (wet-granule compression) is a popular method for preparing pharmaceutical tablets.1) Compared with other methods, such as direct compression and that using dry-granules, wet-granule compression yields better results and reduces the risks of tableting failures, such as capping, lamination, sticking, and die friction. Furthermore, it is easier to increase the quantities of active pharmaceutical ingredients (APIs) in the tablets. However, wet-granule compression involves relatively long and complex manufacturing steps, such as crushing, sieving, mixing, granulation, drying, tableting, and/or coating. Until now, expertise and experience have played an important role in the manufacture of high-quality tablets.
Quality by design (QbD) is an essential concept for modern manufacturing processes of pharmaceutical products.2–5) A scientific understanding of the manufacturing processes is crucial to realizing QbD. However, the mechanism underlying wet-granulation and tableting is unclear because of the complexity of the manufacturing processes, and consequently, it is difficult to identify critical process parameters (CPPs), critical material attributes (CMAs), as well as critical quality attributes (CQAs). According to QbD, quality must be built in the pharmaceutical product when the manufacturing process is designed. In view of risk assessment, it is important to identify CPPs, CMAs, and CQAs based on QbD. In this regard, a preliminary hazard analysis (PHA), a failure mode and effect analysis (FMEA), an Ishikawa diagram, among other methods, have been employed as screening techniques.6–8) These techniques provide systematic means to define CPPs, CMAs, and CQAs; however, a risk priority number (RPN) must be employed based on the expert knowledge.4–7) Because the RPN is arbitrarily determined, we often encounter difficulties in objective scoring of RPN.
Partial least squares regression (PLS) and principal component analysis (PCA) have often been applied to identify CPPs, CMAs, and CQAs in terms of QbD practice.9) Although these techniques are useful, a large amount of data is needed, and their modeling tends to be data-dependent, rather than being mechanistic. A Bayesian network (BN) is also an effective tool for understand the science of manufacturing processes. It is simple and convenient for graphical comprehension of multivariate relationships between causal, intermediate, and output variables.10) However, the construction of mechanistic models is limited because the measured values in all variables are required for applying BN. Structural equation modeling (SEM) is a statistical technique used to elucidate the relationships between observed variables and latent factors, in which no measured values are included.11–14) Based on SEM, we identified a possible conceptual model composed of observed variables together with latent factors. Recently, SEM has received a lot of attention in research areas, such as psychology, sociology, economics, and education.11–14) Furthermore, SEM analysis is often utilized in pharmaceutical practice.15,16) For instance, Yamamura et al. found via SEM analysis, that pharmacists qualified to assess the pain status of patients contributed to improving the QOL of cancer patients.15) Oshima et al. revealed discrepancies in perceptions between patients and pharmacists regarding the use of pharmaceuticals.16) However, SEM is yet to be applied to the manufacturing process of pharmaceutical products. In this study, we attempted to elucidate the latent structure underlying the wet-granule compression process and thereby obtain the information essential for the QbD approach. A tablet containing 100 mg of acetaminophen as the API was employed as the model case. Based on our previous experience, causal variables, such as the kneading time of the moist mass, amount of water used as a binder for granulation, and tableting force, were selected as potential CPPs (p-CPPs). Several characteristics of granules and tablets were determined as potential CMAs (p-CMAs) and potential CQAs (p-CQAs). Finally, we attempted to build a reasonable model that included latent factors for granulation and tableting by employing SEM analysis.
Acetaminophen fine powder was purchased from Mallinckrodt Japan Co., Ltd. (Tokyo, Japan). Lactose (Tablettose® 80) was purchased from Meggle Japan, Co., Ltd. (Tokyo, Japan). Cornstarch (Graflow® M) was purchased from Nippon Starch Chemical Co., Ltd. (Osaka, Japan). Microcrystalline cellulose (MCC; Ceolus® PH-101) was purchased from Asahi Kasei Chemicals Co., Ltd. (Tokyo, Japan). Polyvinylpyrrolidone K-90 was a gift from Nippon Shokubai Co., Ltd. (Osaka, Japan). Low-substituted hydroxypropyl cellulose was purchased from Shin-Etsu Chemical Co., Ltd. (Tokyo, Japan). Magnesium stearate (MgSt) from plants, Wako 1st grade, was purchased from FUJIFILM Wako Pure Chemical Corp. (Osaka, Japan).
Granulation and TabletingTest formulations are listed in Table 1. The kneading time (X1) and amount of purified water (X2) were the p-CPPs for wet-granulation. The compression force (X3) was the p-CPP for tableting. Three levels of X1, X2, and X3 were assigned using the Box-Behnken experimental design (Table 2), and 15 types of test granules and tablets were prepared at random. All ingredients shown in Table 1 except MgSt were dried at 70 °C for 12 h, and then sieved through a 60-mesh screen (250 μm). The ingredients were accurately weighed, and blended for 3 min at 60 rpm using a V-shaped mixer (VM-2, 1000 mL container volume; Tsutsui Scientific Instruments Co., Ltd., Tokyo, Japan). An appropriate amount of purified water (X2 in Table 2) was added to the mixed powder, and then kneaded for an appropriate time (X1 in Table 2) using a kneader with a stirring blade at 300 rpm (KENMIX; Aicohsha Co., Ltd., Toda, Japan). The moist mass thus produced was forcibly sieved through a 12-mesh screen (1400 μm) and then dried for 2 h at 75 °C. The coarse granules obtained were mixed with MgSt (0.5%) in a V-shaped mixer for 1 min before tableting. The granules (200 mg) were compressed with an appropriate compression force (X3 in Table 2) into either flat-faced (FLAT) or convex (CONV) tablets (8 mm in diameter), using a tableting apparatus (HANDTAB 100; Ichihashi-Seiki Co., Ltd., Kyoto, Japan). Hard chrome plating punches with a flat-face and curvature radius of 12 mm were used to prepare FLAT and CONV, respectively.
| Material | Weight (g) |
|---|---|
| Acetaminophen | 100 |
| Lactose | 30 |
| Corn starch | 10 |
| Microcrystalline cellulose | 40 |
| Polyvinylpyrrolidone K-90 | 10 |
| Low-substituted hydroxypropyl cellulose | 10 |
| Trial | X1 | X2 | X3 | |||
|---|---|---|---|---|---|---|
| Code | (min) | Code | (%) | Code | (kN) | |
| 1 | −1 | 10 | −1 | 30 | 0 | 8 |
| 2 | −1 | 10 | 0 | 35 | 1 | 10 |
| 3 | −1 | 10 | 0 | 35 | −1 | 6 |
| 4 | −1 | 10 | 1 | 40 | 0 | 8 |
| 5 | 0 | 15 | −1 | 30 | 1 | 10 |
| 6 | 0 | 15 | −1 | 30 | −1 | 6 |
| 7 | 0 | 15 | 0 | 35 | 0 | 8 |
| 8 | 0 | 15 | 0 | 35 | 0 | 8 |
| 9 | 0 | 15 | 0 | 35 | 0 | 8 |
| 10 | 0 | 15 | 1 | 40 | 1 | 10 |
| 11 | 0 | 15 | 1 | 40 | −1 | 6 |
| 12 | 1 | 20 | −1 | 30 | 0 | 8 |
| 13 | 1 | 20 | 0 | 35 | 1 | 10 |
| 14 | 1 | 20 | 0 | 35 | −1 | 6 |
| 15 | 1 | 20 | 1 | 40 | 0 | 8 |
The Hausner ratio of granules is the index of fluidity.17) Approximately 20 mL of the sample granules was gently poured into the graduated cylinder. The bulk density (ρbulk) was determined as the granule weight divided by the volume of gently poured granules. The graduated cylinder was then tapped up and down repeatedly using a tap density tester (Konishi Seisakusho Co., Ltd., Osaka, Japan), until the powder volume became constant. The powder volume was measured after every 20 tap, and was found to become constant before 100 taps. The tapped density (ρtapped) is defined as the ratio of the powder weight to the tapped volume at 100 taps. The Hausner ratio was then calculated as follows:
 | (1) |
The Hausner ratio was measured in triplicate for each sample granule.
Angle of Repose of GranulesThe angle of repose of sample granules was determined from the circular conic formed on the upper surface of a stainless-steel cylinder (diameter (d) = 50 mm). The height of the circular conic (h) was measured, and the angle of repose was then calculated as follows:
 | (2) |
The angle of repose was measured in triplicate for each sample granule.
Average Diameter of GranulesA Feret diameter of each particle in the sample granules was measured using a digital microscope (VHZ-ST; Keyence Corp., Tokyo, Japan). The average diameter was defined as the arithmetic mean of the diameter of 100 particles. The average diameter was measured in triplicate for each sample granule.
Ratio of Coarse Granules and Fine GranulesThe sample granules were mixed with MgSt (0.5%) in a V-shaped mixer for 1 min. Sample granules (2000 mg) were sifted through 12-mesh (1400 μm) and 60-mesh (250 μm) screens, using a micro vibration sifter (M-3T; Tsutsui Scientific Instruments Co., Ltd., Tokyo, Japan). The granules remaining on the 12-mesh screen and passing through the 60-mesh screen were accurately weighed. The ratios of the weights of granules remaining on the 12-mesh screen and the weights of granules passing through the 60-mesh screen to the total weight of sample granules, were defined as the ratio of coarse granules and the ratio of fine granules, respectively. The measurements were repeated in triplicate for each sample granule.
Yielding Force and Crashing Strength of GranulesThe yielding force of the sample granules was determined using a corpuscle hardness measuring apparatus (New Grano; Okada Seiko Co., Ltd., Tokyo, Japan). The loading speed of the tester probe was set to 15 μm/s. The force onset of the collapse of the test granule was defined as the yielding force. The crushing strength was calculated as follows18):
 | (3) |
where, d is the diameter of each particle. The yielding force and crushing strength were measured in triplicate for each sample granule.
Tablet DensityThe test tablets were accurately weighed, and the tablet density was calculated by dividing the tablet weight with the volume (V). In the case of FLAT, V was calculated as follows:
 | (4) |
where, r is the tablet radius, and h is the tablet thickness. In the case of CONV, V was calculated as follows:
 | (5) |
where, V1 is the volume of the cylindrical part, and V2 is the volume of the cap part on both sides, h1 is the thickness of the cylindrical part, and the h2 is the maximum height of the cap part. The tablet density was measured in triplicate for each tablet.
Tensile Strength of TabletsThe tensile strength of tablets in a diametral compression was determined using a load cell type hardness tester (PC30; Portable Checker, Okada Seiko Co., Ltd.). The tensile strength was calculated as follows19,20):
 | (6) |
where, F is the crushing force of the tablet in the diametral direction, D is the diameter, and w is the thickness in FLAT, and the length of the thickest part of the tablet in CONV.21) The tensile strength was measured in triplicate for each tablet.
Disintegration Test of TabletsThe disintegration test was performed in accordance with the Japanese Pharmacopeia 17 disintegration test for tablets using a disintegration tester (NT-20H; Toyama Sangyo Co., Ltd., Osaka, Japan) and 900 mL of purified water as a test medium at 37 °C ±2 °C. The disintegration time was defined as the time required for the complete disappearance of the tablet and its particles from the tester net. The disintegration time was measured in triplicate for each tablet.
Dissolution Test of TabletsThe dissolution profiles of acetaminophen from the tablets were determined in accordance with the Japanese Pharmacopeia 17 dissolution test no. 2 (paddle method) by using a dissolution tester (NT-6600; Toyama Sangyo Co., Ltd.). As a test medium, a 900 mL of water was used at 37 °C ±0.5 °C at a paddle rotation speed of 50 rpm. Aliquots (5 mL) were withdrawn at 5, 10, 15, 20, 30 and 60 min, and filtered through a membrane filter with a pore size of 0.45 μm. After sampling, the same amount of fresh medium was immediately added to the test medium. The concentration of acetaminophen was determined using HPLC. The HPLC apparatus was assembled as follows: a pump; LC-20AD (Shimadzu Corp., Kyoto, Japan), a detector; SPD-M20A (Shimadzu Corp.), a column; Inertsil® ODS (mean particle size of 3.5 μm) 4.6 × 150 mm (GL Sciences Inc., Tokyo, Japan), a mobile phase; deionized water-acetonitrile (10 : 90 in volume ratio) containing 0.1% (v/v) phosphoric acid, and wavelength of detection; 254 nm. The 50% dissolution time was determined from the dissolution profiles in triplicate for each tablet.
SEM AnalysisPossible models including observed variables and latent factors were built with AMOS 25 (IBM Japan, Ltd., Tokyo, Japan). For SEM analysis, the most likelihood and least squares estimations were applied to fit the data to the proposed models. The improved model has been explored in many trials. Subsequently, a Bayesian estimation incorporating Markov chain Monte Carlo (MCMC) simulation was adopted for a realistic simple model.
Among the various pharmaceutical parameters, the kneading time (X1) of moist mass, amount of water (X2) for granulation, and compression force (X3) of tablets were selected as p-CPPs. These values are controllable, and hence they were assigned using the Box-Behnken experimental design.21) Many variables for the granules and tablets were measured as p-CMAs and p-CQAs (Table 3). The Hausner ratio (G1) of test granules was close to 1 and their angle of repose (G2) was less than 40°, suggesting that granules with good fluidity were prepared. The quantities of crude and fine granules (G3 and G4) were very small, and the average diameter (G5) varied less. These results may have originated from the sample granules being prepared by force-sieving of the moist mass. Although wide deviations in the yielding force (G6) and crushing strength (G7) were observed, all samples were at the level of the soft granules. Variations in these values (G6 and G7) in the same sample were not very large. In terms of tablet properties, the tensile strength (T2) of FLAT was somewhat greater than that of CONV, but other variables in FLAT and CONV were similar. The density (T1) and tensile strength (T2) were reasonably good, derived from the good fluidity of the granules and their ease of plastic deformation during tableting. Both disintegration time (T3) and 50% dissolution time (T4) were unfavorable. This may be due to the high T1 and T2 values of the sample tablets. In addition to p-CMAs (G1–G7) and p-CQAs (T1–T4), we set up two latent factors without observational data for granulation and tableting. Based on the role of each variable, we proposed a tentative early model, as shown in Fig. 1. The model shows that two process parameters, the kneading time (X1) and amount of water (X2) directly affect the latent factor (L1) for granulation, and the compression force (X3) affects the latent factor (L2) for tableting. L1 is linked to the p-CMAs of granules (G1 to G7), and L2 is linked to the p-CQAs of tablets (T1 to T4). Furthermore, L2 is partly affected by L1. Although this model was thought to be proper based on our previous knowledge, no convergence in this model was achieved when the most likelihood and least squares estimations were adopted. This may be due to several reasons, such as incomplete modeling, bias of measured data, and small sample size. In this regard, we conducted several trials of data transformations and modification of modeling. Finally, we found that a discretization of measured data based on the Ward method gave us convergence of models and better approximations.22) The detailed description and discrete of variables are shown in Table 4.
| Variable | Code | Mean ± S.D. | |
|---|---|---|---|
| Granule | Hausner ratio | G1 | 1.057 ± 0.025 |
| Angle of repose | G2 | 38.02 ± 1.94 (°) | |
| Ratio of crude granules | G3 | 1.309 ± 0.126 (%) | |
| Ratio of fine granules | G4 | 1.234 ± 0.421 (%) | |
| Average diameter | G5 | 597.8 ± 35.7 (mm) | |
| Yielding force | G6 | 60.57 ± 21.94 (mN) | |
| Crushing strength | G7 | 348.5 ± 204.1 (kPa) | |
| FLAT | Density | T1 | 1.187 ± 0.025 (g/cm3) |
| Tensile strength | T2 | 1.116 ± 0.316 (MPa) | |
| Disintegration time | T3 | 9.55 ± 6.62 (min) | |
| 50% Dissolution time | T4 | 11.79 ± 7.81 (min) | |
| CONV | Density | T1 | 1.214 ± 0.027 (g/cm3) |
| Tensile strength | T2 | 0.895 ± 0.209 (MPa) | |
| Disintegration time | T3 | 8.83 ± 6.84 (min) | |
| 50% Dissolution time | T4 | 11.02 ± 7.78 (min) |
| Variable | Code | Discrete level | Description |
|---|---|---|---|
| Hausner ratio | G1 | 1, 2, 3, 4 | Smaller G1, higher the score |
| Angle of repose | G2 | 1, 2, 3, 4 | Smaller G2, higher the score |
| Ratio of crude granules | G3 | 1, 2, 3, 4 | Smaller G3, higher the score |
| Ratio of fine granules | G4 | 1, 2, 3, 4 | Smaller G4, higher the score |
| Average diameter | G5 | 1, 2, 3, 4 | Larger G5, higher the score |
| Yielding force | G6 | 1, 2, 3, 4 | Stronger G6, higher the score |
| Crushing strength | G7 | 1, 2, 3, 4 | Stronger G7, higher the score |
| Density | T1 | 1, 2, 3, 4, 5, 6 | Denser T1, higher the score |
| Tensile strength | T2 | 1, 2, 3, 4, 5, 6 | Stronger T2, higher the score |
| Disintegration time | T3 | 1, 2, 3, 4, 5, 6 | Shorter T3, higher the score |
| 50% Dissolution time | T4 | 1, 2, 3, 4, 5, 6 | Shorter T4, higher the score |
e1–e13 represent the error variables.
Figure 2 shows the improved model for FLAT and CONV tablets. The angle of repose (G2), mean diameter (G5), and yielding force (G6) of granules were removed from the early model (Fig. 1), because G2 was correlated with the Hausner ratio (G1), and G6 was correlated with the crushing strength (G7). Moreover, the variation in average diameter (G5) was rather narrow. The improved model shown in Fig. 2 is reasonable and it may be helpful in explaining the wet-granule compression process scientifically, although the goodness-of-fit (GOF) was problematic (Table 5). The goodness of fit index (GFI), adjusted goodness of fit index (AGFI), and chi-square (CMIN/D) predicted by the least squares estimation were acceptable, but these statistics were somewhat poor when the most likelihood estimation was employed. This may suggest that the proposed model (Fig. 2) still includes some statistical problems, such as small sample size, including meaningless factors, and the bias of error variance from a normal distribution. We attempted to improve the models according to the modification index,23) and the mathematically preferable models were obtained with acceptable GOF parameters. However, many of these models were inappropriate in view of realistic meanings. This difficulty often creates unfavorable barriers for the intensive application of SEM.
e1–e13 represent the error variables.
| Statistical parameter | FLAT | CONV | ||
|---|---|---|---|---|
| LSa) | MLb) | LSa) | MLb) | |
| GFIc) | 0.940 | 0.764 | 0.967 | 0.752 |
| AGFId) | 0.898 | 0.601 | 0.944 | 0.581 |
| CMI/DFe) | 1.997 | 2.572 | 1.273 | 2.695 |
| RMSEAf) | 0.186 | 0.196 | ||
a) Least squares estimation, b) most likelihood estimation, c) goodness of fit index, d) adjusted goodness of fit index, e) chi-square. f) root mean square error of approximation.
In order to address the above-mentioned issues, a Bayesian estimation incorporating MCMC simulation has been applied in SEM analysis.24) Several links between error variables such as e3↔e7, e9↔e10, e9↔e11, and e10↔e11 were removed from the improved model, and a simpler model was built as shown in Fig. 3. In the maximum likelihood and least squares estimations, the true values of the model parameters are hypothesized as fixed but unknown, and the estimates of those parameters from a given sample are presumed as random but known. In the case of the Bayesian approach, model parameters are assumed to be unknown as a random variable and they are assigned as a probability distribution. The distribution of parameters before the data become evident is defined as a “prior probability.” According to the Bayesian estimation, the distribution of parameters is updated as a “posterior probability.” Using a MCMC simulation, random values of parameters from high-dimensional joint posterior distributions can be calculated even if the model is complex. That is, sample means and standard deviations of posterior parameters are determined by the Bayesian estimation with MCMC via more than 1000000 iterative calculations. The Bayesian estimation is considered as converged when the autocorrelation coefficient in every path is sufficiently close to 0. As an example, Fig. 4 shows the autocorrelation coefficient of L1→L2 in FLAT as a function of iterative procedure of MCMC simulation. The MCMC simulation had essentially forgotten its starting position, which was equivalent to convergence in distribution. All path coefficients successfully converged as the autocorrelation coefficients approached 0. In addition, the deviance information criterion (DIC) is available as another GOF parameter.25) The DIC is an asymptotic approximation, and it is useful in the model selection problems where the posterior distributions have been obtained by MCMC simulation. The DIC greatly decreased when the early model (Fig. 1) was compared with the simple model (Fig. 3), i.e., 322 to 180 in FLAT and 331 to 224 in CONV. This indicated that better approximation was achieved with the simple model. Path coefficients in the simple model obtained by the Bayesian estimation are summarized in Table 6. To make it easy to compare, the path coefficients of L1→G1 and L2→T1 were fixed at 1. We compared the path coefficients predicted by the least squares and most likelihood estimations in the improved model, and by the Bayesian estimation with MCMC in the simple model. The results are shown in Table 7. The slope of regression equation was almost equal to unity, the intersect was close to 0, and the correlation coefficient was sufficiently high in every case, indicating that path coefficients were acceptable irrespective of a subtle variation in modeling and differences in mathematical algorithms. This also indicates that the latent mechanism underlying the wet-granulation and tableting processes can be determined via the simple model shown in Fig. 3, although it may have limitations in this case study.
e1–e13 represent the error variables.
The autocorrelation coefficient reached 0 with more than 1000000 iterative MCMC simulations.
| FLAT | CONV | |||||
|---|---|---|---|---|---|---|
| LSa) | MLb) | BEc) | LSa) | MLb) | BEc) | |
| X1→L1 | −0.245 | −0.161 | −0.146 | −0.255 | −0.173 | −0.182 |
| X2→L1 | 0.682 | 0.874 | 0.829 | 0.570 | 0.877 | 0.782 |
| X3→L2 | 1.469 | 1.466 | 1.460 | 1.068 | 1.249 | 1.143 |
| L1→G1d) | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 |
| L1→G3 | −1.556 | −1.056 | −1.150 | −1.771 | −1.039 | −1.217 |
| L1→G4 | 1.490 | 1.379 | 1.500 | 1.614 | 1.334 | 1.513 |
| L1→G7 | 0.758 | 0.633 | 0.683 | 0.997 | 0.628 | 0.766 |
| L2→T1d) | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 |
| L2→T2 | 0.329 | 0.485 | 0.491 | 0.459 | 0.744 | 0.806 |
| L2→T3 | −1.145 | −1.036 | −1.036 | −1.701 | −1.314 | −1.519 |
| L2→T4 | −1.043 | −1.021 | −1.008 | −1.472 | −1.267 | −1.479 |
| L1→L2 | 0.758 | 0.677 | 0.710 | 0.797 | 0.463 | 0.491 |
a) Least squares estimation, b) most likelihood estimation, c) Bayesian estimation with MCMC simulation, d) pass coefficients of L1→G1 and L2→T1 were fixed at 1. Least squares estimation and most likelihood estimation were applied to an improved model represented in Fig. 2. Bayesian estimation was applied to a simpler model represented in Fig. 3.
| FLAT | CONV | |||
|---|---|---|---|---|
| Equation | R2 | Equation | R2 | |
| LS vs. ML | y = 1.10x−0.10 | 0.982 | y = 1.15x−0.14 | 0.974 |
| LS vs. BE | y = 1.08x−0.10 | 0.990 | y = 1.03x−0.03 | 0.959 |
| MS vs. BE | y = 0.98x + 0.00 | 0.998 | y = 0.89x + 0.10 | 0.981 |
x is horizontal and y is vertical axes.
Critical parameters of granulation and tableting were identified based on the path coefficients (Table 6). The latent factor of granules (L1) represented the good fluidity (higher G1), larger number of crude particles (lower G3), smaller number of fine powders (lower G4), and high crushing strength (higher G7). L1 was mainly affected by the amount of water (X2), and to a lesser extent, by the kneading time (X1). Specifically, an increase in X2 and a decrease in X1 resulted in an increase in L1. The latent factor of tableting (L2) represented a high density (higher T1), excellent hardness (higher T2), retardation of disintegration time (lower T3) and decrease in dissolution rate (lower T4). L2 was mainly controlled by the compression force (X3), although the effect of L1 on L2 was not negligible. It is well known that an increase in the mechanical strength of tablets results in retardation of disintegration time as well as a decrease in the dissolution rate of API, indicating that L2 is a common feature of mechanically strong tablets.
Bivariate Posterior DensityTo identify the effects of p-CPPs (X1, X2, and X3) on the latent factors of granulation (L1) and tableting (L2), bivariate posterior density was plotted. Figure 5 shows bivariate posterior density plots between path coefficients of X1→L1 and X2→L1. No obvious difference between FLAT and CONV was seen in the densest location in the density plots, indicating that the distribution densities of X1→L1 and X2→L1 were scarcely affected by the indirect effects of the tableting variables (T1, T2, T3, and T4). This is reasonable because no signal backpropagates from tableting to granulation processes. An increase in the path coefficient for X1→L1 resulted in broadening of credible ranges of the distribution density for X2→L1, and vice versa, indicating that causal variables, X1 and X2, mutually complement the granulation process. The credible range of distribution density for CONV (Fig. 5B) was somewhat broader than that of FLAT (Fig. 5A), indicating that the fitting of data to the model was slightly poorer in CONV. It was also confirmed with DIC values (DIC = 180 in FLAT and DIC = 224 in CONV). Bivariate posterior density plots between path coefficients L1→L2 and X3→L2 are shown in Fig. 6. There are specific differences between FLAT (Fig. 6A) and CONV (Fig. 6B). The densest points of the path coefficients L1→L2 and X3→L2 were considerably different. In the case of CONV (Fig. 6B), the credible ranges of the distribution density for X3→L2 were broadened with a decrease in the path coefficient of L1→L2. On the other hand, the credible range of distribution density for X3→L2 was relatively narrow in FLAT (Fig. 6A), indicating that the compression force (X3) of FLAT acted more directly as CPP when the tablet has a flat surface. In our previous studies,26,27) we indicated that the distribution of stress remaining in the flat-faced tablets was considerably different from that in the convex tablets, affecting CQAs, such as the hardness and the disintegration time. The results of this study support previous findings, indicating that a small change in tablet shapes should be considered in addition to process and material variables.
The three shades of gray represent the 50, 90, and 95% credible regions.
The three shades of gray represent the 50, 90, and 95% credible regions.
In view of risk assessment for preparing pharmaceutical products, it is important to identify the CPPs, CMAs, and CQAs based on scientific understanding of the manufacturing process. In this regard, we introduced SEM to reveal CPPs, CMAs, and CQAs from an objective perspective. In the case of the wet-granulation and tableting processes proposed in this study, we revealed that the compression force (X3) was the most important CPP (Table 6), and the amount of water (X2) was effective, as was the kneading time (X1), but to a lesser extent. The fluidity of granules (G1), and the particle size distribution (G3 and G4) were crucial as CMAs. Furthermore, the tablet density (T1), disintegration time (T3), and dissolution rate of API (T4) were key parameters for CQAs. In view of tablet shapes, the compression force (X3) and latent factor of granulation (L1) more directly affected the latent factor of tableting (L2) in FLAT. Although some issues, such as the fitting improvement and the model modification, need to be addressed in the future, the results of this study indicate that SEM is useful for implementing QbD in the manufacturing processes of pharmaceutical products.
This research was supported by AMED under Grant Number 20hm0102083h0001.
The authors declare no conflict of interest.
