# Control Strategy for Excipient Variability in the Quality by Design Approach Using Statistical Analysis and Predictive Model: Effect of Microcrystalline Cellulose Variability on Design Space

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

^{®}, Dusseldorf, Germany), FMC BioPolymer (Avicel

^{®}, Philadelphia, PA, USA), Blanver (MICROCEL

^{®}MC, Farmoquímica, Sao Paulo, Brazil), and JRS Pharma GmbH & Co. KG (PROSOLV

^{®}SMCC (Silicified microcrystalline cellulose), VIVAPUR

^{®}, Heweten

^{®}, Rosenberg, Germany). Polyvinylpyrrolidone (PVP) was purchased from BASF AG (Kolidon

^{®}, Ludwigshafen, Germany). Croscarmellose sodium (CCS) was purchased from FMC BioPolymer (Ac-Di-Sol

^{®}, Philadelphia, PA, USA). Magnesium stearate (St-Mg) was purchased from Sigma-Aldrich Co. (St. Louis, MO, USA). All other reagents were of analytical or high-performance liquid chromatography (HPLC) grade.

#### 2.2. QbD Approach for Formulation Development

#### 2.2.1. Initial Risk Assessment

#### 2.2.2. Experimental Design to Optimize Formulation

^{®}software (version 13; Stat-Ease Inc., Minneapolis, MN, USA) was used to devise an experimental design. Amlodipine besylate (6.94 mg) and St-Mg (1.50 mg) were used as fixed factors. The three control factors included x

_{1}: SMCC 90 (PROSOLV

^{®}SMCC 90), x

_{2}: CCS, and x

_{3}: PVP K25, and their ranges were 66.6–89.6, 1.0–15.0, and 1.0–10.0 mg, respectively. The total amount of control factors was maintained at 91.56 mg. Hardness (y

_{1}); friability (y

_{2}); dissolution at 5 (y

_{3}), 10 (y

_{4}), and 15 min (y

_{5}); assay (y

_{6}); and content uniformity (CU) (y

_{7}) were selected as response factors, and their target values are presented in Table S1. The target values of CQAs were determined using prior knowledge [22]. After the completion of 17 experiments using the D-optimal mixture design, statistical parameters, such as coefficient of determination (R

^{2}), adjusted R

^{2}, and predicted R

^{2}, were assessed to confirm the best-fit model. The adjusted R

^{2}is used for reducing the overestimation of R

^{2}that increases as the number of predictors increases in the model. By employing the best-fit model, the quantitative effect of CMAs on CQAs was confirmed by analysis of variance (ANOVA) and the effect was presented as a coded equation. The coefficient of the coded equation indicated the effect degree of CMAs, and a higher coefficient suggested a significant effect of CMAs on CQAs. A positive coefficient (+) signified that CMAs increase CQAs, whereas a negative coefficient (−) indicated that CMAs decrease CQAs. After employing ANOVA analysis, a design space was established with CMAs that satisfied the optimal range of CQAs.

#### 2.2.3. Tablet Preparation

#### 2.2.4. Evaluation of CQAs

_{1}is the weight before rotation and w

_{2}is the weight after rotation.

#### 2.3. Investigation of the Effect of MCC Variability on the Design Space

#### 2.3.1. Measurement of the Physicochemical Properties of MCC

_{bulk}and ρ

_{tapped}are the bulk density and tapped density, respectively.

_{bulk}and ρ

_{true}are the bulk density and true density, respectively.

#### 2.3.2. Statistical Analysis of the Physicochemical Properties of MCC and CQAs

^{©}software (Sartorius Stedim Biotech., version 15, Umeå, Sweden) and Origin 2022 software (OriginLab, Northampton, MA, USA), respectively. PCA is a multivariate analysis method that transforms numerous datasets into a new system of variables known as principal components (PCs), thereby facilitating data interpretation [27]. The axis with the highest variance is identified as the first PC, and the axis with the second largest variance is identified as the second PC [28]. PCC quantifies the linear relationship between two variables (X and Y) and ranges from −1 to +1 [27]. In the present study, X variables included the physicochemical properties of MCC, whereas the Y variables included CQAs. PCC of −1 indicates a negative linear relationship, i.e., Y decreases as X increases. PCC of +1 indicates a positive linear relationship, i.e., Y increases as X increases. PCC of 0 indicates no correlation between two variables. PCC was calculated using Equation (11):

#### 2.3.3. ANN Modeling

^{2}. MSE and R

^{2}were calculated using Equations (12) and (13) [29,30]:

## 3. Results and Discussion

#### 3.1. QbD Approach for Optimizing the Formulation

#### 3.1.1. Initial Risk Assessment for Formulation Development

#### 3.1.2. Effect of CMAs on CQAs

^{2}, adjusted R

^{2}, and predicted R

^{2}of all response factors were high, indicating that all the models were fit. In addition, the difference between adjusted R

^{2}and predicted R

^{2}was less than 0.2, which indicates these two statistical parameters were considered to be in reasonable agreement. As presented in Table 1, the mutual interaction between SMCC 90 (x

_{1}) and PVP K25 (x

_{3}) had a positive effect on hardness, and a negative effect on friability. Dissolution was affected by the mutual interactions between SMCC 90 (x

_{1}) and CCS (x

_{2}) and between CCS (x

_{2}) and PVP K25 (x

_{3}). In particular, the mutual interaction between CCS (x

_{2}) and PVP K25 (x

_{3}) had a significantly positive impact on dissolution. Nevertheless, the main effect of PVP K25 on dissolution was negative. Plastic deformation is triggered by a particle bed within the cavity inside the die during the compression process, and greater plastic deformation produces a mechanically stronger tablet. Because MCC primarily exhibits plastic deformation during compression [36], when MCC was compressed, its binding area increased, leading to an increase in tablet hardness without increasing tablet friability [34]. In general, PVP is utilized as a binder in the wet granulation and direct compression process because of its high binding strength. In the direct compression process, the moisture content of the ingredients is essential, and in the case of PVP, the water contained in PVP can increase hardness because it provides the bonding force between the particles [37]. In addition, PVP ensures the desired tablet hardness without increasing the tablet friability, and consequently, SMCC 90 and PVP K25 can enhance hardness and reduce friability. When PVP K25 interacts with water, its viscosity increases, and the bonding strength of other ingredients in the tablet also increases [37]. In contrast, the rate of hydration is decreased, and drug release might be delayed [34]. PVP K25 thus exerted a detrimental effect on dissolution. CCS triggers tablet disintegration by generating pores in the tablet matrix via the relaxation of cellulose fibers and by inducing water penetration and the breakdown of hydrogen bonds [35]. PVP K25 and CCS can thus decrease and increase drug release, respectively.

#### 3.1.3. Establishment of the Optimal Setting and Robust Design Space

#### 3.2. Effect of MCC Variability on Drug Product Quality and the Design Space

#### 3.2.1. Risk Assessment for MCC Physicochemical Properties

#### 3.2.2. Effect of MCC Variability on Drug Product Quality

#### 3.2.3. Effect of A Changes in the Manufacturer on Design Space

^{®}112, DFE Pharma) and C4 (MICROCEL

^{®}MC 112, Blanver). As presented in Figure 4a,b, the design spaces of A3 and C4 demonstrated significant differences compared with those of the formulation development. In A3, the design space could not be detected, the yellow region could be observed in C4, but the yellow and dark yellow regions in C4 were smaller than the design space of the formulation development. In addition, the optimal setting for formulation development was not included in the design space. These design space variabilities could possibly be the result of variability in the physicochemical property. As presented in Figure 2b,d, a negative correlation between A3 and C4 was detected in PC4, while PC4 was predominantly affected by SI, LOD, and CBD. C4, which had a positive score in PC4, exhibited high SI and LOD and low CBD (Table 2). In contrast, A3, which exhibited a negative score in PC4, featured low SI and LOD and high CBD (Table 2). These variations might trigger CQA variability. The correlation between the physicochemical properties of MCC and CQAs was based on the use of PCCs, which clarified how the design space variability of A3 and C4 occurred. Based on the PCCs presented in Figure 5 and Table S7, LOD exhibited a negative correlation with dissolution, whereas CBD displayed negative correlations with dissolution and friability. Moreover, SI showed a negative correlation with the assay, dissolution, and friability and a positive correlation with CU. The assay and CU of A3 ranged from 101.91% to 109.64% and from 0.02% to 0.56%, respectively, and those of C4 ranged from 99.43% to 102.67% and from 0.26% to 7.10%, respectively. As A3 had lower SI than C4, the assay of A3 was higher than that of C4, and the CU of A3 was lower than that of C4. The friabilities of A3 and C4 were 0.06–1.78% and 0.05–1.58%, respectively. This could be a result of C4 having higher SI than A3. For A3, dissolution at 5, 10, and 15 min was 9.72–99.34%, 33.52–99.81%, and 38.12–104.36%, respectively, whereas that for C4 was 10.26–104.86%, 35.38–105.36%, and 40.24–110.16%, respectively. This finding demonstrated that A3 had a slower dissolution profile than C4, possibly because A3 exhibited higher CBD than C4.

#### 3.2.4. Effect of Changes in the Grade on Design Space

^{®}200, JRS Pharma GmbH & Co. KG) and D15 (VIVAPUR

^{®}301, JRS Pharma GmbH & Co. KG). Figure 6a,b presents the design space variability triggered by changes in the grade. Significant differences in the design spaces of D13 and D15 were noticed. In both D13 and D15, the design spaces were not observed, possibly because of the variability in the physicochemical properties triggered by a modification of the grade. As presented in Figure 2a,c, a negative correlation was identified between D13 and D15 in PC2, and PC2 was predominantly affected by LOD, SI, HR, CI, tapped density, and PSD (D10, D50, and D90). D15, which had a positive score in PC2, exhibited high LOD and SI and low HR, CI, tapped density, and PSD (Table 2). In contrast, D13, which had a negative score in PC2, exhibited low LOD and SI and high HR, CI, tapped density, and PSD (Table 2). The variations in physicochemical properties could trigger the variability of CQAs that leads to design space variability. As presented in Figure 5 and Table S7, LOD exhibited a negative correlation with dissolution, whereas PSD had negative correlations with dissolution and friability and a positive correlation with hardness. Moreover, HR and CI exhibited positive correlations with dissolution. Dissolution at 5, 10, and 15 min of D13 was 9.61–100.22%, 34.14–101.15%, and 38.69–103.47%, respectively, and that of D15 was 10.04–104.68%, 35.65–105.65%, and 40.41–108.07%, respectively. Despite the fact that LOD, HR, and CI showed a correlation with dissolution, dissolution was primarily affected by PSD. PSD exhibited a robust negative correlation with dissolution and D13, which displayed high PSD and had slower dissolution profiles than D15. The friabilities of D13 and D15 were 0.03–0.84% and 0.10–2.97%, respectively. PSD had a negative correlation with friability and because D15 had lower PSD than D13, it exhibited high friability. The hardness values of D13 and D15 ranged from 9.31 kp to 11.93 kp and between 4.62 kp and 5.92 kp, respectively. Based on the data in Figure 5 and Table S7, a strong positive correlation between PSD (D10, D50, and D90) and hardness was observed. Consequently, D13, which displayed high PSD, exhibited greater hardness than D15. Of note, there was no significant correlation between tapped density and CQAs, whereas SI had a negative correlation with the assay and a positive correlation with CU. The assay and CU of D13 ranged from 97.71% to 105.13% and between 0.04% and 1.11%, respectively, whereas those of D15 were between 95.24% and 101.44% and 0.30% and 8.35%, respectively. As previously mentioned, SI exhibited a positive correlation with CU and a negative correlation with the assay. D13, which had low SI, exhibited a higher assay and lower CU than D15.

#### 3.3. Establishment of a Dissolution Prediction Model Based on PCA-ANNs

#### 3.3.1. Establishment of the PCA-ANN Model

_{1}), pH (a

_{2}), D10 (a

_{3}), D50 (a

_{4}), D90 (a

_{5}), bulk density (a

_{6}), tapped density (a

_{7}), true density (a

_{8}), HR (a

_{9}), CI (a

_{10}), porosity (a

_{11}), BFE (a

_{12}), SI (a

_{13}), FRI (a

_{14}), SE (a

_{15}), and CBD (a

_{16}). The four PCs scores (F1, F2, F3, and F4) were determined using Equations (14)–(17), as presented in Table S10. The four PC scores were selected as the input layer of the ANN model for network training and learning.

_{1}− 0.063a

_{2}+ 0.091a

_{3}+ 0.107a

_{4}+ 0.111a

_{5}+ 0.125a

_{6}+ 0.010a

_{7}+ 0.047a

_{8}− 0.115a

_{9}− 0.111a

_{10}− 0.123a

_{11}+ 0.097a

_{12}− 0.001a

_{13}− 0.130a

_{14}− 0.116a

_{15}+ 0.115a

_{16},

_{1}− 0.029a

_{2}+ 0.240a

_{3}+ 0.225a

_{4}+ 0.194a

_{5}− 0.100a

_{6}+ 0.145a

_{7}− 0.122a

_{8}+ 0.184a

_{9}+ 0.207a

_{10}+ 0.095a

_{11}+ 0.123a

_{12}− 0.192a

_{13}+ 0.010a

_{14}− 0.037a

_{15}− 0.067a

_{16},

_{1}+ 0.217a

_{2}+ 0.005a

_{3}− 0.029a

_{4}− 0.056a

_{5}+ 0.208a

_{6}+ 0.436a

_{7}− 0.250a

_{8}+ 0.144a

_{9}+ 0.116a

_{10}− 0.220a

_{11}− 0.142a

_{12}+ 0.069a

_{13}+ 0.062a

_{14}− 0.039a

_{15}+ 0.184a

_{16},

_{1}+ 0.096a

_{2}+ 0.138a

_{3}+ 0.131a

_{4}+ 0.125a

_{5}− 0.092a

_{6}+ 0.085a

_{7}+ 0.237a

_{8}+ 0.121a

_{9}+ 0.140a

_{10}+ 0.103a

_{11}+ 0.248a

_{12}+ 0.458a

_{13}− 0.048a

_{14}+ 0.066a

_{15}− 0.179a

_{16},

^{2}. The regression analysis obtained from the neural network training tool is presented in Figure 7. The four regression outcomes are presented (training, validation, test, and all). As presented in Figure 7, all regression results revealed R

^{2}values exceeding 0.9, indicating a good fit between the network and the data. Figure 8a presents the MSE and validation performance of the network. The optimal validation performance was 2.6234 at epoch 2 after six error repetitions, and the process ended at epoch 8. The PCA-ANN model training and fitting curve of dissolution at 5, 10, and 15 min are presented in Figure 8b–d. These results revealed that the developed PCA-ANN model was reliable, and it could be employed as an effective predictive model for dissolution in formulation development.

#### 3.3.2. Model Verification

## 4. Conclusions

## Supplementary Materials

_{p}, true density; ρ

_{b}, bulk density; ρ

_{t}, tapped density; HR, Hausner ratio; CI, compressibility index; P, powder porosity; BFE, basic flowability energy; SI, stability index; FRI, flow rate index; SE, specific energy; CBD, conditioned bulk density; CU, content uniformity; Diss., dissolution); Table S8: Explanation of variance; Table S9: Component and score coefficient matrix. (LOD, loss on drying; BFE, basic flowability energy; SI, stability index; FRI, flow rate index; SE, specific energy; CBD, conditioned bulk density); Table S10: Principal component scores and CQAs. (F1–F4 are four PCs scores); Table S11: Comparison of the actual and predicted values of dissolution in the PCA-ANN model. (AE, absolute error; RE, relative error).

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

^{2}, coefficient of determination; ANOVA, analysis of variance; USP–NF, United States Pharmacopeia–National Formulary; CoA, certificate of analysis; LOD, loss on drying; HR, Hausner ratio; CI, compressibility index; BFE, basic flowability energy; SI, stability index; FRI, flow rate index; SE, specific energy; CBD, conditioned bulk density; PCA, principal component analysis; PCC, Pearson correlation coefficient; PCs, principal components; MSE, mean square error; QTPP, quality target product profile; PDG, Pharmacopeial Discussion Group; Ph. Eur., European Pharmacopoeia; JP, Japanese Pharmacopeia; KMO, Kaiser Meyer–Olkin; AE, absolute error; RE, relative error.

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**Figure 1.**Design space in formulation development. The yellow area corresponds to the 95% confidence interval that satisfies the target values of CQAs. (SMCC, silicified microcrystalline cellulose; CCS, croscarmellose sodium; PVP, polyvinylpyrrolidone).

**Figure 2.**Result of principal component analysis; (

**a**) Loading plot with PC1 and PC2; (

**b**) Loading plot with PC3 and PC4; (

**c**) Score plot with PC1 and PC2; (

**d**) Score plot with PC3 and PC4. The yellow area indicates physicochemical properties significantly affecting PC1, the blue area denotes the physicochemical properties significantly affecting PC2, the light green area indicates the physicochemical properties significantly affecting PC3, and the orange area indicates the physicochemical properties significantly affecting PC4. (PC, principal component; LOD, loss on drying; BFE, basic flowability energy; SI, stability index; FRI, flow rate index; SE, specific energy; CBD, conditioned bulk density.)

**Figure 3.**The CQAs of 36 different MCCs; (

**a**) Dissolution; (

**b**) Assay; (

**c**) Content uniformity; (

**d**) Hardness; (

**e**) Friability. The gray dotted lines and box indicate the optimal ranges of CQAs. (CQA, critical quality attribute; MCC, microcrystalline cellulose).

**Figure 4.**Design space variability resulting from changes in the manufacturer; (

**a**) Design space using A3; (

**b**) Design space using C4. The crosshair indicates the optimal setting of formulation development. (SMCC, silicified microcrystalline cellulose; CCS, croscarmellose sodium; PVP, polyvinylpyrrolidone).

**Figure 5.**Pearson correlation coefficient matrix. (LOD, loss on drying; ρ

_{b}, bulk density; ρ

_{t}, tapped density; ρ

_{p}, true density; HR, Hausner ratio; CI, compressibility index; P, powder porosity; BFE, basic flowability energy; SI, stability index; FRI, flow rate index; SE, specific energy; CBD, conditioned bulk density; CU, content uniformity; Diss., dissolution).

**Figure 6.**Design space variability triggered by modifications of the grade; (

**a**) Design space using D13; (

**b**) Design space using D15. The crosshair indicates the optimal setting of formulation development. (SMCC, silicified microcrystalline cellulose; CCS, croscarmellose sodium; PVP, polyvinylpyrrolidone).

**Figure 8.**Training and fitting curve; (

**a**) Performance of neural network during training; (

**b**) Actual vs. Predicted dissolution at 5 min; (

**c**) Actual vs. Predicted dissolution at 10 min; (

**d**) Actual vs. Predicted dissolution at 15 min. For the reader’s clarity, the MCC abbreviations (X-axis) in (

**b**–

**d**) have been defined. The manufacturers of MCC are labeled using uppercase letters: A, DFE Pharma; B, FMC BioPolymer; C, Blanver; D, JRS Pharma GmbH & Co. KG. The details of the abbreviations are shown in Table 2.

**Figure 9.**Prediction model verification and fitting curve; (

**a**) Actual vs. Predicted dissolution at 5 min; (

**b**) Actual vs. Predicted dissolution at 10 min; (

**c**) Actual vs. Predicted dissolution at 15 min.

**Table 1.**The result of the experiment design and summary of the coded equation and statistical analysis. (x

_{1}, silicified microcrystalline cellulose 90; x

_{2}, croscarmellose sodium; x

_{3}, polyvinylpyrrolidone K25; y

_{1}, hardness; y

_{2}, friability; y

_{3}, dissolution at 5 min; y

_{4}, dissolution at 10 min; y

_{5}, dissolution at 15 min; y

_{6}, assay; y

_{7}, content uniformity).

Run Order | Control Factors | Response Factors | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

x_{1} (mg) | x_{2} (mg) | x_{3} (mg) | y_{1} (kp) | y_{2} (%) | y_{3} (%) | y_{4} (%) | y_{5} (%) | y_{6} (%) | y_{7} (%) | |

1 | 85.07 | 1.00 | 5.50 | 9.68 | 0.06 | 30.92 | 56.80 | 70.76 | 100.6 | 1.51 |

2 | 78.07 | 8.00 | 5.50 | 9.35 | 0.10 | 94.27 | 92.18 | 96.26 | 103.9 | 2.48 |

3 | 81.57 | 4.50 | 5.50 | 9.58 | 0.08 | 74.28 | 80.83 | 85.95 | 102.4 | 0.58 |

4 | 75.57 | 15.00 | 1.00 | 7.96 | 0.31 | 89.38 | 96.50 | 84.08 | 99.9 | 0.12 |

5 | 80.57 | 1.00 | 10.00 | 10.20 | 0.01 | 9.37 | 33.29 | 37.73 | 99.7 | 0.38 |

6 | 79.32 | 4.50 | 7.75 | 9.88 | 0.04 | 70.43 | 75.19 | 77.70 | 99.8 | 2.51 |

7 | 71.07 | 15.00 | 5.50 | 9.10 | 0.15 | 98.05 | 99.11 | 92.15 | 97.9 | 1.87 |

8 | 66.57 | 15.00 | 10.00 | 8.86 | 0.05 | 93.36 | 94.92 | 94.27 | 98.9 | 0.81 |

9 | 76.82 | 11.50 | 3.25 | 8.68 | 0.14 | 93.08 | 93.33 | 92.96 | 100.6 | 0.28 |

10 | 73.57 | 8.00 | 10.00 | 9.84 | 0.02 | 95.55 | 96.72 | 95.82 | 100.4 | 1.15 |

11 | 75.82 | 8.00 | 7.75 | 9.65 | 0.05 | 94.56 | 88.39 | 91.54 | 98.0 | 0.86 |

12 | 82.57 | 8.00 | 1.00 | 8.37 | 0.28 | 93.34 | 95.69 | 100.06 | 96.6 | 0.17 |

13 | 83.82 | 4.50 | 3.25 | 9.12 | 0.11 | 74.28 | 86.47 | 98.71 | 103.1 | 0.05 |

14 | 74.57 | 11.50 | 5.50 | 9.24 | 0.13 | 97.73 | 98.64 | 98.51 | 99.6 | 1.59 |

15 | 89.57 | 1.00 | 1.00 | 8.92 | 0.24 | 34.63 | 65.68 | 83.13 | 100.9 | 2.12 |

16 | 80.32 | 8.00 | 3.25 | 8.93 | 0.13 | 95.62 | 96.83 | 100.90 | 98.4 | 1.42 |

17 | 72.32 | 11.50 | 7.75 | 9.64 | 0.07 | 100.63 | 94.63 | 96.19 | 98.3 | 0.09 |

Response factors | Main effects of control factors | Mutual interactions between control factors | Statistical analysis of the coded equation | |||||||

x_{1} | x_{2} | x_{3} | x_{1}x_{2} | x_{1}x_{3} | x_{2}x_{3} | p-value | R^{2} | AdjustedR^{2} | Predicted R^{2} | |

y_{1} | 8.75 | 7.52 | 6.51 | - | 9.76 | 8.50 | <0.0001 | 0.98 | 0.97 | 0.92 |

y_{2} | 0.23 | 0.42 | 0.52 | −0.15 | −1.38 | −1.66 | <0.0001 | 0.95 | 0.93 | 0.88 |

y_{3} | 36.81 | −30.24 | −13.87 | 378.99 | - | 505.78 | <0.0001 | 0.98 | 0.97 | 0.91 |

y_{4} | 66.60 | 28.09 | −2.61 | 207.79 | - | 342.00 | <0.0001 | 0.95 | 0.93 | 0.84 |

y_{5} | 86.55 | −4.84 | −23.92 | 213.72 | - | 457.32 | <0.0001 | 0.94 | 0.93 | 0.81 |

**Table 2.**Physicochemical properties of 36 different MCCs. (LOD, loss on drying; HR, Hausner ratio; CI, compressibility index; BFE, basic flowability energy; SI, stability index; FRI, flow rate index; SE, specific energy; CBD, conditioned bulk density.)

Manufacturer | Brand Name | Abbreviation | LOD | pH | D10 | D50 | D90 | Bulk Density | Tapped Density | True Density | HR | CI | Powder Porosity | BFE | SI | FRI | SE | CBD |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

(%) | (µm) | (µm) | (µm) | (g/mL) | (g/mL) | (g/mL) | (%) | (%) | (mJ) | (mJ/g) | (g/mL) | |||||||

DFE Pharma | Pharmacel^{®} 101 | A1 | 3.0 | 6.1 | 22.00 | 62.20 | 147.0 | 0.31 | 0.43 | 0.800 | 1.39 | 27.91 | 61.25 | 281.0 | 1.32 | 1.53 | 9.420 | 0.332 |

Pharmacel^{®} 102 | A2 | 3.4 | 6.0 | 43.00 | 123.4 | 248.0 | 0.31 | 0.42 | 0.802 | 1.35 | 26.19 | 61.35 | 278.0 | 1.30 | 1.43 | 5.920 | 0.342 | |

Pharmacel^{®} 112 | A3 | 1.1 | 5.7 | 30.00 | 90.00 | 186.0 | 0.33 | 0.47 | 0.791 | 1.42 | 29.79 | 58.28 | 189.0 | 1.00 | 1.33 | 5.950 | 0.379 | |

FMC BioPolymer | Avicel^{®} PH-101 | B1 | 3.2 | 6.1 | 21.40 | 61.70 | 154.0 | 0.30 | 0.51 | 0.802 | 1.70 | 41.18 | 62.59 | 311.0 | 1.32 | 1.72 | 9.720 | 0.322 |

Avicel^{®} PH-102 | B2 | 3.6 | 6.2 | 38.20 | 135.0 | 273.6 | 0.32 | 0.51 | 0.802 | 1.59 | 37.25 | 60.08 | 298.0 | 1.35 | 1.38 | 6.150 | 0.352 | |

Avicel^{®} PH-103 | B3 | 2.6 | 6.3 | 28.20 | 66.30 | 162.8 | 0.28 | 0.49 | 0.793 | 1.75 | 42.86 | 64.69 | 258.0 | 1.15 | 2.13 | 8.920 | 0.380 | |

Avicel^{®} PH-105 | B4 | 2.8 | 6.5 | 9.000 | 28.00 | 62.00 | 0.24 | 0.60 | 0.791 | 2.50 | 60.00 | 69.66 | 38.1 | 1.14 | 3.01 | 10.20 | 0.245 | |

Avicel^{®} PH-112 | B5 | 1.3 | 6.2 | 24.00 | 143.0 | 284.0 | 0.30 | 0.54 | 0.792 | 1.80 | 44.44 | 62.12 | 198.0 | 1.00 | 1.29 | 6.100 | 0.349 | |

Avicel^{®} PH-113 | B6 | 1.2 | 5.9 | 24.00 | 68.00 | 154.0 | 0.28 | 0.55 | 0.803 | 1.96 | 49.09 | 65.13 | 245.0 | 1.03 | 2.05 | 8.710 | 0.380 | |

Avicel^{®} PH-200 | B7 | 2.8 | 5.9 | 114.4 | 248.6 | 400.7 | 0.32 | 0.55 | 0.800 | 1.72 | 41.82 | 60.00 | 395.0 | 1.24 | 1.29 | 7.420 | 0.359 | |

Avicel^{®} PH-200LM | B8 | 1.1 | 6.0 | 168.0 | 247.0 | 439.0 | 0.34 | 0.56 | 0.800 | 1.65 | 39.29 | 57.50 | 392.0 | 1.13 | 1.32 | 7.320 | 0.379 | |

Avicel^{®} PH-301 | B9 | 3.2 | 6.1 | 48.20 | 53.60 | 148.7 | 0.40 | 0.59 | 0.805 | 1.48 | 32.20 | 50.31 | 204.0 | 1.11 | 1.52 | 7.420 | 0.430 | |

Avicel^{®} PH-302 | B10 | 3.1 | 6.3 | 57.80 | 139.4 | 242.3 | 0.42 | 0.59 | 0.795 | 1.40 | 28.81 | 47.17 | 298.0 | 1.14 | 1.25 | 6.120 | 0.420 | |

Blanver | MICROCEL^{®} MC 12 | C1 | 3.1 | 6.1 | 42.10 | 160.0 | 367.8 | 0.37 | 0.49 | 0.802 | 1.32 | 24.49 | 53.87 | 361.0 | 1.01 | 1.32 | 5.410 | 0.376 |

MICROCEL^{®} MC 101 | C2 | 2.8 | 6.3 | 26.50 | 71.10 | 151.8 | 0.30 | 0.46 | 0.801 | 1.53 | 34.78 | 62.53 | 302.0 | 1.21 | 1.66 | 9.680 | 0.322 | |

MICROCEL^{®} MC 102 | C3 | 2.1 | 6.2 | 33.80 | 94.60 | 234.0 | 0.32 | 0.51 | 0.802 | 1.59 | 37.25 | 60.08 | 293.0 | 1.00 | 1.30 | 6.310 | 0.352 | |

MICROCEL^{®} MC 112 | C4 | 3.2 | 6.9 | 27.10 | 102.5 | 245.1 | 0.32 | 0.48 | 0.803 | 1.50 | 33.33 | 60.17 | 221.0 | 1.30 | 1.42 | 7.210 | 0.369 | |

MICROCEL^{®} MC 200 | C5 | 3.1 | 5.8 | 73.00 | 180.0 | 264.0 | 0.35 | 0.47 | 0.801 | 1.34 | 25.53 | 56.31 | 201.0 | 1.17 | 1.47 | 6.070 | 0.418 | |

JRS Pharma GmbH & Co. KG | PROSOLV^{®} SMCC 50 | D1 | 2.8 | 5.6 | 25.00 | 65.00 | 162.4 | 0.33 | 0.44 | 0.809 | 1.33 | 25.00 | 59.22 | 300.0 | 1.13 | 1.59 | 9.250 | 0.352 |

PROSOLV^{®} SMCC 50 LD | D2 | 1.3 | 5.7 | 21.00 | 56.30 | 156.2 | 0.24 | 0.45 | 0.798 | 1.88 | 46.67 | 69.93 | 321.0 | 1.05 | 1.72 | 9.570 | 0.262 | |

PROSOLV^{®} SMCC 90 | D3 | 1.2 | 5.4 | 42.30 | 142.7 | 251.0 | 0.35 | 0.43 | 0.813 | 1.23 | 18.60 | 56.92 | 271.0 | 1.21 | 1.18 | 6.320 | 0.382 | |

PROSOLV^{®} SMCC HD 90 | D4 | 2.1 | 5.8 | 54.20 | 118.5 | 243.0 | 0.42 | 0.53 | 0.798 | 1.26 | 20.75 | 47.37 | 274.0 | 1.05 | 1.21 | 6.410 | 0.452 | |

PROSOLV^{®} SMCC 90 LM | D5 | 2.2 | 5.7 | 46.80 | 125.0 | 251.3 | 0.30 | 0.44 | 0.806 | 1.47 | 31.82 | 62.79 | 219.0 | 1.02 | 1.63 | 6.120 | 0.368 | |

VIVAPUR^{®} 12 | D6 | 3.1 | 6.1 | 67.20 | 198.8 | 420.0 | 0.33 | 0.46 | 0.800 | 1.39 | 28.26 | 58.76 | 388.0 | 1.02 | 1.28 | 5.570 | 0.336 | |

VIVAPUR^{®} 14 | D7 | 1.0 | 6.0 | 78.10 | 170.0 | 428.1 | 0.36 | 0.48 | 0.798 | 1.33 | 25.00 | 54.91 | 332.0 | 0.92 | 1.39 | 6.710 | 0.400 | |

VIVAPUR^{®} 101 | D8 | 2.3 | 5.7 | 26.20 | 75.30 | 167.2 | 0.31 | 0.45 | 0.800 | 1.45 | 31.11 | 61.25 | 289.0 | 1.19 | 1.61 | 9.510 | 0.332 | |

VIVAPUR^{®} 102 | D9 | 2.1 | 5.6 | 34.60 | 103.2 | 252.2 | 0.31 | 0.50 | 0.800 | 1.61 | 38.00 | 61.25 | 301.0 | 1.10 | 1.33 | 6.560 | 0.342 | |

VIVAPUR^{®} 103 | D10 | 1.1 | 6.3 | 29.10 | 65.00 | 123.0 | 0.28 | 0.44 | 0.792 | 1.57 | 36.36 | 64.63 | 226.0 | 0.99 | 1.85 | 8.730 | 0.380 | |

VIVAPUR^{®} 105 | D11 | 1.2 | 6.5 | 8.000 | 26.00 | 32.00 | 0.24 | 0.45 | 0.795 | 1.88 | 46.67 | 69.80 | 41.9 | 1.01 | 3.37 | 11.40 | 0.245 | |

VIVAPUR^{®} 112 | D12 | 1.3 | 6.2 | 38.00 | 147.8 | 294.1 | 0.33 | 0.45 | 0.791 | 1.36 | 26.67 | 58.28 | 204.0 | 1.10 | 1.32 | 6.900 | 0.379 | |

VIVAPUR^{®} 200 | D13 | 1.5 | 5.9 | 138.0 | 250.0 | 325.0 | 0.32 | 0.48 | 0.802 | 1.50 | 33.33 | 60.11 | 380.0 | 1.04 | 1.40 | 7.010 | 0.359 | |

VIVAPUR^{®} XLM200 | D14 | 1.3 | 5.9 | 127.0 | 252.0 | 337.0 | 0.36 | 0.51 | 0.801 | 1.42 | 29.41 | 55.06 | 372.0 | 1.01 | 1.32 | 6.920 | 0.399 | |

VIVAPUR^{®} 301 | D15 | 3.6 | 6.1 | 28.50 | 78.10 | 177.3 | 0.40 | 0.46 | 0.800 | 1.15 | 13.04 | 50.00 | 185.0 | 1.27 | 1.48 | 7.230 | 0.430 | |

VIVAPUR^{®} 302 | D16 | 2.6 | 5.8 | 47.90 | 130.0 | 187.0 | 0.39 | 0.55 | 0.796 | 1.41 | 29.09 | 51.00 | 304.0 | 1.05 | 1.39 | 6.580 | 0.441 | |

Heweten^{®} 101 | D17 | 2.2 | 6.5 | 25.00 | 67.10 | 151.5 | 0.28 | 0.40 | 0.805 | 1.43 | 30.00 | 65.22 | 208.0 | 1.00 | 1.82 | 9.400 | 0.332 | |

Heweten^{®} 102 | D18 | 2.4 | 6.1 | 34.50 | 109.4 | 271.1 | 0.29 | 0.41 | 0.802 | 1.41 | 29.27 | 63.84 | 281.0 | 1.00 | 1.40 | 6.120 | 0.322 |

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**MDPI and ACS Style**

Kim, J.Y.; Choi, D.H. Control Strategy for Excipient Variability in the Quality by Design Approach Using Statistical Analysis and Predictive Model: Effect of Microcrystalline Cellulose Variability on Design Space. *Pharmaceutics* **2022**, *14*, 2416.
https://doi.org/10.3390/pharmaceutics14112416

**AMA Style**

Kim JY, Choi DH. Control Strategy for Excipient Variability in the Quality by Design Approach Using Statistical Analysis and Predictive Model: Effect of Microcrystalline Cellulose Variability on Design Space. *Pharmaceutics*. 2022; 14(11):2416.
https://doi.org/10.3390/pharmaceutics14112416

**Chicago/Turabian Style**

Kim, Ji Yeon, and Du Hyung Choi. 2022. "Control Strategy for Excipient Variability in the Quality by Design Approach Using Statistical Analysis and Predictive Model: Effect of Microcrystalline Cellulose Variability on Design Space" *Pharmaceutics* 14, no. 11: 2416.
https://doi.org/10.3390/pharmaceutics14112416