# A Novel Framework to Aid the Development of Design Space across Multi-Unit Operation Pharmaceutical Processes—A Case Study of Panax Notoginseng Saponins Immediate Release Tablet

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Theory

#### 2.1.1. A Novel Framework to Develop the Design Space across Multi-Unit Operation Pharmaceutical Processes

#### 2.1.2. Partial Least Squares (PLS)

**X**) and response variables matrix (e.g.,

**Y**).The basic idea is that the PLS decomposes the two matrixes (e.g.,

**X**= [

**X**,

_{1}**X**,

_{2}**X**] and

_{3}**Y**as seen in Figure 3) in a reduced latent variable space, in which the covariance between the projection of original samples is maximized.

**T**=

**XW**

**X**=

**TP**+

^{T}**E**

**Y**=

**TQ**+

^{T}**F**

**W**is the weight of matrix

**X**,

**T**represents the scores of matrix

**X**,

**P**and

**Q**stand for the loadings of matrix

**X**and

**Y**, respectively.

**E**and

**F**are the residuals of matrix

**X**and

**Y**, respectively.

#### 2.1.3. Multi-Block Partial Least Squares (MBPLS)

**X**,

_{1}**X**,

_{2}**X**, and

_{3}**Y**) were used to construct the MBPLS model (Figure 3) based on the later version. The MBPLS model is illustrated as follows:

**X**=

_{1}**T**+

_{s}P_{1}^{T}**E**

_{1}**X**=

_{2}**T**+

_{s}P_{2}^{T}**E**

_{2}**X**=

_{3}**T**+

_{s}P_{3}^{T}**E**

_{3}**Y**=

**T**+

_{s}Q^{T}**F**

**T**refers to the super scores;

_{s}**P**,

_{1}**P**, and

_{2}**P**refer to the loadings of matrix

_{3}**X**,

_{1}**X**, and

_{2}**X**, respectively;

_{3}**E**,

_{1}**E**, and

_{2}**E**refer to the residuals of matrix

_{3}**X**,

_{1}**X**, and

_{2}**X**, respectively;

_{3}**Q**refers to the loadings of matrix

**Y**;

**F**refers to the residuals of matrix

**Y**.

#### 2.1.4. Multi-Block Partial Least Squares Path Model (MBPLSPM)

**X**,

_{1}**X**,

_{2}**X**, and

_{3}**Y**) were used to realize the MPLSPM. The pathway between different data blocks is shown in Figure 3. The MBPLSPM is assumed to be logically specified from left to right, where the left end blocks, namely, predictor blocks (e.g.,

**X**and

_{1}**X**), only predict and the right end blocks (e.g.,

_{3}**Y**), namely, predictee blocks, are only predicted. The blocks in the middle, namely, interior blocks (e.g.,

**X**), are both predictor blocks and predictee blocks.

_{2}**t**and

**u**vectors for

**X**,

_{1}**X**and

_{2,}**X**are selected.

_{3}**X**,

_{1}**X**and

_{2}**X**are calculated. Since

_{3}**X**and

_{2}**X**only predict

_{3}**Y**, the

**t**and

_{X2}**t**can be calculated as Equations (8)–(11):

_{X3}**w**=

_{X2}**X**,

_{2′}u_{Y}**w**=

_{X2}**w**/(

_{X2}**w**)

_{X2′}w_{X2}^{1/2}

**t**=

_{X2}**X**

_{2}w_{X2}**w**=

_{X3}**X**,

_{3′}u_{Y}**w**=

_{X3}**w**/(

_{X3}**w**)

_{X3′}w_{X3}^{1/2}

**t**=

_{X3}**X**

_{3}w_{X3}**w**and

_{X2}**w**are weights of

_{X3}**X**and

_{2}**X**.

_{3}**X**predicts both

_{1}**X**and

_{3}**Y**. To calculate

**t**, which predicts both blocks

_{X1}**X**and

_{3}**Y**, a superblock

**U**that contains

**u**and

_{X3}**u**is defined.

_{Y}**U**= [

**u**,

_{X3}**u**]

_{Y}**t**is calculated as follows:

_{X1}**c**=

_{U}**U’t**,

_{X1}**c**=

_{U}**c**/(

_{U}**c**)

_{U}’ c_{U}^{1/2}

**u**=

_{U}**Uc**

_{U}**w**=

_{X1}**X**,

_{1′}u_{U}**w**=

_{X1}**w**/(

_{X1}**w**)

_{X1′}w_{X1}^{1/2}

**t**=

_{X1}**X**

_{1}w_{X1}**c**is the weight of

_{U}**U**,

**u**is the score of

_{U}**U**,

**w**is the weight of

_{X1}**X**.

_{1}**X**and

_{3}**Y**are determined.

**X**is only predicted by

_{3}**X**, so

_{1}**u**can be directly calculated as follows:

_{X3}**c**=

_{X3}**X**,

_{3′}t_{X1}**c**=

_{X3}**c**/(

_{X3}**c**)

_{X3′}c_{X3}^{1/2}

**u**=

_{X3}**X**

_{3}c_{X3}**c**is the weights of

_{X3}**X**.

_{3}**Y**is predicted by

**X**,

_{1}**X**, and

_{2}**X**. A superblock

_{3}**T**is defined which consists of

**t**,

_{X1}**t**, and

_{X2}**t**.

_{X3}**w**and

_{T}**c**are the weights of

_{Y}**T**and

**Y**,

**u**can be calculated.

_{Y}**w**=

_{T}**T’ u**,

_{Y}**w**=

_{T}**w**/(

_{T}**w**)

_{T}’ w_{T}^{1/2}

**t**=

_{T}**T w**

_{T}**c**=

_{Y}**Y’ t**,

_{T}**c**=

_{Y}**c**/(

_{Y}**c**)

_{Y}’ c_{Y}^{1/2}

**u**=

_{Y}**Y c**

_{Y}**u**is tested for convergence within a desired precision (e.g., 10

_{Y}^{−8}).

**p**) and predictee blocks (

**q**) are calculated. As block scores

**t**,

_{X1}**t**and

_{X2}**t**are combined to calculate the super score

_{X3}**t**, there are two methods, namely, the block score update method and the super score update method, to calculate the loadings. In this case, the former is used for calculating loadings of block

_{T}**X**, while the latter is used for block

_{1}**X**and

_{2}**X**.

_{3}**p**=

_{X1}**X**/(

_{1′}t_{X1}**t**)

_{X1′}t_{X1}**p**=

_{X2}**X**/(

_{2′}t_{T}**t**)

_{T}’ t_{T}**p**=

_{X3}**X**/(

_{3′}t_{T}**t**)

_{T}’ t_{T}**q**=

_{X3}**X**/(

_{3′}u_{X3}**u**)

_{X3′}u_{X3}**q**=

_{Y}**Y’ u**/(

_{Y}**u**)

_{Y}’ u_{Y}**b**) are calculated for each block in the prediction.

**b**=

_{X1→U}**u**/(

_{U}’ t_{X1}**t**)

_{X1′}t_{X1}**b**=

_{T→Y}**u**/(

_{Y}’ t_{T}**t**)

_{T}’ t_{T}**b**and

_{X1→U}**b**are used to predict

_{T→Y}**U**and

**Y**, respectively.

**X**, the regression coefficient used to determine the predictor and predictee part of

_{3}**X**is calculated in Equations (30) and (31).

_{3}**b**=

_{X1→X3}**c**/(

_{U}(1) b_{X1→U}**c**)

_{U}’ c_{U}**b**=

_{X3→Y}**w**/(

_{T}(1) b_{T→Y}**w**)

_{T}’ w_{T}**E**,

_{X1}**E**,

_{X2}**E**, and

_{X3}**E**are residuals of

_{Y}**X**,

_{1}**X**,

_{2}**X**, and

_{3}**Y**, respectively, the residuals are calculated for each block.

**E**=

_{X1}**X**−

_{1}**t**

_{X1}p_{X1′}**E**=

_{X2}**X**−

_{2}**t**

_{X2}p_{X2′}**E**=

_{Y}**Y**−

**b**

_{T→Y}t_{T}c_{Y}’**E**=

_{X3}**X**− (

_{3}**s**+

_{X3}t_{X3}p_{X3′}**r**)

_{X3}u_{X3}c_{X3′}_{X3}= b

_{X1→X3}

^{2}/(b

_{X1→X3}

^{2}+ b

_{X3→Y}

^{2}), s

_{X3}

^{2}= 1 − r

_{X3}

^{2},

**u**= b

_{X3}_{X1→X3}

**t**.

_{X1}**X**,

_{1}**X**,

_{2}**X**, and

_{3}**Y**are replaced by

**E**,

_{X1}**E**,

_{X2}**E**, and

_{X3}**E**, respectively.

_{Y}#### 2.2. Materials

^{®}101) was supplied by J. Rettenmaier & Söhne GmbH + CoKG (Rosenberg, Germany; lot No. 2610141813). The crospovidone (PVPP, XL-10) was purchased from ISP Chemicals, LLC (Calvert City, KY, USA; lot No. 0001873448). The magnesium stearate was purchased from Sinopharm Chemical Reagent Co., Ltd. (Shanghai, China; lot No. 20121010).

#### 2.3. Design of Experiment

#### 2.4. PNS IRT Production Process

#### 2.5. Available Data

**M**(11 × 9). The characteristics of PNS extracts included the bulk density (D

_{bm}), tapped density (D

_{tm}), particle size distribution (D

_{10m}, D

_{50m}, D

_{90m}, Span

_{m}), angle of repose (AOR

_{m}), Hausner ratio (HR

_{m}) and specific surface area (SSA

_{m}). During the granulation experiments, five variables were varied and arranged in Block

**P**(52 × 5). Granules from the wet granulation were dried and milled. All the experiments were conducted under the same drying and milling settings. The dried and milled granules were characterized by their bulk density (D

_{1}_{b}), tapped density (D

_{t}), particle size distribution (D

_{10}, D

_{50}, D

_{90}, span), moisture content (MC), angle of repose (AOR) and Hausner ratio (HR). The mean value of each variable across all samples was included corresponding to Block

**X**(52 × 9). The last step was compaction to get tablets. Before compaction, each run of granules was lubricated for a different time and then compressed into tablets by varying the minimal punch tip separation distance. The lubrication and compaction parameters were collected in Block

_{2}**X**(52 × 2). The tablets were measured by tensile strength (TS) and disintegration time (DT). These data were included in Block

_{3}**Y**(52 × 2).

#### 2.6. Multivariate Statistical Analysis

## 3. Results and Discussion

#### 3.1. Data Collection

#### 3.2. Data Management

^{2}ellipse with 95% confidence [50] was calculated to identify potential outliers. As a result, none of the samples were beyond the threshold.

_{i}= 1/(1 − r

_{i}

^{2})

_{i}

^{2}refers to the coefficient of determination of multiple linear regression between i-th variable and other variables.

#### 3.3. Exploratory Analysis

#### 3.3.1. Material Properties (**M**)

^{2}) and cumulative explained variance per PC (R

^{2}

_{cum}) is shown in Table 5. Generally, the appropriate number of PCs should be considered to build the model. In the literature, several methods have been reported. In this case, the eigenvalue-greater-than-one rule was used to determine the number of PCs. Therefore, a PCA model was built by using the first two PCs, which explained 82.6% of the total variability in the input materials.

**M**. It could be seen that D

_{bm}, D

_{tm}, D

_{10m}, D

_{50m}D

_{90m}, and SSA

_{m}made great contributions to the first PC. D

_{bm}, D

_{tm}, D

_{10m}, D

_{50m,}and D

_{90m}had similar loading absolute values, so they were correlated. However, these variables were all inversely related to SSA

_{m}. This indicated that the PNS extracts with large particle size usually had high bulk and tapped density, and low specific surface area. Both D

_{bm}and D

_{tm}characterized the filling performance of the PNS extracts, and D

_{10m}, D

_{50m}, D

_{90m}, and SSA

_{m}characterized the dimensions of the PNS extracts. Therefore, the physical meaning of the first PC can be summarized as the difference in filling performance and dimensions between different lots of PNS extracts. The variables that contributed most to the second PC were AOR

_{m}, HR

_{m}, and Span

_{m}. AOR

_{m}and HR

_{m}were used to evaluate the powder flow-ability and Span

_{m}was the homogeneity index. The second PC mainly described the difference in flow-ability and homogeneity between different lots of PNS extracts. The score plot of the PCA model on Block

**M**is shown in Figure 5B. All lots of PNS extracts were within the Hotelling T

^{2}ellipse with 99% confidence. YNZM, XAHX, Zl1208, ZL0120, ZL0518, ZL0524 and YNSS are projected close to each other in Figure 5B. This confirmed these lots had similar characteristics. The remaining lots, including SXAS, WHYC, and BCTG were located far from them. It was concluded that these three lots of PNS extract had differences in filling performance, dimensions, and flow-ability.

#### 3.3.2. Granulation Procedure ([**P**_{1}, **X**_{2}])

_{1}

_{2}

**P**(wet granulation parameters) and

_{1}**X**(granule properties) were analyzed in order to understand how granulation parameters affected the granule properties. Therefore, a PCA model was built on a joint data block by concatenating the data block

_{2}**P**and

_{1}**X**. The diagnostics from the PCA model on the granulation data are listed in Table 6. It was observed that the first five PCs showed eigenvalues greater than 1 and thus the first five PCs, which accounted for 75.6% of total variance were used to build the model. The variability explained by the first two PCs was much higher than the others. The first two PCs captured a large fraction of the data variability. For this reason, the analysis was focused on the first two PCs.

_{2}_{b}, D

_{t}, D

_{10}, D

_{50}, D

_{90}and binder amount were correlated. This indicated that the first PC mainly represented the influence of binder amount on the granule particle size and density. Granules with large particle size and density should be obtained by wet granulation with more binder. The second PC mainly described MC, HR, and Span. MC usually affected the stability of the granules and controlling the MC of granules was critical to manufacturing desire quality tablets. HR and span were the indexes that characterize the granule flow-ability and homogeneity, respectively. A combined analysis of loading plots with the score plot in Figure 6B gave a deeper understanding of the results. Along the first PC direction, the granules produced with different binder amounts are marked with different symbols or colors. The lots processed with a low amount of binder are located in the region on the left of the score plot, while the lots processed with a high amount of binder fall mainly in the region on the right. The lots processed with a medium amount of binder are projected in the middle of score plot. This further confirmed that the binder amount used was positively correlated with the granule particle size and density.

#### 3.3.3. Compaction Procedure ([**X**_{3}, **Y**])

_{3}

_{3}was combined with data block Y to form the joint data block [

**X**,

_{3}**Y**]. The diagnostics of the PCA model on the joint data block are shown in Table 7. The first two PCs were enough to build the model as 78.6% of total variability was explained by two PCs.

#### 3.4. System Modeling and CPPs Identification

#### 3.4.1. Model Selection

**X**

_{1}= [

**M**,

**P**]) to simplify the modeling procedure. In general, the prediction performance is primarily considered in model development. However, for the pharmaceutical process, the model interpretability is also of equal importance as the underlying information can be obtained to understand the mechanisms acting on the system. The amount of variability of original data explained by the model is usually used to represent the model interpretability, which is quantified by R

_{1}^{2}. The diagnostics of PLS, MBPLS, and MPLSPM model are shown in Table 8. The number of LVs for each model was selected by leave one out cross-validation. Three LVs were used to build the PLS, MBPLS and MBPLSPM models. In Table 8, R

^{2}

_{Xcum}and R

^{2}

_{Ycum}refer to the cumulative explained variance per LV for independent variables and response variables, respectively. Q

^{2}

_{Ycum}refers to the cumulative explained variance per LV for modeling in the cross-validation. Q

^{2}can be seen as a measure of the model predictive ability, and the prediction performance had no significant differences among different models, although the interpretability of the MBPLSPM was much higher than the others. The variation explained by the MBPLSPM for the independent variable matrix was 64.3%, and the model also captured a larger fraction of variability in the response variable matrix.

#### 3.4.2. System Model

**W***of matrix [

**X**,

_{1}**X**,

_{2}**X**], weighted on the variables are showed in Figure 9A. The bar plots of loadings

_{3}**Q**of

**Y**, which indicated the contribution of each variable in LVs are reported in Figure 9B.

**X**and

_{2}**X**, i.e., D

_{3}_{b}, D

_{t}, D

_{10}, D

_{50}, D

_{90}and compaction process parameters. There appeared to be positive correlations between the granule size and the granule density. As expected, large granules after compaction resulted in tablets with lower TS. Decreasing the lubrication time and minimal punch tip separation distance resulted in tablets with higher TS. The second LV showed that increasing the minimal punch tip separation distance led to tablets faster disintegration. The third LV showed that the granule size and lubrication time also contributed to the DT, which was an expected occurrence; tablets compressed with large granules and longer lubrication time may disintegrate faster.

#### 3.4.3. CPPs Identification

_{Y,k}

^{2}is the variance of tablet properties explained by the k-th latent variable, and w

_{i,k}

^{s}is the weight of i-th block on the k-th latent variable calculated from the MBPLSPM.

**X**and

_{2}**X**were larger than 1. The granule properties and compaction process parameters contributed most to the tablet properties.

_{3}_{Y,k}

^{2}is the variance of tablet properties explained by the k-th latent variable, while w

_{i,k}is the weight of i-th variable on the k-th latent variable.

_{b}, D

_{t}, D

_{10}, D

_{50}, D

_{90}, lubrication time and minimal punch tip separation distance were identified as the critical variables.

#### 3.5. Design Space Development

_{t}, D

_{b}, D

_{10}, D

_{50}, D

_{90}, lubrication time and minimal punch tip separation distance. The CPPs covered the wet granulation and compaction process and an integrated design space can be developed to control the CQAs of tablets. As the granule density (D

_{t}, D

_{b}) and granule size (D

_{10}, D

_{50}, and D

_{90}) were correlated with binder amount, controlling the binder amount in the wet granulation resulted in desire granules. For this reason, binder amount, lubrication time and minimal punch tip separation distance were determined to be the final variables for developing the design space. The prediction formula of each CQA is shown below.

^{2}= 0.863, R

^{2}

_{adj}= 0.836.

^{2}= 0.828, R

^{2}

_{adj}= 0.8096.

^{2}) and the adjusted coefficient of determination (R

^{2}

_{adj}) for the prediction model of TS were 0.863, and 0.836, respectively, while the coefficient of determination and the adjusted coefficient of determination for the prediction model of DT were 0.828, and 0.8096, respectively. In addition, the analysis of variance was performed on the regression models. It was confirmed that the models were statistically significant with a p value <0.5. These results indicated that the established models were acceptable and suitable for building the design space. Based on the established regression models, the contour plots were constructed to visualize the effects of the binder amount, lubrication time and minimal punch tip separation distance on the DT and TS in Figure 12. It could be inferred from contour plots that increasing the binder amount, lubrication time, and the minimal punch tip separation distance would result in tablets with higher TS while decreasing the binder amount and lubrication time, and increasing the minimal punch tip separation distance would result in tablets with faster disintegration.

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**A novel framework to develop the design space across multi-unit operation pharmaceutical processes. DoE refers to design of experiment.

**Figure 3.**The schematic diagram of the partial least squares (PLS), multi-block partial least squares (MBPLS), and multi-block partial least squares path model (MBPLSPM) algorithm.

**Figure 6.**(

**A**) Loading bar plots of PCA model on Block [

**P**,

_{1}**X**]; (

_{2}**B**) Score plot of PCA model on Block [

**P**,

_{1}**X**]. A–E refer to the pre-mixing time, impeller rate, binder amount, liquid additive rate and granulation time, respectively.

_{2}**Figure 7.**(

**A**) Loading bar plots of PCA model on data block [

**X**,

_{3}**Y**]; (

**B**) Score plot of PCA model on data block [

**X**,

_{3}**Y**]. F and G refer to lubrication time and minimal punch tip separation distance, respectively.

**Figure 8.**The relationships between the score of supermatrix

**T**and that of matrix

**Y**under the latent variables space of the MBPLSPM. (

**A**) t

_{T}1 vs. u1; (

**B**) t

_{T}2 vs. u2; (

**C**) t

_{T}3 vs. u3.

**Figure 9.**(

**A**) Bar plots of the weights

**W***of [

**X**,

_{1}**X**,

_{2}**X**] in the MBPLSPM; (

_{3}**B**) Bar plots of the loadings

**Q**of

**Y**in the MBPLSPM. A–F refers to pre-mixing time, impeller rate, binder amount, liquid additive rate, granulation time, lubrication time and minimal punch tip separation distance, respectively.

**Figure 11.**Variable importance in the projection (VIP) indexes of each variable in the MBPLSPM. A–F refers to pre-mixing time, impeller rate, binder amount, liquid additive rate, granulation time, lubrication time and minimal punch tip separation distance, respectively.

**Figure 12.**Contour plot showing the effects of the binder amount, lubrication time, and minimal punch tip separation distance on the tensile strength and disintegration time.

**Figure 13.**The design space for the PNS IRT production process; (

**A**) binder amount vs. lubrication time; (

**B**) binder amount vs. minimal punch tip separation distance; (

**C**) lubrication vs. minimal punch tip separation distance.

Factors | Levels | |
---|---|---|

Low-Level | High-Level | |

A (min) | 5 | 15 |

B (rpm) | 400 | 600 |

C (%) | 20 | 24 |

D (mL/min) | 10 | 20 |

E (min) | 3 | 5 |

F (min) | 10 | 20 |

G (mm) | 3.0 | 3.2 |

**Table 2.**D-optimal design for the Panax Notoginseng Saponins immediate release tablet (PNS) IRT production process with different lots of PNS extracts.

Run | Lot No. | Granulation | Compaction | |||||
---|---|---|---|---|---|---|---|---|

A (min) | B (rpm) | C (%) | D (mL/min) | E (min) | F (min) | G (mm) | ||

1 | ZL0518 | 15 | 400 | 20 | 19.9 | 5 | 10 | 3.2 |

2 | SXAS | 5 | 410 | 22.8 | 18.9 | 4.3 | 20 | 3.0 |

3 | XAHX | 5 | 400 | 20 | 20 | 3 | 10 | 3.0 |

4 | YNZW | 8.8 | 500 | 24 | 10 | 5 | 10 | 3.1 |

5 | ZL0524 | 15 | 400 | 24 | 20 | 5 | 20 | 3.0 |

6 | WHYC | 5 | 400 | 22.2 | 20 | 5 | 10 | 3.1 |

7 | YNYK | 8.1 | 500 | 20 | 17.5 | 3 | 10 | 3.1 |

8 | BCTG | 15 | 455 | 22 | 14.5 | 4.1 | 13.4 | 3.1 |

9 | ZL0518 | 15 | 500 | 24 | 10 | 3 | 20 | 3.1 |

10 | BCTG | 13.4 | 500 | 24 | 10 | 5 | 20 | 3.0 |

11 | YNZZ | 5 | 400 | 24 | 20 | 3 | 15.9 | 3.2 |

12 | ZL0518 | 5 | 400 | 22 | 10 | 5 | 10 | 3.2 |

13 | ZL1208 | 5 | 400 | 20 | 10 | 5 | 14.8 | 3.1 |

14 | ZL0524 | 5 | 500 | 24 | 20 | 3.9 | 20 | 3.1 |

15 | YNZW | 5 | 500 | 20 | 20 | 3 | 20 | 3.0 |

16 | SXAS | 15 | 500 | 22.1 | 20 | 3 | 20 | 3.2 |

17 | SXAS | 5 | 400 | 24 | 10 | 5 | 20 | 3.0 |

18 | WHYC | 15 | 400 | 20 | 20 | 3 | 20 | 3.1 |

19 | ZL1208 | 15 | 400 | 24 | 10 | 4.2 | 20 | 3.2 |

20 | BCTG | 15 | 433 | 24 | 15.2 | 3 | 20 | 3.0 |

21 | ZL0120 | 15 | 500 | 22.1 | 20 | 3 | 20 | 3.2 |

22 | BCTG | 10.75 | 400 | 24 | 14.3 | 5 | 20 | 3.1 |

23 | ZL1208 | 5 | 434 | 21.6 | 15.1 | 3.6 | 14 | 3.1 |

24 | YNSS | 15 | 400 | 20 | 10 | 5 | 20 | 3.0 |

25 | SXAS | 5 | 400 | 20 | 12.9 | 3 | 20 | 3.2 |

26 | BCTG | 5 | 486 | 24 | 10 | 3 | 20 | 3.2 |

27 | ZL0518 | 5 | 400 | 24 | 10 | 3 | 10 | 3.1 |

28 | YNSS | 5.7 | 441 | 20 | 20 | 5 | 20 | 3.2 |

29 | YNSS | 15 | 500 | 20 | 20 | 5 | 10 | 3.0 |

30 | ZL0120 | 5 | 500 | 21.4 | 10 | 5 | 20 | 3.1 |

31 | ZL0518 | 15 | 400 | 24 | 10 | 4.2 | 20 | 3.2 |

32 | YNSS | 15 | 400 | 24 | 20 | 3 | 10 | 3.1 |

33 | YNYK | 15 | 500 | 20 | 20 | 5 | 20 | 3.1 |

34 | WHYC | 15 | 464 | 24 | 20 | 5 | 10 | 3.2 |

35 | ZL0120 | 7.05 | 500 | 21.2 | 19.7 | 5 | 14.6 | 3.1 |

36 | ZL0518 | 8.5 | 500 | 21.6 | 10.3 | 3.8 | 13.7 | 3.2 |

37 | YNSS | 5 | 500 | 24 | 20 | 3 | 10 | 3.0 |

38 | YNYK | 15 | 400 | 20 | 10 | 3 | 10 | 3.1 |

39 | XAHX | 15 | 400 | 20 | 20 | 5 | 10 | 3.2 |

40 | XAHX | 5 | 500 | 20 | 20 | 3.8 | 10 | 3.2 |

41 | YNZW | 11.5 | 478 | 20 | 13.6 | 4 | 20 | 3.0 |

42 | ZL0120 | 15 | 500 | 20 | 10 | 3 | 10 | 3.0 |

43 | ZL1208 | 10.75 | 400 | 24 | 14.3 | 5 | 20 | 3.1 |

44 | XAHX | 15 | 444 | 20 | 10 | 3 | 15.3 | 3.2 |

45 | YNYK | 15 | 500 | 20 | 10 | 5 | 10 | 3.2 |

46 | YNSS | 5 | 500 | 20 | 10 | 5 | 10 | 3.0 |

47 | XAHX | 5 | 500 | 24 | 15.2 | 5 | 15.4 | 3.2 |

48 | WHYC | 15 | 500 | 24 | 10.2 | 3 | 10 | 3.2 |

49 | SXAS | 9 | 400 | 24 | 20 | 4.2 | 10 | 3.0 |

50 | ZL0120 | 9.6 | 400 | 22.2 | 10 | 3 | 16.2 | 3.0 |

51 | WHYC | 15 | 400 | 24 | 10 | 5 | 10 | 3.0 |

52 | YNZW | 5 | 400 | 20 | 12.9 | 3 | 20 | 3.2 |

Blocks | Dimensions | Variables Included |
---|---|---|

M | 11 × 9 | D_{tm}, D_{bm}, D_{10m}, D_{50m}, D_{90m}, Span_{m}, AOR_{m}, HR_{m}, SSA_{m} |

P_{1} | 52 × 5 | pre-mixing time (A), impeller rate (B), binder amount (C), additive rate (D), granulation time (E) |

X_{2} | 52 × 9 | D_{t}, D_{b}, AOR, HR, MC, D_{10}, D_{50}, D_{90}, Span |

X_{3} | 52 × 2 | lubrication time (F), minimal punch tip separation distance (G) |

Y | 52 × 2 | DT, TS |

Data Block | Variable | VIF |
---|---|---|

M | D_{bm} | 8.906 × 10^{3} |

D_{tm} | 6.016 × 10^{3} | |

HR_{m} | 353.1 | |

SSA_{m} | 22.09 | |

AOR_{m} | 5.026 | |

D_{10m} | 32.37 | |

D_{50m} | 1.338 × 10^{3} | |

D_{90m} | 1.554 × 10^{3} | |

Span_{m} | 72.03 | |

P_{1} | Pre-mixing time (A) | 1.250 |

Impeller rate (B) | 1.554 | |

binder amount (C) | 3.429 | |

liquid additive rate (D) | 1.457 | |

granulation time (E) | 1.632 | |

X_{2} | MC | 1.611 |

AOR | 1.520 | |

Db | 520.4 | |

Dt | 467.0 | |

HR | 118.2 | |

D_{10} | 13.39 | |

D_{50} | 394.5 | |

D_{90} | 501.0 | |

Span | 48.36 | |

X_{3} | Lubrication time (F) | 1.228 |

Minimal punch tip separation distance (G) | 7.101 | |

Y | TS | 1.006 |

DT | 1.006 |

PCs | Eigenvalues | R^{2} (%) | R^{2}_{cum} (%) |
---|---|---|---|

1 | 5.65 | 62.8 | 26.8 |

2 | 1.78 | 19.8 | 82.6 |

3 | 0.967 | 10.7 | 93.3 |

PCs | Eigenvalues | R^{2} (%) | R^{2}_{cum} (%) |
---|---|---|---|

1 | 4.52 | 32.3 | 32.3 |

2 | 2.40 | 17.1 | 49.4 |

3 | 1.51 | 10.8 | 60.2 |

4 | 1.16 | 8.3 | 68.5 |

5 | 1.01 | 7.1 | 75.6 |

6 | 0.94 | 6.7 | 82.3 |

PCs | Eigenvalues | R^{2} (%) | R^{2}_{cum} (%) |
---|---|---|---|

1 | 1.73 | 43.3 | 43.3 |

2 | 1.41 | 35.3 | 78.6 |

3 | 0.67 | 16.7 | 95.3 |

Model | LVs | R^{2}_{Xcum} (%) | R^{2}_{Ycum} (%) | Q^{2}_{Ycum} (%) |
---|---|---|---|---|

PLS | 3 | 47.0 | 76.1 | 62.5 |

MBPLS | 3 | 47.4 | 77.7 | 70.8 |

MBPLSPM | 3 | 64.3 | 79.8 | 63.5 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Sun, F.; Xu, B.; Dai, S.; Zhang, Y.; Lin, Z.; Qiao, Y.
A Novel Framework to Aid the Development of Design Space across Multi-Unit Operation Pharmaceutical Processes—A Case Study of *Panax Notoginseng* Saponins Immediate Release Tablet. *Pharmaceutics* **2019**, *11*, 474.
https://doi.org/10.3390/pharmaceutics11090474

**AMA Style**

Sun F, Xu B, Dai S, Zhang Y, Lin Z, Qiao Y.
A Novel Framework to Aid the Development of Design Space across Multi-Unit Operation Pharmaceutical Processes—A Case Study of *Panax Notoginseng* Saponins Immediate Release Tablet. *Pharmaceutics*. 2019; 11(9):474.
https://doi.org/10.3390/pharmaceutics11090474

**Chicago/Turabian Style**

Sun, Fei, Bing Xu, Shengyun Dai, Yi Zhang, Zhaozhou Lin, and Yanjiang Qiao.
2019. "A Novel Framework to Aid the Development of Design Space across Multi-Unit Operation Pharmaceutical Processes—A Case Study of *Panax Notoginseng* Saponins Immediate Release Tablet" *Pharmaceutics* 11, no. 9: 474.
https://doi.org/10.3390/pharmaceutics11090474