Rational Function-Based Approach for Integrating Tableting Reduced-Order Models with Upstream Unit Operations: Dry Granulation Case Study
Abstract
:1. Introduction
2. Materials and Methods
2.1. Preparation and Characterization of Granules
2.2. Preparation and Characterization of Tablets
3. Tableting Reduced-Order Models
4. Model Selection and Parameter Estimation
5. Reduced-Order Models to Integrate Dry Granulation and Tableting Processes
6. Results and Discussion
6.1. Tablet Weight
6.2. Compaction Force
6.3. Elastic Recovery and Tablet Density
6.4. Tensile Strength
6.5. Discussion
Granule Properties | Tablet Weight | Compaction Force | Elastic Recovery | Tensile Strength |
---|---|---|---|---|
1 | 1 | 1 | 1 | |
— | 2 | 2 | — | |
1 | — | — | 2 | |
2 | — | — | — |
Weight | |
, | |
; ; | |
, | |
; | |
Compaction force | |
; | |
; | |
; | |
Elastic recovery | |
; | |
; ; | |
Tensile strength | |
; | |
; ; ; | |
; ; ; |
7. Conclusions
8. Future Work
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
QbD | Quality by Design |
FDA | Food and Drug Administration |
QbC | Quality by Control |
API | Active Pharmaceutical Ingredients |
CPP | Critical Process Parameters |
CQA | Critical Quality Attributes |
ROMs | Reduced-Order Models |
NMPC | Nonlinear Model Predictive Control |
CMAs | Critical Material Attributes |
MCC | Microcrystalline Cellulose Avicel PH-102 |
APAP | Acetaminophen Grade 0048 |
GSD | Granule Size Distributions |
ML | Machine-learning |
NIR | Near-infrared |
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Roll Pressure [bar] | Roll Gap [mm] | [m] | [m] | [m] | [m] | [m] | ||||
---|---|---|---|---|---|---|---|---|---|---|
30 | 2 | 0.54 | 524 | 1055 | 2.25 | 5.32 | 457 | 991 | 696 | 0.640 |
30 | 3 | 0.57 | 518 | 1019 | 2.25 | 5.43 | 325 | 999 | 667 | 0.613 |
60 | 2 | 0.46 | 541 | 1170 | 2.24 | 4.98 | 479 | 1074 | 800 | 0.739 |
60 | 3 | 0.58 | 517 | 1009 | 2.26 | 5.46 | 458 | 931 | 658 | 0.708 |
90 | 2 | 0.44 | 546 | 1202 | 2.23 | 4.89 | 484 | 1102 | 830 | 0.803 |
90 | 3 | 0.50 | 533 | 1114 | 2.24 | 5.15 | 472 | 1024 | 747 | 0.770 |
Roller Compactor Settings | Tablet Press Settings | |||
---|---|---|---|---|
Batch | Roll Pressure [bar] | Roll Gap [mm] | Dosing Position [mm] | Main Compression Thickness [mm] |
1 | 30 | 2 | 7.0–8.5 | 2.5–3.0 |
2 | 30 | 3 | 7.0–8.0 | 2.5–3.2 |
3 | 60 | 2 | 7.5–9.0 | 2.5–3.0 |
4 | 60 | 3 | 7.0–8.0 | 2.5–3.2 |
5 | 90 | 2 | 8.0–9.0 | 3.5–4.0 |
6 | 90 | 3 | 7.0–7.3 | 3.0–3.3 |
Lower Bound () | Upper Bound () | Normalized | |
---|---|---|---|
Ribbon relative density: | 1 | ||
Mean granule size: | 0 |
Compaction Force | Elastic Recovery | Tensile Strength | |
---|---|---|---|
Model Number | Rational Function | No. of Parameters |
---|---|---|
1 | 9 | |
2 | 7 | |
3 | 7 | |
4 | 5 | |
5 | 7 | |
6 | 5 | |
7 | 5 | |
8 | 3 | |
9 | Constant − | 1 |
Function Variant | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
---|---|---|---|---|---|---|---|---|---|
1 | ✓ | ✓ | |||||||
2 | ✓ | ✓ | |||||||
3 | ✓ | ✓ | |||||||
4 | ✓ | ✓ | |||||||
5 | ✓ | ✓ | |||||||
6 | ✓ | ✓ | |||||||
7 | ✓ | ✓ | |||||||
8 | ✓ | ✓ | |||||||
9 | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |
SSE | AIC | ||||
---|---|---|---|---|---|
7 | 7 | 9 | 5.539 | 0.985 | −79.37 |
6 | 9 | 7 | 6.707 | 0.982 | −74.57 |
4 | 9 | 7 | 6.79 | 0.982 | −74.00 |
4 | 4 | 11 | 5.903 | 0.984 | −72.44 |
8 | 8 | 7 | 7.053 | 0.981 | −72.26 |
SSE | AIC | ||||
---|---|---|---|---|---|
4 | 9 | 7 | 0.004 | 0.976 | −185.5 |
8 | 9 | 5 | 0.005 | 0.968 | −182.6 |
2 | 9 | 9 | 0.004 | 0.977 | −181.6 |
3 | 9 | 9 | 0.004 | 0.976 | −181.5 |
6 | 9 | 7 | 0.005 | 0.970 | −180.3 |
SSE | AIC | ||||||
---|---|---|---|---|---|---|---|
1 | 1 | 0.913 | 177 | 16 | −5302 | ||
1 | 1 | 0.906 | 193 | 16 | −5123 | ||
3 | 3 | 0.903 | 197 | 12 | −5082 | ||
3 | 3 | 0.900 | 205 | 12 | −5004 | ||
7 | 7 | 0.881 | 243 | 8 | −4639 | ||
2 | 2 | 0.873 | 259 | 14 | −4497 | ||
5 | 5 | 0.873 | 260 | 12 | −4491 | ||
1 | 9 | 0.862 | 281 | 10 | −4327 | ||
2 | 2 | 0.856 | 293 | 14 | −4229 | ||
4 | 4 | 0.848 | 309 | 10 | −4122 |
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Bachawala, S.; Lagare, R.B.; Delaney, A.B.; Nagy, Z.K.; Reklaitis, G.V.; Gonzalez, M. Rational Function-Based Approach for Integrating Tableting Reduced-Order Models with Upstream Unit Operations: Dry Granulation Case Study. Pharmaceuticals 2024, 17, 1158. https://doi.org/10.3390/ph17091158
Bachawala S, Lagare RB, Delaney AB, Nagy ZK, Reklaitis GV, Gonzalez M. Rational Function-Based Approach for Integrating Tableting Reduced-Order Models with Upstream Unit Operations: Dry Granulation Case Study. Pharmaceuticals. 2024; 17(9):1158. https://doi.org/10.3390/ph17091158
Chicago/Turabian StyleBachawala, Sunidhi, Rexonni B. Lagare, Abigail B. Delaney, Zoltan K. Nagy, Gintaras V. Reklaitis, and Marcial Gonzalez. 2024. "Rational Function-Based Approach for Integrating Tableting Reduced-Order Models with Upstream Unit Operations: Dry Granulation Case Study" Pharmaceuticals 17, no. 9: 1158. https://doi.org/10.3390/ph17091158