Mathematical Tools for the Quantitative Definition of a Design Space

  • Amanda Rogers
  • Marianthi G. IerapetritouEmail author
Part of the Methods in Pharmacology and Toxicology book series (MIPT)


This chapter focuses on the application of process modeling to determination of design space for pharmaceutical manufacturing processes. The first two sections define design space and related terms from a regulatory perspective and discuss how these apply in practice during pharmaceutical process development. In Sect. 3, a variety of mathematical techniques that can be used to guide design space development are introduced. An emphasis is placed on the use of feasibility analysis and the relationship between process feasibility and design space. Statistical techniques, including latent variable and Bayesian methods, are also discussed in detail. For methods that have been reported in the literature for pharmaceutical manufacturing applications, an overview of the relevant case studies is provided. If methods have not yet been applied to pharmaceutical processes, potential applications for these techniques are indicated. To illustrate the applicability of these concepts to pharmaceutical manufacturing processes, a brief case study is presented in Sect. 4. A discussion of design space verification and issues related to scale-up is provided in Sect. 5. Finally a brief summary of the concepts presented and their potential role in design space development for pharmaceutical processes is given in Sect. 6.

This chapter is intended to provide readers with an understanding of mathematical techniques that can be used during process development to assist in the determination of process design space. An overview of the problem formulation and solution approaches for each method are presented. More detailed mathematical developments for each technique are available in the references provided. Table 1 provides a list of symbols that are used throughout this chapter, while Table 2 describes acronyms used within this chapter.

Key words

Design space Feasibility analysis Flexibility analysis Black-box feasibility Derivative-free optimization Bayesian reliability Partial least squares (PLS) Principal component analysis (PCA) Pharmaceutical process development Process modeling 



The authors would like to acknowledge financial support from Bristol-Myers Squibb as well as from the Engineering Research Center for Structured Organic Particulate Systems at Rutgers University (NSF-0504497, NSF-ECC 0540855).


  1. 1.
    ICH (2005) ICH Q8 pharmaceutical developmentGoogle Scholar
  2. 2.
    McKenzie P, Kiang S, Tom J, Rubin E, Futran M (2006) Can pharmaceutical process development become high tech? AIChE J. 52 (12)Google Scholar
  3. 3.
    ICH Harmonised Tripartite Guideline: Pharmaceutical Development Q8(R2) Current Step 4 Version (2009) International Conference on Harmonisation of Technical Requirements for Registration of Pharmaceuticals for Human UseGoogle Scholar
  4. 4.
    Guidance for Industry (2006) Q8 pharmaceutical development, USAGoogle Scholar
  5. 5.
    Yu LX (2008) Pharmaceutical quality by design: product and process development, understanding, and control. Pharm Res 25(4):781–791. doi: 10.1007/s11095-007-9511-1CrossRefPubMedGoogle Scholar
  6. 6.
    ICH (2005) ICH Q9 quality risk managementGoogle Scholar
  7. 7.
    ICH (2005) ICH Q10 pharmaceutical quality systemsGoogle Scholar
  8. 8.
    Chatterjee S (2008) Overview of models used in design space determination: a regulatory perspective. Paper presented at the AIChE annual meeting, Philadelphia, PAGoogle Scholar
  9. 9.
    Chatterjee S (2012) Design space considerations. In: AAPS annual meeting, Chicago, IlGoogle Scholar
  10. 10.
    Degerman M, Westerberg K, Nilsson B (2009) A model-based approach to determine the design space of preparative chromatography. Chem Eng Technol 32(8):1195–1202. doi: 10.1002/ceat.200900102CrossRefGoogle Scholar
  11. 11.
    Leopore J, Spavins J (2008) PQLI design space. J Pharm Innov 3(2):79–87Google Scholar
  12. 12.
    Peterson JJ (2008) A Bayesian approach to the ICH Q8 definition of design space. J Biopharm Stat 18(5):959–975. doi: 10.1080/10543400802278197CrossRefPubMedGoogle Scholar
  13. 13.
    Guidance for Industry (1995) Immediate release solid oral dosage forms scale-up and postapproval changes: chemistry, manufacturing, and controls, in vitro dissolution testing, and in vivo bioequivalence documentation, USAGoogle Scholar
  14. 14.
    Guidance for Industry (1997) Modified release solid oral dosage forms scale-up and postapproval changes: chemistry, manufacturing, and controls, in vitro dissolution testing, and in vivo bioequivalence documentation, USAGoogle Scholar
  15. 15.
    Guidance for Industry (1997) Nonsterile semisolid dosage forms scale-up and postapproval changes: chemistry, manufacturing, and controls, in vitro dissolution testing, and in vivo bioequivalence documentation, USAGoogle Scholar
  16. 16.
    Guidance for Industry (2004) Changes to an approved NDA or ANDA, USAGoogle Scholar
  17. 17.
    Charoo NA, Shamsher AA, Zidan AS, Rahman Z (2012) Quality by design approach for formulation development: a case study of dispersible tablets. Int J Pharm 423(2):167–178. doi: 10.1016/j.ijpharm.2011.12.024CrossRefPubMedGoogle Scholar
  18. 18.
    Kenett R, Kenett D (2008) Quality by design applications in biosimilar pharmaceutical products. Accredit Qual Assur 13(12):681–690. doi: 10.1007/s00769-008-0459-6CrossRefGoogle Scholar
  19. 19.
    Lionberger RA, Lee SL, Lee L, Raw A, Yu LX (2008) Quality by design: concepts for ANDAs. AAPS J 10(2):268–276. doi: 10.1208/s12248-008-9026-7CrossRefPubMedPubMedCentralGoogle Scholar
  20. 20.
    Airaksinen S, Karjalainen M, Shevchenko A, Westermarck S, Leppanen E, Rantanen J, Yliruusi J (2005) Role of water in the physical stability of solid dosage formulations. J Pharm Sci 94(10):2147–2165. doi: 10.1002/jps.20411CrossRefPubMedGoogle Scholar
  21. 21.
    Wu H, White M, Khan MA (2011) Quality-by-Design (QbD): an integrated process analytical technology (PAT) approach for a dynamic pharmaceutical co-precipitation process characterization and process design space development. Int J Pharm 405(1-2):63–78. doi: 10.1016/j.ijpharm.2010.11.045CrossRefPubMedGoogle Scholar
  22. 22.
    am Ende D, Bronk KS, Mustakis J, O’Connor G, Santa Maria CL, Nosal R, Watson TNJ (2007) API quality by design example from the torcetrapib manufacturing process. J Pharm Innov 2:71–86Google Scholar
  23. 23.
    Cimarosti Z, Bravo F, Castoldi D, Tinazzi F, Provera S, Perboni A, Papini D, Westerduin P (2010) Application of the QbD principles in the development of the casopitant mesylate manufacturing process. Process research studies for the definition of the control strategy of some drug substance-CQAs for stages 2a, 2b, and 2c. Org Process Res Dev 14(4):805–814. doi: 10.1021/Op1000622CrossRefGoogle Scholar
  24. 24.
    Dach R, Song JHJ, Roschangar F, Samstag W, Senanayake CH (2012) The eight criteria defining a good chemical manufacturing process. Org Process Res Dev 16(11):1697–1706. doi: 10.1021/Op300144gCrossRefGoogle Scholar
  25. 25.
    Adeyeye MC (2008) Drug-excipient interaction occurrences during solid dosage form development. Drugs Pharm Sci 178:357–436Google Scholar
  26. 26.
    Campisi B, Chicco D, Vojnovic D, Phan-Tan-Luu R (1998) Experimental design for a pharmaceutical formulation: optimisation and robustness. J Pharm Biomed Anal 18(1-2):57–65PubMedGoogle Scholar
  27. 27.
    Muzzio FJ, Alexander A, Goodridge C, Shen E, Shinbrot T (2004) Solids Mixing. In: Paul EL, Atiemo-Obeng VA, Kresta SM (eds) Handbook of Industrial mixing: science and practice. Wiley, Hoboken, NJ, pp 887–985Google Scholar
  28. 28.
    Faldu B, Sharma A, Sharma A, Chauhan CS (2012) Roller compaction: imperative process for tablet manufacturing: a review. Int J Pharm Res Dev 4(10):40–47Google Scholar
  29. 29.
    Lee KT, Ingram A, Rowson NA (2013) Comparison of granule properties produced using twin screw extruder and high shear mixer: a step towards understanding the mechanism of twin screw wet granulation. Powder Technol 238:91–98Google Scholar
  30. 30.
    Rogers AJ, Hashemi A, Ierapetritou MG (2013) Modeling of particulate processes for the continuous manufacture of solid-based pharmaceutical dosage forms. Processes 1(2):67–127Google Scholar
  31. 31.
    Ng KM (2002) Design and development of solids processes – a process systems engineering perspective. Powder Technol 126(3):205–210Google Scholar
  32. 32.
    Strong J (2009) Scale-up of pharmaceutical manufacturing operations of solid dosage forms. In: Qiu Y, Chen Y, Zhang GZ, Liu L, Porter WR (eds) Developing solid oral dosage forms: pharmaceutical theory and practice. Academic Press, New York, NY, USA, pp 615–636. doi: 10.1016/B978-0-444-53242-8.00027-8, An Imprint of ElsevierCrossRefGoogle Scholar
  33. 33.
    Järvinen MA, Paaso J, Paavola M, Leivisk K, Juuti M, Muzzio F, Järvinen K (2013) Continuous direct tablet compression: effects of impeller rotation rate, total feed rate and drug content on the tablet properties and drug release. Drug Dev Ind Pharm 39(11):1802–1808Google Scholar
  34. 34.
    Boukouvala F, Niotis V, Ramachandran R, Muzzio FJ, Ierapetritou MG (2012) An integrated approach for dynamic flowsheet modeling and sensitivity analysis of a continuous tablet manufacturing process. Comput Chem Eng 42:30–47. doi: 10.1016/j.compchemeng.2012.02.015CrossRefGoogle Scholar
  35. 35.
    Gentis ND, Betz G (2012) Compressibility of binary powder formulations: investigation and evaluation with compaction equations. J Pharm Sci 101(2):777–793. doi: 10.1002/jps.22794CrossRefGoogle Scholar
  36. 36.
    Faure A, York P, Rowe RC (2001) Process control and scale-up of pharmaceutical wet granulation processes: a review. Eur J Pharm Biopharm 52:269–277Google Scholar
  37. 37.
    Vervaet C, Remon JP (2005) Continuous granulation in the pharmaceutical industry. Chem Eng Sci 60:3949–3957Google Scholar
  38. 38.
    Iveson SM, Litster JD, Hapgood K, Ennis BJ (2001) Nucleation, growth and breakage phenomena in agitated wet granulation processes: a review. Powder Technol 117:3–39Google Scholar
  39. 39.
    Kleinebudde P (2004) Roll compaction/dry granulation: pharmaceutical applications. Eur J Pharm Biopharm 58:317–326Google Scholar
  40. 40.
    Lecompte T, Doremus P, Thomas G, Perier-Camby L (2005) Dry granulation of organic powders – dependence of pressure 2D-distribution on different process parameters. Chem Eng Sci 60:3933–3940Google Scholar
  41. 41.
    Hlinak AJ, Kuriyan K, Morris KR, Reklaitis GV, Basu PK (2006) Understanding critical material properties for solid dosage form design. J Pharm Innov 1(1):12–17Google Scholar
  42. 42.
    Jornitz MW (2008) Vendor qualification and validation. In: Agalloco J, Carleton FJ (eds) Validation of pharmaceutical processes, 3rd edn. Informa Healthcare, New York, NY, USA, p 529Google Scholar
  43. 43.
    Zhang X, Lionberger RA, Davit BM, Yu LX (2011) Utility of physiologically based absorption modeling in implementing quality by design in drug development. AAPS J 13(1):59–71. doi: 10.1208/s12248-010-9250-9CrossRefPubMedPubMedCentralGoogle Scholar
  44. 44.
    Jivraj M, Martini LG, Thomson CM (2000) An overview of the different excipients useful for the direct compression of tablets. Pharm Sci Technol Today 3(2):58–63PubMedGoogle Scholar
  45. 45.
    Pifferi G, Santoro P, Pedrani M (1999) Quality and functionality of excipients. Farmaco 54(1–2):1–14PubMedGoogle Scholar
  46. 46.
    Morin G, Briens L (2013) The effect of lubricants on powder flowability for pharmaceutical application. AAPS PharmSciTech 14(3):1158–1168PubMedPubMedCentralGoogle Scholar
  47. 47.
    Wang J, Wen H, Desai D (2010) Lubrication in tablet formulations. Eur J Pharm Biopharm 75(1):1–15. doi: 10.1016/j.ejpb.2010.01.007CrossRefPubMedGoogle Scholar
  48. 48.
    Onuki Y, Kawai S, Arai H, Maeda J, Takagaki K, Takayama K (2012) Contribution of the physicochemical properties of active pharmaceutical ingredients to tablet properties identified by ensemble artificial neural networks and Kohonen’s self-organizing maps. J Pharm Sci 101(7):2372–2381. doi: 10.1002/jps.23134CrossRefPubMedGoogle Scholar
  49. 49.
    Herting MG, Kleinebudde P (2007) Roll compaction/dry granulation: effect of raw material particle size on granule and tablet properties. Int J Pharm 338(1-2):110–118. doi: 10.1016/j.ijpharm.2007.01.035CrossRefPubMedGoogle Scholar
  50. 50.
    Kushner J, Langdon BA, Hiller JI, Carlson GT (2011) Examining the impact of excipient material property variation on drug product quality attributes: a quality-by-design study for a roller compacted, immediate release tablet. J Pharm Sci 100(6):2222–2239. doi: 10.1002/jps.22455CrossRefPubMedGoogle Scholar
  51. 51.
    Nosal R, Schultz T (2008) PQLI definition of criticality. J Pharm Innov 3(2):69–78Google Scholar
  52. 52.
    Garcia T, Cook G, Nozal R (2008) PQLI key topics: criticality, design space, and control strategy. J Pharm Innov 3(2):60–68Google Scholar
  53. 53.
    Saltelli A, Chan K, Scott EM (2000) Sensivivity analysis. Wiley, ChichesterGoogle Scholar
  54. 54.
    Saltelli A, Annoni P, Azzini I, Campolongo F, Ratto M, Tarantola S (2010) Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index. Comput Phys Commun 181(2):259–270. doi: 10.1016/j.cpc.2009.09.018CrossRefGoogle Scholar
  55. 55.
    Rogers AJ, Inamdar C, Ierapetritou MG (2013) An integrated approach to simulation of pharmaceutical processes for solid drug manufacture. Ind Eng Chem Res 131015102838009. doi:  10.1021/ie401344aGoogle Scholar
  56. 56.
    Kikuchi S, Takayama K (2009) Reliability assessment for the optimal formulations of pharmaceutical products predicted by a nonlinear response surface method. Int J Pharm 374(1-2):5–11. doi: 10.1016/j.ijpharm.2009.02.016CrossRefPubMedGoogle Scholar
  57. 57.
    Grossmann IE, Calfa B, Garcia-Herreros P (2014) Evolution of concepts and models for quantifying resiliency and flexibility of chemical processes. Comput Chem Eng. doi: 10.1016/j.compchemeng.2013.12.013CrossRefGoogle Scholar
  58. 58.
    Lima FV, Jia Z, Lerapetritou M, Georgakis C (2010) Similarities and differences between the concepts of operability and flexibility: the steady-state case. AIChE J 56(3):702–716. doi: 10.1002/Aic.12021CrossRefGoogle Scholar
  59. 59.
    Boukouvala F, Muzzio FJ, Ierapetritou MG (2010) Design space of pharmaceutical processes using data-driven-based methods. J Pharm Innov 5(3):119–137. doi: 10.1007/s12247-010-9086-yCrossRefGoogle Scholar
  60. 60.
    Morari M (1983) Flexibility and resiliency of process systems. Comput Chem Eng 7(4):423–437Google Scholar
  61. 61.
    Swaney RE, Grossmann IE (1985) An index for operational flexibility in chemical process design. Part II: computational algorithms. AIChE J 31(4):631–641Google Scholar
  62. 62.
    Swaney RE, Grossmann IE (1985) An index for operational flexibility in chemical process design. Part II: computational algorithms. AIChE J 31(4):631–641Google Scholar
  63. 63.
    Boukouvala F, Ierapetritou MG (2012) Feasibility analysis of black-box processes using an adaptive sampling Kriging-based method. Comput Chem Eng 36:358–368. doi: 10.1016/j.compchemeng.2011.06.005CrossRefGoogle Scholar
  64. 64.
    Grossmann IE, Floudas CA (1987) Active constraint strategy for flexibility analysis in chemical processes. Comput Chem Eng 11(6):675–693Google Scholar
  65. 65.
    Biegler LT, Grossmann IE, Westerberg AW (1997) Systematic methods of chemical process design. Prentice Hall, Upper Saddle River, NJGoogle Scholar
  66. 66.
    Halemane KP, Grossmann IE (1983) Optimal process design under uncertainty. AIChE J 49:425Google Scholar
  67. 67.
    Kuhn HW, Tucker AW (1950) Nonlinear programming. In: Proceedings of the second Berkeley symposium on mathematical statistics and probability. University of California Press, Berkeley, CA, pp 481–492Google Scholar
  68. 68.
    Ostrovsky GM, Volin YM, Barit EI, Senyavin MM (1994) Flexibility analysis and optimization of chemical plants with uncertain parameters. Comput Chem Eng 18:755–767Google Scholar
  69. 69.
    Ostrovsky GM, Achenie LEK, Wang Y, Volin YM (2002) A unique approach for solving sub-problems in flexibility analysis. Chem Eng Comm 189(1):125–149Google Scholar
  70. 70.
    Ostrovsky GM, Achenie LEK, Wang Y (2000) A new algorithm for computing process flexibility. Ind Eng Chem Res 39:2368–2377Google Scholar
  71. 71.
    Floudas CA, Gümüs ZH, Ierapetritou MG (2001) Global optimization in design under uncertainty: feasibility test and flexibility index problems. Ind Eng Chem Res 40:4267–4282Google Scholar
  72. 72.
    Floudas CA (2000) Nonconvex optimization and its applications. In: Floudas CA (ed) Deterministic global optimization: theory, methods and applications, vol 37. Kluwer Academic Publishers, Dordrecht, The NetherlandsGoogle Scholar
  73. 73.
    Subrahmanyam S, Peknyt JF, Reklaitis GV (1994) Design of batch chemical-plants under market uncertainty. Ind Eng Chem Res 33(11):2688–2701. doi: 10.1021/Ie00035a019CrossRefGoogle Scholar
  74. 74.
    Vin JP, Ierapetritou MG (2001) Robust short-term scheduling for multiproduct batch plants under demand uncertainty. Ind Eng Chem Res 40:4543–4554Google Scholar
  75. 75.
    Linninger AA, Chakraborty A (2001) Pharmaceutical waste management under uncertainty. Comput Chem Eng 25(4–6):675–681. doi: 10.1016/S0098-1354(01)00668-8CrossRefGoogle Scholar
  76. 76.
    Pistikopoulos EN, Mazzuchi TA (1990) A novel flexibility analysis approach for processes with stochastic parameters. Comput Chem Eng 14(9):991–1000Google Scholar
  77. 77.
    Straub DA, Grossmann IE (1990) Integrated stochastic metric of flexibility for systems with discrete state and continuous parameter uncertainties. Comput Chem Eng 14(9):967–985Google Scholar
  78. 78.
    Straub DA, Grossmann IE (1993) Design optimization of stochastic flexibility. Comput Chem Eng 17(4):339–354Google Scholar
  79. 79.
    Grossmann IE, Straub DA (1996) Recent developments in the evaluation and optimization of flexible chemical processes. In: Reklaitis GV, Sunol AK, Rippin DWT, Hortacsu O (eds) Batch processing systems engineering fundamentals and applications for chemical engineering, vol 143, Fundamentals and applications for chemical engineering. Springer in Collaboration with NATO Scientific Affairs Division, Heidelberg, Berlin, pp 495–516Google Scholar
  80. 80.
    Bansal V, Perkins JD, Pistikopoulos EN (2000) Flexibility analysis and design of linear systems by parametric programming. AIChE J 46(2):335–354. doi: 10.1002/aic.690460212CrossRefGoogle Scholar
  81. 81.
    Bansal V, Perkins JD, Pistikopoulos EN (2002) Flexibility analysis and design using a parametric programming framework. AIChE J 48(12):2851–2868Google Scholar
  82. 82.
    Pistikopoulos EN, Ierapetritou MG (1995) Novel-approach for optimal process design under uncertainty. Comput Chem Eng 19(10):1089–1110. doi: 10.1016/0098-1354(94)00093-4CrossRefGoogle Scholar
  83. 83.
    Bansal V, Perkins JD, Pistikopoulos EN (1998) Flexibility analysis and design of dynamic processes with stochastic parameters. Comput Chem Eng 22(Suppl):S817–S820. doi: 10.1016/S0098-1354(98)00156-2CrossRefGoogle Scholar
  84. 84.
    Boukouvala F, Ierapetritou M (2012) Simulation-based derivative-free optimization for computationally expensive function. In: AIChE annual meeting, Pittsburgh, PAGoogle Scholar
  85. 85.
    Myers RH, Montgomery DC (2002) Response surface methodology process and product optimization using designed experiments. Wiley, New YorkGoogle Scholar
  86. 86.
    Box GEP, Wilson KB (1951) On the experimental attainment of optimum conditions. J Roy Stat Soc B 13(1):1–35Google Scholar
  87. 87.
    Jia ZY, Davis E, Muzzio FJ, Ierapetritou MG (2009) Predictive modeling for pharmaceutical processes using Kriging and response surface. J Pharm Innov 4(4):174–186. doi: 10.1007/s12247-009-9070-6CrossRefGoogle Scholar
  88. 88.
    Calder CA, Cressie N (2009) Kriging and variogram models. In: Kitchin R, Thrift N (eds) International encyclopedia of human geography, vol 1. Elsevier, Oxford, pp 49–55Google Scholar
  89. 89.
    Kleijnen JPC (2009) Kriging metamodeling in simulation: a review. Eur J Oper Res 192(3):707–716. doi: 10.1016/j.ejor.2007.10.013CrossRefGoogle Scholar
  90. 90.
    Metheron G (1963) Principles of geostatistics. Econ Geol 58(8)Google Scholar
  91. 91.
    Agatonovic-Kustrin S, Beresford R (2000) Basic concepts of artificial neural network (ANN) modeling and its application in pharmaceutical research. J Pharm Biomed Anal 22(5):717–727PubMedGoogle Scholar
  92. 92.
    Basheer IA, Hajmeer M (2000) Artificial neural networks: fundamentals, computing, design, and application. J Microbiol Methods 43(1):3–31PubMedGoogle Scholar
  93. 93.
    Li G, Rosenthal C, Rabitz H (2001) High dimensional model representations. J Phys Chem A 105(33)Google Scholar
  94. 94.
    Li GY, Wang SW, Rabitz H (2002) Practical approaches to construct RS-HDMR component functions. J Phys Chem A 106(37):8721–8733. doi: 10.1021/Jp014567tCrossRefGoogle Scholar
  95. 95.
    Li G, Rabitz H, Hu J, Chen Z, Ju Y (2008) Regularized random-sampling high dimensional model representation (RS-HDMR). J Math Chem 43(3):1207–1232Google Scholar
  96. 96.
    Boukouvala F, Muzzio FJ, Ierapetritou MG (2011) Dynamic data-driven modeling of pharmaceutical processes. Ind Eng Chem Res 50(11):6743–6754. doi: 10.1021/Ie102305aCrossRefGoogle Scholar
  97. 97.
    Jia Z, Davis E, Muzzio FJ, Ierapetritou MG (2009) Predictive modeling for pharmaceutical processes using Kriging and response surface. J Pharm InnovGoogle Scholar
  98. 98.
    Boukouvala F, Ierapetritou MG (2014) Derivative-free optimization for expensive constrained problems using a novel expected improvement objective function. AIChE J 60(7):2462–2474Google Scholar
  99. 99.
    Johanson JR (1965) A rolling theory for granular solids. ASME J Appl Mech E32(4):842–848Google Scholar
  100. 100.
    Samsatli NJ, Papageorgiou LG, Shah N (1999) Batch process design and operating using operational envelopes. Comput Chem Eng Suppl 5887–5890Google Scholar
  101. 101.
    Ierapetritou MG (2001) A new approach for quantifying process feasibility: convex and one dimensional quasi-convex regions. AIChE J 47(6):1407–1417Google Scholar
  102. 102.
    Goyal V, Ierapetritou MG (2002) Determination of operability limits using simplicial approximation. AIChE J 48(12):2902–2909Google Scholar
  103. 103.
    Director SW, Hachtel GD (1977) The simplicial approximation approach to design centering. IEEE Trans Circ Syst 24(7)Google Scholar
  104. 104.
    Banarjee I, Ierapetritou MG (2005) Feasibility evaluation of nonconvex systems using shape reconstruction techniques. Ind Eng Chem Res 44:3638–3647Google Scholar
  105. 105.
    Wold S, Sjostrom M, Eriksson L (2001) PLS-regression: a basic tool of chemometrics. Chemometr Intell Lab 58(2):109–130. doi: 10.1016/S0169-7439(01)00155-1CrossRefGoogle Scholar
  106. 106.
    López-Negrete de la Fuente R, García-Muñoz S, Biegler LT (2010) An efficient nonlinear programming strategy for PCA models with incomplete data sets. J Chemometr 24(6):301–311Google Scholar
  107. 107.
    Burnham AJ, MacGregor JF, Viveros R (1999) Latent variable multivariate regression modeling. Chemometr Intell Lab 48(2):167–180. doi: 10.1016/S0169-7439(99)00018-0CrossRefGoogle Scholar
  108. 108.
    Hoskuldsson A (1988) PLS regression methods. J Chemometr 2:211Google Scholar
  109. 109.
    García-Muñoz S, Polizzi M (2012) WSPLS – a new approach towards mixture modeling and accelerated product development. Chemometr Intell Lab 15:116–121Google Scholar
  110. 110.
    García-Muñoz S, MacGregor JF, Kourti T (2005) Product transfer between sites using Joint-Y PLS. Chemometr Intell Lab 79:101–114Google Scholar
  111. 111.
    Huang J, Kaul G, Cai C, Chatlapalli R, Hernandez-Abad P, Gosh K, Nagi A (2009) Quality by design case study: an integrated multivariate approach to drug product and process development. Int J Pharm 382:23–32PubMedGoogle Scholar
  112. 112.
    MacGregor JF, Bruwer M-J (2008) A framework for the development of design and control spaces. J Pharm Innov 3:15–22Google Scholar
  113. 113.
    García-Muñoz S, Dolph S, Ward HWI (2010) Handling uncertainty in the establishment of a design space for the manufacture of a pharmaceutical product. Comput Chem Eng 34:1098–1107Google Scholar
  114. 114.
    García-Muñoz S (2009) Establishing multivariate specifications for incoming materials using data from multiple scales. Chemometr Intell Lab 98(1):51–57Google Scholar
  115. 115.
    Duchesne C, Macgregor JF (2004) Establishing multivariate specification regions for incoming materials. J Qual Technol 36(1):78–94Google Scholar
  116. 116.
    Nasr M (2007) The FDA’s initiative on pharmaceutical quality for the 21-st century: emphasizing quality by design. In: IFPAC, Baltimore, MDGoogle Scholar
  117. 117.
    Garcia-Munoz S, MacGregor JF, Kourti T, Apruzzece F, Champagne M (2006) Optimization of batch operating policies. Part I. Handling multiple solutions. Ind Eng Chem Res 45(23):7856–7866Google Scholar
  118. 118.
    García-Muñoz S, MacGregor JF, Neogi D, Latshaw BE, Mehta S (2008) Optimization of batch operating policies. Part II. Incorporating process constraints and industrial applications. Ind Eng Chem Res 47(12):4202–4208Google Scholar
  119. 119.
    Jaeckle CM, MacGregor JF (1998) Product design through multivariate statistical analysis of process data. AIChE J 44(5):1105–1118. doi: 10.1002/aic.690440509CrossRefGoogle Scholar
  120. 120.
    Montgomery DC, Bettencourt VMJ (1977) Multiple response surface methods in computer simulation. Simulation 29:113–121Google Scholar
  121. 121.
    Park KS, Kim KJ (2005) Optimizing multi-response surface problems: how to use multi-objective optimization techniques. IIE Trans 37(6):523–532. doi: 10.1080/07408170590928992CrossRefGoogle Scholar
  122. 122.
    Khuri AI, Conlon M (1981) Simultaneous optimization of multiple responses represented by polynomal regression function. Technometrics 23:363–375Google Scholar
  123. 123.
    Pignatiello JJ (1993) Strategies for robust multiresponse quality engineering. IIE Trans 25(3):5–15. doi: 10.1080/07408179308964286CrossRefGoogle Scholar
  124. 124.
    Vining GG (1998) A compromise approach to multi-response optimization. J Qual Technol 30:309–313Google Scholar
  125. 125.
    Peterson JJ (2004) A posterior predictive approach to multiple response surface optimization. J Qual Technol 36(2):139–153Google Scholar
  126. 126.
    Dimitriadis VD, Pistikopoulos EN (1995) Flexibility analysis of dynamic-systems. Ind Eng Chem Res 34(12):4451–4462. doi: 10.1021/Ie00039a036CrossRefGoogle Scholar
  127. 127.
    Holt BR, Morari M (1985) Design of resilient processing plants V – the effect of deadtime on dynamic resilience. Chem Eng Sci 40:1229Google Scholar
  128. 128.
    Holt BR, Morari M (1985) Design of resilient processing plants VI – the effect of right half plane zeros on dynamic resilience. Chem Eng Sci 40:59Google Scholar
  129. 129.
    Skogestad S, Morari M (1987) Design of resilient processing plants IX – the effect of model uncertainty on dynamic resilience. Chem Eng Sci 42:1765Google Scholar
  130. 130.
    Soroush M, Kravaris C (1993) Optimal-design and operation of batch reactors. 1. Theoretical framework. Ind Eng Chem Res 32(5):866–881. doi: 10.1021/Ie00017a015CrossRefGoogle Scholar
  131. 131.
    Soroush M, Kravaris C (1993) Optimal-design and operation of batch reactors. 2. A case-study. Ind Eng Chem Res 32(5):882–893. doi: 10.1021/Ie00017a016CrossRefGoogle Scholar
  132. 132.
    Vassiliadis VS, Sargent RWH, Pantelides CC (1994) Solution of a class of multistage dynamic optimization problems. 1. Problems without path constraints. Ind Eng Chem Res 33(9):2111–2122. doi: 10.1021/Ie00033a014CrossRefGoogle Scholar
  133. 133.
    Vassiliadis VS, Sargent RWH, Pantelides CC (1994) Solution of a class of multistage dynamic optimization problems. 2. Problems with path constraints. Ind Eng Chem Res 33(9):2123–2133. doi: 10.1021/Ie00033a015CrossRefGoogle Scholar
  134. 134.
    Biegler LT (2007) An overview of simultaneous strategies for dynamic optimization. Chem Eng Process 46(11):1043–1053. doi: 10.1016/j.cep.2006.06.021CrossRefGoogle Scholar
  135. 135.
    Biegler LT, Cervantes AM, Wächter A (2002) Advances in simultaneous strategies for dynamic process optimization. Chem Eng Sci 57(4):575–593, Doi: Pii S0009-2509(01)00376-1Google Scholar
  136. 136.
    Kameswaran S, Biegler LT (2006) Simultaneous dynamic optimization strategies: recent advances and challenges. Comput Chem Eng 30:1560–1575Google Scholar
  137. 137.
    Betts JT (2001) Practical methods for optimal control using nonlinear programming. Advances in design and control. SIAM, Philadelphia, PAGoogle Scholar
  138. 138.
    Bahri PA, Bandoni JA, Romagnoli JA (1997) Integrated flexibility and controllability analysis in design of chemical processes. AIChE J 43(4):997–1015. doi: 10.1002/aic.690430415CrossRefGoogle Scholar
  139. 139.
    Mohideen MJ, Perkins JD, Pistikopoulos EN (1996) Optimal design of dynamic systems under uncertainty. AIChE J 42(8):2251–2272Google Scholar
  140. 140.
    Engisch WE, Muzzio FJ (2012) Method for characterization of loss-in-weight feeder equipment. Powder Technol 228:395–403. doi: 10.1016/j.powtec.2012.05.058CrossRefGoogle Scholar
  141. 141.
    Zhou H, Li X, Qian Y, Kraslawski A (2009) Optimizing the initial conditions to improve the dynamic flexibility of batch processes. Ind Eng Chem Res 48:6321–6326Google Scholar
  142. 142.
    Luus R, Hennessy D (1999) Optimization of fed-batch reactors by the Luus-Jaakola optimization procedures. Ind Eng Chem Res 38:1948–1955Google Scholar
  143. 143.
    Huang W, Li X, Yang S, Qian Y (2011) Dynamic flexibility analysis of chemical reaction systems with time delay: Using a modified finite element collocation method. Chem Eng Res Des 89:1938–1946Google Scholar
  144. 144.
    Uchida K, Shimemura E, Kubo T, Abe M (1988) The linear-quadratic optimal control approach to feedback control design for systems with delay. Automatica 24:773–780Google Scholar
  145. 145.
    Kim AV, Han SH, Kwon WH, Pimenov VG (1998) Explicit numerical methods and LQR control algorithms for time-delay systems. In: International conference on electrical engineering, Korea, pp 21–25Google Scholar
  146. 146.
    Bindhumadhavan G, Seville JPK, Adams MJ, Greenwood RW, Fitzpatrick S (2005) Roll compaction of a pharmaceutical excipient: experimental validation of rolling theory for granular solids. Chem Eng Sci 60:3891–3897Google Scholar
  147. 147.
    Reynolds G, Ingale R, Roberts R, Kothari S, Gururagan B (2010) Practical application of roller compaction process modeling. Comput Chem Eng 34:1049–1057Google Scholar
  148. 148.
    Hsu SH, Reklaitis GV, Venkatasubramanian V (2010) Modeling and control of roller compaction for pharmaceutical manufacturing. Part I: process dynamics and control framework. J Pharm Innov 5:14–23Google Scholar
  149. 149.
    Garcia T, McCurdy V, Watson TNJ, Ende MA, Butterell P, Vukovinsky K, Chueh A, Coffman J, Cooper S, Schuemmelfeder B (2012) Verification of design spaces developed at subscale. J Pharm Innov 7(1):13–18. doi: 10.1007/s12247-012-9123-0CrossRefGoogle Scholar
  150. 150.
    Plumb K (2005) Continuous processing in the pharmaceutical industry – changing the mind set. Chem Eng Res Des 83(A6):730–738. doi: 10.1205/Cherd.04359CrossRefGoogle Scholar
  151. 151.
    Brone D, Alexander A, Muzzio FJ (1998) Quantitative characterization of mixing of dry powders in V-blenders. AIChE J 44(2):217–278Google Scholar
  152. 152.
    Ahmend SU, Katdare A, Naini V, Wadgaonkar D (2014) Scale-up, technology transfer, and process performance qualification. In: Shargel L, Kanfer I (eds) Generic drug product development: solid oral dosage forms, vol 129, 2nd edn, Drugs and the pharmaceutical sciences. CRC Press Taylor & Francis Group, Boca Raton, FLGoogle Scholar
  153. 153.
    Hallow DM, Mudryk BM, Braem AD, Tabora JE, Lyngberg OK, Bergum JS, Rossano LT, Tummala S (2010) An example of utilizing mechanistic and empirical modeling in quality by design. J Pharm Innov 5(4):193–203. doi: 10.1007/s12247-010-9094-yCrossRefGoogle Scholar
  154. 154.
    Burt JL, Braem AD, Ramirez A, Mudryk B, Rossano L, Tummala S (2011) Model-guided design space development for a drug substance manufacturing process. J Pharm Innov 6(3):181–192. doi: 10.1007/s12247-011-9109-3CrossRefGoogle Scholar
  155. 155.
    Shah N (2004) Pharmaceutical supply chains: key issues and strategies for optimisation. Comput Chem Eng 28(6-7):929–941. doi: 10.1016/j.compchemeng.2003.09.022CrossRefGoogle Scholar
  156. 156.
    Gao Y, Muzzio FJ, Ierapetritou MG (2011) Characterization of feeder effects on continuous solid mixing using Fourier series analysis. AIChE J 57(5):1144–1153Google Scholar
  157. 157.
    Yang S, Evans JRG (2007) Metering and dispensing of powder; the quest for new solid freeforming techniques. Powder Technol 178:56–72Google Scholar
  158. 158.
    Nakach M, Authelin J-R, Chamayou A, Dodds J (2004) Comparison of various milling technologies for grinding pharmaceutical powders. Int J Miner Process 74S:S173–S181Google Scholar
  159. 159.
    Reynolds GK (2010) Modelling of pharmaceutical granule size reduction in a conical screen mill. Chem Eng J 164:383–392Google Scholar
  160. 160.
    Verheezen JJAM, van der Voort Maarschalk K, Faassen F, Vromans H (2004) Milling of agglomerates in an impact mill. Int J Pharm 278:165–172Google Scholar
  161. 161.
    Vendola TA, Hancock BC (2008) The effect of mill type on two dry-granulated placebo formulations. Pharm Technol. 32(11)Google Scholar
  162. 162.
    Pernenkil L, Cooney CL (2006) A review on the continuous blending of powders. Chem Eng Sci 61(2):720–742. doi: 10.1016/j.ces.2005.06.016CrossRefGoogle Scholar
  163. 163.
    Portillo PM, Ierapetritou MG, Muzzio FJ (2008) Characterization of continuous convective powder mixing processes. Powder Technol 182(3):368–378. doi: 10.1016/j.powtec.2007.06.024CrossRefGoogle Scholar
  164. 164.
    Marikh K, Berthiaux H, Gatumel C, Mizonov V, Barantseva E (2008) Influence of stirrer type on mixture homogeneity in continuous powder mixing: a model case and a pharmaceutical case. Chem Eng Res Des 86(9A):1027–1037. doi: 10.1016/j.cherd.2008.04.001CrossRefGoogle Scholar
  165. 165.
    Vanarase AU, Muzzio FJ (2011) Effect of operating conditions and design parameters in a continuous powder mixer. Powder Technol 208(1):26–36. doi: 10.1016/j.powtec.2010.11.038CrossRefGoogle Scholar
  166. 166.
    Dhenge RM, Cartwright JJ, Hounslow MJ, Salman AD (2012) Twin screw wet granulation: effects of properties of granulation liquid. Powder Technol 229:126–136Google Scholar
  167. 167.
    Betz G, Junker-Burgin P, Leuenberger H (2003) Batch and continuous processing in the production of pharmaceutical granules. Pharmaceut Dev Tech 8(3):289–297Google Scholar
  168. 168.
    Vercruysse J, Córdoba Díaz D, Peeters E, Fonteyne M, Delaet U, Van Assche I, De Beer T (2012) Continuous twin screw granulation: influence of process variables on granule and tablet quality. Eur J Pharm Biopharm 82:205–211PubMedGoogle Scholar
  169. 169.
    Yu S, Gururajan B, Reynolds G, Roberts R, Adams MJ, Wu CY (2012) A comparative study of roll compaction of free-flowing and cohesive pharmaceutical powders. Int J Pharm 428:39–47PubMedGoogle Scholar
  170. 170.
    Kudra T, Mujumdar AS (2009) Advanced drying technologies, 2nd edn. Taylor & Francis Group, Boca Raton, FLGoogle Scholar
  171. 171.
    Paltzer S (2007) Drying of wet agglomerates in a continuous fluid bed: influence of residence time, air temperature and air-flowrate on the drying kinetics and the amount of oversize particles. Chem Eng Sci 62:463Google Scholar
  172. 172.
    Mortier ST, De Beer T, Gernaey KV, Vercruysse J, Fonteyne M, Remon JP, Vervaet C, Nopens I (2012) Mechanistic modelling of the drying behaviour of single pharmaceutical granules. Eur J Pharm Biopharm 80(3):682–689. doi: 10.1016/j.ejpb.2011.12.010CrossRefPubMedGoogle Scholar
  173. 173.
    Hovmand S (1995) Fluidized bed drying. In: Mujumdar AS (ed) Handbook of industrial drying, 2nd edn. Marcel Dekker, Inc., New York, NYGoogle Scholar
  174. 174.
    Carstensen JT, Zoglio MA (1982) Tray drying of pharmaceutical wet granulations. J Pharm Sci 71(1):35–39PubMedGoogle Scholar
  175. 175.
    McLoughlin CM, McMinn WAM, Magee TRA (2003) Microwave-vacuum drying of pharmaceutical powders. Dry Technol 21(9):1719–1733. doi: 10.1081/Drt-120025505CrossRefGoogle Scholar
  176. 176.
    Patel S, Kaushal AM, Bansal AK (2007) Effect of particle size and compression force on compaction behavior and derived mathematical parameters of compressibility. Pharm Res 24(1):111–124. doi: 10.1007/s11095-006-9129-8CrossRefPubMedGoogle Scholar
  177. 177.
    Jackson S, Sinka IC, Cocks AC (2007) The effect of suction during die fill on a rotary tablet press. Eur J Pharm Biopharm 65(2):253–256. doi: 10.1016/j.ejpb.2006.10.008CrossRefPubMedGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Chemical and Biochemical Engineering, School of EngineeringRutgers, The State University of New JerseyPiscatawayUSA

Personalised recommendations