Processes 2018, 6,82
24. Fadda, S.; Cincotti, A.; Cao, G. A novel population balance model to investigate the kinetics of in vitro cell
proliferation: Part I. model development. Biotechnol. Bioeng. 2012, 109, 772–781. [CrossRef][PubMed]
25. Jandt, U.; Platas Barradas, O.; Pörtner, R.; Zeng, A.P. Synchronized Mammalian Cell Culture: Part
II—Population Ensemble Modeling and Analysis for Development of Reproducible Processes. Biotechnol.
Prog. 2015, 31, 175–185. [CrossRef][PubMed]
26. Craven, S.; Whelan, J.; Glennon, B. Glucose concentration control of a fed-batch mammalian cell bioprocess
using a nonlinear model predictive controller. J. Process Control 2014, 24, 344–357. [CrossRef]
27. Sbarciog, M.; Coutinho, D.; Wouwer, A.V. A simple output-feedback strategy for the control of perfused
mammalian cell cultures. Control Eng. Pract. 2014, 32, 123–135. [CrossRef]
28. Amribt, Z.; Niu, H.X.; Bogaerts, P. Macroscopic modelling of overflow metabolism and model based
optimization of hybridoma cell fed-batch cultures. Biochem. Eng. J. 2013, 70, 196–209. [CrossRef]
29. Mantzaris, N.V.; Liou, J.J.; Daoutidis, P.; Srienc, F. Numerical solution of a mass structured cell population
balance model in an environment of changing substrate concentration. J. Biotechnol. 1999, 71, 157–174.
[CrossRef]
30. Farzan, P.; Mistry, B.; Ierapetritou, M.G. Review of the Important Challenges and Opportunities related to
Modeling of Mammalian Cell Bioreactors. AIChE J. 2017, 63, 398–408. [CrossRef]
31. Rocha, I. Model-Based Strategies for Computer-Aided Operation of Recombinant E. coli Fermentation; Universidade
do Minho: Braga, Portugal, 2003.
32. Lopez-Meza, J.; Araíz-Hernández, D.; Carrillo-Cocom, L.M.; López-Pacheco, F.; del Refugio Rocha-Pizaña, M.;
Alvarez, M.M. Using simple models to describe the kinetics of growth, glucose consumption, and monoclonal
antibody formation in naive and infliximab producer CHO cells. Cytotechnology 2016, 68, 1287–1300.
[CrossRef][PubMed]
33. Cachaza, E.M.; Díaz, M.E.; Montes, F.J.; Galán, M.A. Simultaneous Computational Fluid Dynamics (CFD)
simulation of the hydrodynamics and mass transfer in a partially aerated bubble column. Ind. Eng. Chem. Res.
2009, 48, 8685–8696. [CrossRef]
34. Wang, H.N.; Jia, X.; Wang, X.; Zhou, Z.; Wen, J.; Zhang, J. CFD modeling of hydrodynamic characteristics of
a gas-liquid two-phase stirred tank. Appl. Math. Model. 2014, 38, 63–92. [CrossRef]
35. Azargoshasb, H.; Mousavi, S.M.; Amani, T.; Jafari, A.; Nosrati, M. Three-phase CFD simulation coupled
with population balance equations of anaerobic syntrophic acidogenesis and methanogenesis reactions in
a continouos stirred bioreactor. J. Ind. Eng. Chem. 2015, 27, 207–217. [CrossRef]
36. Kerdouss, F.; Bannari, A.; Proulx, P.; Bannari, R.; Skrga, M.; Labrecque, Y. Two-phase mass transfer coefficient
prediction in stirred vessel with a CFD model. Comput. Chem. Eng. 2008, 32, 1943–1955. [CrossRef]
37. Micale, G.; Montante, G.; Grisafi, F.; Brucato, A.; Godfrey, J. CFD simulation of particle distribution in stirred
vessels. Chem. Eng. Res. Des. 2000, 78, 435–444. [CrossRef]
38. Farzan, P.; Ierapetritou, M.G. Integrated Modeling to Capture the Interaction of Physiology and Fluid
Dynamics in Biopharmaceutical Bioreactors. Comput. Chem. Eng. 2017, 97, 271–282. [CrossRef]
39. Bezzo, F.; Macchietto, S.; Pantelides, C.C. A general methodology for hybrid multizonal/CFD models: Part I.
Theoretical framework. Comput. Chem. Eng. 2004, 28, 501–511. [CrossRef]
40. Delafosse, A.; Collignon, M.L.; Calvo, S.; Delvigne, F.; Crine, M.; Thonart, P.; Toye, D. CFD-based
compartment model for description of mixing in bioreactors. Chem. Eng. Sci. 2014, 106, 76–85. [CrossRef]
41. Kagoshima, M.; Mann, R. Development of a networks-of-zones fluid mixing model for an unbaffled stirred
vessel used for precipitation. Chem. Eng. Sci. 2006, 61, 2852–2863. [CrossRef]
42. Vrabel, P.; Van der Lans, R.G.J.M.; Cui, Y.Q.; Luyben, K.C.A. Compartment model approach: Mixing in large
scale aerated reactors with multiple impellers. Chem. Eng. Res. Des. 1999, 77, 291–302. [CrossRef]
43. Bashiri, H.; Heniche, M.; Bertrand, F.; Chaouki, J. Compartmental modelling of turbulent fluid flow for the
scale-up of stirred tanks. Can. J. Chem. Eng. 2014, 92, 1070–1081. [CrossRef]
44. Vrabel, P.; van der Lans, R.G.; Luyben, K.C.A.; Boon, L.; Nienow, A.W. Mixing in large-scale vessels stirred
with multiple radial or radial and axial up-pumping impellers: Modelling and measurements. Chem. Eng.
Sci. 2000, 55, 5881–5896. [CrossRef]
45. Ishii, M.; Hibiki, T. Thermo-Fluid Dynamics of Two-Phase Flow; Springer: Berlin, Germany, 2011.
46. ANSYS Inc. ANSYS Fluent Theory Guide, Release 15.0 ed.; ANSYS Inc.: Canonsburg, PA, USA, 2013.
47. Schmalzriedt, S.; Jenne, M.; Mauch, K.; Reuss, M. Integration of physiology and fluid dynamics. In Process
Integration in Biochemical Engineering; Springer: Berlin, Germany, 2003; pp. 19–68.
128
24. Fadda, S.; Cincotti, A.; Cao, G. A novel population balance model to investigate the kinetics of in vitro cell
proliferation: Part I. model development. Biotechnol. Bioeng. 2012, 109, 772–781. [CrossRef][PubMed]
25. Jandt, U.; Platas Barradas, O.; Pörtner, R.; Zeng, A.P. Synchronized Mammalian Cell Culture: Part
II—Population Ensemble Modeling and Analysis for Development of Reproducible Processes. Biotechnol.
Prog. 2015, 31, 175–185. [CrossRef][PubMed]
26. Craven, S.; Whelan, J.; Glennon, B. Glucose concentration control of a fed-batch mammalian cell bioprocess
using a nonlinear model predictive controller. J. Process Control 2014, 24, 344–357. [CrossRef]
27. Sbarciog, M.; Coutinho, D.; Wouwer, A.V. A simple output-feedback strategy for the control of perfused
mammalian cell cultures. Control Eng. Pract. 2014, 32, 123–135. [CrossRef]
28. Amribt, Z.; Niu, H.X.; Bogaerts, P. Macroscopic modelling of overflow metabolism and model based
optimization of hybridoma cell fed-batch cultures. Biochem. Eng. J. 2013, 70, 196–209. [CrossRef]
29. Mantzaris, N.V.; Liou, J.J.; Daoutidis, P.; Srienc, F. Numerical solution of a mass structured cell population
balance model in an environment of changing substrate concentration. J. Biotechnol. 1999, 71, 157–174.
[CrossRef]
30. Farzan, P.; Mistry, B.; Ierapetritou, M.G. Review of the Important Challenges and Opportunities related to
Modeling of Mammalian Cell Bioreactors. AIChE J. 2017, 63, 398–408. [CrossRef]
31. Rocha, I. Model-Based Strategies for Computer-Aided Operation of Recombinant E. coli Fermentation; Universidade
do Minho: Braga, Portugal, 2003.
32. Lopez-Meza, J.; Araíz-Hernández, D.; Carrillo-Cocom, L.M.; López-Pacheco, F.; del Refugio Rocha-Pizaña, M.;
Alvarez, M.M. Using simple models to describe the kinetics of growth, glucose consumption, and monoclonal
antibody formation in naive and infliximab producer CHO cells. Cytotechnology 2016, 68, 1287–1300.
[CrossRef][PubMed]
33. Cachaza, E.M.; Díaz, M.E.; Montes, F.J.; Galán, M.A. Simultaneous Computational Fluid Dynamics (CFD)
simulation of the hydrodynamics and mass transfer in a partially aerated bubble column. Ind. Eng. Chem. Res.
2009, 48, 8685–8696. [CrossRef]
34. Wang, H.N.; Jia, X.; Wang, X.; Zhou, Z.; Wen, J.; Zhang, J. CFD modeling of hydrodynamic characteristics of
a gas-liquid two-phase stirred tank. Appl. Math. Model. 2014, 38, 63–92. [CrossRef]
35. Azargoshasb, H.; Mousavi, S.M.; Amani, T.; Jafari, A.; Nosrati, M. Three-phase CFD simulation coupled
with population balance equations of anaerobic syntrophic acidogenesis and methanogenesis reactions in
a continouos stirred bioreactor. J. Ind. Eng. Chem. 2015, 27, 207–217. [CrossRef]
36. Kerdouss, F.; Bannari, A.; Proulx, P.; Bannari, R.; Skrga, M.; Labrecque, Y. Two-phase mass transfer coefficient
prediction in stirred vessel with a CFD model. Comput. Chem. Eng. 2008, 32, 1943–1955. [CrossRef]
37. Micale, G.; Montante, G.; Grisafi, F.; Brucato, A.; Godfrey, J. CFD simulation of particle distribution in stirred
vessels. Chem. Eng. Res. Des. 2000, 78, 435–444. [CrossRef]
38. Farzan, P.; Ierapetritou, M.G. Integrated Modeling to Capture the Interaction of Physiology and Fluid
Dynamics in Biopharmaceutical Bioreactors. Comput. Chem. Eng. 2017, 97, 271–282. [CrossRef]
39. Bezzo, F.; Macchietto, S.; Pantelides, C.C. A general methodology for hybrid multizonal/CFD models: Part I.
Theoretical framework. Comput. Chem. Eng. 2004, 28, 501–511. [CrossRef]
40. Delafosse, A.; Collignon, M.L.; Calvo, S.; Delvigne, F.; Crine, M.; Thonart, P.; Toye, D. CFD-based
compartment model for description of mixing in bioreactors. Chem. Eng. Sci. 2014, 106, 76–85. [CrossRef]
41. Kagoshima, M.; Mann, R. Development of a networks-of-zones fluid mixing model for an unbaffled stirred
vessel used for precipitation. Chem. Eng. Sci. 2006, 61, 2852–2863. [CrossRef]
42. Vrabel, P.; Van der Lans, R.G.J.M.; Cui, Y.Q.; Luyben, K.C.A. Compartment model approach: Mixing in large
scale aerated reactors with multiple impellers. Chem. Eng. Res. Des. 1999, 77, 291–302. [CrossRef]
43. Bashiri, H.; Heniche, M.; Bertrand, F.; Chaouki, J. Compartmental modelling of turbulent fluid flow for the
scale-up of stirred tanks. Can. J. Chem. Eng. 2014, 92, 1070–1081. [CrossRef]
44. Vrabel, P.; van der Lans, R.G.; Luyben, K.C.A.; Boon, L.; Nienow, A.W. Mixing in large-scale vessels stirred
with multiple radial or radial and axial up-pumping impellers: Modelling and measurements. Chem. Eng.
Sci. 2000, 55, 5881–5896. [CrossRef]
45. Ishii, M.; Hibiki, T. Thermo-Fluid Dynamics of Two-Phase Flow; Springer: Berlin, Germany, 2011.
46. ANSYS Inc. ANSYS Fluent Theory Guide, Release 15.0 ed.; ANSYS Inc.: Canonsburg, PA, USA, 2013.
47. Schmalzriedt, S.; Jenne, M.; Mauch, K.; Reuss, M. Integration of physiology and fluid dynamics. In Process
Integration in Biochemical Engineering; Springer: Berlin, Germany, 2003; pp. 19–68.
128