Adv Biochem Eng Biotechnol (2021) 177: 229–254
https://doi.org/10.1007/10_2020_133
© Springer Nature Switzerland AG 2020
Published online: 26 September 2020
Euler-Lagrangian Simulations: A Proper
Tool for Predicting Cellular Performance
in Industrial Scale Bioreactors
Christopher Sarkizi Shams Hajian, Julia Zieringer, and Ralf Takors
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
2 Embedding Cells in Microenvironmental Heterogeneities of Bioreactors . . . . . . . . . . . . . . . . . 231
2.1 The Core Idea of Lifeline Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
2.2 How to Get Biologically Sound Readouts? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236
3 Lifeline Analysis in Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237
3.1 Eulerian Simulation Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238
3.2 Eulerian Simulation Outputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
3.3 Lagrangian Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
3.4 Lagrangian Readouts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
4 Scale-Down Examples and Methods from the Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
5 Advantages and Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
6 Conclusion and Outlook . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250
Abstract Eulerian-Lagrangian approach to investigate cellular responses in a bioreactor has become the center of attention in recent years. It was introduced to
biotechnological processes about two decades ago, but within the last few years, it
proved itself as a powerful tool to address scale-up and -down topics of bioprocesses.
It can capture the history of a cell and reveal invaluable information for, not only,
bioprocess control and design but also strain engineering. This way it will be
possible to shed light on the actual environment that cell experiences throughout
its lifespan. Lifelines of a microorganism in a bioreactor can serve as the missing link
that encompasses the biological timescales and the physical timescales. For this
purpose digitalization of bioreactors provides us with new insights that are not
C. S. S. Hajian, J. Zieringer, and R. Takors (*)
Institute of Biochemical Engineering, University of Stuttgart, Stuttgart, Germany
e-mail: takors@uni-stuttgart.de