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Mechanistic Mathematical Models as a Basis for Digital Twins

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Digital Twins

Part of the book series: Advances in Biochemical Engineering/Biotechnology ((ABE,volume 176))

Abstract

A future-oriented approach is the application of Digital Twins for process development, optimization and finally during manufacturing. Digital Twins are detailed virtual representations of bioprocesses with predictive capabilities. In biotechnology, Digital Twins can be used to monitor processes and to provide data for process control and optimization. Central and crucial components of Digital Twins are mathematical process models, which are capable to describe and predict cultivations with high fidelity. Detailed mechanistic models in particular are suitable for both use in Digital Twins and for the development of process control strategies.

In this chapter the requirements that process models must fulfil in order to be used for process optimization and finally in Digital Twins will be described. Different types of models, including mechanistic as well as compartmentalized models, are outlined and their application in Digital Twins and for process optimization is explained. Finally, a structured, compartmentalized process model, which was specifically designed for process optimization and has already been used in Digital Twins, is highlighted.

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Notes

  1. 1.

    “State variables” is a set of variables describing the (dynamic) state of a system. “State variables” are resulting from differential or algebraic equations, often the corresponding real quantities are measureable. “Parameters” in models are constant values in time. “Influencing factors” are factors that have an impact on the bioprocess quantities, examples are feeding rates, pH, temperature, etc.

Abbreviations

AA:

Amino acids

AI:

Artificial intelligence

Amm:

Ammonia

ANMPC:

Adaptive nonlinear model predictive control

ANN:

Artificial neural network

CHO:

Chinese hamster ovary

DNA:

Deoxyribonucleic acid

DO:

Dissolved oxygen

DTP:

Digital twin prototype

EtOH:

Ethanol

GFP:

Green fluorescent protein

Glc:

Glucose

Gln:

Glutamine

GSM:

Generalized structured modular

HAc:

Acetic acid

Ind:

Induction

IPTG:

Isopropyl-β-D-thiogalactopyranoside

Lac:

Lactate

mAb:

Monoclonal antibody

Mal:

Maltose

MPC:

Model predictive controller

NaCl:

Sodium chloride

NMPC:

Nonlinear model predictive control

OLFO:

Open-loop-feedback-optimal strategy

OTS:

Operator training simulator

OUR:

Oxygen uptake rate

P:

Product

PAT:

Process analytical technology

PC:

Product carbon

RNA:

Ribonucleic acid

SAA:

Substrate amino acid

SC:

Substrate carbon

SCM:

Structured compartment model

SM:

Structured model

SN:

Substrate nitrogen

Str:

Striatine

UI:

User interface

USM:

Unstructured model

YE:

Yeast extract

FV, in [m3 s−1]:

Total feed rate

Fi [m3 s−1]:

Feed rate of component i

KS [kg L−1]:

Half saturation constant

Ksl [−]:

Slope parameter (sigmoidal parameter)

X50, h [unit of x]:

Location parameter, high side of function (sigmoidal parameter)

X50, l [unit of x]:

Location parameter, low side of function (sigmoidal parameter)

Yh [−]:

Value at high x (sigmoidal parameter)

Yi/S [−]:

Yield coefficient

Yl [−]:

Value at low x (sigmoidal parameter)

Ymid [−]:

Value between X50,l and X50,h (sigmoidal parameter)

cS [g L−1]:

Concentration of substrate

ci, Feed [g L−1]:

Feed concentration of component i

ci [g L−1]:

Concentration of component i

ri− [s−1]:

Uptake rate

ri+ [s−1]:

Production rate

vi [−]:

Stoichiometric coefficient

μd [s−1]:

Specific death rate

F [m3 s−1]:

Feed rate

MWi [kg mol−1]:

Molecular weight of component i

S [g L−1]:

Substrate concentration

T [K]:

Temperature

V [m3]:

Volume

X [g L−1]:

Biomass

Xd [g L−1]:

Dead biomass

Xi [g L−1]:

Inactive biomass

Xp [g L−1]:

Product forming biomass

Xpri [g L−1]:

Active primary biomass

Xs [g L−1]:

Structural biomass

Xsi [g L−1]:

Structural inactive biomass

Xv [g L−1]:

Viable Biomass

n [−]:

Kinetic parameter

r [s−1]:

Rate

t [s]:

Time

α, β, γ, δ, ε [−]:

Stoichiometric parameters

μ [s−1]:

Specific growth rate

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Acknowledgments

The authors would like to thank C. Fittkau and M. Meissner for their laboratory work at Furtwangen University. We gratefully acknowledge the funding by the German Federal Ministry of Education and Research (BMBF) (mDoE-Toolbox-2; Grant No. 031B0577C).

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Authors and Affiliations

  1. Faculty of Medical and Life Sciences, Furtwangen University, Villingen-Schwenningen, Germany

    André Moser, Christian Appl & Volker C. Hass

  2. Department of Biochemical Engineering, University College London, London, UK

    Christian Appl & Volker C. Hass

  3. Thuenen Institute of Sea Fisheries, Bremerhaven, Germany

    Simone Brüning

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  1. André Moser
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  2. Christian Appl
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  3. Simone Brüning
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  4. Volker C. Hass
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Correspondence to Volker C. Hass .

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Editors and Affiliations

  1. Institute of Chemical, Environmental and Bioscience Engineering, Vienna University of Technology, Wien, Austria

    Christoph Herwig

  2. Institute of Bioprocess and Biosystems Engineering, Hamburg University of Technology, Hamburg, Germany

    Ralf Pörtner

  3. Institute of Bioprocess and Biosystems Engineering, Hamburg University of Technology, Hamburg, Germany

    Johannes Möller

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Moser, A., Appl, C., Brüning, S., Hass, V.C. (2020). Mechanistic Mathematical Models as a Basis for Digital Twins. In: Herwig, C., Pörtner, R., Möller, J. (eds) Digital Twins. Advances in Biochemical Engineering/Biotechnology, vol 176. Springer, Cham. https://doi.org/10.1007/10_2020_152

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