model structure should be kept as simple as possible in the initial process design
phase and should then be extended if more data becomes available or novel
biological effects are identified.
In the application of digital twins within mDoE (see Fig. 3) during process design
and optimization with only a low number of available data, they structurally include
rather simple mathematical process models. These are based on the formulation of
mathematical links (i.e., equations) between cell growth, metabolism, and
corresponding product formation [63]. If partial mechanistics are unknown, they
can be modeled to gain a systematic understanding, although they might not be
measurable (e.g., in systems biology) [17, 41]. Such a mathematical process model
mainly works as an initial starting point to obtain a deeper process understanding
during the bioprocess life cycle.
3.1.1 Mathematical Model Structures
Mathematical modeling has already been the subject of controversial discussions in
recent years, and several models of varying complexity have been described in
literature [64–66]. In the early phases of bioprocess development, the mathematical
models used in mDoE mainly consist of simple model structures and should then be
extended stepwise. The model parameters considered should be determinable by
simple experiments since these include known mechanistics (e.g., ammonia formation based on glutamine uptake). It is favorable if models used for process optimization are applicable to a broad range of bioreactor scales [12, 64, 67]. Although the
application of mathematical process models for the development of sophisticated
processes has many advantages, it is still not commonly applied in bioprocess
development. Reasons for this include the variety and complexity of mathematical
models, e.g., different mechanistics and quality of predictions (recently reviewed in
[64]). Due to the complexity of biological processes, simple models might be
unsuitable for representing real phenomena. However, it has been suggested that
the growth of a cell line follows the same kinetics regardless of the cultivation
method, such as batch and fed-batch processes [65]. Nevertheless, even with complex models, the behavior of cells may change, and predictions can differ from
observed behavior. Reasons are the inadequate precision of the approximated model
coefficients and the complexity during the determination of the model parameters.
Therefore, a compromise between the accuracy of the model and the required
experimental effort for the determination of the parameters needs to be agreed on
for each application [68].
Bioprocess-related mathematical models are either classified according to the
description of the biophase, which is seen as an engineering-type approach or
based on the implemented model structure (e.g., neural networks, fuzzy logic).
This chapter focuses on biophase-classified models, which are historically sorted
according to their structural complexity, as shown in Fig. 4. Even if this classification was made in the 1990s, it is still valid for the class of models here discussed.
42
K. B. Kuchemüller et al.
phase and should then be extended if more data becomes available or novel
biological effects are identified.
In the application of digital twins within mDoE (see Fig. 3) during process design
and optimization with only a low number of available data, they structurally include
rather simple mathematical process models. These are based on the formulation of
mathematical links (i.e., equations) between cell growth, metabolism, and
corresponding product formation [63]. If partial mechanistics are unknown, they
can be modeled to gain a systematic understanding, although they might not be
measurable (e.g., in systems biology) [17, 41]. Such a mathematical process model
mainly works as an initial starting point to obtain a deeper process understanding
during the bioprocess life cycle.
3.1.1 Mathematical Model Structures
Mathematical modeling has already been the subject of controversial discussions in
recent years, and several models of varying complexity have been described in
literature [64–66]. In the early phases of bioprocess development, the mathematical
models used in mDoE mainly consist of simple model structures and should then be
extended stepwise. The model parameters considered should be determinable by
simple experiments since these include known mechanistics (e.g., ammonia formation based on glutamine uptake). It is favorable if models used for process optimization are applicable to a broad range of bioreactor scales [12, 64, 67]. Although the
application of mathematical process models for the development of sophisticated
processes has many advantages, it is still not commonly applied in bioprocess
development. Reasons for this include the variety and complexity of mathematical
models, e.g., different mechanistics and quality of predictions (recently reviewed in
[64]). Due to the complexity of biological processes, simple models might be
unsuitable for representing real phenomena. However, it has been suggested that
the growth of a cell line follows the same kinetics regardless of the cultivation
method, such as batch and fed-batch processes [65]. Nevertheless, even with complex models, the behavior of cells may change, and predictions can differ from
observed behavior. Reasons are the inadequate precision of the approximated model
coefficients and the complexity during the determination of the model parameters.
Therefore, a compromise between the accuracy of the model and the required
experimental effort for the determination of the parameters needs to be agreed on
for each application [68].
Bioprocess-related mathematical models are either classified according to the
description of the biophase, which is seen as an engineering-type approach or
based on the implemented model structure (e.g., neural networks, fuzzy logic).
This chapter focuses on biophase-classified models, which are historically sorted
according to their structural complexity, as shown in Fig. 4. Even if this classification was made in the 1990s, it is still valid for the class of models here discussed.
42
K. B. Kuchemüller et al.