The number of runs is taken into account at the penultimate level. BBD is most
efficient with three or four factors. Compared to other designs, they require the least
number of runs [44]. However, even with optimal designs, the number of experiments can be user-defined and thus minimized. Only a model-dependent minimum
number must be included. For a quadratic regression model with four factors, e.g.,
the minimum number is 15, one term for the intercept, four linear terms, four purely
quadratic terms, and six cross-product terms must be taken into account. In the BBD
or CCD, the number of runs varies between 25 and 30, depending on the number of
center points [85]. LHSDs, on the other hand, require a large number of experiments
to fill the space and are therefore mainly used for computer simulations [86–88].
Finally, the choice of factor levels is decisive. In order to evaluate designs
optimally, they require at least three levels per factor [43]. In the BBD, the factors
are examined at three levels. However, no factor-level combinations are investigated
at the corner points, and thus, only a low prediction quality for extrema is available
[89]. LHSDs are also not suitable for the investigation of extrema [41]. The CCDs
contain five levels per factor [28]. In the optimal designs, the factor levels can also be
set user-specifically and combined as desired. However, it can happen that very few
test points are generated in the middle of the test area, which means that no
statements can be made concerning this area [38].
The selected design can then be implemented experimentally or in the mDoE (see
Sect. 4.3). It should be noted that the application of the selection scheme (Fig. 5) is
not limited to mDoE solely and it can be generally applied for the selection of DoE
designs.
4 Case Study: mDoE for Medium Optimization
As previously mentioned in Sect. 3.1, digital twins are used within the mDoE
concept to simulate and evaluate statistical DoE designs in silico. The application
of mDoE with a strong reduction in the number of experiments has been shown so
far for medium optimization, fed-batch design, and scale-up studies for antibodyproducing CHO cells, algae, and yeasts [11, 12, 61, 90]. During these studies, the
process understanding is stepwise increased and captured in the digital twin (i.e.,
mathematical process model). In the following, the application of mDoE is exemplarily discussed for the reduction of the factor boundary values for the optimization
of the glucose and glutamine concentrations in an antibody-producing cell culture
process. The specific workflow applied in this study is shown in Fig. 6.
In this case study, the dynamics of the bioprocess are modeled first, and the model
parameters are based on a few experimental data points. Then, the boundary values
of experimental designs are defined, and experimental settings are planned. Each
planned experiment is simulated, the responses (e.g., maximal product titer) are
calculated, and the response surfaces are determined. Based on these response
surfaces, the initially defined factor boundary values and the planned experiments
are evaluated, and only a few experiments are recommended to be performed. This
46
K. B. Kuchemüller et al.
efficient with three or four factors. Compared to other designs, they require the least
number of runs [44]. However, even with optimal designs, the number of experiments can be user-defined and thus minimized. Only a model-dependent minimum
number must be included. For a quadratic regression model with four factors, e.g.,
the minimum number is 15, one term for the intercept, four linear terms, four purely
quadratic terms, and six cross-product terms must be taken into account. In the BBD
or CCD, the number of runs varies between 25 and 30, depending on the number of
center points [85]. LHSDs, on the other hand, require a large number of experiments
to fill the space and are therefore mainly used for computer simulations [86–88].
Finally, the choice of factor levels is decisive. In order to evaluate designs
optimally, they require at least three levels per factor [43]. In the BBD, the factors
are examined at three levels. However, no factor-level combinations are investigated
at the corner points, and thus, only a low prediction quality for extrema is available
[89]. LHSDs are also not suitable for the investigation of extrema [41]. The CCDs
contain five levels per factor [28]. In the optimal designs, the factor levels can also be
set user-specifically and combined as desired. However, it can happen that very few
test points are generated in the middle of the test area, which means that no
statements can be made concerning this area [38].
The selected design can then be implemented experimentally or in the mDoE (see
Sect. 4.3). It should be noted that the application of the selection scheme (Fig. 5) is
not limited to mDoE solely and it can be generally applied for the selection of DoE
designs.
4 Case Study: mDoE for Medium Optimization
As previously mentioned in Sect. 3.1, digital twins are used within the mDoE
concept to simulate and evaluate statistical DoE designs in silico. The application
of mDoE with a strong reduction in the number of experiments has been shown so
far for medium optimization, fed-batch design, and scale-up studies for antibodyproducing CHO cells, algae, and yeasts [11, 12, 61, 90]. During these studies, the
process understanding is stepwise increased and captured in the digital twin (i.e.,
mathematical process model). In the following, the application of mDoE is exemplarily discussed for the reduction of the factor boundary values for the optimization
of the glucose and glutamine concentrations in an antibody-producing cell culture
process. The specific workflow applied in this study is shown in Fig. 6.
In this case study, the dynamics of the bioprocess are modeled first, and the model
parameters are based on a few experimental data points. Then, the boundary values
of experimental designs are defined, and experimental settings are planned. Each
planned experiment is simulated, the responses (e.g., maximal product titer) are
calculated, and the response surfaces are determined. Based on these response
surfaces, the initially defined factor boundary values and the planned experiments
are evaluated, and only a few experiments are recommended to be performed. This
46
K. B. Kuchemüller et al.