Determination of culture design spaces in shaken disposable cultivation systems for CHO suspension cell cultures

Abstract Processes involving mammalian cell cultures - especially CHO suspension cells - dominate biopharmaceutical manufacturing. These processes are usually developed in small scale orbitally shaken cultivation systems, and thoroughly characterizing these cultivation systems is crucial to their application in research and the subsequent scale-up to production processes. With the knowledge of process engineering parameters such as oxygen transfer rate, mixing time, and power input, in combination with the demands set by the biological production system, biomass growth and product yields can be anticipated and even increased. However, the available data sources for orbitally shaken cultivation systems are often incomplete and thus not sufficient enough to generate suitable cultivation requirements. Furthermore, process engineering knowledge is inapplicable if it is not linked to the physiological demands of the cells. In the current study, a simple yet comprehensive approach for the characterization and design space prediction of orbitally shaken single-use cultivation systems is presented, including the “classical” Erlenmeyer shake flask, the cylindrical TubeSpin bioreactor and the alternately designed Optimum Growth flask. Cultivations were performed inside and outside the design space to validate the defined culture conditions, so that cultivation success (desired specific growth rates and viable cell densities) could be achieved for each cultivation system.


Introduction
The steadily growing biopharmaceuticals market is dominated by products produced from mammalian cell cultures, and this approach is used by more than three quarters of biopharmaceutical manufacturers [1]. Currently, the primary driver for the development of new processes is through the use of Chinese hamster ovary (CHO) cells, from which monoclonal antibodies for therapeutic use and biosimilars are produced [1]. In most cases, studies investigating these new processes are carried out in small orbital shaken cultivation systems, such as multiwell plates, tubes, and shake flasks, allowing for cost-effective and efficient parallelized screening. The most widely used and best characterized orbital shaken cultivation system is the Erlenmeyer flask, which was developed by Emil Erlenmeyer in the 19th century and named after him years later [2,3]. Since, the material that is used, as well as the design of the Erlenmeyer flask, has undergone a number of adaptations. There are, for example, versions with narrow and wide necks, and with or without baffles. A wide variety of sterile barriers are also available [4]. Especially for CHO cells, unbaffled single-use Erlenmeyer flasks have proven to be the best option, as they reduce the likelihood of (cross-)contamination and preparation time. Since the basic geometric shape of unbaffled Erlenmeyer flasks causes the surface area of its contents to consistently decline as volume increases, this tapering can restrict the exchange of oxygen. As a result of this, the filling volume of CHO cell cultures in Erlenmeyer flasks is usually restricted to less than 40% of the nominal volume. In order to ensure a sufficiently large surface area at filling volumes over 40%, alternative geometries have been developed, such as the TubeSpin bioreactor [5][6][7] from TPP -Techno Plastic Products AG, which is based on centrifuge tubes, or the Optimum Growth flask [8,9] from Thomson Instrument Company, which increases the surface area and thus the filling volume through a higher angle of inclination compared to the conventional Erlenmeyer flask. However, it should be noted that the surface-to-volume ratio of TubeSpin bioreactors and Thomson flasks also decreases as the filling volume increases. This leads to a reduced specific interfacial area and consequently to a decrease in the oxygen transfer rate [10]. In addition, small scale stirred bioreactor systems have emerged, easing the challenges associated with scaling up and down.
Considering these alternatives, why should processes in orbitally shaken cultivation systems be further developed? Well, in tandem with the advantages of low price and effort, an understanding of the process engineering characteristics of shaken cultivation systems can allow for the investigation of the potential limiting factors of a cell line-medium combination. This knowledge can be utilized to multiparametrically determine the technical limitations of a bioprocess, allowing for process transfer/scale-up within a given design space, whereby the design space predicts cultivation success with a certain failure probability. The design space, which is described as a concept in the International Council for Harmonisation of Technical Requirements for Pharmaceuticals for Human Use (ICH) Q8 guideline, is a hypercube in which all factor combinations (e.g. shaking rate, filling volume, shaking diameter) can be applied without affecting the response specification (e.g. mixing time, specific power input). ICH defines the design space as "the multidimensional combination and interaction of input variables (e.g. material attributes) and process parameters that have been demonstrated to provide assurance of quality" [11]. Design spaces are increasingly used in the pharmaceutical industry as a tool for Quality by Design (QbD) [12]. QbD aims to meet customer demands consistently and efficiently. In contrast to Quality by Testing, QbD aims to build quality into the process, and ultimately the final product, during its development [13]. The above mentioned definition of a design space is exemplified by Abu-Absi et al. through the example of a CHO based monoclonal antibody production process [14]. In this study, the authors were able to determine critical process parameters in a scale-down model by varying process (e.g. dissolved oxygen, pH, agitation rate) and cell physiological (e.g. inital viable cell density, temperature shift) parameters [14].
The definition of a design space is based on the regression models Workflow for creating process engineering based cell culture design spaces. Suitable data from the literature and experiments are required to determine the demands of the biological system (combination of cell line and medium, left side) as well as the capabilities of the cultivation system being investigated (right side). Both must be connected and aligned with each other in order to determine critical and limiting process conditions. Here, a comparison is made between the oxygen uptake rate (OUR) of the suspension culture and the oxygen transfer rate (OTR) of the system (subsection 2.4), the critical mixing time at which metabolic changes in the cell culture can be expected (Θ M,crit ) with the 95% mixing time in the system (Θ M , subsection 2.3), and the cell size (l cell ) with the Kolmogorov scale of micro turbulence (λ K , subsection 2.5). Based on this data, the design space can be generated, which is subsequently verified through cultivation. If necessary, the cultivation data obtained in this way can be used to improve cell line characterization.
created and an estimate of the failure probability. For the former, a design of experiments (DoE) approach is preferably used. The probability of obtaining predictions outside the response specifications corresponds to the failure probability and can be calculated according to Kane [15]. For the development of a design space, the Monte Carlo simulation method may be used [16,17]. In this study, process engineering and cell physiological data are combined to create a culture design space for orbitally shaken cultivation systems. Using a 500 mL Erlenmeyer flask for the cultivation of a CHO cell line (CHO XM111-10), all process steps are described. First, the capacities of the cultivation system and potential limitations of the cell line are identified. Subsequently, the design space is created based on the determined data. Afterwards, cultivations are performed within and outside the selected limits, along with a process transfer to a TubeSpin and Optimum Growth flask.

General approach
The approach of this work is depicted in Fig. 1. Both literature and experimental data can be used to characterize the cell line (left side) and the cultivation system (right side), so both will be compared in the following subsections. In the case of doubt, self-obtained experimental values are to be preferred, since deviations due to modified cell lines, measurement techniques etc. can have a considerable influence. For orbitally shaken cultivation systems, three critical parameters have been defined for which the demands of the cell line can be compared with the procedural properties of the cultivation system: • The cell specific oxygen demand and thus the oxygen uptake rate (OUR) must be matched by the oxygen transport capabilities of the cultivation system (oxygen transfer rate OTR). • A metabolic response to substrate limitation, accumulation of inhibiting metabolites or pH-gradients has to be avoided and thus, a sufficient degree of uniformity must be guaranteed.
• Cell damage or growth reduction caused by fluid mechanical stress has to be avoided. This can be achieved by predicting the minimal eddy size by means of volumetric power input calculation and thus ensure eddy sizes greater than the cell sizes.
With all the data gathered, a design space can be created which depicts the risk of not meeting the selected criteria. Cultivations can then be performed at presumably favorable and unfavorable conditions to verify the concept in one cultivation system. Experiments can be assessed in different ways, such as by evaluating biomass growth over maximum specific growth rate and maximum cell density or productivity over product quality and quantity. To reduce the effects of media variation and ensure comparability with other studies, the maximum specific growth rate μ max is used as the main comparison criterion for evaluating the process engineering effects [18]. In the case of significant deviations, the assumptions made (especially on the cell line characterization side) have to be reviewed. Otherwise, the concept can be transferred to other process engineering characterized cultivation systems.
However, it must be noted that various factors besides the process engineering settings can limit growth and product formation in a biotechnological process [19]. Therefore, to evaluate the influence of process engineering parameters on cultivation success, variations resulting from media and inoculum preparation must be avoided. The following sections describe how characteristics of the engineering and cell line data were determined and design spaces were created.

Investigation space
All of the examined cultivation systems are depicted in Fig. 2. The investigation space that was utilized for the 50 mL TubeSpin (TS50), the 500 mL Erlenmeyer flask (EF500), the 500 mL Optimum Growth flask (OG500), the 600 mL TubeSpin (TS600) and the 5000 mL Optimum Growth flask (OG5000) is summarized in Table 1. All process engineering characterizations and cultivations were set within these limits. The selected attributes (filling volume, shaking rate, and shaking diameter) all had a significant influence on the investigated engineering parameters. The chosen limits were based on frequently used literature values, except for the maximum shaking rate, which was set higher to investigate the shear sensitivity of the cells. The distribution of individual measuring points in the process engineering characterization design space was realized via a central composite face centered (CCF) DoE approach. A central composite design was chosen because it produces similar results to full factorial designs with a reduced number of experiments [20]. The CCF solution is a compromise: a larger process space is covered compared to a central composite inscribed (CCI) design, while at the same time all experiments are conducted within the technical limits (for example, the maximum shaking rate), which are exceeded using a broader central composite circumscribed (CCC) design [21]. Using the DoE software MODDE 12 (Sartorius AG, Göttingen, Germany), models were created to interpolate the mixing time, k L a, and power input values between the measuring points.

Mixing time
In contrast to oxygen saturation or fluid dynamic stress considerations, exact values regarding limiting respectively critical mixing times are rarely published. In general, mixing times below 30 s at laboratory scale (≤ 10 L) [22] and 2 min at production scale (≥ 100 L) [23] seem to be important to avoid the potential limitations of oxygen, pH, and nutrient gradients. With an unspecified CHO cell line which was exposed to an oxygen gradient, Anane et al. were able to demonstrate that a mixing time greater than 90 s resulted in a clear-cut metabolic switch [24]. Thus, when this mixing time was exceeded, lactate accumulation increased and the viable cell density was lower compared to the control process. This, however, had no effect on productivity, but it did have an impact on product purity. Xu et al. also showed that insufficient mixing and high CO 2 concentrations caused lactate accumulation [25]. However, lactate did not accumulate at lower mixing times. The effect of pH fluctuations on cell growth and product formation rates with two different CHO cell lines was investigated by Paul et al. [26]. Such pH fluctuations are expected especially in large bioreactors with high mixing times and resulted in reduced, maximum cell densities in the scale-down model. Platas Barradas et al. found the highest growth rates at lab scale at mixing times between 10 and 12 s and already detected reduced growth rates at mixing times of 20 s [18]. When considering mixing, constant suspension of the cells should be assumed, since cell sedimentation leads to insufficient mass transfer and thus to reduced growth or cell death.
Experimentally determined mixing time values for orbitally shaken cultivation systems have been published by Tan et al. [27], Rodriguez et al. [28,29], and Monteil et al. [30]. However, as the literature data was incomplete for the investigated systems, the mixing time was determined by the decolorization method [27,31,32], based on the recommendation of the DECHEMA expert group for single-use technology [33]. To accomplish this, flasks were filled with water and 5 mL L −1 of a 10 g L −1 starch (Sigma-Aldrich, St. Louis, USA) solution, together with 2 mL L −1 iodide/potassium iodide (Sigma-Aldrich) solution (consisting of 20 g L −1 iodine and 40 g L −1 potassium iodide), resulting in a dark blue bulk solution. The decolorization process commenced with the sudden addition of sodium thiosulfate (Sigma-Aldrich) solution (24.8 g L −1 sodium thiosulfate pentahydrate). The mixing time was defined as the period between the addition of the thiosulfate and the complete decolorization of the bulk solution. The decolorization times were measured manually in triplicate, at 25 ∘ C within the designated investigation space (Table 1) in a Multitron Cell shaking incubator (Infors AG, Bottmingen, Switzerland).

Cell oxygen demand and oxygen transfer rate
A sufficient supply and avoidance of fluctuations in dissolved oxygen concentration are critical for optimal growth of CHO cell suspension cultures. Adequate oxygen supply can be achieved if the oxygen transfer rate (OTR) is greater or equal to the oxygen uptake rate (OUR). The OTR consists of the volumetric mass transfer coefficient k L a, the dissolved oxygen concentration at the gas liquid interphase c * O2,L and the measured or desired dissolved oxygen concentration in the liquid c O2,L . The OUR can be calculated as the product of the viable biomass concentration c x and the cell specific oxygen uptake rate q O2 (Eq. 1).
The cell specific oxygen uptake rate must first be measured or obtained from suitable sources in the literature. A thorough overview of the oxygen demand of different cell lines is provided by Wagner et al. [34], and extensive summaries of different measurement methods and values are provided by Garcia-Ochoa et al. [35] and Seidel et al. [36]. A synopsis of literature q O2 -values is depicted in Fig. 3. It can be seen that for CHO cells, the outliers extend over two orders of magnitude, which can be explained among other things by different clones (e.g. DG44, SSF3, K1), process modes (batch, fed-batch, perfusion) and measurement methods (e.g. by gas-phase mass balance, dynamic evaluation or dissolved oxygen concentration profile calculation). Measuring the cell specific oxygen uptake rate for an investigated CHO clone is therefore recommended.
The dependence of the volumetric mass transfer coefficient k L a from process conditions in orbitally shaken cultivation systems has been extensively investigated over the past decades. Different approaches have been summarized by Meier et al., including a new correlation for estimating the OTR in unbaffled Erlenmeyer flasks [81]. However, the oxygen transfer in shaken vessels is significantly influenced by a thin layer build of the liquid on the inside of the flask. Maier and Büchs were able to show that hydrophilic surfaces (e.g. classic glass Erlenmeyer flasks) generate higher oxygen transfer rates compared to vessels with hydrophobic surfaces (e.g. plastic flasks) [82], proving that the material should not be ignored when taking literature data into consideration. No complete data on the k L a-value could be found for the single-use systems investigated. Therefore, the determination of the k L a-values was performed according to the DECHEMA expert group recommendations for single-use technology [33], whereby the gassing-out method [83,84] was used. The dissolved oxygen concentration was measured using the shake flask reader and the selected shaken vessel with SP-PSt3-NAU oxygen sensor spots (PreSens Precision Sensing GmbH, Regensburg, Germany). The sensor spots have a response time t 63%,crit of approximately 14 s, which allows for the measurement of k L a-values up to 250 h −1 using the van't Riet criterion [85] or up to 50 h −1 using the more restrictive approach by Zlokarnik [86]. The cultivation system was filled to the appropriate volume with 1 x phosphate buffered saline (PBS) solution (Sigma-Aldrich) and tempered to 37 ∘ C. Afterwards, oxygen was removed from the system by gassing the bulk solution with nitrogen until a concentration of less than 5% was achieved. Then, by shaking the system, it was (passively) gassed with air until an air saturation of more than 95% was reached. The k L a-values were calculated between 10% and 90% air saturation.

Specific power input and potential of fluid dynamic stress
Several publications deal with the potential impairments of growth and product expression in CHO cell cultures due to fluid dynamic stress (often called mechanical/shear stress) [18,[87][88][89][90], but the concepts which quantify this stress vary. Often used approaches are based on the volumetric power input, the energy dissipation rate or the size of the micro-turbulence generated. Chalmers has summarized various studies with lethal and sub-lethal cell responses to mechanical stress, with lethal responses ranging from energy dissipation rates of 6 ⋅ 10 6 W m −3 (CHO-GS cells) to 10 8 W m −3 (wild type suspended CHO-K1 cells) [87]. Such a wide data range is another example of the problems associated with literature values for dramatically varying experimental conditions. Another approach utilizes the Kolmogorov scale of turbulence. Kolmogorov's microscale theory describes the formation of smaller eddies by the breakup of large scale turbulent eddies as a cascading process. At the Kolmogorov scale of turbulence, viscous and inertial forces compensate each other and the energy from the eddies dissipates [91]. Cell damage arising from the fluid dynamics is thought to occur if the micro eddies produced by the cultivation system are smaller or similar in size to the cells [90,92]. Thus, keeping the eddy size above 18 μm -the typical upper size of CHO cells -should prevent fluid dynamic damage [91].
Büchs et al. determined the power input in glass Erlenmeyer flasks with torque measurements in the shaking incubator while counterbalancing the friction losses, whereby power inputs up to 6 kW m −3 were measured [93]. Utilizing the power input P/V and the liquid density ρ L , the average energy dissipation rate ε in unbaffled Erlenmeyer flasks can be calculated using Eq. 2 [94].
In unbaffled flasks, the ratio between the average and maximum energy dissipation rate below the critical Reynolds number of 60 000 is approximately 1 and indicates non-turbulent flow [95]. For baffled shake flasks and for Reynolds numbers above 60 000, the maximum energy dissipation rate ε max can be calculated analogous to stirred tanks, using the relative motion of the liquid π ⋅ N ⋅ d i (with the shaking rate N and the maximum inner diameter d i ) and the height of the liquid h L as the characteristic length (Eq. 3) [95].
Finally, the length of the microscale λ K can be calculated according to the Kolmogorov approach (Eq. 4), using the maximum energy dissipation rate and the kinematic viscosity of the liquid ν L .
The volumetric power input was determined using computational fluid dynamics (CFD). All simulations were carried out with the open source software OpenFOAM (www.openfoam.org), version 5. The underlying simulation method was validated by Klöckner et al., where the method is described in detail [96]. The computer aided design (CAD) geometry was manually generated using Autodesk Inventor, version 2020. The number of grid cells generated was 213 297 for the 500 mL Optimum Growth flask and 824 261 cells for the 5000 mL flask, 34 804 for the 50 mL TubeSpin and 156 626 for the 600 mL TubeSpin as well as 137 452 for the 500 mL Corning Erlenmeyer flask. Physical properties were set to conditions at 25 ∘ C, which corresponds with a water density of 997.05 kg m −3 , a dynamic viscosity of water of 890.02 ⋅ 10 −6 Pa s −1 , an air density of 1.17 kg m −3 , and a dynamic viscosity of air of 18.93 ⋅ 10 −6 Pa s −1 [97, p. 201-220]. The water-surface contact angle was set to 83 ∘ for polycarbonate (Corning) and 97 ∘ for polypropylene cultivation systems (Optimum Growth and TubeSpin) [98]. The applied transient solver interDyMFoam was used with the k-ω SST turbulence model [99]. Twenty seconds were simulated to anticipate stationary conditions. For every shaking rate, one further period was simulated for power input evaluation.

Cultivation of CHO suspension cells
The utilized CHO suspension cell line XM111-10 (established by Prof. Dr. Martin Fussenegger and team, ETH Zürich, Switzerland [100]; CCOS 837) was cultivated in all investigated cultivation systems. CHO XM111-10 is a model cell line that produces secreted alkaline phosphatase (SEAP) using a tetracycline induced switch-off system (tet-off) [101]. Under non-limiting conditions, the suspension cell culture grown in chemically defined minimal media has a doubling time of approximately 18 h and a peak viable cell density of 4 ⋅ 10 6 cells mL −1 , as demonstrated in a traveling wave [102] or stirred tank bioreactor [103]. After a further 48 h, the cell suspension was transferred into orbitally shaken 1 L flasks (Corning Inc.) for 72 h and finally into the investigated cultivation system, whereby seeding cell densities of 0.5 ± 0.1 ⋅ 10 −6 cells mL −1 were used. The ChoMaster HP-1 medium (Cell Culture Technologies), supplemented with 1 mmol L −1 L-glutamine (G5792, Sigma-Aldrich), 10mL L −1 Pluronic F68 (A1288, Appli-Chem GmbH, Darmstadt, Germany) and 2.5 mg L −1 tetracycline (T7660, Sigma-Aldrich) was used for all orbitally shaken experiments. All cultivations were performed at 37 ∘ C with 7.5% CO 2 saturation and 80% humidity (measured within the shaker unit) at shaking diameters of 25 and 50 mm (Multritron Cell, Infors AG). The filling volume and the shaking rate were varied in an expedient range set by the process engineering characterization, except for the inoculum preparation, which was carried out at 120 rpm, 50 mm and 300 mL filling volume. Cell density (Innovatis Cedex, Roche Diagnostics, Rotkreuz, Switzerland) was measured every 24 h.

Design space creation and Monte Carlo simulation
To predict the cultivation success, and conversely the probability of failure, a two-dimensional design space was created for each cultivation system and shaking diameter using the filling volume and shaking rate. The response used was the combination of mixing time Θ M , k L a-value and volumetric power input P/V. This design space corresponds to the concept of ICH [11]. To calculate the probability of failure in the design space, a partitioning into 500 × 500 parts was carried out, followed by a Monte Carlo simulation with 10 000 steps in each case. A normally distributed error was added for each factor with a standard deviation of ± 5% of the factor range [104]. Using a confidence interval of 95% and a standard deviation of 5%, 9 604 iterations are required to obtain a maximum error of 0.1% [105]. In order to undercut the error, 10 000 iterations were chosen. Simulations with at least one value outside the acceptance range were marked as errors, resulting in a probability of error. The boundaries of the individual factors (shaking rate, filling volume) for the design space correspond to the experimental space (see Table 1). The acceptance range was defined by the authors (subsection 3.3) and was a maximum of 20 s for the mixing time, a maximum of 900 W m −3 for the volumetric power input and a minimum of 10.5 h −1 for the volumetric mass transfer coefficient. The process capability indices and therefore the probabilities of failure were calculated according to Kane [15]. The Monte Carlo simulation was carried out in parallel using the message passing interface on a high-performance computer (Linux CentOS 7.5.1804) with Python 3.6.5 [106].

Results and discussion
In this section, the process engineering results are first evaluated and the Kolmogorov approach for orbital shaken cultivation systems is reviewed. Subsequently, the creation of a design space is shown using the 500 mL Erlenmeyer flask as an example before presenting the evaluation of the cultivation systems studied. A detailed review of all cultivation systems is provided in the appendix.

Process engineering characterization
In Fig. 4, the ranges in values that were found in the process engineering investigations are summarized for all systems. In the investigated space, major differences in the process engineering parameters occurred. In each cultivation system, mixing times below 3 s could be achieved, yet, especially in the 5 L Optimum Growth flask, mixing times could reach several minutes and thus may negatively affect cell growth. At low shaking rates and high filling volumes, all systems were characterized by low k L a values. Nevertheless, using high shaking rates and low filling volumes, both 500 mL flasks produced k L a values over 100 h −1 whilst the 600 mL TubeSpin and the 5000 mL Optimum Growth flask reached values above 60 h −1 . It should be mentioned that oxygen transfer in the TubeSpin bioreactors could be further increased by using even lower filling volumes or an angled mount inside the shaker [107], but these conditions were not investigated in this study. The volumetric power input varied between 1 W m −3 (maximum filling volume, minimum shaking rate, 25 mm shaking diameter) and several kW m −3 , whereby by far the highest values could be achieved in the 600 mL TubeSpin (2.3 kW m −3 ) and the 5000 mL Optimum Growth (3.7 kW m −3 ). Thus, a wide range of favorable and unfavorable conditions could be found in the five selected cultivation systems.

CHO XM111-10 suspension culture limitations
The inoculum preparation approach described in subsection 2.6 was also used for cell growth limitation studies. Hence, the success of a cultivation should only be affected by process engineering variations. The preliminary experiments were performed in 500 mL Erlenmeyer flasks, as these often serve as a standard cultivation vessel for comparative studies. As can be seen in Fig. 3, the oxygen demand of a CHO cell line varies significantly, depending on the clone and cultivation conditions. Thus, for the investigated CHO XM 111-10 cell line, the specific oxygen demand of 2.8 ⋅ 10 −13 mol O2 cell −1 h −1 was experimentally determined. This can be translated to a minimal k L a using Eq. 1. If, for example, a minimum oxygen concentration of 30% with a maximum expected cell density of 5 ⋅ 10 6 cells mL −1 is required, a k L a of 10.5 h −1 is needed to ensure oxygen supply. Please note that this k L a-value is slightly higher as it would be in an acid controlled stirred bioreactor (9.7 h −1 ) due to the 7.5% CO 2 in the incubator atmosphere. The maximum tolerable mixing time was set to 20 s according to Platas Barradas et al. [18]. Determining a critical power input or energy dissipation rate proved to be difficult because (as Chalmers was able to impressively show [87]) limitations or (sub-)lethal effects occur at different values. Therefore, the Kolmogorov microturbulence concept was adopted (Eq. 4) and the maximum energy dissipation rate (Eq. 3) was calculated. The threshold proposed by Peter [95] was used and compared against the created eddy sizes for given volumetric power inputs (Fig. 5). Only with the onset of full turbulent flow and thus an ε max > ε, a vortex size in the order of magnitude of CHO XM111-10 cells was reached. The micro eddies thus reached a critical size in the range of 1 kW m −3 , a value that occurred at 275 rpm, 50 mm and 100 mL in 500 mL Erlenmeyer flaks, for example.

Creating of cell culture design spaces
The limits found in the previous section can now be used to create design spaces. This allows for the verification of all process engineering parameters at the same time. In summary, the following threshold values are used: • A mixing time Θ M of 20 s as the upper limit • A k L a-value of at least 10.5 h −1 based on a q O2 of 2.8 ⋅ 10 −13 mol O2 cell −1 h −1 and a maximum cell density of 5 ⋅ 10 6 cells mL −1 • A maximum volumetric power input P/V of 900 Wm −3 , leading to eddy sizes above 20 μm Utilizing these limitations, a design space for every cultivation system was created from which the probability of failure (green to red) with all specifications is visible. As an example, the design space for the 500 mL Erlenmeyer flask is depicted in Fig. 6. Cultivations (presented as white dots) were performed inside and outside the recommended parameter combinations (green area) to evaluate the chosen limitations. If the selected parameter combination cannot be achieved at any point in the system (no green area), a successful cultivation is still possible, but cannot be expected with certainty. Experiments were evaluated primarily by the maximum specific growth rate, which was determined by maximizing the fit of an exponential function. The maximum viable cell density (VCD max ) was used as a plausibility check, so that an experiment with μ max > 0.04 h −1 (doubling time t d of 17.33 h and VCD max > 3⋅10 6 cells mL -1 could be considered successful.

Cultivation results
To verify the design space approach, the 500 mL Erlenmeyer flask was investigated in a first step (with 50 mm shaking diameter, Fig. 7). It was quite clearly demonstrated that experiments within the sweet spot (the green zone in Fig. 7, defined by a probability of failure below 1%) performed as desired (μ max > 0.04 h −1 , t d < 17.33 h), whereas the experiments in the peripheral areas resulted in a reduced maximum specific growth rate (μ max < 0.04 h −1 ). The experiments at 110 rpm (outside of the sweet spot but with error probabilities < 50%) also showed the desired maximum specific growth rates, illustrating that exceeding the sweet spot is not immediately associated with a loss of specific growth rate. This can be explained by the still sufficiently high k L a values (> 10 h −1 ) and low mixing times (< 25 s). However, at 80 rpm and 200 mL filling volume, reduced maximum specific growth rates were measurable (0.03 h −1 < μ max < 0.04 h −1 ), which can be explained by the lower k L a value (50% of the target at 200 mL) and mixing times above 30 s. At 300 rpm, in contrast, the cells stopped growing almost completely, which can be explained by the high energy input and the resulting fluid dynamic stress caused by the small eddies. Similar results can be seen using a shaking diameter of 25 mm, where in the case of 80 rpm and 200 mL, sedimentation of the cells could be observed (see appendix). In  summary, the growth of CHO cells in the 500 mL Erlenmeyer flask can be well predicted using the process engineering characterization based design space.
The TubeSpin bioreactors behaved somewhat differently due to their basic cylindrical shape, as the example of the 600 mL TubeSpin at 25 mm shaking diameter demonstrates (Fig. 8). Within the design space (at 160, 200 and 250 rpm), the cultivations proceeded as desired. However, at 110 rpm (corresponding to a mixing time of approximately one minute), the cells sedimented, causing the experiment to fail. Utilizing a shaking rate of 300 rpm and hence power inputs from 0.9 (400 mL) to 1 kW m −3 (200 mL), the cells formed macroscopically visible agglomerates and minor growth. Again, the high predictability of the cultivation success was shown by the process engineering limits set in the design space. However, the failure rate in the extreme ranges was much more pronounced compared to the Erlenmeyer flask, which can be explained by the cylindrical shape and the associated significantly increased filling height. Similar effects could be seen for the 50 mL and the 600 mL TubeSpin with 50 mm shaking diameter, whereas sedimentation was more pronounced at 25 mm (see appendix for the design spaces).
The 500 mL Optimum Growth flask showed similar behavior to the 500 mL Erlenmeyer flask, although the higher maximum filling volume may have a negative effect on cultivation success at low shaking rates and high filling volumes (e.g. at 90 rpm, 250 mL and 25 mm shaking diameter), which can be justified by poorer mixing. This effect is even more visible with the 5 L Optimum Growth flask, so it is recommended to avoid combining a high filling volume with a lower shaking rate when using these flasks. At the same time, the larger inner diameter leads to high power inputs at shaking rates > 200 rpm, through which the sweet spot in this cultivation system is significantly smaller (the corresponding design spaces can be found in the appendix.) Interestingly, the 5 L flask with a 3 L filling volume could not achieve the desired maximum specific growth rates and cell densities within the sweet spot, revealing a weakness in the design space concept. At the maximum filling volume and shaking rates > 110 rpm, a foam layer several centimeters high formed, which limited the oxygen transfer and was not evident from the process engineering investigations. Comparing the maximum specific growth rates of all experiments, it can be seen that the median for all is between 0.033 and 0.042 h −1 . The 500 mL Erlenmeyer and Optimum Growth flask are characterized by the highest median specific growth rates (0.041 and 0.043 h −1 , respectively) with a smaller interquartile range, which demonstrates the relative independence of the selected process engineering parameter combinations. Both TubeSpin bioreactors are distinguished by more outliers and failed experiments due to cell sedimentation, reflecting a more limited set of parameters.

Conclusion
The application of characterization-based process engineering, multi parameter design spaces is a promising way to improve cultivation success in orbitally shaken cultivation systems. This was demonstrated with the investigation of differently shaped cultivation systems (Erlenmeyer flask, TubeSpin bioreactor and Optimum Growth flask) utilizing CHO XM111-10 cells. Within the sweet spot (the region in the design space with an error probability below 1%), the experiments showed targeted maximum specific growth rates (μ max > 0.04 h −1 ) and cell densities (VCD max > 3⋅10 6 cells mL −1 ). In its immediate vicinity, both ideal and slightly reduced maximum specific growth rates were observed, whereas cultivations in the peripheral areas often led to failures due to lack of mixing, sedimentation, reduced oxygen availability or high fluid dynamic stress. Extreme conditions atypical for mammalian cell cultures (for example, volumetric power inputs exceeding 1 kW m −3 ) were selected to demonstrate the applicability of the Kolmogorov eddy size concept for predicting stress-induced limitations in shake flasks. As predicted, growth reduction occurred once the minimum vortex size equaled the cell size. This may be less of a limiting factor for CHO suspension cells in shake flasks, but may be critical when applying the approach of this case study to highly aggregating (e.g. HEK 293) or larger cells (e.g. plants suspension cultures) or microcarrier-dependent cell lines (e.g. stem cells).
For the user, this means that combinations of shaking rate, filling volume and shaking diameter which ensure results within the sweet spot can be used for this investigated cell line to achieve comparable results with targeted growth rates and cell densities. For implementation, the process engineering data of the cultivation systems as well as potentially critical factors of the cell lines must be known or determined. It should be noted that in this study, broad design spaces were deliberately selected, which require an increased number of process engineering experiments. This has the advantage that no further characterization is necessary when transferring to other cell lines. However, the process engineering experimental effort can be significantly reduced by appropriately preselecting parameters. After the initial characterization step, the approach can be used in different ways: First, cultivation success can be ensured in orbitally shaken systems (for instance for inoculum production), even if factors such as vessel size, shaking rate or filling volume change. Furthermore, the approachby adapting the cell line-specific limitations (cell size and associated sensitivity to fluid dynamic stress, cell-specific oxygen demand, and metabolic influences due to insufficient mixing) -can be used for other cell lines with little effort. The data required for this purpose can be obtained from suitable literature or experiments and compared with the already known characteristics of the cultivation systems, although proof-of-concept cultivations are recommended. Finally, the chosen approach can also be used for non-shaken cultivation systems, since the mixing time, k L a value or power input can be determined for stirred or well-mixed bioreactors as well. This allows for better comparability between differently powered cultivation systems as well as a simplified scale-up, since the used and confirmed cell specific limits for oxygen supply, mixing time and mechanical damage can be transferred. The chosen approach thus allows for cultivations with the desired growth in different orbital shaken cultivation systems, a characterization of the selected cell line and hence knowledge for the transfer to larger systems, just with simple means and without additional sensorsbased on procedural characterization alone.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
The approach outlined in this publication is applied in this digital appendix to all systems as a case study to ensure replicability and to enable application to other cell lines. The process characterization (Θ M , k L a, P/V) is performed as described in chapter 2. Based on this, mathematical derivations are created, which can be used for the selected system for all potential cell lines. For CHO XM111-10 (the selected cell line for this case study), we defined the following critical parameters: Knowing the limitations of the cell line, the process engineering parameters can be set accordingly to create the design spaces with the following desirable conditions: • A mixing time Θ M below 20 s • A k L a-value above 10.5 h −1 • A volumetric power input P/V below 900 W m −3 , leading to eddy sizes above 20 μm With these settings, the design spaces were created (adapted to the engineering parameters of every system and the requirements for the CHO XM111-10 cell line) and cultivations were conducted. The following evaluation was applied: • Successful cultivations with a μ max > 0.04 h −1 and a VCD max > 3 ⋅ 10 6 cells mL −1 are indicated with green dots.
• Cultivations with poor performance μ max < 0.03 h −1 are indicated with red squares.
• Black squares indicate experiments without growth, e.g. due to cell sedimentation.

mL Erlenmeyer flask
The design space of the 500 mL Erlenmeyer flask proved to be robust (Fig. 9). In the range of 80-250 rpm, successful cultivations can be expected at both shaking diameter regardless of the filling volume. The only exception is the combination of the minimum shaking rate (80 rpm) with the maximum filling volume (200 mL), which leads to sedimentation at 25 mm shaking diameter and reduced growth at 50 mm. At the maximum shaking rate (300 rpm), the critical vortex size of 20 μm is undercut, resulting in slow growth with maximum cell densities of 1 ⋅ 10 6 cells mL −1 and a 3-4 d lag phase.

mL Optimum Growth flask
Compared to the 500 mL Erlenmeyer flask, the sweet spot for the 500 mL Optimum Growth flask at 25 mm shaking diameter is smaller (Fig. 10).
Especially at high filling volumes (250 mL) with low shaking rates, the cells may grow poorly (VCD max of 1.67 ⋅ 10 6 cells mL −1 and μ max of 0.02 h −1 at 90 rpm) or with a reduced maximum specific growth rate (μ max of 0.038 h −1 at 150 rpm). Due to the higher k L a values and the lower mixing times, the growth at 50 mm shaking diameter is still good at low shaking rates and high filling volumes, so the use of the 500 mL Optimum Growth flask with 50 mm shaking diameter is recommended. At shaking rates of 250 rpm and filling volumes of 50 mL (corresponding to power input values of approx. 0.7 kW m −3 ), a reduced maximum specific growth rate (μ max of 0.036 h −1 ) was observed independent of the shaking diameter, thus setting the upper limit. Fig. 9. Evaluation of the 500 mL Erlenmeyer flask design spaces with 25 mm (top) or 50 mm (bottom) shaking diameter based on the maximum specific growth rate.

mL Optimum Growth flask
The 5000 mL Optimum Growth flask has the narrowest sweet spot of all investigated cultivation systems (Fig. 11). This can be explained by the high volumetric power input (e.g. above 1 kW m −3 at 180 rpm and filling volumes of 1200 mL) for the upper limit as well as the high mixing times at low shaking rates and high filling volumes (e.g. above 7 min at 90 rpm and filling volumes of 3000 mL with 25 mm shaking diameter). Furthermore, increased foaming was observed for parameter combinations with high filling volumes and high shaking rates (e.g. 200 and 250 rpm with 3000 mL using a shaking diameter of 25 mm or 150 and 170 rpm with 3000 mL using a shaking diameter of 50 mm). This seems to be a limitation of the design space approach, as foam formation could not be predicted by the process engineering characterization. Fig. 10. Evaluation of the 500 mL Optimum growth flask design spaces with 25 mm (top) or 50 mm (bottom) shaking diameter based on the maximum specific growth rate.

mL TubeSpin
The sweet spot for the 50 mL TubeSpin bioreactor is primarily within the range of high shake rates (> 160 rpm at 25 mm and > 110 rpm at 50 mm shaking diameter, Fig. 12). The lower boundaries are marked by cell sedimentation, which is even more pronounced in this cylindrical vessels at higher filling volumes (see results of 10 and 30 mL at the boarder of the sweet spots). At the maximum shaking rate (300 rpm), the formation of macroscopic aggregates was observed, which was accompanied by a reduction in the maximum specific growth rate.

mL TubeSpin
The 600 mL TubeSpin bioreactor has a design space comparable to the 500 mL Erlenmeyer and Optimum Growth flask (Fig. 13). However, cultivations outside the sweet spot lead to unfavorable conditions more quickly. Shaking rates below 110 rpm at 25 mm shaking diameter led to cell sedimentation. Utilizing the maximum shaking rate of 300 rpm caused a reduced maximum specific growth rate (μ max < 0.030 h −1 at 25 mm and μ max < 0.023 h −1 at 3.0 mm shaking diameter with VCD max < 2⋅10 6 cells mL −1 and VCD max < 1.6⋅10 6 cells mL −1 respectively). The transition from optimal to fluid mechanically damaging conditions is observable at 250 rpm at 50 mm shaking diameter, where the maximum specific growth rate is reduced to 0.032 h −1 with VCD max of 2.5 ⋅ 10 6 cells mL −1 .

Cell size distribution
To assess the effect of eddy-generated shear stress on the cells, the cell size distribution had to be determined at different time points. The measurements were made with a Cedex HiRes, by which the class width of 1 μm was fixed. The data was subsequently applied to a Gaussian normal distribution function in order to make simpler numerical statements about the cell size distribution over the course of cultivation (Fig. 14). On average, the expected value μ of cell size was 14.45 μm with a standard deviation σ of 1.40 μm, which means that 99% of the cells can be assumed to be smaller than 20 μm, the selected upper cell size limit in this study.