Implementation of mDoE‐methods to a microcarrier‐based expansion processes for mesenchymal stem cells

The need for advanced therapy medicinal products (ATMPs) has gained increased attention in recent years. In this respect, a well‐designed cell expansion process is needed to efficiently manufacture the required number of cells with the desired product quality. This step is challenging due to the biological complexity of the respective primary cell (e.g., mesenchymal stem cells (MSC)) and the usage of microcarrier‐based expansion systems. One accelerating approach for process design is model‐assisted Design of Experiments (mDoE) combining mathematical process models and statistical tools. In this study, the mDoE workflow was used for the development of an expansion processes with human immortalized mesenchymal stem cells (hMSC‐TERT) and the aim of maximizing cell yield assuming only a limited amount of prior knowledge at a very early stage of development. First, suitable microcarriers for expansion in shake flasks were screened and the differentiation of the cells was proven. Second, initial experiments were performed to generate prior knowledge, which was then used to set up the mathematical model and to estimate the model parameters. Finally, the mDoE was used to determine and evaluate the design space to be performed experimentally. Overall, a cell expansion process using microcarriers in a shake flask culture was successfully implemented and a significant increase in cell yield (up to 6,2‐fold) was achieved compared to literature.

1][12] However, the novelty of ATMPs is accompanied by special challenges in their development, the design of a manufacturing process and the regulatory approval.The final in vivo therapeutic efficacy of cell products depend to a large extend on the manufacturing process. 13,147][18][19] This represents a major challenge especially for cell and gene therapy, as final cell product doses up to 50-100 billion T-cells are required. 20erefore, the focus here will be on cell expansion for this purpose.
Techniques used for cell expansion have been reviewed extensively by References [15].In brief, on a smaller scale, static culture dishes (e.g., well plates, T-flasks, stacked plate systems, mostly single-use) are mainly used for cell expansion.For these systems monitoring and control of parameters such as temperature, pH, and oxygen supply can be difficult.Moreover, the typical cell concentrations (25,000-30,000 cells/cm 2 ) provided by common planar cultivation systems with up to 40 layers cannot achieve the desired cell numbers (e.g., > billions of cells per batch required for cell therapy) and consistent quality, even with a high degree of automation and parallelization. 21,22As plates and flasks allow for a limited expansion only, scalable bioreactor systems based on matrices to provide cell attachment have been established in the past.
These cover hollow fiber bioreactors, bioreactors for macrocarriers (e.g., fixed bed), meander type bioreactors, and, microcarriers for use in stirred tank reactors, either re-usable or single use (reviewed by 23 ).
Although stirred tank reactors operated with microcarriers have shown promising results, they were originally designed for mammalian cellbased productions of therapeutic proteins. 24However, stem cells are less robust and more sensitive than the therapeutic production cells. 25 addition, the stem cell culture media differ in compositions, particularly in their supplements, and serum (up to 20%) is usually present. 26,27th respect to the before mentioned requirements, the stem cell expansion processes needs to be standardized based on the process understanding with a special focus on process robustness and scalability to ensure the desired product quality. 7,9,28However, this requires immense efforts during process development, industrial implementation and transfer with challenging development procedures and long timelines. 29During process development, specifically dedicated to the cell number required for clinical application, trial-and-error and one-factorat-a-time (OFAT) methods are still "state of the art".However, these inevitably require a large number of experiments to be performed and analytically evaluated. 30,313][34] At the same time, there is a risk that experiments are incorrectly selected by the heuristic design of a DoE, having insufficient explanatory power.This additionally increases costs and leads to time delays. 32,35,36more advanced approach for the reduction of development times and the related costs of cell propagation processes is the combination of mathematical growth models with statistical optimization methods, called mDoE. 37In mDoE, the process understanding is captured in a mathematical model which is used to evaluate experimental designs in silico before they are performed in the laboratory.Recommended experiments are thus implemented experimentally in a significantly reduced number and product quality and quantity can be better ensured. 33,38The successful application of mDoE has been demonstrated for the optimization of medium and feeding strategies for antibody-producing mammalian cell culture and Saccharomyces cerevisiae expansion processes including a whole-cell biocatalysis. 32,33Additionally, the use of mathematical process models is nowadays seen as a sustainable part of process development.This has been discussed extensively for production of recombinant therapeutic proteins (e.g., antibodies). 37,39,40Examples for model-assisted development of cell therapeutics and tissue engineered products have been recently reviewed by References [15,41].
Recently, we showed the successful application of mDoE for the development of an expansion process for an adherent cell line (L929). 42Additionally, a mathematical model to describe cell growth of adherent cells on microcarriers was presented. 42Based on the previous developments, the intention of this study was to evaluate, if the mDoE workflow is beneficial for the development of expansion processes for ATMPs.As test system, an expansion process for hMSC-TERT cells was developed with the aim of maximizing cell yield assuming only a limited amount of prior knowledge at a very early stage of development.In this respect, the mDoE-assisted workflow for process development for an ATMP cell line includes the following elements: choice of microcarriers, relevant analytical quality control of the cell line differentiation, model set-up and calibration.Building on these results, the design space will be elaborated with a special focus on bead-to-bead transfer.Following these specific tasks, suitable microcarriers for expansion in shake flasks were screened first and the differentiation of the cells according to ISCT-guidelines was proven.
Second, initial experiments were performed to generate prior knowledge and determine cause-effect relationships, which was then used to set-up the mathematical model and to determine kinetic parameters.Finally, the mDoE was used to determine and evaluate the design space to be performed experimentally.
A critical step for the chosen microcarrier-based cell expansion is the transfer of cells between different scales, which is often accomplished by bead-to-bead-transfer.Design of this critical process step usually requires significant experimental effort.The mDoE was used to determine the start time of the bead-to-bead transfer and the concentration of MC in the bead-to-bead transfer focusing on a maximum cell concentration, first in silico to determine a suitable design space for the required experiments and then experimentally for verification.
For the design of the cell expansion process the previously published mDoE software toolbox was used. 33,42 | MATERIALS AND METHODS

| Cell lines, pre-cultivation and passaging in T-flasks
Adherent-growing hMSC-TERT cells (kindly provided by Prof. M. Kassem, University of Southern Denmark, Denmark and Prof. D. Salzig, Technical University of Applied Sciences Mittelhessen, Germany) were cultivated in static (e.g., T-flasks) and in dynamic (e.g., shaken) bioreactors.For the static cultivations, cryo-cultures containing 1 Â 10 6 cells were thawed and transferred to 10 mL phosphate-buffered saline (PBS) (Carl Roth, Germany).The cell suspension was centrifuged for 4 min at 200g (Avanti J-26SXP, Beckmann Coulter, USA) and the supernatant was removed.The cell pellet was resuspended in pre-warmed Dulbecco's Modified Eagle Medium (DMEM) (PAN-Biotech GmbH, Germany) and transferred to a cell culture T-flask (Greiner Bio-One, Austria) at a seed density of 5000 cells cm À2 in DMEM with 10 vol% FBS (FBS Superior, Biochron GmbH, Germany).
The cells were cultivated at 37 C and 5 vol% CO 2 in an incubator (HeraCell 150i, Thermo Fisher, USA).Depending on the experimental setup, the glucose (Sigma-Aldrich, USA) and glutamine (Lonza Group AG, Switzerland) concentrations were adjusted in the medium.
Reaching a confluence of 80%-90%, the cells were proteolytically solubilized from the growth surface with 1 vol% trypsin (Lonza Group AG, Switzerland) in PBS.For this, the medium was removed, and the T-flask was washed twice with PBS (V PBS = V medium ).Then, the trypsin solution was applied and incubated for 5-7 min.Enzymatic proteolysis was stopped by the addition of medium (V Trypsin = V medium ), so that new cultivation systems were subsequently inoculated with the obtained cell solution.

| Cultivation in shake flasks
Dynamic cultivations were performed in shake flasks (glass, Schott AG, USA) with working volumes of 25, 40, and 60 mL cultivation medium (DMEM; same as in Section 2.1) and different types and concentrations of microcarriers (MC).hMSC-TERT were inoculated at a cell density of 5000 cells cm À2 of microcarriers, as low attachment densities are recommended for this cell type. 18,43,44The shake flasks were incubated for one night without agitation at the beginning and subsequently the shaker speed (GFL 3005, GFL, Germany) was set to 60 rpm (shaking diameter = 10 mm).For bead-to-bead-transfer, 100% fresh medium and 25%, 50%, 75% or 100% fresh MC were added after 3, 5 or 7 days.
Siliconization of all glass culture vessels (shake flasks and bioreactor) was necessary to avoid adhesion of the microcarriers and cells to the vessel wall.For this purpose, a few mL of Sigmacote (Sigma-Aldrich, USA) were transferred to the respective vessel under a fume hood and rotated and swirled at regular intervals to distribute the solution.The respective vessel was then rinsed with ultrapure water and dried overnight in a 60 C heating oven (Thermo Scientific Heratherm, ThermoFisher Scientific, USA).

| Cell harvest and lysis
For the enzymatic as well as cell lysing methods, 1 mL sample was taken, and the MCs were sedimented (1-3 min, depending on the respective MC).The supernatant was collected and stored for suspension cell count determination.Subsequently, the respective MC cell pellet was washed two times with PBS or with PBS + 2 mmol L À1 Ethylendiaminetetraacetic acid (EDTA).Samples were incubated with enzyme solution for 5-7 min.The first enzyme solution is based on a 1 vol% trypsin mixture in PBS, while the second is composed of a 1:1 mixture of 0.25 vol% trypsin in PBS and 0.02 vol% EDTA in PBS.Further instructions can be found in Reference [15].For the IGEPAL method, the protocol from Reference [16] was adopted, but no sieve was used.

| Cell counting
Cell nuclei were stained by propidium iodide (Sigma-Aldrich, USA) and quantified using a flow cytometer (CytoFLEX, Beckman Coulter, USA) with the 585/42 filter and a 488 nm laser.Debris were excluded using SSC-A versus FSC-A gating and doublets were excluded with FSC-H versus FSC-A gating.
A Z2 Coulter Particle Count and Size Analyzer (Beckmann Coulter, USA) was used for cell counting.For measuring, a total volume of 10 mL was diluted with PBS and 2 mmol L À1 EDTA according to the expected cell concentration.For quantification of fluorescence by the SYBR Green I (SG) (Sigma-Aldrich, USA) method, samples were centrifuged for 4 min at 200g, and the supernatant was removed and replaced with PBS.Subsequently, fluorescence measurements were performed in a black 96-well plate (Corning, Germany) threefold using a microplate reader (Tecan Infinite Nano+, Tecan, Switzerland).Further details can be found in Reference [17].
Samples were centrifuged at 200g for 3 min and washed with PBS.
The centrifugation step was then repeated, and the samples resuspended in 70 vol% ethanol.Intermediate storage was performed in a À20 C freezer (Bauknecht, Germany).
For microscopy, the ethanol supernatant of the samples was removed and replaced with PBS + 1 vol% Triton X-100 + 0.1 vol% DAPI.The fluorescent dye was incubated at room temperature in the dark for a period of 5 min.Subsequently, 50 μL of sample was pipetted onto a slide with coverslip.Microscopy was performed at 358 nm using a violet filter on the Eclipse 80i fluorescence microscope.

| Quantification of glucose, glutamine, lactate and ammonia
Concentrations of glucose (c Glc ), glutamine (c Gln ), and lactate (c Lac ) were measured with the YSI 2900D (Yellow Springs Instruments) biochemistry analyzer.The concentration of ammonium (c Amm ) was determined with an enzymatic test kit (AK00091; NZYTech, Portugal).

| Differentiation and characterization of hMSC-TERT
For differentiation and characterization, hMSC-TERT of different passages (40+ and 88+) were used.The ability of the cells for specialization was checked after static as well as dynamic cultivation.
Differentiation kits from Miltenyi Biotec (Germany) were used for differentiation studies.Cells were prepared and treated as described in the manual, with deviations listed below.
To initiate adipogenesis and osteogenesis, cells were differently seeded in a ClipMax (Faust, Switzerland) as stated in the protocol.
Additionaly, cells for adipogenesis were cultivated in standard cell culture medium and replaced with adipogenesis differentiation medium after an incubation period of 48 h.Finally, cells were cultivated for 13-28 days, with medium changes every 2-3 days.For osteogenic differentiation, cells were incubated for 14-21 days in osteogenic differentiation medium.Medium was changed every 2-3 days.The formation of a bone matrix as a result of calcium accumulation was confirmed by alizarin red staining after ethanol fixation.Chondrogenesis was stained with Alcian blue and nuclear red stain.For better visualization of the cartilage, sections of the nodules were prepared in advance.
To detect the surface markers of hMSC-TERT, an MSC phenotyping kit from Miltenyi Biotec was used.The integrated CD73-APC conjugate was replaced with a CD73-PE conjugate.The respective sample was labeled with the phenotyping cocktail and measured in CytoFLEX using 585/42, PB450, FITC and KOS525 filters at 488 nm.Simultaneously, one sample each was prepared as an isotype control and measured to determine non-specific binding.

| Mathematical process model and estimation of model parameters
The mathematical model to describe the growth behavior of adherent-growing cells on microcarriers is described in Reference [42].
In brief, the model is based on our experience in modeling suspension-growing mammalian cell lines (see References [45]   and [32]).The main advantage of this model is the modeling of the initial attachment phase of cells onto the microcarriers and the incorporation of growth limitation due to contact inhibition and cell metabolism.The model structure was chosen due to its simple design and the possibility to extract all model parameters estimated from a few cultivations.The model is shown in Supplement, Table S1.Least square methods were used to determine the specific model parameters, which were used as initial values to determine the expected process variability.For this purpose, the model parameters were varied 1000-fold based on the experimental uncertainty (e.g., measurement error) and thus the measurement errors were simulated.Please see References [13,14] for further details.

| mDoE toolbox
The combination of a mathematical process model, including modelparametric uncertainties with the computational planning and evaluation of DoE designs are the main parts of the mDoE software toolbox.
Please see References [33] and [42] for more details about the toolbox and its application.In brief, the biotechnological system is mod- The desirability is 0 if the optimization criteria is not fulfilled and the desirability tends toward 1 if the optimization is highly desirable.

| RESULTS AND DISCUSSION
The aim of this study was the evaluation of the applicability of the mDoE workflow for the development of an expansion process for hMSC-TERT cells with only a limited amount of prior knowledge at a very early stage of development.First, suitable microcarriers for expansion in shake flasks were screened and the differentiation of the cells according to ISCT-guidelines was proven.Second, initial experiments were performed to generate prior knowledge and determine cause-effect relationships.Finally, the model parameters of the mathematical process model were adapted and the mDoE was used to determine the start time of the bead-to-bead transfer and the concentration of MC in the bead-to-bead transfer focusing on a maximum cell concentration.As can be seen in Figure 1  Surface marker analysis of hMSC-TERT (passage 90) were done on Cytodex 3 MCs.The hMSC-TERTs were negative (<2%) for hematopoietic markers such as CD45, CD34, CD14, CD19, and HLA-DR and positive (>90%) for stromal markers such as CD73, CD105, and CD90.
Overall, relevant surface markers, plastic adherence and differentiation of hMSC-TERT were successfully detected according to ISCT guidelines. 46

| MC-screening
Despite many studies involving MSCs and microcarrier culture investigating various aspects of the culture process, there is no unified set of culture conditions for MSC microcarrier expansion.However, many different types of microcarriers exist, each with different particle sizes, as well as a different structures (i.e., solid bead, macroporous, enzymatically digestible), and coatings (fibronectin, collagen, gelatin).The selection of the appropriate microcarrier is a fundamental component of microcarrier/stirred-tank bioreactor cell expansion.Therefore, it is of importance that the optimal microcarrier is selected from the outset based on a stringent selection methodology. 47The use of MSCs in allogeneic cell therapy requires a scalable, cost-efficient manufacturing process including a well-chosen MC (17).In this study, six different MC were investigated regarding the growth of hMSC-TERT cells and the fluorescencestained images can be seen in Figure 2  As shown in Figure 2, the cells attach to all surfaces and different cell growth was observed for the MCs.Compared to the Collagen-Coated and Cytodex 3 MCs, the FACT, Plastic, PlasticPlus, and Star-Plus MCs are sparsely overgrown.Smaller cell-cell-agglomerates and MC-cell-agglomerates were detected in the CollagenCoated MCs (Figure 2A).Only MC-cell-agglomerates were detected in Cytodex 3 MCs (Figure 2B).The FACT MC are barely overgrown, instead forming cell-cell-agglomerates up to 260 μm in size (Figure 2C).MCcell-agglomerates are a typical phenomenon, as documented by Jossen et al. 44 and Abraham et al., 21 among others.It was emphasized there that limitations occur due to the formation of concentration gradients within MC-cell-agglomerates.According to Abraham et al., these should be avoided. 21Due to the efficient growth of hMSC-TERTs on Cytodex 3 MCs, they were further used in this study.

| Prior knowledge and determination of cause-effect relationships
The basis of mathematical process modeling is the determination of cause-effect relationships as previously published. 42For hMSC-TERT, no dynamic cultivation data was available at the beginning of the study.To generate a first understanding about the dynamic cultivation behavior of hMSC-TERT, multiple shake flask growth cultures were experimentally performed.Based on our experience, typical medium components such as c Glc , c Gln , and c MC were examined since these have the main impact on the expansion process.The initial concentration of glucose (c Glc,I ) varied in the range of 5-60 mmol L À1 and the initial concentration of glutamine (c Gln,I ) varied in the range of 2-12 mmol L À1 based on our prior knowledge in the field of cell expansion processes. 32The range of c MC was 1-5 g L À1 based on previous studies. 42In addition, the feasibility of bead-to-bead transfer was also tested.The investigated factors were the freshly added microcarriers (c F,MC ), which represents the percentage of added fresh MCs in relation to the initial medium concentration and the time of the addition (t feed ).Experiments were selected to best cover the expected experimental space based on our experience with adherent growing cells and typical medium components.
For comparison of the results, the growth rates up to the beadto-bead transfer (μ max,before,btb ) and after the bead-to-bead transfer (μ max,after,btb ), the maximum cell number X v,max and the multiplication factor VF are summarized in Table 1.
By analyzing these six experiments the following cause-effect relationships were derived.The highest maximum cell numbers were   Note: Bead-to-bead transfer was performed after 120 h with a 100% medium and a 50% MC addition.Cells were innoculated with 5000 cells cm À2 in each experiment.No Bead to Bead transfer was performed in experiment 1.The specific cultivation data can be seen in Figure S1.
achieved in Experiment 4 and Experiment 5 (Table 1) with an MC concentration of 1 g L À1 .Based on the determined growth rates, a mean maximum specific growth rate of μ max = 0.027 h À1 was assumed for the hMSC TERT cells with a c MC = 1 g L À1 before bead-to-bead transfer.For all other c MC , a decreased growth with an approximated reduction of μ max by 30% was determined before and after beadto-bead transfer (Exp.2, 3, 6 in Table 1).Furthermore, a variation of c Glc,I and c Gln,I have only a small influence on cell growth.As long as both substrates are present, no limiting effects are present.

| Estimation of model parameters
Based on the determined cause-effect relationships, the model parameters were estimated for the experimental hMSC TERT cultivation data.A previously published mathematical model developed for adherent-growing L929 cells was used in this study to model the growth and main metabolism for hMSC TERT cells (see Table S1).
Starting from this model, no differential equations had to be changed and only the initial parameters and the boundary conditions of the mathematical model were adjusted.To apply the uncertainty distribution in the mDoE toolbox, the initial values were varied 1000-fold by ±5% and the parameters were determined using Monte-Carlo simulations.The initial values and the estimated model parameters can be seen in Table 2.
To assess the goodness of the adapted mathematical model including the estimated model parameters, the model was used to simulate all experiments mentioned in Table 1 and the coefficient of determination was calculated for each simulated variable.As can be seen in Figure 3a,b, X v was simulated with a coefficient of determination (R 2 ) > 0.80.The data points are close to the identity line indicating a high representation of the simulated to the experimental data.The uptake of glucose and glutamine as main sources of energy can be expressed well with a R 2 of 0.85 (c Glc ) and 0.69 (c Gln ).Lactate, as main metabolic waste product, is described with R 2 = 0.69 (Figure 3e).No correlation was detected for the decrease in ammonium concentration, so this phenomenon was only simulated poorly and was not considered for the process development (Figure 3f).

| Process optimization with mDoE toolbox
Based on previously described results (Table 1), it was shown that a c MC = 1 g/L led to improved cell growth.The aim of process optimization in this study was to identify the best start time of feeding of MC (t feed ) and an appropriate MC concentration (c F,MC ) in the feed.For this purpose, a mDoE was performed based on the previously introduced mathematical process model.The factor limits were set broadly so that a large experimental space was studied using the simulations.
Freshly added MC during bead-to-bead transfer varied in the range of 25%, 50% and 100% (0.25-1 g L À1 ) and the start time of the feed from 72 to 168 h.The minimum limit of the feed start time was set at 72 h to allow the cells to adhere to the MCs and to transition to the exponential phase.After 168 h, a transition to stationary phase was already observed in isolated cases, so this was set as the maximum limit.Additionally, c Glc,I was set to 12 mmol L À1 , c Gln,I to 4 mmol L À1 and c MC to 1 g L À1 .A D-optimal experimental design was chosen as the experimental design, since effective experimental designs can be generated with a small number of factor combinations, as was shown in Reference [48].
Using mDoE, a response surface was predicted with a maximal desirability (maximizing cell concentration) to be at intermediate as well as maximum c F,MC and early to intermediate t feed .For c F,MC lower than 0.6 g L À1 , a strong decrease in the desirability is predicted whereas the influence of t feed seems to be rather low.Out of the planned experimental conditions (blue points in Figure 4a), 6 conditions were chosen and experimentally tested (Figure 4b).The growth  All in all, before bead-to-bead transfer, a maximum cell concentration up to 4 Â 10 4 cells cm À2 (m-3) and 5.25 Â 10 4 cells cm À2 (m-5) could be reached.After bead-to-bead transfer, a maximum cell concentration of 18.8 Â 10 4 cells cm À2 was achieved after 360 h of cultivation (m-5).Leber et al. 28 investigated the growth of hMSC-TERT cells using different microcarriers.They reported a maximal cell concentration of 3 Â 10 4 cells cm À2 in spinner cultures using glass-coated  microcarriers (Solohill Glass Coated, Pall), both before and after beadto-bead transfer.In comparison to this maximal cell number, a slightly higher cell yield was achieved here before bead-to-bead transfer (m-3 and m-5).After bead-to-bead transfer, up to 6 times more cells per cm 2 were cultivated in m-5 using different microcarriers and an optimized bead-to-bead transfer protocol.
Additionally, it is important to highlight the successful cultivation of hMSC-TERT-cells on microcarriers under shake flask conditions.So far, mostly spinner cultures have been reported for small scale suspension cultures of hMSC-TERT cells.Wyrobnik et al. 49 summarized cell expansion processes in stirred tank bioreactors with a typical range of cell densities between 1 Â 10 5 cells mL À1 and 1 Â 10 6 cells mL À1 and a cell viability above 90% Â 10 6 cells mL À1 (converted from cell cm À2 to cells mL À1 ), which is comparable to the previously described range in stirred tank bioreactors.Therefore, the small-scale expansion in shake flasks is an appropriate tool for process development and investigation.

| CONCLUSION
The objective of this research was to assess the efficacy of using the mDoE concept in enhancing the expansion processes for ATMPs, such as MSC cells.To achieve this, a workflow for model-assisted process development was set up.First, various microcarriers were compared, and Cytodex 3 microcarriers were selected for further cultivation due to their favorable handling characteristics.The study then progressed by elaborating cause-effect relationships based on six preliminary experiments.These relationships were utilized to define the parameters of a mathematical model, forming the basis for implementing the mDoE.By utilizing the mDoE approach, the range of possible experimental was narrowed down.This facilitated the optimization of eled first based on the objective of the study.After defining the mathematical model, Monte-Carlo based parametric uncertainties are derived and, process variability is simulated to be later used in the DoE evaluation.Experimental factors and responses are defined as well as a DoE design is subsequently planned.For each recommended factor combination, the time courses of the modeled state variables are simulated multiple times and used for the computational evaluation.The design plan is analyzed, and response surface plots are generated automatically for visualization and experiments are recommended to be performed.After defining the response surface plots, user-defined constraints are chosen and the desirability function is calculated for each response individually.With the desirability function the multidimensional optimization problem is standardized to just one desirability function, which will be reduced with the multiplication of the different desirability function values to one overall desirability.

3. 1 |
Characterization of MSCs and microcarrier-screening 3.1.1| Characterization of hMSC-TERT According to the ISCT guidelines, MSCs are characterized by plastic adherence, differentiation into adipocytes, chondrocytes and osteoblasts as well as the expression of certain surface markers. 46Plastic adherence was confirmed by T-flasks cultures (not specifically shown).
(Part I A), osteocyte differentiation was successfully demonstrated with alizarin red staining of intracellular calcium deposits.Differentiated adipocytes were confirmed by oil red O staining of the lipid vacuoles (Figure 1, Part I, B).Alcian blue staining of proteoglycans was used to detect chondrogenic differentiation (Figure 1, Part I, C).Overall, differentiation into adipocytes, osteoblasts, and chondrocytes was demonstrated successfully.
with different magnification.F I G U R E 1 Part I: Differentiation of mesenchymal stem cells into osteoblasts (A), adipocytes (B) and chondrocytes (C).Differentiation was performed in T-flasks (A, B) and conical centrifugation tubes (C) in differentiation medium.Alizarin red staining highlights calcium accumulation in osteoblasts (A), whereas lipids are stained in adipocytes by oil red OR staining (B).The aggrecan of the extracellular matrix is stained by Alcian blue and the nuclei with a nuclear red stain (C).Part II: Surface marker analysis of hMSC-TERT expanded on Cytodex 3-MCs in DMEM.Positive markers CD90, CD105, and CD73 (A-C) and the negative cocktail with CD45, CD34, CD14, CD19 (D), and HLA-DR (E).Isotype controls are shown in gray.hMSC-TERT of passage 90 were characterized.

curves can be seen in Figure 5 A
with different characteristic behavior.For m-1 (low c F,MC and low t feed ), cells grew up to a maximum of 14.5 Â 10 4 cells cm À2 at 312 h.For the next hours the cell number declined to 12.7 Â 10 4 cells cm À2 .A low t feed and a high c F,MC (Figure5, m-2) resulted in a higher X v = 17.5 Â 10 4 cells cm À2 at 360 h and an average t feed and c F,MC (Figure5, m-3) led to a little bit smaller maximal X v = 15.2Â 10 4 cells cm À2 .The lowest maximal cell number of 9.1 Â 10 4 cells cm À2 was achieved for an average t feed and high c F,MC (Figure5, m-4) whereas the highest X v = 18.8 Â 10 4 cells cm À2 was determined for a high t feed and a low c F,MC (Figure5, m-5).For a high t feed and c F,MC , an rather low X v = 10.9Â 10 4 cells cm À2 was measured (Figure5, m-6).c Glc and c Gln was steadily taken up by the cells during growth and c Glc was consumed after 360 h of cultivation.c Gln was given in excess and was not fully consumed.Overall, a low c F,MC and a late t feed is recommended for an efficient cell expansion, as was tested in experiment m-5.Additionally, this results showed that c F,MC <1 g L À1 are not yet optimally described with the mathematical model.Modifications would be necessary for further usage.However, this corresponds to the concept of the mDoE, to increase the process knowledge in a short time with a smaller number of experiments.

F
I G U R E 4 (a) Response surface plot of mDoE for the optimization of c F,MC and t feed , blue points are simulated experimental conditions for mDoE, the surface is simulated.(b) contour plot of c F,MC and t feed , experimentally implemented conditions (m means mDoE).

R 2 V 5
parameters like feeding rate (t feed ) and microcarrier concentration (c F,MC ) through six additional experiments only.This optimization process led to a significant increase in cell yield compared to existing literature.It is noteworthy that the successful results were accomplished without the need for iterative DoE cycles.This was possible due to a comprehensive analysis of cultivation data and a refined iterative modification of the mathematical process model.Consequently, only experiments that held substantial informational value were conducted, leading to a reduction in the time required for optimizing the bead-to-bead transfer process.With focus on the manufacturing of ATMPs, which often demands tailored, individualized processing, a significantly reduced effort for processes is essential, setting it apart from the production of traditional biopharmaceuticals.Utilizing the mDoE techniques holds significant promise in harnessing a wide array of diverse data and knowledge sources.This, in turn, contributes to an enhanced comprehension of cell culture methodologies and has the potential to accelerate the progression through the clinical development phases, thus speeding up the market entry of ATMPs.NOMENCLATURE List of Symbols c Amm , [mmol L À1 ] concentration of ammonia c F,MC , [g L À1 ] freshly added microcarriers c Glc , [mmol L À1 ] concentration of glucose c Glc,I , [mmol L À1 ] initial glucose concentration c Gln , [mmol L À1 ] concentration of glutamine c Gln,I , [mmol L À1 ] initial glutamine concentration c MC , [g L À1 ] concentration of microcarrier c Lac , [mmol L À1 ] concentration of lactate c LS , [mmol L À1 ] concentration of limiting substrate k att , [h À1 ] attachment constant K S,LS , [mmol L À1 ] kinetic parameter K d,LS , [mmol L À1 ] kinetic parameter q Glc , [mmol cell À1 h À1 ] cell specific uptake rate of glucose q Gln , [mmol cell À1 h À1 ] cell specific uptake rate of glutamine Medium , [mL] volume Medium V Trypsin , [mL] volume Trypsin X Inokulum , [cells cm À2 ] inoculation cell concentration X V , [cells cm À2 ] cells growing on microcarrier X v,max , [cells cm À2 ] maximum cell number X SUS , [cells mL À1 ] cells growing in suspension Experimentally tested cultivations, based on Figure 4b.

Table 1 .
The identity line (dashed) is given as reference.Statistical information (R 2 ) is presented for all curves.
Y X/Glc , [cells mmol À1 ] ratio of growth to cell yield for glucoseY X/Gln , [cells mmol À1 ]ratio of growth to cell yield for glutamine max,before,btb , [h À1 ] growth rates up to the bead-to-bead transfer μ max,after,btb , [h À1 ] growth rate after the bead-to-bead transfer