**Lactate-Based Model Predictive Control Strategy of Cell Growth for Cell Therapy Applications**

**Kathleen Van Beylen 1,2, Ali Youssef 1, Alberto Peña Fernández 1, Toon Lambrechts 1,2, Ioannis Papantoniou 2,3,4 and Jean-Marie Aerts 1,\***


Received: 30 May 2020; Accepted: 15 July 2020; Published: 20 July 2020

**Abstract:** Implementing a personalised feeding strategy for each individual batch of a bioprocess could significantly reduce the unnecessary costs of overfeeding the cells. This paper uses lactate measurements during the cell culture process as an indication of cell growth to adapt the feeding strategy accordingly. For this purpose, a model predictive control is used to follow this a priori determined reference trajectory of cumulative lactate. Human progenitor cells from three different donors, which were cultivated in 12-well plates for five days using six different feeding strategies, are used as references. Each experimental set-up is performed in triplicate and for each run an individualised model-based predictive control (MPC) controller is developed. All process models exhibit an accuracy of 99.80% ± 0.02%, and all simulations to reproduce each experimental run, using the data as a reference trajectory, reached their target with a 98.64% ± 0.10% accuracy on average. This work represents a promising framework to control the cell growth through adapting the feeding strategy based on lactate measurements.

**Keywords:** model predictive control; bio-process; cell growth; lactate; advanced therapy medicinal products

#### **1. Introduction**

Cell-based products receiving market approval are increasing over the last years. The European Medicine Agency (EMA) has approved 14 medicinal products based on gene therapies, cell therapies or tissue engineering, also called advanced therapies for the European market [1]. The U.S. Food and Drug Administration (FDA) has approved 17 cellular or gene therapy products [2]. Compared to other pharmaceuticals such as small molecule drugs or biologics, the active pharmaceutical ingredient (API) of these cell-based therapies is living cells. An example of such a cell-based therapy is chimeric antigen receptor (CAR) T-cell therapy, where the patient is injected with human immune cells, which are modified to target cancer cells [3]. Another type of cell-based therapy is skeletal tissue engineering, where a cell-based implant is used to regenerate cartilage or bone in the patient instead of using a prosthetic implant, which has the disadvantage that it will need to be replaced within 10–15 years [4]. Besides being the active component of the final medicinal product, cells can also be used as a tool in the manufacturing process to produce the final product, such as extracellular vesicles [5].

With the introduction of this promising group of cell-based or cell-derived products, the necessity to transform the emerging cell therapy and regenerative medicine industrial sector towards a BioPharma 4.0 sector is growing. This revolution should build on a strong IT infrastructure combined with automation technologies in order to use continuous data to steer and optimise bioprocesses in real-time without the need for human interaction [6]. Closely monitoring and controlling the bioprocess tackles the challenge of irreproducible manufacturing processes that are often seen for (personalised) cell-based therapies. This bioprocess variability is inherent to donor variability, the time-varying characteristics of progenitor cells (such as phenotype) and the complexity of living systems [7].

Progenitor cell expansion is a crucial process step whereby clinically relevant numbers are produced typically ranging between 5 <sup>×</sup> 107–108 [8,9]. Currently, progenitor cell expansion relies on fixed protocols which do not take into account the particularities of the cell type, donor characteristics or the batch, leading to suboptimal outcomes [10]. In order to reduce this variability, the process has to remain within predefined boundaries during the whole production process, which is possible by actively adapting critical process parameters (CPP) during the cell expansion process, based on the characteristics and individual needs of a batch. The retuning of the process parameters should be done in a way that would enable the process to follow a predefined (reference) trajectory, providing optimal conditions for the cultured cells. Due to the inherent variability of cells and the time-varying dynamics of the process, modelling and controlling the cell growth is challenging [11].

Active control of cell culture bioprocesses will also result in lower batch-to-batch variability. Without any monitoring or control of cell culture, there could be a high amount of batch rejections due to results of in-process or finished product testing falling out of the predefined boundaries of the validated process. These specifications are described in quality control documents approved by health authorities and are set to assure product quality and safety. The amount of "out of specifications" test results of two different commercial cell therapies was recently described in the biologics license application (BLA) submission of Kymriah® and Yescarta®. Novartis reported 7% and 9% manufacturing failures for Kymriah batches, whereas Kite reported 1% for Yescarta batches [12]. Novartis disclosed that all out of specifications (OOS) results were caused by viability problems, resulting in final products with a viability lower than 80%. The challenge lies in the nature of cell products having an inherent variability and complexity.

Therefore, in this work, a model-based predictive control (MPC) system is proposed as a potential solution to the aforementioned challenges of inherent variability and time-varying dynamics of the cell culture process [13]. MPC exhibits several interesting features, such as intuitive concepts, easy tuning and the ability to control a range of simple and complex phenomena, including systems with time delays, non-minimum phase dynamics, dead times, multivariable cases and instability [14]. While dealing with all these challenges, the MPC can easily incorporate constraints and tailor formulated control objectives [12,13]. Model predictive control offers several important advantages: (1) the process model captures the dynamic and static interactions between input, output and disturbance variables; (2) constraints on inputs and outputs are considered in a systematic manner in the cost function and (3) accurate model predictions can provide early warnings of potential problems [13].

Several studies have investigated the benefits of controlling the environment of cell culture vessels such as dissolved oxygen tension (dO2), temperature and CO2 [15]. Instead of using these standard physicochemical process parameters to control the bioprocess, this paper will develop a method to control the metabolic responses of the cells. This metabolic response is measured off-line and is used as an indication of the cell growth, which can only be measured at the end of the bioprocess of adherent cells. An interesting metabolic response to use as an indirect measure for cell growth in a high glucose medium is the cumulative lactate production of the cells over the culture period. Using lactate measures has the advantage, in an environment with excess amount of glucose, that the ratio between lactate production and glucose consumption is a known value (two) based on the anaerobic glycolysis pathway [16]. In high glucose environments, measurements of glucose have a low sensitivity compared to lactate. Lactate concentrations are low in fresh medium and are produced

by the cells, resulting in higher sensitivity and indication of whether or not cells are alive. Another advantage is controlling the pH, since this is related to the lactate concentration [17,18]. The control of this pH is important because an increase in extracellular acidosis, i.e., a value below 6.7, leads to a higher amount of apoptosis [19,20].

Furthermore, lowering the lactate concentration by replacing the media for 100%, 50% or 0% of the total working volume has been reported to have a significant effect on the cell growth [15].

The aim of this paper is to describe a framework for controlling process parameters of the cell expansion process based on lactate measurements in combination with a model predictive control approach. As a proof of concept we used lactate measures, but depending on the considered application, the input and output could be chosen differently, taking into account specific process parameters and quality attributes. For example, in low glucose environments, it would be interesting to change the measurement to glucose. By controlling the process parameters, the cell growth can be directed towards a predefined reference trajectory. This research demonstrated the intended goal using experimental data in combination with control strategy simulations.

#### **2. Materials and Methods**

#### *2.1. Cell Culture Experiments*

In order to develop this framework, we performed experiments on human periosteum-derived cells (hPDCs) and studied their metabolic responses during their cell expansion process. Cell proliferation was the aimed output. This cell growth was represented here by the cumulative lactate produced by the cells. As an input to control the cell growth, we investigated the effect of the total amount of replaced medium.

#### 2.1.1. Cell Culture

The hPDCs used in this study were obtained from periosteal biopsies with patients' informed consent. The performed biopsy procedures, as described by [21], were approved by the Ethics Committee for Human Medical Research (KU Leuven). These cells were expanded until passage 4 and frozen. Culture medium consisted of high glucose Dulbecco's modified Eagle's medium (DMEM + GlutaMAXTM + pyruvate, GibcoTM by Thermo Fisher Scientific, Waltham, MA, USA), supplemented with 10% (v/v) heparin-free pooled human platelet lysate (StemulateTM by Cook Regentec, Indianapolis, IN, USA) and 1% antibiotic-antimycotic (GibcoTM by Thermo Fisher Scientific).

The cell culture experiment started by thawing three frozen vials, each containing 1 million hPDC cells from a different donor. The cells from these three donors were seeded in three different T175 flask at passage 5 with 27 mL culture medium and incubated in a humidified atmosphere of 90% at 37 ◦C and 5% CO2. The culture medium used during the experiment was DMEM supplemented with only 7.5% hPL instead of 10%, which was used for general cell culture expansion and storage. The reason for lowering the amount of hPL is based on knowledge from previous experiments, indicating cells cultured in 7.5% hPL as the condition with the lowest medium cost per population doubling (data not included). Cells were subjected to a 100% medium replacement on day 2 and harvested on day 4 with TrypLE (GibcoTM by Thermo Fisher Scientific). This passaging was repeated once again, with the same seeding density of 5700 cells·cm<sup>−</sup>2.

#### 2.1.2. Experimental Set-Up

Cells were harvested after the second expansion step and seeded into 6 different 12-well plates (72 wells), each well with a density of 3300 cells·cm−<sup>2</sup> in 1 mL of DMEM medium supplemented with 7.5% hPL. Reducing the seeding density from the previous 5700 cells·cm<sup>−</sup>2, which was used for expanding and storing of cells, to 3300 cells·cm−<sup>2</sup> was, on the one hand, based on previous experiments. These experiments indicated a seeding density of 3300 cells·cm−<sup>2</sup> to be a more cost-effective use of the culture vessel, due to a lower population doubling time and similar cell number harvested at the end

of the cell culture. On the other hand, a lower seeding density would also provide more cell culture time before reaching 80% of confluency, resulting in a higher amount of input and output data points. The cells were cultured during 5 days while the medium was replaced according to 6 different medium replacement strategies, as indicated in Table 1.


**Table 1.** Overview of medium replacement strategies. The amount of medium replaced is indicated as a percentage of the total working volume of the well, which changed over the different days.

All conditions were performed for three different donors in triplicates (54 wells). In addition a control condition was set up in each of the six 12-well plates in triplicates (18 wells), which had the same medium replacement scheme as condition 6, but the cells were from a pool of the three different donors to account for possible well plate differences.

#### 2.1.3. Lactate Measurements and Cell Counts

During the 5 days of cell culture, 100 μL medium samples were taken every day from each and stored at −80 ◦C. Therefore, a minimum of 10% medium replacement was required. The medium samples were analysed for lactate with the CEDEX medium analyser (Roche, Custom Biotech, Belgium) after thawing. After five days of cell culture expansion, the cells were harvested using TrypLE express and counted with trypan blue 0.25% using a Bürker haemocytometer.

#### *2.2. Model-Based Control and Optimisation*

#### 2.2.1. System Identification and Modelling

The main goal of this work is to (1) optimise the cell proliferation, combined with (2) minimising the use of medium, which can be achieved by tuning a process parameter to steer the process towards a defined growth trajectory. In order to solve this optimisation problem, a model-based predictive control (MPC) approach is used, which is shown in Figure 1.

The control strategy consists of a dynamic model to forecast the future behaviour of the system (predicted outputs *y*ˆ(*k* + *Np* - - *k*), at time k with prediction horizon *Np*). This predictive knowledge is used in combination with the past knowledge of previous input and output measurements of the system and a reference trajectory (*r k* + *Np* ) to calculate the future errors (*e*ˆ(*k* + *Np* - - *k*)). The optimiser will take these errors in to account, together with the cost function (J) and the constraints, to formulate the optimal control decision (future inputs *u*ˆ(*k* + *Nc*|*k*), estimated at time k with control horizon *Nc*) to be used as inputs to minimise the deviation from the reference trajectory [23].

**Figure 1.** Model predictive controller scheme [22].

A first step in developing a model-based controller is to develop a model of the process. When no readily available mechanistic model or knowledge is available, a model can be identified based on measuring process inputs and outputs. Several methods can be used, but an approach that has been proven successful in many applications is system identification. This approach assumes that the observed input–output relations of the system are the manifestation of the dominant processes occurring within the system under study. Typically, a transfer function (TF) model structure is estimated as an objective and the parsimonious mathematical description of the process is considered [24].

The reason for using a data-based model predictive controller is based on the multiple advantages it has regarding controlling and optimising systems compared to classical proportional–integral–derivative (PID) controllers [25]. The model will predict the lactate increase and use time varying parameters combined with an a priori defined reference trajectory required for the complex and time-varying nature of the cells. Furthermore, the model is able to include feedback knowledge of experiments and extract the main processes to see the effect on the growth. In addition, it can take into account constraints on the input and output variables, use short prediction horizons and avoid time delay problems.

#### 2.2.2. Interpolated Data

One of the challenges faced during the present study was the sparsity of the data points, with only one data point every 24 h. Therefore, an interpolation step was needed, for which the method of piecewise linear interpolation was used. In order to do this, all collected data points are used and the data in between are estimated using a linear function [26]. For a dataset of *n* points (*t*1, *y*1), .., (*tn*, *yn*) with *t*<sup>1</sup> < *tn*, the piecewise linear interpolation for point *t* situated at *tk* < *t* < *tk*+1, is described by

$$\mathbf{y}(\mathbf{t}) = y\_k + \frac{y\_{k+1} - y\_k}{t\_{k+1} - t\_k} \cdot (t - t\_k),\tag{1}$$

where *y* (mmol) is again the accumulated lactate produced and *t* (days) is the culture period in days. The values (*tk*, *yk*) and (*tk*+1, *yk*+1) are collected data points, whereas (*t*, y(t)) is an interpolated data point. The resulted interpolated data were used as a reference trajectory in the simulation step for the developed model predictive controller.

#### 2.2.3. Prediction Model

The MPC approach requires a dynamic model which forecasts the output, in this case the cell growth. Furthermore, the model relates the process parameters, used as inputs, to this desired output. The goal of this work is to estimate the growth of the cells during the cell culturing phase. However, since adherent cells cannot be measured directly in this phase, an indirect measure of cell growth is used, namely, accumulated lactate produced by the cells during proliferation.

The advantage of the previous mentioned system-identification methods, such as transfer function models, is that they develop the process models directly based on measured process data and thus can take into account differences between cell types and/or time-varying characteristics.

Figure 2 shows a representation of the lactate concentrations over time, with medium replacements at certain time points *k*.

**Figure 2.** Simplified lactate concentration graph during a cell expansion period with medium replacements at time points *k*, *k* + 1 *and k* + 2.

At time zero, the cell culture has an initial lactate concentration which is equal to the concentration in fresh medium and is called the baseline concentration *C*0. While the cells proliferate, they consume nutrients such as glucose and produce waste products such as lactate. Therefore, the lactate concentration increases between time zero and *k* from the initial *C*<sup>0</sup> until *C*1(*k*). At time *k*, the medium is replaced with *U*(*k*) as a percentage of the working volume of the vessel. After medium replacement, the lactate concentration *C*1(*k*) decreases to *C*2(*k*) as described in the following equation:

$$C\_2(k) = C\_1(k) - C\_1(k)\mathcal{U}(k) + C\_0 \mathcal{U}(k). \tag{2}$$

To control this lactate production, the amount of medium used to replenish the cells can be used as the manipulated process parameter (or control input).

A data-based mechanistic model approach was used to describe the effect of changing the medium replacement on the cumulative lactate production. A transfer function input–output model structure is used for system model identification, as little knowledge of the complex cell behaviour is required a priori.

In this research, dynamic auto-regressive exogenous (DARX) variables are estimated using the CAPTAIN toolbox [27] in MATLAB version 2018b. The DARX model is used in the analysis to allow a changing relation between medium replacement and accumulated lactate during the cell culture period [28]. The model structure is described as follows [22,23]:

$$y\_t = \frac{B\{\mathbf{z}^{-1}, \mathbf{t}\}}{A(\mathbf{z}^{-1}, \mathbf{t})} u\_{t-\delta} + \frac{1}{A(\mathbf{z}^{-1}, t)} e\_{t\prime} \tag{3}$$

where *yt* is the output (accumulated lactate (mmol)) of the system and *ut*−<sup>δ</sup> the input (accumulated medium replaced (mL) with a certain time delay δ. The additive noise *et* is assumed to have a zero mean and uncorrelated variance *N* 0, σ<sup>2</sup> . The series *A* and *B* have time varying parameters described by the following equations:

$$A\left(\mathbf{z}^{-1}, \mathbf{t}\right) = 1 + a\_{1,l}\mathbf{z}^{-1} + a\_{2,l}\mathbf{z}^{-2} + \cdots + a\_{n,l}\mathbf{z}^{-n\_x} \tag{4}$$

$$B(\mathbf{z}^{-1}, t) = b\_{0,t} + b\_{1,t}\mathbf{z}^{-1} + b\_{2,t}\mathbf{z}^{-2} + \cdots + b\_{m,t}\mathbf{z}^{-n\_b},\tag{5}$$

where the backward shift operator z<sup>−</sup>1, applied on the model parameters *a*i,*<sup>t</sup>* and *b*i,*t*, can also be expressed as:

$$a\_{\mathbf{i},t} \mathbf{z}^{-t} = a\_{\mathbf{i},t}(\mathbf{t} - \mathbf{i}). \tag{6}$$

To obtain the relation between input and output, estimated by the polynomials *A* and *B*, experiments were performed. These experiments changed the process parameter (*u*, medium replacement) while measuring the effect on the output (*y*, cumulative lactate concentration). The model parameters were estimated using refined instrumental variable (RIV) algorithms [27]. The most suitable reduced order model structure was selected based on two identification criteria, namely, the coefficient of determination *R*<sup>2</sup> and Young identification criterion (YIC). The orders of these polynomials in Equations (4) and (5) are *na* and *nb*. For these data, model orders between 1 and 2 for *n* and *m* respectively were evaluated, including time delays between 0 and 1. The best fit was obtained using first order polynomials with a fixed *a*<sup>1</sup> parameter in time and a variable *b*<sup>0</sup> during all the different time points. The accuracy of this fit is measured with MATLAB version 2018b using normalised root mean square error (NRMSE) with the goodness of fit function. This method is described as follows:

$$\text{NRMSE} = 1 - \frac{\left\| y\_{ref} - y\_{fit} \right\|}{\left\| y\_{ref} - mean(y\_{ref}) \right\|} \tag{7}$$

where *yfit*, the modelled data, compared to *yre f* , the reference data. The NRMSE equals 1 for a perfect fit.

#### 2.2.4. Cost Function

The optimal process parameter values are those which steer the system towards the reference trajectory function. These values are calculated as the ones minimising a controller's cost function. This cost function consists of one term to minimise the difference between the predicted output (*y*ˆ) and the reference trajectory (r), and another term to minimise the change of the control signal (Δ*u*) (i.e., the replaced medium volume). This equation is as follows:

$$f(\text{Nc}, \text{Np}) = \sum\_{j=1}^{\text{Np}} \delta(j) \left[ \mathfrak{H}(k+j|k) - r(k+j) \right]^2 + \sum\_{j=1}^{\text{Nc}} \lambda(j) \left[ \Delta u(k+j-1) \right]^2,\tag{8}$$

where *Nc* is the control horizon, *Np* is the prediction horizon (time points where *y* is controlled to follow *r*) and δ, λ are used as weights to create a relevance ranking [22,29].

#### 2.2.5. Constraints

The solutions to optimise the system are subject to constraints. The input, manipulated to control the system, could be restricted by physical boundaries. For example, replacing the medium for 100% in certain vessels is impossible without the risk of removing cells together with the medium. In addition, the output of the system could also be restricted to assure product quality, feasibility or safety. For example, the lactate concentration of the cell culture system is limited to avoid toxic lactate levels, meaning a value of 20 mM [30]. There was no need to implement these constraints in the current work, since the toxic lactate threshold was never reached in these experiments, not even for the condition of minimal lactate replacement.

#### 2.2.6. Simulation

In this paper, the use of a model-based predictive control approach was evaluated for cell growth control by quantifying the performance of the controller based on simulated control actions. More specifically, the experimental data were used to identify time-varying transfer function models describing the dynamic relations between cumulative lactate concentrations and medium refreshments and these models were used in combination with the control algorithms to simulate the needed medium refreshments. The reference trajectory for cumulative lactate concentration was assumed to be the cumulative lactate concentrations actually measured for each condition.

#### **3. Results**

#### *3.1. Collected Data*

Figure 3 shows the amount of accumulated lactate produced and the cell number after the five days of cell expansion. These results are summarised in Table 2, and show the average of the triplicates for the different donors and different medium replacement conditions, which were explained in Table 1.

**Figure 3.** Average results with error bars for the triplicate experiments of each individual donor with each specific medium replacement strategy. (**a**) Total accumulated lactate produced after 5 days of cell culture (mM). (**b**) Cell numbers counted at the end of the cell culture period.


**Table 2.** Total amount of cells harvested after the cell culture expansion, which is averaged over the triplicates for each donor and condition (100,000 cells).

Figure 4 represents an example of measured lactate concentration over time, similar to Figure 2, but adapted to the data from the experiments with donor 1, condition 5 and triplicate 1.

**Figure 4.** Lactate concentration over time (days) for the results of donor 1, condition 5 and triplicate 1.

Table 3 represents how efficiently the amount of medium is used for proliferation by the cells. This is calculated by dividing the total amount of cells by the total amount of medium supplied during the cell expansion. The table indicates that the most efficient medium replacement strategy, meaning the most cells per amount of medium used, is donor- and not method-dependent. All three different donors require different medium replacement strategies. However, giving the cells the highest amount of medium (condition 6 with 100% medium replacement every 24 h) always results in the highest amount of cells at the end of the expansion. Also, the lowest amount of medium replacement always results in the lowest amount of cells at the end of the expansion.


**Table 3.** Efficiency of medium used over the total cell culture period, calculated by dividing the total cell numbers by the total amount of medium used (10,000 cells mL<sup>−</sup>1).

Therefore, to develop a model predictive controller, it is always necessary to keep in mind what the goal or reference is. If the goal is to predict the feeding strategy of the cells in order to reach the highest amount of cells, the controller would suggest to replace the medium as much as possible. The downside is that resources are wasted due to unnecessary medium replacements. A more interesting question would be to ask the controller how much medium should be replaced to reach, for example, 80% of the total amount of cells according to a maximum medium replacement strategy (condition 6) in the same amount of time. Or another question could be, in a case where a patient has a procedure scheduled in fixed amount of time, e.g., eight weeks: how much medium should be provided to the cells to reach the therapeutically-required amount of cells in eight weeks?

Table 4 represents the results of the average amount of lactate produced by each cell at the end of the cell expansion. This relation is interesting for translating the accumulated amount of lactate produced to the amount of cells. However, this number differs for each donor and differs even more between different medium-replacement strategies. Condition 6, in which the medium is replaced 100% every day, could be a representation of how the cells produce lactate in an optimal environment. Condition 4, in which only 10% of the medium is replaced every day, has a significantly higher amount

of lactate produced over the expansion period, which is due to either a lack of nutrients and growth factors, or inhibiting factors such as lactate itself.


**Table 4.** The accumulated lactate divided by the cell numbers at the end of the cell culture period and divided by total culture time (120 h), averaged over the triplicates for each donor and condition (10,000,000 mM cell−<sup>1</sup> h<sup>−</sup>1).

One of the biological reasons for this difference in lactate produced by cells could be that cells die due to this lactate inhibition or nutrient and growth factor depletion. Therefore, less cells are counted in the end than actually lived, causing a higher lactate·cell−<sup>1</sup> ratio [31]. Another reason could be that cells are changing their metabolic profiles [32].

#### *3.2. Interpolated Data*

When using the piecewise linear interpolation method, the fit was 100%, since all data points are being used. The piecewise linear interpolation methods were further used to interpolate the sparse data set. Instead of using only one data point every day, the data are interpolated to one data point every hour, which reflects a more realistic approach for field conditions.

#### *3.3. Prediction Model*

The model parameters for the DARX model, represented in Equation (3), were obtained using first order polynomials with a fixed *a*<sup>1</sup> parameter (cf. Equation (4)) in time and a variable *b*<sup>0</sup> (cf. Equation (5)) during all the different time points. The accuracy of this DARX model compared to the piecewise interpolated output is shown in Table 5 and visualised in Figure 5.

**Figure 5.** Visualisation of dynamic auto-regressive exogenous (DARX) model for accumalated lactate (mM) compared to the interpolated data for the experiment of donor 1, condition 5 and triplicate 1.


**Table 5.** Accuracy measured using normalised root mean square error (NRMSE) of DARX model compared to output of the interpolated data for each condition, donor and triplicates. The DARX model used is either the one based on the corresponding experimental data (diagonal values) or on the data of an experimental triplicate. The value is NRMSE multiplied by 100 and expressed as a percentage, with 100 being a perfect fit.

Using a fixed parameter *a*<sup>1</sup> and a dynamic parameter *b0,t* results in only one parameter adjusting to the dynamics of the system, making the interpretation of the changes easier. From Figure 6 it can be deducted that *b0,t* is an indicator of how much the cells are competing for the medium. On one hand, if the parameter exhibits an overall low absolute value, as seen in Figure 6a, it indicates that the cells have leftover medium that is not used and will be replaced unnecessarily, which means that resources are wasted. On the other hand, if an overall higher absolute value is attained, as seen in Figure 6b, then the cells do not have enough medium to fulfil their potential growth.

**Figure 6.** Graphs exhibiting the *b0,t* values over time. (**a**) *b0,t* values for triplicates of donor 1 under condition 6, which means 100% medium replacement every 24 h. (**b**) *b0,t* values for triplicates of donor 1 under condition 4, which means only 10% medium replacement every 24 h.

#### *3.4. Simulation of the Model Predictive Controller*

MPC simulations were performed based on the identified prediction models for each type of medium replacement strategy. An example for condition 1 and condition 6 are given in Figure 7, with accumulated lactate produced by the cells as target output and accumulated amount of medium replacement as an input variable.

**Figure 7.** Top graph shows the interpolated output (accumulated lactate (mM)) compared to the simulated output. Bottom graph represents the interpolated input (total replaced medium (mL)) compared to the simulated input. (**a**) model-based predictive control (MPC) simulation applied to donor 1, condition 1 and triplicate 1; (**b**) MPC simulation applied to donor 3, condition 6 and triplicate 3.

The goodness of fit between the controller's input suggestions and output and the experimental data are summarised in Tables 6 and 7.

**Table 6.** The accuracy of the MPC simulation is measured using NRMSE and multiplied by 100 to be expressed as a percentage, with 100 being a perfect fit. The accuracy of the MPC simulation is represented for the difference in input (accumulated replaced medium (mL)) of the experimental data compared to the input of the simulated data. All NRMSE values calculated for all three donors and all three triplicates are equal for the same condition of medium replacement.


**Table 7.** The accuracy of the MPC simulation is measured using NRMSE and multiplied by 100 to be expressed as a percentage, with 100 being a perfect fit. The accuracy of the MPC simulation is represented as the difference between output (accumulated lactate (mM)) of the experimental data compared to the output of the simulated data. The DARX model used to perform the simulation is either the one based on the corresponding experimental data (diagonal values) or on the data of an experimental triplicate.


#### **4. Discussion**

Monitoring and controlling the cell growth is crucial when developing a large-scale reproducible cell culture process. However, there are currently no standardised methods to sample the amount of cells during a cell culture expansion in tissue flasks or hollow fibre bioreactors. Previous studies have therefore investigated the benefits of controlling the environment of the cell culture vessels using standard physicochemical process parameters [15]. In addition, other studies developed potential soft sensors using the metabolic responses of the cells to control the process, mostly glucose concentration [33,34]. This work used this metabolic soft sensor concept by measuring the lactate concentration off-line and used it as an indication of the cell growth, which can otherwise only be measured at the end of the bioprocess.

Choosing the correct control strategy for this framework results in high accuracy between the experimental data and the simulated data. Many different control strategies have been explored in fermentation processes [35], some for mammalian cells [15,17], and a few for human cells [36]. These control strategies are built on either user experience, a process model or historical data [35]. Each strategy has its own benefits and disadvantages. Using an approach based only on user experience has the advantage that it can be quickly applied to a new system without the need for historical data or a process model. However, these approaches, such as probing control [37] or fuzzy control [38], are running behind the action, because they act when the current state is not ideal, without an optimal strategy for the whole process. When there is a large amount of historical data, interesting approaches are artificial neural networks [20,21] or statistical process controls [39]. However, for cell therapy bioprocesses this is mostly not the case, since these data are very process-specific and cannot be extrapolated for different cell types, batch sizes or in autologous applications, which are donor-specific. Mechanistic mathematical approaches encounter the same difficulty, because their specific sets of kinetic parameters have to be redefined for each specific process, requiring many specific data sets. A mathematical model, for example, one that describes the exponential growth of cells in combination with consumption nutrients and production waste products [36], is useful for the prediction of an average control strategy for that cell type. However, the downside of these mathematical models is that they contain cell-lineage-specific kinetics parameters from literature and should be updated for every stage of that cell lineage, e.g., proliferation or differentiation [40].

In cases where there is a process model available, the preferred choice would be to use model-based predictive control (MPC), because it can deal with non-linear dynamics, unpredictable disturbances and provides insight for the user [35]. Other attempts at controlling bioprocesses using an MPC have been made. One of them consisted of controlling the glucose concentration to maintain more than a certain threshold of 11 mM in a 15 L fed-batch system [34]. To achieve this, they used a non-linear model-based predictive control to adapt the feed rate based on a mechanistic mathematical model which describes the cell growth and metabolism. However, the main problem was the process–model mismatch, which is inherent to the variability of a bioprocess. They also compared an off-line measurement method with 12 h between samples to an on-line spectroscopy technique sampling every six minutes. The problem with on-line glucose methods was a high sample-to-noise ratio. Another study tried to avoid this problem of the high cost and noise of on-line glucose sensors by developing a soft sensor [33]. This soft sensor uses cumulative oxygen transfer rates, calculated using several on-line measured variables. It defines the correlation between the on-line soft sensor and the real glucose concentration by comparing off-line measures of glucose every 24 h to recalculate the correlation.

What was still missing from most current control strategies is the combination of a model predictive control with an adaptive control strategy to avoid the process–model mismatch [34]. Therefore, this paper uses the MPC approach and implements an adaptive prediction model. This allows the model to predict the next input to achieve the desired output based on all previous inputs and outputs, taking into account unpredictable disturbances or inherent batch variability in bioprocesses by updating the model parameters in real-time. The accuracy of the model fit when using the same model over different medium replacement conditions or different donors can even be below 50%. This is represented in Table A1 where the model for donor 2 is fitted on data of donor 3. This points out the variability between donors and realisations. However, the potential of the approach developed in this work is that the model is estimated and adapted in real-time solely using data for that specific realisation/individual, and thus guarantees a personalised approach.

This work also uses the concept of a soft sensor by using another measurable variable (lactate concentration) to estimate a desired critical quality attribute of the bioprocess (cell number). The flexibility of the controller to react to disturbances as well as process variability is shown by successfully applying the controller to three different donors and six different control strategies in triplicate.

The next step for this work is to implement the controller in real-time to the system and re-evaluate the performance of the controller. The prediction model will be updated with every new data point received from the current experimental run. In future experiments, the idea is to start from the known model structure, which was found to be the best representation for that bioprocess. In this case, the model would be a DARX model with a fixed *a*<sup>1</sup> parameter and a variable *b*<sup>0</sup> over time. After gathering enough data points, depending on the measuring frequency, this could be one day. The model will be developed based on the parameters defined by the process at hand. After this initial data gathering period, the model and controller will be updated in real-time using only the data from the current experiment. Using only the fixed model structure from previous experiments would lead to better results compared to other modelling techniques, where the parameter values of previous experiments are also used without tuning them based on experiment-specific data. The MPC approach presented in this work, which uses the data of each specific realisation, results in a model that adapts well to the process at hand.

In addition, this MPC model could potentially address a case study based on giving the process just enough medium to reach a certain percentage of the maximum cell number at harvest. This maximum cell number is estimated when supplying the process with 100% medium every day. However, to practically perform such a controlled process, additional knowledge about the system is required, which can be gained by performing follow-up experiments. One strategy to consider for these experiments is to observe the *b*<sup>0</sup> values of the DARX model, which is continuously re-estimated with every new data point collected from the experiment at hand. Further analysis could lead to finding certain thresholds for this parameter that would result in reaching a predefined percentage of the maximum achievable cell number at harvest.

Another additional path to explore is to correlate the cumulative lactate produced back to the biomass growth, in order to use the measurements as a soft sensor and estimate the amount of biomass at each lactate sample time point. However, the relation between the number of cells and lactate produced can differ not only between cell types, but also between different medium replacement strategies. In cases where cells receive a very low amount of medium, cells could die due to nutrient and growth factor depletion. Another possibility which could lead to a change in the relation between the amount of cells and the amount of lactate produced is a metabolic alteration (a by-product of glycolysis) by the cells when the amount of replaced medium is low [41]. Therefore, it would also be important in additional experiments to assess different quality attributes of the cells to check whether all process parameters are possible or if certain thresholds on medium replacement are required to avoid changing the quality and characteristics of the cells. The quality could be assessed with live/dead analysis, additional measures such as Lactate Dehydrogenase (LDH) and flow cytometry for MSC markers or the trilineage potential, determining the osteogenic, chondrogenic or adipogenic potential.

When these two steps of real time implementation and translation into cell numbers are combined, the controller could potentially solve case studies using an adaptive reference trajectory where a specific number of cells is required by a specific realistic time period using a minimal amount of medium. This approach is also capable of implementing different manipulated and controlled variables, in case new sensor techniques come onto the market.

Finally, instead of using well plates as a way to keep process costs low and experimental time short for a large amount of experiments, we envisage the use of such tools for suspension bioreactors where progenitor cell populations can be scaled-up for clinical production, allowing, at the same time, the capacity for real-time process adaptation [10,40].

#### **5. Conclusions**

The model predictive controller developed in this work is a generic algorithm which requires minimal effort to implement different process parameters and different responses of the system. This controller has the potential to be an inexpensive tool to minimise the costs and time of cell expansions in combination with assured product quality by design (QbD) [42]. Using cumulative lactate concentrations as an output measurement of the controller has proven to be useful in this specific bioprocess setting, where high glucose DMEM was used. However, it is important, when applying this method to a different bioprocess, to first assess which output measurement and related process parameter would suit that specific bioprocess.

Six different combinations of medium replacement were tested on three different donors in triplicate in order to model the dynamical response of medium replacement on cell proliferation. This dynamic response is best modelled using a DARX prediction model, resulting in an overall high R<sup>2</sup> of 99.80% ± 0.02% for the DARX model on the same experimental data. The process–model mismatch is also low when applying a model based on experimental data from one triplicate to experimental data from another one of the triplicates. The average fit for the triplicates in DARX models on all the triplicates of experimental data is 96.57% ± 3.26%.

Based on simulations, the model predictive controller designed in this work shows promising results to accurately predict the effect of medium replacement on cell growth. The medium change input suggested by the simulation has a 86.45% ± 0.78% accuracy compared to the real experimental data, whereas the accumulated lactate output has an accuracy of 98.64% ± 0.10% compared to the target experimental data.

The results in this work show that this lactate-based model predictive controller can be applied to different donors as well as different medium-replacement strategies. The parameters are estimated for each individual experimental run, resulting in a high accuracy fit between the simulated data and the experimental data. Using these individualised parameters is the main advantage compared to other control strategies, which are more focused on a suitable prediction for the average bioprocess [14,17].

**Author Contributions:** Conceptualisation, K.V.B., T.L.; methodology, K.V.B., T.L., A.Y., I.P., A.P.F., J.-M.A.; software, K.V.B., A.P.F., A.Y.; validation, K.V.B.; formal analysis, K.V.B.; investigation, K.V.B., I.P.; resources, I.P., J.-M.A.; data curation, K.V.B.; writing—original draft preparation, K.V.B.; writing—review and editing, K.V.B., A.Y., A.P.F., T.L., I.P. and J.-M.A.; visualisation, K.V.B.; supervision, I.P. and J.-M.A.; project administration, J.-M.A.; funding acquisition, I.P., J.-M.A. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by KU Leuven, grant number C24/17/077.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Appendix A**

**Table A1.** Model mismatch example, where the DARX models of donor 2 are applied to experimental data from donor 3. The results are the NRMSE multiplied by 100, between the DARX model and the data.


#### **References**


© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Article* **An Approach towards a GMP Compliant In-Vitro Expansion of Human Adipose Stem Cells for Autologous Therapies**

#### **Valentin Jossen 1,\*, Francesco Muoio 2, Stefano Panella 2, Yves Harder 3,4, Tiziano Tallone <sup>2</sup> and Regine Eibl <sup>1</sup>**


Received: 12 June 2020; Accepted: 15 July 2020; Published: 20 July 2020

**Abstract:** Human Adipose Tissue Stem Cells (hASCs) are a valuable source of cells for clinical applications (e.g., treatment of acute myocardial infarction and inflammatory diseases), especially in the field of regenerative medicine. However, for autologous (patient-specific) and allogeneic (off-the-shelf) hASC-based therapies, in-vitro expansion is necessary prior to the clinical application in order to achieve the required cell numbers. Safe, reproducible and economic in-vitro expansion of hASCs for autologous therapies is more problematic because the cell material changes for each treatment. Moreover, cell material is normally isolated from non-healthy or older patients, which further complicates successful in-vitro expansion. Hence, the goal of this study was to perform cell expansion studies with hASCs isolated from two different patients/donors (i.e., different ages and health statuses) under xeno- and serum-free conditions in static, planar (2D) and dynamically mixed (3D) cultivation systems. Our primary aim was I) to compare donor variability under in-vitro conditions and II) to develop and establish an unstructured, segregated growth model as a proof-of-concept study. Maximum cell densities of between 0.49 and 0.65 <sup>×</sup> 105 hASCs/cm<sup>2</sup> were achieved for both donors in 2D and 3D cultivation systems. Cell growth under static and dynamically mixed conditions was comparable, which demonstrated that hydrodynamic stresses (*P*/*<sup>V</sup>* <sup>=</sup> 0.63 W/m3, <sup>τ</sup>*nt* <sup>=</sup> 4.96 <sup>×</sup> <sup>10</sup>−<sup>3</sup> Pa) acting at *Ns1u* (49 rpm for 10 g/L) did not negatively affect cell growth, even under serum-free conditions. However, donor-dependent differences in the cell size were found, which resulted in significantly different maximum cell densities for each of the two donors. In both cases, stemness was well maintained under static 2D and dynamic 3D conditions, as long as the cells were not hyperconfluent. The optimal point for cell harvesting was identified as between cell densities of 0.41 and 0.56 <sup>×</sup> 10<sup>5</sup> hASCs/cm<sup>2</sup> (end of exponential growth phase). The growth model delivered reliable predictions for cell growth, substrate consumption and metabolite production in both types of cultivation systems. Therefore, the model can be used as a basis for future investigations in order to develop a robust MC-based hASC production process for autologous therapies.

**Keywords:** human adipose stem cells (hASCs); serum- and xeno-free conditions; UrSuppe stem cell culture medium; autologous therapy; kinetic growth modeling; segregated and unstructured growth model

#### **1. Introduction**

The successful development and application of cell-based therapies has the potential to treat a number of currently incurable diseases and to improve patient care. It is therefore not surprising that many research activities [1,2] are taking place all over the world in the field of regenerative medicine. However, despite the progress in this field, there are a number of challenges that remain before cell-based therapies can be performed more routinely in clinical practice.

Human Adipose Tissue Stem Cells (hASCs) have demonstrated their potential to target a number of currently incurable clinical conditions [2]. This is not surprising since adipose tissue has recently been discovered to be a novel abundant source of adult stem cells, which can be collected by minimally invasive, low risk procedures for the donors/patients and processed by different techniques [3–5]. Moreover, results from recently performed clinical trials have indicated possible applications in the treatment of acute myocardial infarction, stroke and a host of inflammatory and immune disorders [6]. Human ASCs are also gaining increasing interest in plastic and reconstructive surgical procedures, where a trend towards stem cell-based tissue-engineering strategies is evident. However, the majority of these clinical applications require in-vitro expansion of the cells to deliver an effective therapeutic dose. The intention of the in-vitro expansion step is to manufacture a sufficient number of hASCs under Good Manufacturing Practice (GMP) conditions and in a cost-effective manner [7–10]. The processing of hASCs must be performed in accordance with the Directive 2003/94/EC for cell-based medicinal products [11]. In general, hASC-based therapies can be broadly divided into two categories: patient-specific therapies (autologous) and off-the-shelf therapies (allogeneic). From an economic point of view, the allogeneic therapy approach seems to be the most attractive option at present [12–14]. However, a crucial factor for the economic success of allogeneic cell-based therapies in terms of affordability will depend on whether the patient receiving the stem cell therapy will require immunosuppressive medication. A combined treatment with immunosuppressive drugs will significantly increase the overall life cycle cost of the treatment. In contrast, autologous therapies require careful consideration of regulatory challenges as well as the distribution and delivery of a safe and effective cell-based therapeutic. Furthermore, it is crucial to consider how a cell therapy manufacturing process can be developed to consistently manufacture products from multiple patients/donors [15]. Therefore, technical and biological characterizations of different cultivation technologies, different donors and other biological aspects are important and will support the development of descriptive and predictive models in the future. Achieving consistency and reproducibility in the manufacture of medicinal products is a key requirement for regulatory approval [16,17] and can be achieved to some extent by a reduction in process variations. A key aspect in reducing process variation is the elimination of fetal bovine serum (FBS) in the cell culture medium [18]. Various studies have already shown that serum-free cell culture media can be used in combination with stirred bioreactors and Microcarrier (MC) technology [19–22] in order to expand human mesenchymal stem cells (hMSCs). In addition to the MC-based expansion technology, hollow fiber bioreactors are also frequently used for the hMSC expansion, with which total cell densities of up to 109 hMSC can be achieved [23,24]. In contrast to the MC-based expansion, hMSC cell growth occurs inside the hollow fibers, which are permanently flown through with cell culture medium. However, cell harvest could be problematic in these systems and must be carefully developed based on the expansion process. Amini et al. [25] developed a static, wicking matrix bioreactor that provides a thing film of medium that drips onto cells on the scaffold. They used this new bioreactor concept successfully for the expansion of hiPSC-derived pancreatic cells for the production of insulin. Thus, such new bioreactor concepts are also interesting for the expansion of hMSCs.

In contrast to traditional planar and static cultivation systems, MCs (typically in the range of 100–300 μm) provide a surface on which the strictly adherent hASCs can grow in stirred and instrumented bioreactors. The MCs consist of different materials (e.g., polystyrene and gelatin), including synthetic/organic or natural polymers that are synthesized with different porosities and topographies. The careful selection and tuning of the MCs and the serum-free cell culture medium is important and has an influence on the success of in-vitro cultivation.

The aim of this proof-of-concept study was to perform cell expansion experiments with hASCs isolated from two different patients/donors (i.e., different age and health status) under xeno- and serum-free conditions in static, planar (2D) and dynamically mixed (3) cultivation systems. In so doing, we (I) compared the donor variability under in-vitro conditions in two different cultivation systems and (II) developed and established an unstructured, segregated growth model for future investigations. However, due to the limited accessibility of the donor/patient material, only two donors were considered in the present study in order to establish first versions of the growth model. Special emphasis was placed on determining growth-related parameters (i.e., parameters for growth rate and metabolic flux) and comparing cell-specific Critical Quality Attributes (CQAs) during the processing of the hASCs under the static 2D and dynamic 3D process conditions. The growth-related parameters were subsequently used to establish a mathematical growth model for donor-dependent cell growth description, substrate consumption and metabolite production under static 2D and dynamic 3D process conditions.

#### **2. Materials and Methods**

#### *2.1. Procurement of Subcutaneous Adipose Tissue from Human Donors*

The human adipose tissue samples used in this study (*n* = 2 donors, referred to as 080 and 085) were obtained from tissue excess originating from surgical interventions performed at the Department of Plastic, Reconstructive and Aesthetic Surgery at the Ospedale Regionale di Lugano (Switzerland). All patients who donated their adipose tissue provided written agreement in compliance with the directives of the local Ethics Committee of the Canton of Ticino (Switzerland), which approved the project and its procedures (project reference number: CE 2915).

The cellular sources used in this study originate from subcutaneous adipose tissue harvested from the abdominal region of female patients undergoing autologous breast reconstruction under general anesthesia. Firstly, depending on the position of the deep inferior epigastric artery and its perforating vessels (DIEP-flap), a symmetrical diamond-shaped abdominal flap was dissected between the umbilicus and the pubis. Any excess subcutaneous adipose tissue, not used for breast reconstruction, was packed into two sterile bags to avoid any contamination and was delivered for further processing of the tissue. The adipose tissue samples were stored at room temperature and processed within 24 h [26] to obtain the Stromal Vascular Fraction (SVF).

#### *2.2. Isolation and Establishment of a Serum-Free hASC Culture*

The extraction of the SVF from human adipose tissue and the in-vitro expansion and cryopreservation of the isolated hASCs was performed in accordance with the ethical principles outlined in the Declaration of Helsinki and in compliance with the directives of the Ethics Committee of the Canton of Ticino (Switzerland). The isolated tissue samples were firstly separated from the skin tissue, washed in PBS and homogenized in a blender for 10–15 s (100–400 g of fat tissue). After this initial step, the tissue was digested for 45 min at 37 ◦C with 0.28 Wünsch Unit/mL of Collagenase AB [27] (Worthington Biochemical Corp., Lakewood, NJ, USA). The enzymatic reaction was stopped by the addition of PBS supplemented with 1% human albumin (CSL Behring AG, Bern, Switzerland). After separating the aqueous phase from the lipid phase, the aqueous phase was collected in a new sterile tube. The cells were subsequently centrifuged and filtered to obtain a fresh SVF.

In order to characterize the SVF, the cells were stained with anti-CD34-BV650, anti-CD45-PC7, anti-CD73-FITC (BioLegend, San Diego, CA, USA), anti-CD146-PE, anti-CD36-APC (Miltenyi BioTech, Bergisch Gladbach, Germany), 7-amino-actinomycin D (7-AAD) (Becton Dickinson, Franklin Lakes, NJ, USA) and Syto40 (Life Technologies from Thermo Fisher Scientific, Waltham, MA, USA). All of the antibodies were titrated to optimize the signal–to–noise ratio and used at a specific concentration (further information can be found in "Supplementary Materials Table S2"). After 20 min of incubation, the erythrocytes were lysed with 1 mL of VersaLyse solution (Beckman Coulter Inc., Brea, CA, USA). A Forward Scatter Time-of-Flight channel was used to select single cell events, Syto40 DNA marker was used to exclude cellular debris and 7-AAD was used to discriminate between dead and living cells. Cells were acquired using a Cytoflex flow cytometer (Beckman Coulter Inc., Brea, CA, USA). The ASC cell population was defined as CD45−, CD146−, CD36−, CD34<sup>+</sup> and CD73+.

After characterization, cells were seeded at a density of 30,000 ASCs/cm2 in fibronectin precoated plates (Corning Inc., New York City, NY, USA) with our chemically defined serum- and xeno-free stem cell culture medium, called UrSuppe. The stem cell culture medium was changed every 2–3 days, always keeping 50% of the conditioned medium, until the cells reached a confluency of 80–90%. For passaging, the cells were detached from the growth surface by incubating them for 2 min at 37 ◦C in TrypLE Select [28] (Life Technologies from Thermo Fisher Scientific, MA, USA). After discarding the supernatant, the cells were resuspended in UrSuppe and passaged or used for other experimental investigations in this study.

#### *2.3. hASC Growth Characterization under Planar, Static Conditions (2D Monolayer Expansion)*

2D growth characterization of previously isolated hASCs was performed in precoated T25-flasks (5 μg/cm<sup>2</sup> r-fibronectin; Sigma Aldrich, St. Louis, MO, USA) with the UrSuppe stem cell culture medium (5 mL). For this purpose, the cryopreserved, patient-derived hASCs (P1, 080-PDLcum. 3.9, 085-PDLcum. 3.7) were thawed and precultured in T75-flasks (10,000 hASCs/cm2; 37 ◦C, 5% CO2, 80% rH) in order to achieve the required cell numbers to inoculate 22 × T25-flasks per donor (P2, 080-PDLcum. 6.3, 085-PDLcum. 6.5, 10,000 cells/cm2). The hASC growth characteristics were assessed over 11 days by harvesting two T25-flasks per donor (2 mL TrypLE Select at 37 ◦C, 2 min) every day. The cell density, substrate and metabolite measurements were carried out using a NucleoCounter NC-200 (Chemometec, Allerod, Denmark) and a Cedex Bio (Roche Diagnostics, Rotkreuz, Switzerland), respectively. In addition to standard T25-flasks, T25-flasks equipped with pH and DO sensor spots (PreSens, Regensburg, Germany) were also inoculated in parallel for each donor in order to assess the pH and DO profiles during cell growth (37 ◦C, 5% CO2, 80% rH). In each case, partial medium exchanges of 40% and 60% were performed for each donor on days 4 and 8.

#### *2.4. hASC Growth Characterization under Dynamically Mixed Conditions (Microcarrier-Based Expansion)*

3D growth characterization was performed for each donor (P3, 080-PDLcum. 11.5, 085-PDLcum. 11.6) using fibronectin-coated polystyrene beads (ProNectin® F-COATED, Pall SoloHill, New York City, NY, USA) in 125 mL disposable Corning spinner flasks (=100 mL UrSuppe). An initial cell density of 15,000 cells/cm<sup>2</sup> (=54,000 cells/mL) and a Microcarrier (MC) concentration of 10 g/L (=1 g, 360 cm2) were used to inoculate the spinner flasks. The MC concentration of 10 g/L was defined based on previous investigations by Schirmaier et al. [29] and Jossen et al. [1,30]. The cell inoculum was prepared in T75-flasks coated with r-fibronectin (5 μg/cm2) and with cells from P1 (=080-PDLcum. 3.9, 085-PDLcum. 3.7). Before inoculation, the MCs were prepared and sterilized according to the vendor recommendations one day before usage. After cell inoculation, a static cell attachment phase of 24 h was performed in a cell culture incubator (37 ◦C, 5% CO2, 80% rH) to allow the cells to attach to the MC surface. After the static attachment phase, the culture was continuously stirred at 49 rpm. The selected impeller speed, which corresponded to the *Ns1u* criterion for 10 g/L MCs in the 125 mL disposable Corning spinner flask, was defined based on experimental and numerical fluid flow investigations by Kaiser et al. [31] and Jossen et al. [1,30]. The *Ns1u* suspension criterion defines the lower limit of *Ns1* (=*Njs*), meaning that some MC beads are still in contact with the reactor bottom, but none of them were at rest [32]. On day 5, a partial medium exchange of 50% was performed. For this purpose, the impeller was switched off and the MCs were allowed to settle. Fifty percent of the working volume was replaced with fresh preheated UrSuppe stem cell culture medium, and the impeller was restarted. No MC feeds were performed during the cultivations.

Off-line samples were taken daily to measure substrate and metabolite concentrations (Glc, Lac and Amn) with a Cedex Bio (Roche Diagnostics, Rotkreuz, Switzerland). After the cells had been detached from the MC surface by the enzymatic treatment (15 min with TrypLE Select), the hASC cell number was measured using a NucleoCounter NC-200. The measured cell specific values were used to calculate the growth-related parameters as described in Section 2.6. In addition to the cell measurements, 1 mL of the MC-cell suspension was fixed immediately after sampling with a 3% paraformaldehyde solution for 4 ,6-diamidin-2-phenyliondol (DAPI) staining.

#### *2.5. Cell Analytics*

#### 2.5.1. Flow Cytometric Analysis

Flow cytometric measurements were performed at the end of the growth characterization experiments (10th day of cultivation): 2D monolayer and MC-based expansion. The flow cytometric measurements contained different mixtures of the following antibodies: CD26-FITC, CD73-FITC, CD90-APC, CD105-PE (BioLegend, San Diego, CA, USA), CD36-APC, CD146-PE (Miltenyi Biotec, Bergisch Gladbach, Germany), CD55-BV421 (Becton Dickinson, Franklin Lakes, NJ, USA) and CD54-PE (Thermo Fisher Scientific, Waltham, USA). All of the antibodies were titered in advance in order to improve the signal-to-noise ratio; the final measurements were carried out with 50 ng/test (respective mAbs and Isotype controls). A Zombie Yellow™ Fixable Viability Kit (BioLegend, San Diego, CA, USA) was used to distinguish between live and dead cells after fixation (1% paraformaldehyde in DPBS for 1 min at RT). For the staining procedure, 50,000 cells in 100 μL FACS buffer (PBS supplemented with 1% albumin and 50 ng/μL human immunoglobulin, Privigen Immunogobulin, CSL Behring AG, Bern, Switzerland) were pipetted into a well, gently mixed and subsequently incubated in the dark for 15 min at room temperature. After the incubation step, the samples were diluted with 100 μL FACS buffer. Sample acquisition and analysis were performed using a Cytoflex flow cytometer (Beckam Coulter Inc., Brea, CA, USA) and Kaluza analysis software. The spectral spill-over from the different fluorochromes was assessed by spectral compensation of the individual fluorescence channels. For this purpose, single stained control particles (VersaComp Antibody Capture Bead Kit, Beckman Coulter, Brea, CA, USA) or cells in combination with the different fluorochromes were used. The compensation matrix was automatically calculated using the dedicated software function integrated into the Kaluza analysis software. Flow cytometer functionality, including the control of the optical alignment and fluidics, was verified routinely with fluorospheres (CytoFLEX Daily QC fluorospheres, Beckman Coulter, Brea, CA, USA). Further information about the different antibodies can be found in "Supplementary Materials Table S2".

#### 2.5.2. RT-qPCR Analysis

RT-qPCR measurements were carried out at different times (day 1, day 5 and day 10) after daily harvesting of the hASCs. The different RT-qPCR measurement times represent distinct phases of cell proliferation; day 1: start of cell proliferation, day 5: exponential cell growth and day 10: plateau due to cellular confluence (end of cultivation). For this purpose, RNAs were extracted from the cell pellets or from the MCs covered with cells by using a Nucleospin®RNA kit (Macherey-Nagel, Düren, Germany). The RNA purification process included an on-column digestion step with DNase I and was performed according to the manufacturer instructions. The RNA purity and quantity was assessed with a NanoDrop microvolume spectrophotometer (Thermo Fisher, Waltham, MA, USA) and the total RNA integrity was periodically verified by agarose gel analysis. cDNA was obtained from 900 ng RNA using a GoScriptTM Reverse Transcription System (Promega, CA, USA). Detailed information about the protocol can be found in "Supplementary Materials Table S3". RT-qPCR of the *PREF1, SOX9, WISP1, WISP2, NOTCH1, DLL1, CD26, CD55, CD248, CD142, ZP521, ZFP423, PPARG, DKK1, RUNX2, CD34, CD36* and *CD146* genes was performed using 20 ng cDNA for each gene of interest and a SsoAdvancedTM Universal SYBR® Green Supermix kit (Biorad, Hercules, CA, USA) in combination with a CFX Connect System for signal detection. An overview of the different primer sequences is shown in Table 1, where ACTB was used as an internal control for all measurements. Each primer pair

product was checked for proper amplification using agarose gel electrophoresis and only single sharp bands of the expected size were used for further analysis. The RT-qPCR process was divided into 5 phases: (I) initial denaturation (95 ◦C, 120 s), (II) cycle denaturation (95 ◦C, 5 s), (III) cycle annealing and extension (60 ◦C, 20 s), (IV) final denaturation (95 ◦C, 5 s) and (V) melting curve (65–95 ◦C, 18 min), where phases II and III were repeated 40 times in the sequence. The resulting data were analyzed using CFX software in order to evaluate the ΔΔCt values, which were normalized using the value of the housekeeping gene ACTB as the reference gene. The relative fold changes of the analyzed genes are related to the beginning of the culture (day 1).


**Table 1.** Overview of primer sequences used for RT-qPCR measurements.

#### *2.6. Determination of Cell Biological Kinetic Parameters: Growth Dynamics and Metabolic Activity*

Based on regular measurements of cell density and substrate/metabolite concentration, growth-dependent parameters were calculated for the planar and MC-based cultivations as follows:

(I) Specific growth rate (μ):

$$\mu = \frac{\ln(X\_A(t)) - \ln(X\_A(0))}{\Delta t} \tag{1}$$

where μ is the net specific growth rate (d<sup>−</sup>1), *XA(t)* and *XA(0)* are the cell numbers (cells/cm2) at the end and the beginning of the exponential growth phase, respectively, and *t* is the time (d).

(II) Doubling time (*td*):

$$t\_d = \frac{\ln(2)}{\mu} \tag{2}$$

where *td* is the doubling time, *ln(2)* the binary logarithm of 2 and μ the specific cell growth rate.

(III) Population Doubling Level (*PDL*):

$$\text{PDL} = \frac{1}{\log(2)} \cdot \log\left(\frac{X\_A(t)}{X\_A(0)}\right) \tag{3}$$

where *PDL* is the number of population doublings, and *XA(0)* and *XA(t)* are the cell numbers (cells/cm2) at the beginning and the end of the cultivation, respectively.

(IV) Expansion factor (*EF*):

$$EF = \frac{X\_A(t\_{\text{max}})}{X\_A(t=1)} \tag{4}$$

where *EF* is the expansion factor and *XA(tmax)* is the maximum cell number and *XA(t*=*1)* is the cell number on day 1 (i.e., after cell attachment phase).

(V) Lactate yield from glucose (*YLac*/*Glc*):

$$\chi\_{\text{Lac/Glc}} = \frac{\Delta \text{Lac}}{\Delta \text{Glc}} \tag{5}$$

where *YLac*/*Glc* is the lactate yield from glucose, Δ*Lac* is the lactate production over a specific time period and Δ*Glc* is the glucose consumption over the same time period (=exponential growth phase).

(VI) Specific metabolic flux (*qmet*):

$$q\_{mct} = \left(\frac{\mu}{X\_A(t)}\right) \left(\frac{\mathbb{C}\_{mct}(t) - \mathbb{C}\_{mct}(0)}{e^{\mu t} - 1}\right) \tag{6}$$

where *qmet* is the net specific metabolite consumption or production rate (for Glc, Lac and Amn), μ is the specific cell growth rate (d<sup>−</sup>1), *XA(t)* is the cell number (cells/cm2) at the end of the exponential growth phase, *Cmet(t)* and *Cmet(0)* are the metabolite concentrations (mmol/L) at the end and the beginning of the exponential growth phase, respectively, and *t* is the time (d).

#### *2.7. Modelling of hASC Growth Kinetics in 2D Culture Systems (T25-Flasks)*

Based on the findings from the static, planar growth experiments, an unstructured, segregated, simplistic growth model was developed and used to describe the hASC growth kinetics in the T25-flask cultures. A comparable model approach has already been successfully used by Jossen et al. [1] to simulate the anchorage-dependent growth of hASCs on MCs during serum-reduced (5% FBS) expansion in single-use spinner flasks. The same model approach as that employed by Jossen et al. [1] was also used with only minor modifications to simulate MC-based hASCs growth kinetics in this study. Detailed information about the MC-based growth model can be found in Jossen et al. [1] and in "Supplementary Materials".

The general concept for the growth model and the factors that influence the T25-flask cultures are shown in Figure 1. Since hASC growth is anchorage-dependent, possible formation of spheroids in the suspension was not considered in the model. This simplification was justified since no spheroid formation was observed in any of the 2D cultivations that employed an appropriate surface coating (data not shown). Thus, it can be assumed that cells in suspension do not contribute to an increase in the overall cell number, with cell growth restricted to the planar growth surface. To define the starting conditions, it was assumed that initial cell attachment took place during the cell attachment phase, which can be described by the attachment constant *kat*. After the cells had attached themselves to the planar growth surface, a short cell adaption phase was considered, before the cells began to proliferate.

**Figure 1.** Principle of the growth model and influencing factors.

The cell adaption phase was considered by introducing the coefficient α(*t*) (see Equation (7)),

$$a(t) = \frac{t^n}{t\_l^n + t^n} \tag{7}$$

where *tl* defines the lag time and the point at which α(*t*) is half of the maximum. The exponent *n* in Equation (7) affects the slope of *f*(α(*t*)). If *n* = 1, α(*t*) is described by Michaelis–Menten kinetics. Otherwise, a sigmoidal curve is obtained that becomes steeper as *n* increases. Both variables (*tl* and *n*) were obtained from experimental growth studies using different donor cells.

The specific cell growth rate (μ) was calculated based on Monod-type kinetics. Hence, glucose (Glc), lactate (Lac), ammonium (Amn) and the available growth surface (*Xmax*) were considered to be influencing factors (see Equation (8)). However, analysis of microscopic pictures from time lapse microscopic investigations indicated that cell growth restriction based on the maximum available growth surface does not follow a normal Monod-type kinetic (data not shown). This observation can mainly be ascribed to cell migration during cell growth. Thus, the effect of the growth surface restriction term becomes more significant towards the end of the cell growth phase. For this reason, the exponent *n* was also introduced in Equation (8) as a growth surface restriction term.

$$
\mu = \mu\_{\text{max}} \cdot \left(\frac{Glc}{K\_{\text{Glc}} + Glc}\right) \cdot \left(\frac{K\_{\text{Lac}}}{K\_{\text{Lac}} + Lac}\right) \cdot \left(\frac{K\_{\text{Amm}}}{K\_{\text{Amm}} + Amm}\right) \cdot \left(\frac{X\_{\text{max}}{}^{n} - X\_{\text{A}}{}^{n}}{X\_{\text{max}}{}^{n}}\right) \tag{8}
$$

The cell number on the planar growth surface (*XA*) increased through mitotic cell division and the attachment of cells from the suspension (see Equation (9)). However, this cell number increase was affected by the detachment of hASCs from the planar growth surface, which was accounted for by the detachment constant (−*kdet*).

$$\frac{dX\_A}{dt} = a \cdot \mu \cdot X\_A + k\_{\text{alt}} \cdot \frac{(X\_{\text{max}}^{\prime}{}^n - X\_A{}^n)}{X\_{\text{max}}^{\prime}{}^n} \cdot X\_{\text{Sus}} - k\_{\text{del}} \cdot X\_A \tag{9}$$

Since T25-flasks are static systems, *kdet* is not substantially affected by changing hydrodynamic stresses and can be assumed to be constant. hASC growth in suspension was negligible and therefore *Bioengineering* **2020**, *7*, 77

changes in cell number were only affected by cell attachment to or detachment from the growth surface (see Equation (10)).

$$\frac{dX\_{\text{Sus}}}{dt} = k\_{\text{det}} \cdot X\_A - k\_{\text{at}} \cdot \frac{(X\_{\text{max}}^n - X\_A{}^n)}{X\_{\text{max}}^n} \cdot X\_{\text{Sus}} \tag{10}$$

Glucose consumption was assumed to be limited by the glucose concentration itself (see Equation (11)). In other words, glucose consumption was the result of glucose uptake by the mitotic cells and the maintenance metabolism of the mitotic and non-mitotic cells (*XV*). A step response (δ*Glc*) was implemented in Equation (11) to avoid negative glucose concentrations, even though it was highly improbable that *Glc* was completely consumed during the culture time. This was mainly due to the frequent partial medium exchanges and the theoretically low maximum ratio of cells to *Glc* in the T25-flasks.

$$\frac{d\text{Glc}}{dt} = -\frac{1}{Y\_{\frac{X}{\text{Glc}}}} \cdot \alpha \cdot \mu \cdot \frac{\left(X\_{\text{max}}\,\,^n - X\_A\,^n\right)}{X\_{\text{max}}\,\,^n} \cdot X\_A - m\_{\text{Glc}} \cdot \delta\_{\text{Glc}} \cdot X\_V \tag{11}$$

L-glutamine (Gln) consumption was not considered in this model, since metabolic measurements indicated that Gln was not a limiting factor in the T25-flask cultures. Moreover, UltraGlutamine (L-alanyl-L-glutamine) was used in the UrSuppe stem cell culture medium, which had undergone a series of complex degradation steps (i.e., (I): cleavage by extracellular peptidases, (II) degradation of free L-glutamine or absorption into the cells and metabolization). The production of lactate (Lac) and ammonium (Amn) was accounted for by Equations (12) and (13).

$$\frac{d\text{Lac}}{dt} = q\_{\text{Lac}} \cdot \mathbf{X}\_A \cdot \mathbf{a} + p\_{\text{Lac}} \cdot \mathbf{X}\_V \tag{12}$$

$$\frac{d A m n}{d t} = q\_{A m n} \cdot X\_A \cdot \alpha + p\_{A m n} \cdot X\_V \tag{13}$$

All growth-related simulations were performed using MATLAB 2019a (MathWorks Inc., Natick, MA, USA). The set of model equations were solved using the ode15s solver in MATLAB.

#### **3. Results and Discussion**

#### *3.1. Isolation of hASCs from Subcutaneous Adipose Tissue (SAT)*

The SVF obtained from human subcutaneous adipose tissue is a heterogeneous mixture of cells, which are isolated by enzymatic dissociation. In general, adipocytes represent roughly two-thirds of the total cells extracted and the rest are blood-derived cells, vascular cells, endothelial cells, smooth muscle cells, pericytes, fibroblasts and hASCs. A multiparameter flow cytometric assay was used in the study to determine the absolute cell number for every cell population and to characterize the cells in the SVF. For this purpose, the target hASC population was defined as being positive for CD34<sup>+</sup> and CD73+, and negative for CD36−, CD45<sup>−</sup> and CD146<sup>−</sup> [33,34]. Table 2 provides an overview of the two patients/donors (080 = healthy patient, 085 = post-chemotherapy patient) investigated in this study and the number of living hASCs isolated from their biopsies. For both investigated cases, the number of isolated hASCs was in the range of 5.7–7.7% of the total living cell population and the fraction of hASCs obtained from donor 085 was 35% greater than from donor 80. Based on the information about the number of live hASCs per patient biopsy, the cells were directly seeded in precoated T-flasks (30,000 cells/cm2) with our xeno- and serum-free UrSuppe stem cell culture medium in order to establish P0.


**Table 2.** Results obtained from the two different patients.

#### *3.2. hASC Growth under Planar, Static Conditions*

Figure 2 shows light microscopic pictures of the patient-derived hASCs (a = donor 080, b = donor 085) during the growth characterization study in the T25-flasks. It is clear that cell attachment occurred during the first 4–6 h after cell inoculation. In both cases, ≥98% of the inoculated cells attached to and spread out across the growth surface under the xeno- and serum-free conditions. These cells exhibited typical fibroblast-like or fibroblastoid cell morphology, with minimum and maximum cell diameters in the range of 12–54 μm and 30–291 μm. Interestingly, analysis of the light microscopic pictures showed that the hASCs isolated from donor 085 had a higher average cell area (2480 μm2, + 24–30%) compared to those from donor 080 (1810 μm2). Therefore, lower maximum cell densities (= cells/cm2) can be expected for donor 085, which has an effect on the total cell yield and future process designs. Qualitative analysis of the microscopic pictures showed that the cells began to migrate and proliferate immediately after the cell attachment phase. As expected, cell confluency increased in both cases as a function of the cell number. This resulted in a cell confluency of nearly 80–90% in both cultures after day 5. From day 5 to day 10, the increase in cell confluency slowed down due to the reduced cell proliferation rate, which was caused by the higher frequency of cell contact inhibition. A maximum cell confluency of 95–100% was achieved in both cases by the end of the cultivation studies (=day 10). From a visual point of view, no significant differences in morphology (i.e., shape, granularity) were found between the two donors or during the culture time.

**Figure 2.** Light microscopic pictures of patient-derived Human Adipose Tissue Stem Cells (hASCs; **a** = donor 080, **b** = donor 085) during cell growth in T25-flasks. Scale bar = 275 μm.

Figure 3a–d shows a quantitative analysis of cell growth and substrate/metabolite concentrations. It is clear that in both cases, the hASCs followed a classical exponential growth curve, which was characterized by four different growth phases: (I) cell adaption phase, (II) exponential growth phase, (III) cell growth restriction phase and (IV) stationary growth phase. A maximum cell density of 0.65 <sup>±</sup> 0.02 <sup>×</sup> 105 hASCs/cm2 (=3.25 <sup>±</sup> 0.1 <sup>×</sup> 10<sup>5</sup> hASCs/mL) and 0.52 <sup>±</sup> 0.02 <sup>×</sup> 105 hASCs/cm2 (<sup>=</sup> 2.60 <sup>±</sup> 0.1 <sup>×</sup> 105 hASCs/mL) was achieved for donors 080 and 085, respectively. Consequently, the peak cell density of the hASCs from donor 080 was 25% higher than for donor 085. As already mentioned, the differences in the maximum cell densities may be explained by the higher average hASC cell areas from donor 085 compared to donor 080. Interestingly, cell size could be a "consequence" of

slow cell growth, in which some cells increase their volume by an increased DNA content and/or other macromolecules [35]. However, these observations need to be further investigated in future studies. During the culture period, cell viability was in both cases always > 95%. The maximum cell densities corresponded to maximum PDLs and EFs in the range of 2.79–3.22 and 7.4–9.9, respectively. Hence, the hASC PDL and EF from donor 080 were 15% and 33% higher, respectively, than for the hASCs from donor 085. Due to the metabolic activity of the cells during the growth phase, glucose was consumed, and lactate and ammonium were produced (Figure 3b,d). In both cultures, the glucose concentration did not drop below 14.04 mmol/L due to the regular partial medium exchanges. Maximum lactate and ammonium concentrations were measured in both cultures in the range of 6.2–6.8 mmol/L and 1.13–1.16 mmol/L. Based on data from Higuera et al. [36] and Schop et al. [37,38] lactate and ammonium did not, however, reach growth-inhibiting concentrations (Lac = 25–35 mM, Amn = 2.5 mM). The online measured pH values (data not shown) agreed well with offline measured data (± 1%) and indicated stable pH values in the region of 7.2–7.3 during the entire cultivation. Cellular respiration caused oxygen to be consumed during cell growth. However, the oxygen supply in the T25-flasks was not a limiting factor and the DO values did not drop below 80% (data not shown). It is clear that by using the developed growth model (see Figure 3a–d lines), the time courses of the cell densities on the MC surface, and the substrate and metabolite concentrations could be well approximated. As indicated by the light microscopic pictures, only a few cells were observed in the supernatant during the static 2D cultivations. Hence, cell density in the supernatant was negligible (simulation results see "Supplementary Material"). Maximum deviations between the measured and simulated cell densities in both cultures were in the range of 8–16%, while slightly higher deviations of up to 21% were found between the measured and simulated substrate/metabolite concentrations. These higher deviations can be explained by (I) uncertainties in substrate/metabolite measurements, (II) error propagation in the calculation of the specific consumption/production rates and (III) slightly different behavior in the real cellular metabolism. Nevertheless, based on growth-dependent parameters, the model successfully describes and predicts cellular growth, substrate consumption and metabolite production in the static 2D cultivation systems.

Table 3 summarizes the calculated growth-dependent parameters for donors 080 and 085. It is clear that with a specific growth rate of 0.52 d−<sup>1</sup> (td = 32 h), the hASCs from donor 080 grew 33% faster than the hASCs from donor 085 (μ*max* = 0.39 d<sup>−</sup>1, *td* = 42.7 h). Salzig et al. [20] reported specific growth rates for human bone marrow-derived mesenchymal stem cells (hBM-MSCs) cultivated in a serum-free culture medium in the range of 0.38–0.45 d−<sup>1</sup> (*td* = 36.9–43.7 h). Comparable specific growth rates (0.31–0.47 d<sup>−</sup>1) were also reported by Heathman et al. [22] for hBM-MSCs from different donors and over different passages. Therefore, specific hASC growth rates obtained in this study were in a comparable range or even slightly higher (+15%). However, a direct comparison of the specific growth rates is critical since the hMSCs were from different tissue sources and donors and were grown in different serum-free cell culture media. Specific glucose consumption rates (*-qGlc*) were between 1.35 and 1.98 pmol/cell/d and demonstrated that the glucose was more efficiently metabolized by the cells from donor 080. As a result, hASCs from donor 085 produced more lactate for the same equivalent amount of glucose (*YLac*/*Glc*: 1.14 vs. 1.05 mmol/mmol). Ammonium production (0.28–0.32 pmol/cell/d) was comparable in both cultures.

**Figure 3.** Time-dependent profiles of cell densities (**a**,**c**) and substrate/metabolite concentrations (**b**,**d**) in T25-flasks. Donor 080 (upper row) and 085 (lower row). Partial medium exchanges of 40% and 60% were performed on days 4 and 8, respectively. The symbols represent the experimentally measured values collected from offline measurements. The lines represent the simulated time courses.


**Table 3.** Overview of the main growth-dependent parameters in the 2D cultivations.

( \*) Value was calculated based on the values of the stationary growth phase (mean ± σ*cells*). (\*\*) Value was calculated based on *Xmin* and *Xmax*.

#### *3.3. MC-Based hASC Expansion in Single-Use Spinner Flasks*

Based on the growth-related parameters obtained from the planar growth characterization studies, cell growth was also characterized for dynamic conditions in MC-based cultivations. Figure 4a,d shows the time-dependent profiles of the cell density and the substrate/metabolite concentrations for hASCs from donors 080 (upper row) and 085 (lower row). After the 24 h cell attachment phase, a cell attachment efficiency of 137% (080) and 118% (085) was achieved. These results indicate that a portion of the cell population had already started to divide within the static cell attachment phase. A peak cell density of 0.61 <sup>±</sup> 0.01 <sup>×</sup> 105 hASCs/cm2 (=2.16 <sup>±</sup> 0.04 <sup>×</sup> 10<sup>5</sup> hASCs/mL) was achieved for donor 080. At 0.49 <sup>±</sup> 0.01 <sup>×</sup> 105 hASCs/cm<sup>2</sup> (=1.76 <sup>±</sup> 0.04 <sup>×</sup> 105 hASCs/mL), the maximum cell density for donor 085 was again lower (−19%), but nonetheless agreed well with the data from the planar 2D cultivations. In both cases, the maximum cell densities in the MC-based cultivations agreed well with those achieved in the planar cultivation systems. In both cultures, maximum PDLs and EFs

were in the range of 1.58–1.72 and 3.2–3.3, respectively. During the cultivation, glucose concentrations decreased to 15.2 mmol/L (080) and 14.3 mmol/L (085), meaning glucose was not a limiting factor in either cultivation. As a result of glucose metabolization, lactate concentration increased to maximum values of 4.5 mmol/L (080) and 5.9 mmol/L (085), and ammonium concentrations remained relatively low during the entire cultivation (080-*Amn* = 0.94 mmol/L, 085-Amn = 0.99 mmol/L). Both lactate and ammonium levels were below critical concentrations [36–38]. From the time-dependent profiles of Figure 4, it can be seen that the growth model can also be used to describe the growth kinetics and substrate/metabolite profiles in MC-based hASC cultivations. The simulated and measured values differed only slightly. Maximum deviations in cell density of ≤7% were found, and deviations in the substrate/metabolite concentrations were only slightly higher (≤15%). Nonetheless, the model can be used in the future to describe hASC growth kinetics in different cultivation settings.

**Figure 4.** Time-dependent profiles of cell densities (**a**,**c**) and substrate/metabolite concentrations (**b**,**d**) in the Corning spinner flasks. Donor 080 (upper row) and 085 (lower row). A partial medium exchange of 50% was performed on day 5. The symbols represent the experimentally measured values collected by offline measurements. The lines represent the simulated time courses.

Table 4 provides an overview of the main growth-dependent parameters calculated for the two different hASC cultivations. The hASCs from the two different donors grew at comparable specific growth rates of between 0.42 and 0.44 d−<sup>1</sup> (*td* = 37.8–39.6 h). The calculated specific growth rates were in a comparable range to literature data for MC-based expansions of hBM-MSCs in serum-free cell culture media [20–22,39]. In both cases, glucose was metabolized less efficiently by the hASCs, although -*qGlc* values (1.34–1.96 pmol/cell/d) were comparable to those in the 2D cultures. Therefore, *YLac*/*Glc* was in the range of 1.39–1.68 mmol/mmol. The less efficient metabolism of glucose was caused by a higher *qLac*, which might be a consequence of the hydrodynamic stresses acting on the cells in dynamically mixed systems. The rates of ammonium production in both cultures (0.26–0.27 pmol/cell/d) were comparable with those in the 2D culture systems.

**Table 4.** Overview of the main growth-dependent parameters in the Corning spinner flasks.


( \*) Value was calculated based on the values of the stationary growth phase (mean ± σ*cells*). ( \*\*) Value was calculated based on *Xmin* and *Xmax*.

Cell growth in the MC-based cultivations was mainly restricted by the growth surface. Figure 5a,b shows fluorescence microscopic pictures of DAPI-stained hASCs on MCs during cultivation in the spinner flasks. It is clear that on day 1 (after the cell attachment phase) nearly all of the MCs were covered by 2–5 cells. On day 4, some of the MCs were already partially covered with cells and the cells had started to form initial MC-cell-aggregates. By the end of the cultivation, almost all of the MCs were part of a MC-cell-aggregate and only a few MCs were floating around as single beads.

**Figure 5.** Fluorescence microscopic images during cell growth in Corning spinner flasks. Donors 080 (**a**) and 085 (**b**). DAPI-stained cells on Microcarriers (MCs) on day 1 (left), day 4 (middle) and day 9 (right). Scale bars: 275 μm (left and middle) and 650 μm (right).

Figure 6a,b shows the MC-cell-aggregates at the end of the cultivations (=day 10) and the results of the size distribution analysis of the maximum MC-cell-aggregate diameters. It can be seen that a comparable MC-cell-aggregate size distribution was obtained at the end of both cultivations, with mean MC-cell-aggregate diameters of 1.95 mm (085) and 1.97 mm (080). Minimum and maximum MC-cell-aggregate diameters were measured at 0.8 mm and 5.7 mm for donor 080 and 0.7 mm and 5.0 mm for donor 085. This indicates local volume-weighted hydrodynamic stresses (τ*nt* <sup>=</sup> 4.96 <sup>×</sup> <sup>10</sup>−<sup>3</sup> Pa, <sup>τ</sup>*nn* <sup>=</sup> 1.15 <sup>×</sup> <sup>10</sup>−<sup>3</sup> Pa, Jossen et al. [1]) acting on the MC-cell-aggregates controlled their size to some extent. This observation also agreed well with literature findings [40,41]. Furthermore, the results indicated that increased MC-cell-aggregation mainly took place during the stationary growth phase. Therefore, the cell harvest point should also be defined based on MC-cell-aggregate size data.

**Figure 6.** MC-cell-aggregate diameter distributions (**a**) and photographic images (**b**,**c**) of MC-cell aggregates at the end of the cultivations (day 9). Donor 080 (**b**) and 085 (**c**).

#### *3.4. Flow Cytometric Analysis of Standard Markers Expressed by hASCs Cultured in 2D or 3D*

Figure 7a,b shows the flow cytometry expression profiles of selected markers analyzed at the end of the cultivation studies (2D vs. 3D). There was no significant difference between the marker expression profile of cells cultured in 2D and those cultured in 3D on MCs. Moreover, no significant differences in the expression profiles were observable between the two donors, which agreed with our expectations. Positive hASC markers (CD26+, CD54+, CD55+, CD73<sup>+</sup> and CD90+) were strongly expressed, while negative markers (CD36− and CD146−) were only weakly expressed. CD105 was the only positive marker that was weakly expressed, which might be caused by the hyperconfluence of the cells after 10 days of cultivation [42–44].

**Figure 7.** Flow cytometry expression profile of selected markers. hASCs from donor 080 (**a**) and donor 085 (**b**) cultivated in 2D (T25-flasks) or 3D (MC). hASCs were analyzed after harvesting on day 10. Mean fluorescence was calculated based on specific isotype controls (=relative marker expression).

#### *3.5. Monitoring the Expression of Selected Stemness or Cell Di*ff*erentiation Genes Measured by RT-qPCR*

The cells used in this study were extracted from subcutaneous adipose tissue. It is therefore logical to assume that the "default differentiation pathway" of hASCs, in the event of unwanted and uncontrolled spontaneous maturation, is towards adipogenesis. In recent years, several important genes have been discovered that are crucial for the maintenance of stemness and for the differentiation of hASCs [34,45,46]. Further information about the different genes, including their relationships to each other and a short description, can be found in "Supplementary Materials" or in the literature [47–83]. The selected genes can be used as markers in RT-qPCR tests to assess and compare the differentiation status of hASCs expanded in static 2D (see Section 3.2) and/or dynamic 3D conditions (see Section 3.3). To facilitate analysis, the genes were subdivided into three groups:


Figure 8 shows the results of the RT-qPCR measurements. In the category, "Stemness Maintenance" (Figure 8a), the cells of both donors on day 5 of the dynamic 3D cultivations had a better profile (high expression of *Pref-1* and *ZFP521*) than the hASCs grown in static 2D conditions. However, after 10 days, the cells were hyperconfluent in both cases. Consequently, the expression of almost all genes decreased [42–44]. Nonetheless, the cells on the MCs performed well and their gene expression pattern was similar to that of those obtained from hASCs grown in static 2D conditions.

In the second category, "Differentiation Regulators/Markers" (Figure 8b), it is clear that for the 3D dynamic conditions, the expression of *PPAR*γ, *RUNX2*, *DKK1*, *CD34*, *CD36* and *WISP1* on day 5 was lower or very similar to the standard 2D set-up. Thus, it can be concluded that the cells retained their "stemness" under the dynamic 3D conditions. As already mentioned, on day 10, the cells were hyperconfluent in both cases. In this situation it is normal that the stemness genes are downregulated, while the differentiation genes are induced [42,44]. However, it is worth noting that the expression of *PPAR*γ, the master regulator of adipogenesis, was lower for both donors (080, 085) under dynamic 3D conditions.

In the last category, "Lineage Hierarchy Markers" (Figure 8c), on day 5, the hASCs grown in standard 2D conditions displayed a better gene expression profile than the cells in 3D. However, on day 10, both cell culture systems showed similar satisfactory profiles. It should be noted that the expression of the four genes tested increased during the last days in the 3D spinner system, whereas in the 2D set-up it remained similar between days 5 and 10.

The results of the RT-qPCR measurements clearly showed that the stemness of the hASCs was very well preserved when the cells were grown on xeno-free polystyrene-based MCs with the serum-free UrSuppe stem cell culture medium. The differences in the gene expression profiles were more pronounced on day 5. However, on day 10, due to the very high cell density, most of the stemness genes decreased and most of the differentiation genes increased in both systems, resulting in similar profiles [42–44]. These results clearly demonstrated that for both donors, the optimum point of harvest was on day 5–6 (see Section 3.3). This quality-related observation also agreed very well with the growth-related results and will have an influence on future growth investigations. Hence, higher MC amounts are required to provide the desired cell density, even at lower levels of cell confluency.

**Figure 8.** Results of RT-qPCR measurements of donors 080 (I) and 085 (II). The investigated genes were subdivided into 3 groups: (**a**) stemness maintenance genes, (**b**) differentiation regulators/markers and (**c**) lineage hierarchy markers. Data are represented as 2(-ΔΔCt) and related to the beginning of the culture (day 1). A single value for each experimental condition was calculated with this method. This figure is also depicted as "heat maps" and is shown in the "Supplementary Materials" (Figure S3).

#### **4. Conclusions**

In this proof-of-concept study, growth- and quality-related investigations were performed under xeno- and serum-free conditions in planar 2D and dynamic 3D cultivation systems with hASCs isolated from two different patients/donors (080 and 085). In order to collect donor-dependent data, two donors of different ages (26 vs. 46 years) and with different health statuses (healthy and post-chemotherapy) were selected for this proof-of-concept study. The hASCs were isolated from the *SVF* under fully serum-free conditions in order to fulfill the regulatory requirements for future hASC manufacturing processes for autologous therapies. The results demonstrated that by using the serum-free UrSuppe stem cell culture medium, hASCs from both donors could be successfully isolated and cultured. The observed tissue frequency of living hASCs was comparable for both donors, although differences in age and health status existed. This is very important for future autologous therapies, as most patients/donors are older or unhealthy. However, further investigations in terms of the biological variation (e.g., gender, broad age range and health conditions) between donors and its effects on successful in-vitro cultivation at different production scales are necessary.

Growth characterization under static 2D conditions revealed differences in the growth performance and the maximum achievable cell densities for the two donors. Due to the higher mean cell areas for donor 085, maximum cell densities were lower, which reduced the overall total cell number per cultivation. The same observations were also performed during the MC-based cultivations. Information about cell morphology (i.e., cell size and area) and the maximum achievable cell density

per donor under static 2D conditions is crucial for process scale-up in order to achieve the cell densities required for autologous therapies within the shortest time and number of passages (e.g., issue of cellular senescence). Due to the restricted maximum cell densities for individual donors, high amounts of MCs are necessary in order to increase the total cell number per process step. However, this has an effect on the choice of the stirred bioreactor type and the process conditions. As a result of the shear sensitivity of hASCs, the number of MCs can only be increased up to a certain point, where the occurring hydrodynamic stresses do not negatively affect cell growth or quality. The MC-based expansions clearly showed that the hydrodynamic stresses at *Ns1u* did not significantly affect cell growth or cell quality, even though the stem cell culture medium did not contain FBS. The flow cytometric and RT-qPCR measurements highlighted the maintenance of the stemness during the static 2D and dynamic 3D cultivations of cells from both donors. Surface marker and gene expression profiles under dynamically mixed conditions were comparable for both donors and partially even better than for static 2D conditions. The results also clearly indicate that careful determination of the correct harvest point is important in order to retain stemness. A hyperconfluent culture would increase the total cell density per cultivation but lead to a downregulation of stemness maintenance genes and an upregulation of differentiation marker genes. Thus, optimal cell harvest densities for both donors were determined to be between 0.41 and 0.56 <sup>×</sup> <sup>10</sup><sup>5</sup> hASCs/cm2, which were on average 14–22% lower than the maximum cell densities. Consequently, the required MC surface area per cultivation should in the future be defined based on the optimal cell harvest density.

The unstructured, segregated growth model very clearly showed time courses for cell growth, glucose consumption, lactate production and ammonium production that were similar to experimental data from the planar 2D and dynamic 3D cultivations. Maximum deviations for cell density and substrate/metabolite concentrations were in the range of 7–16% and 15–21%, respectively. This means that the descriptiveness power of the model was satisfactory, especially when considering the accuracy of the experimentally measured values. The intensified MC-cell-aggregate formation during the MC-based expansion was not considered in the growth model. Nevertheless, good agreement has been achieved. Therefore, the model can serve as basis for further investigations with hASCs. For this purpose, comprehensive growth studies with hASCs from a larger number of patient/donors (*n* = 12–20) are planned in stirred, instrumented single-use bioreactors (i.e., BioBLU 0.3c) based on a Design of Experiment approach.

**Supplementary Materials:** The following are available online at http://www.mdpi.com/2306-5354/7/3/77/s1. Growth model principle and influencing factors in MC-based hASC expansions; Figure S1. Factors that positively or negatively regulate adipogenesis; Figure S2. Time-dependent profiles of cell density in the supernatant of the T25-flasks for donor 080 (a) and 085 (b); Figure S3. Results of RT-qPCR measurements ("heat maps") of donors 080 (I) and 085 (II); Table S1. Parameters used for the kinetic growth model (2D and 3D); Table S2. Detailed information of the antibodies used for the flow cytometric measurements; Table S3. Reverse transcription detailed procedure; Table S4. Overview of measured stemness maintenance genes; Table S5. Overview of measured differentiation regulators/markers; Table S6. Overview of measured lineage hierarchy markers.

**Author Contributions:** V.J., R.E. and T.T. conceived and designed the experiments; Y.H. selected and recruited the adipose tissue donors, collected the biopsies and prepared the sterile tissue samples for shipment; F.M., S.P. and T.T. processed the human adipose tissue samples and isolated the hASCs; V.J. performed the planar 2D and dynamic 3D cultivation studies; F.M., S.P. and T.T. carried out the cell analytical measurements/analysis (flow cytometry, RT-qPCR); V.J. developed the unstructured, segregated growth model and completed all growth-related simulations and calculations; V.J. wrote the original draft of the paper; F.M., S.P., T.T., R.E. and V.J. wrote, reviewed, and edited the original manuscript. All authors have read and agreed to the published version of the manuscript.

**Funding:** The cell biology experiments in this study were supported by the Cardiocentro Ticino Foundation (CCTF), and the Foundation for Cardiological Research and Education (FCRE).

**Acknowledgments:** We are grateful to Dante Moccetti (Director of Cardiocentro Ticino) for his interest and continuous support with the project. We also thank Fabio D'Auria, Fabio Ferri, Giorgio Gaiatto, Luca Perini, and Andreja Petkovic (Logistics Cardiocentro Ticino) for the collection and transport of the biopsies and for the organization of all shipments between Lugano and Wädenswil.

**Conflicts of Interest:** The authors declare that there is no conflict of interests regarding the publication of this paper.

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