Application of a simple unstructured kinetic and cost of goods models to support T‐cell therapy manufacture

Manufacturing of cell therapy products requires sufficient understanding of the cell culture variables and associated mechanisms for adequate control and risk analysis. The aim of this study was to apply an unstructured ordinary differential equation‐based model for prediction of T‐cell bioprocess outcomes as a function of process input parameters. A series of models were developed to represent the growth of T‐cells as a function of time, culture volumes, cell densities, and glucose concentration using data from the Ambr®15 stirred bioreactor system. The models were sufficiently representative of the process to predict the glucose and volume provision required to maintain cell growth rate and quantitatively defined the relationship between glucose concentration, cell growth rate, and glucose utilization rate. The models demonstrated that although glucose is a limiting factor in batch supplied medium, a delivery rate of glucose at significantly less than the maximal specific consumption rate (0.05 mg 1 × 106 cell h−1) will adequately sustain cell growth due to a lower glucose Monod constant determining glucose consumption rate relative to the glucose Monod constant determining cell growth rate. The resultant volume and exchange requirements were used as inputs to an operational BioSolve cost model to suggest a cost‐effective T‐cell manufacturing process with minimum cost of goods per million cells produced and optimal volumetric productivity in a manufacturing settings. These findings highlight the potential of a simple unstructured model of T‐cell growth in a stirred tank system to provide a framework for control and optimization of bioprocesses for manufacture.

T-cells as a function of time, culture volumes, cell densities, and glucose concentration using data from the Ambr ® 15 stirred bioreactor system. The models were sufficiently representative of the process to predict the glucose and volume provision required to maintain cell growth rate and quantitatively defined the relationship between glucose concentration, cell growth rate, and glucose utilization rate. The models demonstrated that although glucose is a limiting factor in batch supplied medium, a delivery rate of glucose at significantly less than the maximal specific consumption rate (0.05 mg 1 Â 10 6 cell h À1 ) will adequately sustain cell growth due to a lower glucose Monod constant determining glucose consumption rate relative to the glucose Monod constant determining cell growth rate. The resultant volume and exchange requirements were used as inputs to an operational BioSolve cost model to suggest a cost-effective T-cell manufacturing process with minimum cost of goods per million cells produced and optimal volumetric productivity in a manufacturing settings. These findings highlight the potential of a simple unstructured model of T-cell growth in a stirred tank system to provide a framework for control and optimization of bioprocesses for manufacture.

K E Y W O R D S
cost analysis, modeling framework, process optimization, scalable T-cell manufacturing, T-cell processing

| INTRODUCTION
The launch of CAR-T cell therapy products including Kymriah and Yescarta are the first in a significant pipeline of T-cell based therapeutic products. 1,2 Such cell-based immunotherapies are set to change the treatment options for a range of previously hard to treat or fatal hematological malignancies. 3,4 However, as a new therapeutic class based on a relatively unexplored bioprocess input material, primary T-cells manufacturing technology is particularly immature. 3 The knowledge of process control and its impacts on product quality, such as population distributions and yield, are significantly understudied relative to more established biopharmaceuticals. 5 This lack of knowledge restricts the opportunity for operational optimization that might drive down costs and/or create more consistent product. 6 Recent work in manufacturing processes has shown amenability to suspension scaled production and described some of the changes in the environment. 7 However, these descriptions fall short of providing the level of process understanding required for risk assessment of process deviations or selection of optimal process operation. 8,9 For example, given process constraints, such as a restricted bioreactor volume, the optimal medium exchange or concentrated batch feed strategy and the risk of any associated control deviations. 10,11 The current manufacturing process for CAR-Ts uncovers how a cellular therapy with a complex manufacturing process has been successfully scaled out, streamlined, and optimized to ensure supply of the high-quality T-cell product to the global market. 9 The CAR-T cell therapy manufacturing process begins by collecting the nonmobilized peripheral blood mononuclear cells (PBMC) from a patient through leukapheresis. 10 The leukapheresed PBMC is cryopreserved within 24 h after collection at À120 C for further processing. Dependent upon the patient's need PBMCs are then thawed under controlled conditions, followed by cell washing and T-cells selection and enrichment. T-cells are activated using CD3/CD28 antibody-coated paramagnetic beads before a transduction step using viral vectors. Following transduction and removal of excess vector and other residuals the cells are expanded in static cultures and then in bioreactors. 8,12 Cell expansion continues ex vivo until sufficient number of cells that meet the final product dose requirements have been achieved. To harvest the cells, the CAR-Ts are isolated from the beads, washed, and formulated in infusible media. The critical quality attributes of cells are evaluated to determine multiple parameters including: appearance, identity, safety, purity, potency, and quality of the final product.
During the industrial manufacturing of CAR-Ts for global clinical trial applications, multiple steps were taken to improve process performance and robustness and to maintain the quality of the product. The key process changes included: enhancement of process control to ensure product consistency, introducing the automation process and closed systems to ensure reproducibility while preventing the risk of contamination. Further validation of analytical methods was also applied to improve the consistency of the final product. 13 T-cell based immunotherapy will require a consistent quality product in a suitable bioprocess format for manufacturing at scale. In order to ensure and maintain the quality of clinically relevant T-cell populations, a variety of quality control (QC) panel tests have been carried out by manufacturers to evaluate the expression levels of multiple T-cell surface antibodies including: CD4 + /CD8 + , CD45, and CCR7. 14,15 The presence or absence of these phenotypic markers will determine the diversity of T-cell subpopulations hence mandate the process condition including: feeding composition and rates to achieve targeted sub populations of T-cells that can be clinically relevant. For example, Naive T-cells are CD45RA + , CD45RO À , CD62L + , and CCR-7 + . These markers change to CD45RA 0 , CCR-7 0 in CD8 + TEM cells. Thus, based on the expression level of these and other phenotypic markers T-cell subsets and subpopulations can be sorted, expanded, and analyzed for functional activities during immune responses against pathogenic agents or CAR-T cell therapies. 16,17 The ongoing, continuous process improvements will result in further enrichment in the manufacturing of CAR-Ts including reduction in the throughput time from receipt of leukapheresis material to patient bedside. 8 One example of process improvement was demonstrated by the collaborative study conducted by National Cancer Institute and Kite Pharma, a Gilead company which underlined the significant correlation between the functionality of an anti-CD19 CAR-T-cell product before treatment, polyfunctional strength index, and response in non-Hodgkin lymphoma patients. Their findings show a high potential to predict the cancer patients objective response to CAR-T cell therapy before treatment, while highlighting the improvement achieved both in preinfusion product potency testing and cell product optimization. 4 In common with all therapeutics, the industry standard for process development is a risk-based approach driven by robust experimental data. 16 Mathematical models that describe process outcomes in terms of process control variables are at the heart of such an approach. 17 They can support quantitative estimates of risk based on simulations of operating variation, either via methods such as the Monte-Carlo analysis of model parameters or control variable distributions, or extrapolation/interpolation to assess alternative operating conditions. Diverse outcomes will develop from variation in input cells and reagent indicating that process is highly dependent on process operation and specific autocrine and paracrine responses of T-cell subsets and sub populations. 16,17 Applying mathematical modeling, therefore, is a cost-effective approach that untangle, and control T-cells bioprocesses by predicting variability in process outcomes with respect to input variability thus identify process operation with acceptable risk and opportunities for process optimization.
Independent modeling approaches have previously been developed to provide a framework for bioprocess optimization of cell therapy manufacturing (Advanced Bioprocess Design, UK), 17,18 and, separately, the cost analysis of cell therapy manufacture (BioSolve, Biopharm Services, UK). 19,20 The bioprocess optimization is based on an ordinary differential equation approach to describe key process mechanisms in a low parameter (and generally unstructured) form that directly relate to process operation. The application of this framework in providing insight to T-cell manufacturing process optimization is reported in this article. The aim of this study was to describe how this modeling approach can be applied, with limited process data, to define medium exchange process operation limits in a stirred tank culture format. Therefore, to show how the approach can be evolved to provide further process insight as more analytical data, such as nutrient concentrations, becomes available. Gaining these insights will further assist in evaluation of the process optimization and risk understanding in cell therapy applications.
The second modeling approach was to use BioSolve commercial software as an independent model to provide an insight into the cost impact of defined optimized T-cell process choices and scale-up. Previous work in this area focused on cell therapy manufacturing processing platforms that relied on scale-out. 19,20 Most autologous cell therapies will require low-batch volumes, typically less than 5 L and hence do not take advantage of economies of scale. The smaller volumes, the larger number of batches and the variability of starting and finished cell materials pose a challenge to current processing platforms that rely on unscalable processing platforms. 21 Using scalable technologies would provide maximum flexibility, control, and monitoring in the cell culture platform to accommodate for the heterogeneity in the type and number of cells available initially from the patient. 22 Using modeling approaches such as the ones shown in this article would enable a preliminary analysis of the optimal way to process cells for a given starting cell number, best feeding strategy, and cost impact, before any experimentation or processing is undertaken. With further data, such a model could also indicate how cell growth can be sustained while selectively affecting the growth of specific sub-population of T-cells, hence would be highly applicable in T-cell/ CAR-T cell therapy manufacturing processes. 22 2 | MATERIALS AND METHODS 2.1 | CD3 + /CD28 + cell culture Cells were cultured in T25 tissue culture flasks in humidified atmospheric O 2 and 5% CO 2 conditions at 37 C (5% CO 2 in air) for 7 days prior to bioreactor culture; they were fed daily from day 2 of culture by addition of 5 ml fresh medium. On day 7, dynabeads were removed from cells, cells were centrifuged at 300g for 10 min and were re stimulated by addition of fresh dynabeads with ratio of 1:1.

| Ambr ® 15
Ambr ® 15 is an automated parallel processing bioreactor that can be employed in capturing data, monitoring, controlling culture

| Specific consumption/production rate of Metabolites
Duplicate metabolites samples were collected daily from each vessel (500 μl) and were centrifuged at 300 g for 10 min. The supernatant containing spent media was collected and stored at À20 C prior to analysis. Spent media was analyzed for glucose and lactate using the Cedex Bio-HT (Roche, DE) to calculate the specific metabolite rate mmol cell À1 days À1 .

| Unstructured ODE model
Hypotheses for alternative mechanisms of cell growth and growth inhibition were proposed (as described in the results) and expressed mathematically using a tailored Ordinary Differential Equation (ODE) modeling framework previously described. 18,19 T-cells in the Ambr ® 15 bioreactor were subject to varying media exchange and initial density culture regimes and cell counts recorded. Candidate models were fitted to minimize least squares deviation. The model was iterated to both validate original parameters and include additional explanatory elements such as the nutrient glucose.
In brief, an ODE paradigm was used to model the evolution of system components over time. Media or cell density change operations were modeled as step changes in, with forward Euler used to obtain model variable evolution between these time-points. Optimization was performed via an exhaustive search of parameter space (i.e., a brute force screen of all combinations of parameter values). An acceptable model fit was considered to show no gross systematic deviations in residuals across the model experimental space.

| BioSolve process
The economics of optimal process options for media exchange regimes and initial culture densities were modeled using BioSolve Process (Biopharm Services, UK) commercial software. BioSolve is a Microsoft ® Excel-based software used in the pharmaceutical industry for modeling monoclonal antibodies, vaccines, cell and gene therapies, and products derived from mammalian and microbial production processes. 24,25 This software has an extensive database with default costs, equipment, consumable, and material details, which are updated yearly. The BioSolve Process version 8.0 was used for this evaluation.
The cost analysis presented in this work focused on the cost of goods (CoGs) per million cells generated, and materials categories which included: culture media, dynabeads addition, the starting PBMC material, and in-process QC tests. The PBMC cost was obtained from Biosolve model and assumed to be 201.38 USD/vial. The process used in Biosolve for the generation of PBMC has been previously described. 26,19 The entire experimental set-up, protocol and results for the T-cell process described in Step 1 of the Materials and Methods section was simulated in BioSolve. This was also the case for the QC tests performed, namely viable cell count and identity by flow cytometry analysis, accounting for 1388.60 USD/batch. The smallscale model based on the Ambr ® 15 bioreactor system (Sartorius Stedim) used for the experiments shown in this article were scaled-up to a standard 2 L single-use stirred tank reactor cell culture system to quantify the cost impact of optimized process options on a target 2 L scale for autologous T-cell therapy manufacture.

| RESULTS AND DISCUSSION
Our initial objective was to develop a model that described the T-cell number in the bioprocess over time (yield) in terms of change in the culture environment by the cells. The aim was to determine the quality impact on T-cells of exceeding the point at which growth could be maintained to mirror a manufacturing scenario where medium exchange was delayed or poorly optimized. Modeling the system in terms of unstructured parameters describing cell generated inhibition, rather than in terms of specific nutrients and metabolites, could represent a common scenario early in the process development path. Therefore, this modeling approach is based on growth data that are available in the absence of significant analytical data on the process environment ( Figure 1).

| Constructing a simple feed model for T-cell growth and inhibition
A growth rate, a constant specific production rate of an inhibitory factor (arbitrarily set at 1 inhibitory unit produced per 1 Â 10 6 cell h À1 ), an inhibition of growth rate by generated inhibitory factor units (defined by a threshold and sensitivity parameter), and a cell decay promoted by the same mechanism, were modeled as previously described. Model parameters were optimized by simultaneous fitting of experimental datasets obtained from T-cells cultured in the Ambr ® 15 system under diverse operational scenarios including two start culture densities: high-cell density: 1.1 Â 10 6 cell ml À1 and lowcell density: 0.6 Â 10 6 cell ml À1 and different medium dilution timings: at 24 or 37 h post inoculation that was described as model 1.
Results from Figure 2 and Table 1

| Development of a glucose dependent Monod model for T-cell growth and inhibition
Given the initial model suggested cell activity driven was by growth inhibition, it was probable that this was due to depletion of a key nutrient or accumulation of a toxic metabolites (Figure 2a Table 2 and Figure 3. The glucose dependent model predicted cell growth based on variation in initial cell density and feeding rates and indicated that cell growth linked to metabolites specific consumption/production rate. The parameter optimization for the Monod kinetics indicated that the concentration of glucose at which the specific rate of glucose use rate is half the maximal (half-effect…) was significantly higher than the glucose concentration that was inhibitory for growth or caused cell death (half-effect, threshold) (Figure 3a-e). These findings suggested that delivery of glucose at a feed rate significantly under the maximum specific consumption parameter value of 0.05 mg 1 Â 10 6 cell h À1 should adequately sustain growth as consumption rate of glucose will reduce before detrimental concentrations are reached.

| Validation of glucose supply model
To validate the effect of glucose concentration on T-cell growth, a further culture was conducted in which glucose was provided using different feed strategies including: a 1% h À1 dilution of standard glucose medium (glucose concentration: 2.06 mg ml À1 ), a 1.13% h À1 dilution with high-glucose medium (glucose concentration: 4.11 mg ml À1 ) and a 0.57% h À1 dilution with extra high-glucose medium (glucose concentration: 8.22 mg ml À1 ) (Figure 4a-c). In the latter 2 conditions the total glucose delivery remained the same and targeted to initially deliver the 0.05 mg 1 Â 10 6 cell h À1 which was consumed by the cells in the previous experiment and in the presence of excess glucose. The first scenario of standard medium at 1% h À1 would deliver 0.02 mg ml À1 h À1 glucose to the cells which was approximately 50% under the calculated T-cells glucose consumption rate in the previous experiment. The design of experimental conditions was based on the ODE model calculations that the initial seeding density of T-cell culture at 0.8 Â 10 6 cell ml À1 would require 0.04 mg ml À1 h À1 glucose supplementation from the start with assumption of 0.05 mg 1 Â 10 6 cell h À1 for glucose consumption rate.
The data were tested against the same model and optimized parameter values as previously defined. The growth rate required adjusting due to faster proliferation (0.17 h À1 ) but all other model parameters with respect to metabolic behavior remained the same.
Data fit to the model was reasonable for the low-glucose delivery, suggesting an adequate parameter optimization from the initial data set and confirming that an 'undersupply' of glucose sustained the continual growth rate over the full culture period-even though by the end of the culture period delivery rate was approximately 25% of the suggested feed based on optimized specific consumption rate parameter ( Figure 2a). Further, the cultures with glucose delivered closer to the measured consumption rate both became growth inhibited early, seen as a lack of fit of cell numbers and glucose relative to the model predictions. Inhibition at a similar time point despite the different bulk dilutions suggested that this is related to the glucose supply (which was matched) rather than any other factor (Table 3).

| Development of an optimized glucose supply model of T-cell growth and inhibition
To confirm the robustness of the model to multiple inputs, and further establish the sensitivity of the system to glucose supply, a further experiment was conducted in which 1% h À1 dilution feeds with glucose at 2.056, 2.467, and 2.878 mg ml À1 were supplied to each vessel. Once again, the lower rate of glucose provision sustained the culture in line with the model predictions, with the higher glucose provision causing earlier growth reduction (Figure 5a-c).   (Table 4).

| Monod Kinetics model
In the Monod Kinetics model, Comparison of phenotypic data between static culture and Ambr ® 15 system's different feeding frequency and seeding density conditions showed sensitivity of SCM/TCM, TEM and effector populations in both CD4 + and CD8 + subsets (Figure 6a,b).
However, CD8 + subpopulations changed more significantly over time  CD4 + /CD8 + ratio was significantly changed over time in all feeding dilution condition (p value: 0.049 and 0.001) while no meaningful phenotypic changes were reported between different feeding dilutions and glucose supply conditions (Figure 6c,d). This was evident as only CD8 + TEM subpopulation showed significant sensitivity to different dilution rate and glucose supply conditions between day 3 and day 6 (p value: 0.045) (Table S2).

| Optimized glucose supply model
In the optimized glucose supply model, CD8 + subpopulations showed more sensitivity to variation in feeding dilution and additional glucose in T-cell culture at later timepoints in comparison with CD4 + (Table S3) Despite some commonalities between the effect of different feeding and glucose supply conditions on selection of CD4 + and Note: This validation reveals that glucose was not restrictive and approximately the same restriction points in all three conditions imply total dilution rather than glucose concentration being the issue. 17 Abbreviations: Glc, glucose; Glc Sp rate, glucose specific consumption rate; GR, specific growth rate; Monod Glc_GR, Monod constant determining specific growth rate as a function of Glc concentration (i.e., concentration of glucose at which specific growth rate is half maximal [half-effect]); Monod Glc_GLc use, Monod constant determining specific glucose consumption as a function of glucose concentration (i.e., concentration of glucose at which specific glucose consumption rate is half maximal).

| Scaling up T-cell process: Applications of a cost model in manufacturing settings
The ODE model data were used to inform volumes and densities as input to a Biosolve process model operating at a theoretical 2 L scale ( Figure 7). The volume productivity of a cell culture medium (cells that can be produced per ml of volume exhausted) defines the F I G U R E 6 Results of phenotype variation in CD4 + and CD8 + T-cells cultured under different dilution rates and glucose concentration in the bulk medium for (a and b) Monod kinetics model, (c and d) glucose supply, and (e and f) optimized glucose supply models. Adjusting the feeding rates did not appear to have any effect on diverging the T-cells' subpopulation growth. Variation in T-cells' starting subpopulations seems to dictate the outcome of process regardless of provision of glucose supply and feeding strategies combination of bioreactor volume and volume exchange rate required to deliver a given yield of product (Figure 7). Without a change in volume productivity of medium, then a reduction in bioreactor volume must be matched with a proportional increase in fluid exchange. The initial model of batch exchange, both nonspecific and glucose dependent, indicated a volume productivity of approximately 1.5 Â 10 6 cell ml À1 . The low-glucose feed has a significant impact on volume productivity. The 1% h À1 feed rate with 2.056 g L À1 glucose supported 3 Â 10 6 cell ml À1 , increasing the number of cells that can be yielded from a given bioreactor scale for a given rate of medium exchange (Figure 7).
The results of the BioSolve process model indicated that the materials cost category was the biggest cost driver of T-cell process ranging between 23% and 30% after fixed Labor costs (48%-53%), in line with previous published work. 26,19 Scaling up to 2 L scale reduced the resulting CoGs, improved productivity and involved relatively less materials consumption, as it took advantage of economies of scale (results not shown). Perfusion process was found to be the most costeffective process with highest volumetric productivity and the lowest  (Table S4).
The results of CoGs, volumetric productivity and costs of materials derived from BioSolve process model (Biopharm Services, UK) for optimal T-cell processes at 2 L bioreactor scale. Perfusion process was the most cost-effective process with lowest CoGs per million cells and highest volumetric productivity. Optimal T-cell processes: Baseline protocol with no media addition and low-cell density of 0.5 Â 10 6 cells ml À1 . Low-cell density: 0.5 Â 10 6 cells ml À1 , high-cell density: 1.0 Â 10 6 cells ml À1 , perfusion culture with dilution rate of 2% was assumed to be consisted of low-cell density: 0.5 Â 10 6 cells ml À1 Initially, the rate at which culture medium would need to be exchanged to maintain cell growth was determined (simple feed growth and proliferation in thymocytes. 33,34 Following immune activation, metabolic rates significantly increase in T-cells as a result of proliferative expansion and the production of cytokines. 35,36 This process demands substantial amounts of energy and cellular biosynthesis which leads to an increased demand for nutrients, including glucose, glutamine and amino acids such as serine and arginine, to supply fuel for bioenergetic and biosynthetic pathways. 37,38 Effector T-cells have high rates of glucose and glutamine uptake, which are metabolized by aerobic glycolysis and the tricarboxylic acid cycle. 39,40 Operational costs will be driven down with a smaller unit with less reagents and volume; particularly if allogeneic products take off large batch production costs are driven down. While CD4 + T-cells appear to have selectively increased capacity for mitochondrial respiration of glucose, both CD4 + and CD8 + Tcells can oxidize alternative fuels such as glutamine if required. 41,35 The results of phenotype analysis of CD4 + versus CD8 + population % revealed that the number CD8 + subset increased from $14% at day 0 to $22% at day 4 which was followed by a substantial decrease to $12% at day 7. This indicated that the CD8 + subset might be more sensitive to the effect of inhibitory agents and prior to reaching the growth inhibition at day 7 as shown in optimized glucose model experiment (Figure 6c,d). These findings are aligned with the results of other T-cell studies which suggest that different T-cell subsets and populations may require a more tailored and specific culture conditions and medium composition in order to support cell growth and to prevent initiation of an premature/undesirable exhaustion. 39,42,43 Previous cost analysis of cell therapy products using BioSolve saw the same trends seen here, whereby fixed costs were the main cost driver for small-scale operations, irrespective of the type of technology used. 26,19 Secondary drivers were materials costs, highlighting the importance of the optimization of process parameters such as: the quantities of media added, media components, among others. When compared to the author's previous work, the most noticeable impact of the introduction of scalable bioreactor technology in T-cell processing, was the reduction of the costs per million cells produced, 19,20 achieved by the ability to optimize, and improve volumetric productivities. In the context of autologous cell therapies, the resulting cost per batch (or per patient) could be three times higher using these scalable technologies (results not shown). 44 However, the cost benefit of being able to accommodate for the inherent variability of starting cell densities related to the patient cells collected, and the value to maintain tight control over product quality attributes, are yet to be defined upon the cost-effectiveness of the therapeutic. These would be expected to play a significant role in the final process configuration.

| CONCLUSION
A simple ODE model of cell growth was introduced to specify key parameters for efficient culture operation. It has also demonstrated that this user-friendly model is simple enough to be built and tested with low data and represent the complexity of cell dynamic and biology to a degree that is acceptable for manufacturing applications.
The data from our model indicated that culture growth rate could be approximated as a function of cell time in the system and both starting cell density and timing of feed have a great influence on T-cell system growth and point of growth inhibition. Furthermore, our model showed that glucose is linked to the growth rate and that a delivery of glucose at a feed rate substantially under the maximal specific consumption parameter value of 0.05 mg 1 Â 10 6 cell h À1 will adequately sustain cell growth in the system.

DATA AVAILABILITY STATEMENT
The data that support the findings of this study are available in