Hybrid Approach to State Estimation for Bioprocess Control

Physics-informed neural networks for biopharmaceutical cultivation processes: Consideration of varying process parameter settings

We present a new modeling approach for the study and prediction of important process outcomes of biotechnological cultivation processes under the influence of process parameter variations. Our model is based on physics-informed neural networks (PINNs) in combination with kinetic growth equations. Using Taylor series, multivariate external process parameter variations for important variables such as temperature, seeding cell density and feeding rates can be integrated into the corresponding kinetic rates and the governing growth equations. In addition to previous approaches, PINNs also allow continuous and differentiable functions as predictions for the process outcomes. Accordingly, our results show that PINNs in combination with Taylor-series expansions for kinetic growth equations provide a very high prediction accuracy for important process variables such as cell densities and concentrations as well as a detailed study of individual and combined parameter influences. Furthermore, the proposed approach can also be used to evaluate the outcomes of new parameter variations and combinations, which enables a saving of experiments in combination with a model-driven optimization study of the design space.

Hybrid modeling in bioprocess dynamics: Structural variabilities, implementation strategies, and practical challenges

Hybrid modeling, with an appropriate blend of the mechanistic and data-driven framework, is increasingly being adopted in bioprocess modeling, model-based experimental design (digital-twin), identification of critical process parameters, and optimization. However, the development of a hybrid model from experimental data is an inherently complex workflow, involving designed experiments, selection of the data-driven process, identification of model parameters, assessment fitness, and generalization capability. Depending on the complexity of the process system and purpose, each piece of these modules can flexibly be incorporated into the puzzle. However, this extra flexibility can be a cause of concern to trace an "optimal" model structure. In this paper, the development of hybrid models in a common bioprocess system, selection of data-driven components and their mapping to states, choice of parameter identification techniques, and model quality assurance are revisited. The challenges associated with hybrid-model development, and corrective actions have also been reviewed. The review also suggests the lack of data, and code sharing in communal repositories can be a hurdle in the exploration, and expansion of those tools in a bioprocess system.

An adaptive soft-sensor for advanced real-time monitoring of an antibody-drug conjugation reaction

In the production of antibody-drug conjugates (ADCs), the conjugation reaction is a central step defining the final product composition and, hence, directly affecting product safety and efficacy. To enable real-time monitoring, spectroscopic sensors in combination with multivariate regression models have gained popularity in recent years. The extended Kalman filter (EKF) can be used as so-called soft-sensor to fuse sensor predictions with long-horizon forecasts by process models. This enables the dynamic update of the current state and provides increased robustness against experimental noise or model errors. Due to the uncertainty associated with sensor and process models in biopharmaceutical applications, the deployment of such soft-sensors is challenging. In this study, we demonstrate the combination of an uncertainty-aware sensor model with a kinetic reaction model using an EKF to monitor a site-directed ADC conjugation reaction. As the sensor model, a Gaussian process regression model is presented to realize a time-variant determination of the sensor uncertainty. The EKF fuses the time-discrete predictions of the amount of conjugated drug from the sensor model with the time-continuous predictions from the kinetic model. While the ADC species are not distinguishable by on-line recorded UV/Vis spectra, the developed soft-sensor is able to dynamically update all relevant reaction species. It could be shown that the use of time-variant process and sensor noise computation approaches improved the performance of the EKF and achieved a reduction of the prediction error of up to 23% compared with the kinetic model. The developed framework proved to enhance robustness against noisy sensor measurements or wrong model initialization and was successfully transferred from batch to fed-batch mode. In future, this framework could be implemented for model-based process control and be adopted for other ADC conjugation reaction types.

rAAV Manufacturing: The Challenges of Soft Sensing during Upstream Processing

Recombinant adeno-associated virus (rAAV) is the most effective viral vector technology for directly translating the genomic revolution into medicinal therapies. However, the manufacturing of rAAV viral vectors remains challenging in the upstream processing with low rAAV yield in large-scale production and high cost, limiting the generalization of rAAV-based treatments. This situation can be improved by real-time monitoring of critical process parameters (CPP) that affect critical quality attributes (CQA). To achieve this aim, soft sensing combined with predictive modeling is an important strategy that can be used for optimizing the upstream process of rAAV production by monitoring critical process variables in real time. However, the development of soft sensors for rAAV production as a fast and low-cost monitoring approach is not an easy task. This review article describes four challenges and critically discusses the possible solutions that can enable the application of soft sensors for rAAV production monitoring. The challenges from a data scientist's perspective are (i) a predictor variable (soft-sensor inputs) set without AAV viral titer, (ii) multi-step forecasting, (iii) multiple process phases, and (iv) soft-sensor development composed of the mechanistic model.

The use of predictive models to develop chromatography-based purification processes

Chromatography is the workhorse of biopharmaceutical downstream processing because it can selectively enrich a target product while removing impurities from complex feed streams. This is achieved by exploiting differences in molecular properties, such as size, charge and hydrophobicity (alone or in different combinations). Accordingly, many parameters must be tested during process development in order to maximize product purity and recovery, including resin and ligand types, conductivity, pH, gradient profiles, and the sequence of separation operations. The number of possible experimental conditions quickly becomes unmanageable. Although the range of suitable conditions can be narrowed based on experience, the time and cost of the work remain high even when using high-throughput laboratory automation. In contrast, chromatography modeling using inexpensive, parallelized computer hardware can provide expert knowledge, predicting conditions that achieve high purity and efficient recovery. The prediction of suitable conditions in silico reduces the number of empirical tests required and provides in-depth process understanding, which is recommended by regulatory authorities. In this article, we discuss the benefits and specific challenges of chromatography modeling. We describe the experimental characterization of chromatography devices and settings prior to modeling, such as the determination of column porosity. We also consider the challenges that must be overcome when models are set up and calibrated, including the cross-validation and verification of data-driven and hybrid (combined data-driven and mechanistic) models. This review will therefore support researchers intending to establish a chromatography modeling workflow in their laboratory.

Modern Sensor Tools and Techniques for Monitoring, Controlling, and Improving Cell Culture Processes

The growing biopharmaceutical industry has reached a level of maturity that allows for the monitoring of numerous key variables for both process characterization and outcome predictions. Sensors were historically used in order to maintain an optimal environment within the reactor to optimize process performance. However, technological innovation has pushed towards on-line in situ continuous monitoring of quality attributes that could previously only be estimated off-line. These new sensing technologies when coupled with software models have shown promise for unique fingerprinting, smart process control, outcome improvement, and prediction. All this can be done without requiring invasive sampling or intervention on the system. In this paper, the state-of-the-art sensing technologies and their applications in the context of cell culture monitoring are reviewed with emphasis on the coming push towards industry 4.0 and smart manufacturing within the biopharmaceutical sector. Additionally, perspectives as to how this can be leveraged to improve both understanding and outcomes of cell culture processes are discussed.

Generic and specific recurrent neural network models: Applications for large and small scale biopharmaceutical upstream processes

The calculation of temporally varying upstream process outcomes is a challenging task. Over the last years, several parametric, semi-parametric as well as non-parametric approaches were developed to provide reliable estimates for key process parameters. We present generic and product-specific recurrent neural network (RNN) models for the computation and study of growth and metabolite-related upstream process parameters as well as their temporal evolution. Our approach can be used for the control and study of single product-specific large-scale manufacturing runs as well as generic small-scale evaluations for combined processes and products at development stage. The computational results for the product titer as well as various major upstream outcomes in addition to relevant process parameters show a high degree of accuracy when compared to experimental data and, accordingly, a reasonable predictive capability of the RNN models. The calculated values for the root-mean squared errors of prediction are significantly smaller than the experimental standard deviation for the considered process run ensembles, which highlights the broad applicability of our approach. As a specific benefit for platform processes, the generic RNN model is also used to simulate process outcomes for different temperatures in good agreement with experimental results. The high level of accuracy and the straightforward usage of the approach without sophisticated parameterization and recalibration procedures highlight the benefits of the RNN models, which can be regarded as promising alternatives to existing parametric and semi-parametric methods.

Bridging Offline Functional Model Carrying Aging-Specific Growth Rate Information and Recombinant Protein Expression: Entropic Extension of Akaike Information Criterion

This study presents a mathematical model of recombinant protein expression, including its development, selection, and fitting results based on seventy fed-batch cultivation experiments from two independent biopharmaceutical sites. To resolve the overfitting feature of the Akaike information criterion, we proposed an entropic extension, which behaves asymptotically like the classical criteria. Estimation of recombinant protein concentration was performed with pseudo-global optimization processes while processing offline recombinant protein concentration samples. We show that functional models including the average age of the cells and the specific growth at induction or the start of product biosynthesis are the best descriptors for datasets. We also proposed introducing a tuning coefficient that would force the modified Akaike information criterion to avoid overfitting when the designer requires fewer model parameters. We expect that a lower number of coefficients would allow the efficient maximization of target microbial products in the upstream section of contract development and manufacturing organization services in the future. Experimental model fitting was accomplished simultaneously for 46 experiments at the first site and 24 fed-batch experiments at the second site. Both locations contained 196 and 131 protein samples, thus giving a total of 327 target product concentration samples derived from the bioreactor medium.

About Model Validation in Bioprocessing

In bioprocess engineering the Qualtiy by Design (QbD) initiative encourages the use of models to define design spaces. However, clear guidelines on how models for QbD are validated are still missing. In this review we provide a comprehensive overview of the validation methods, mathematical approaches, and metrics currently applied in bioprocess modeling. The methods cover analytics for data used for modeling, model training and selection, measures for predictiveness, and model uncertainties. We point out the general issues in model validation and calibration for different types of models and put this into the context of existing health authority recommendations. This review provides a starting point for developing a guide for model validation approaches. There is no one-fits-all approach, but this review should help to identify the best fitting validation method, or combination of methods, for the specific task and the type of bioprocess model that is being developed.

Parameter and state estimation of backers yeast cultivation with a gas sensor array and unscented Kalman filter

Real-time information about the concentrations of substrates and biomass is the key to accurate monitoring and control of bioprocess. However, on-line measurement of these variables is a challenging task and new measurement systems are still required. An alternative are software sensors, which can be used for state and parameter estimation in bioprocesses. The software sensors predict the state of the process by using mathematical models as well as data from measured variables. The Kalman filter is a type of such sensors. In this paper, we have used the Unscented Kalman Filter (UKF) which is a nonlinear extension of the Kalman filter for on-line estimation of biomass, glucose and ethanol concentration as well as for estimating the growth rate parameters in S. cerevisiae batch cultivation, based on infrequent ethanol measurements. The UKF algorithm was validated on three different cultivations with variability of the substrate concentrations and the estimated values were compared to the off-line values. The results obtained showed that the UKF algorithm provides satisfactory results with respect to estimation of concentrations of substrates and biomass as well as the growth rate parameters during the batch cultivation.

Monitoring and control of E. coli cell integrity

Soluble expression of recombinant proteins in E. coli is often done by translocation of the product across the inner membrane (IM) into the periplasm, where it is retained by the outer membrane (OM). While the integrity of the IM is strongly coupled to viability and impurity release, a decrease in OM integrity (corresponding to increased "leakiness") leads to accumulation of product in the extracellular space, strongly impacting the downstream process. Whether leakiness is desired or not, differential monitoring and control of IM and OM integrity are necessary for an efficient E. coli bioprocess in compliance with the guidelines of Quality by Design and Process Analytical Technology. In this review, we give an overview of relevant monitoring tools, summarize the research on factors affecting E. coli membrane integrity and provide a brief discussion on how the available monitoring technology can be implemented in real-time control of E. coli cultivations.

The Kalman Filter for the Supervision of Cultivation Processes

In the era of technology and digitalization, the process industries are undergoing a digital transformation. The available process models, advance sensor technologies, enhanced computational power and a broad set of data analytical techniques enable solid bases for digital transformation in the biopharmaceutical industry.Among various data analytical techniques, the Kalman filter and its non-linear extensions are powerful tools for prediction of reliable process information. The combination of the Kalman filter with a virtual representation of the bioprocess, called digital twin, can provide real-time available process information. Incorporation of such variables in process operation can provide improved control performance with enhanced productivity.In this chapter the linear discrete Kalman filter, the extended Kalman filter and the unscented Kalman filters are described and a brief overview of applications of the Kalman filter and its non-linear extensions to bioreactors are presented. Furthermore, in a case study an example of the digital twin of the backer's yeast batch cultivation process is presented. A digital twin of a bioreactor mirrors the processes of the real bioreactor. It contains the physical parts, the process model and prediction algorithm to predict the bioprocess variables. These values could be used for optimization and control of the process.

When Is an In Silico Representation a Digital Twin? A Biopharmaceutical Industry Approach to the Digital Twin Concept

Digital twins (DTs) are expected to render process development and life-cycle management much more cost-effective and time-efficient. A DT definition, a brief retrospect on their history and expectations for their deployment in today's business environment, and a detailed financial assessment of their attractive economic benefits are provided in this chapter. The argument that restrictive guidelines set forth by regulatory agencies would hinder the adoption of DTs in the (bio)pharmaceutical industry is revisited, concluding that those companies who collaborate with the agencies to further their technical capabilities will gain significant competitive advantage. The analyzed process development examples show high methodological readiness levels but low systematic adoption of technology. Given the technical feasibilities, financial opportunities, and regulatory encouragement, concerns regarding intellectual property and data sharing, though required to be taken into account, will at best delay an industry-wide adoption of DTs. In conclusion, it is expected that a strategic investment in DTs now will gain an advantage over competition that will be difficult to overcome by late adopters.

Adaptive Control of Biomass Specific Growth Rate in Fed-Batch Biotechnological Processes. A Comparative Study

This article presents a comparative study on the development and application of two distinct adaptive control algorithms for biomass specific growth rate control in fed-batch biotechnological processes. A typical fed-batch process using Escherichia coli for recombinant protein production was selected for this research. Numerical simulation results show that both developed controllers, an adaptive PI controller based on the gain scheduling technique and a model-free adaptive controller based on the artificial neural network, delivered a comparable control performance and are suitable for application when using the substrate limitation approach and substrate feeding rate manipulation. The controller performance was tested within the realistic ranges of the feedback signal sampling intervals and measurement noise intensities. Considering the efforts for controller design and tuning, including development of the adaptation/learning algorithms, the model-free adaptive control algorithm proves to be more attractive for industrial applications, especially when only limited knowledge of the process and its mathematical model is available. The investigated model-free adaptive controller also tended to deliver better control quality under low specific growth rate conditions that prevail during the recombinant protein production phase. In the investigated simulation runs, the average tracking error did not exceed 0.01 (1/h). The temporary overshoots caused by the maximal disturbances stayed within the range of 0.025–0.11 (1/h). Application of the algorithm can be further extended to specific growth rate control in other bacterial and mammalian cell cultivations that run under substrate limitation conditions.

From Physics to Bioengineering: Microbial Cultivation Process Design and Feeding Rate Control Based on Relative Entropy Using Nuisance Time

For historic reasons, industrial knowledge of reproducibility and restrictions imposed by regulations, open-loop feeding control approaches dominate in industrial fed-batch cultivation processes. In this study, a generic gray box biomass modeling procedure uses relative entropy as a key to approach the posterior similarly to how prior distribution approaches the posterior distribution by the multivariate path of Lagrange multipliers, for which a description of a nuisance time is introduced. The ultimate purpose of this study was to develop a numerical semi-global convex optimization procedure that is dedicated to the calculation of feeding rate time profiles during the fed-batch cultivation processes. The proposed numerical semi-global convex optimization of relative entropy is neither restricted to the gray box model nor to the bioengineering application. From the bioengineering application perspective, the proposed bioprocess design technique has benefits for both the regular feed-forward control and the advanced adaptive control systems, in which the model for biomass growth prediction is compulsory. After identification of the gray box model parameters, the options and alternatives in controllable industrial biotechnological processes are described. The main aim of this work is to achieve high reproducibility, controllability, and desired process performance. Glucose concentration measurements, which were used for the development of the model, become unnecessary for the development of the desired microbial cultivation process.