Hybrid predictive modelling for the control of cell cultures

Abstract

A method for controlling a cell culture process uses hybrid predictive modeling in a model predictive controller. The method includes obtaining current values ​​of relevant cell culture attributes for a plurality of time intervals and generating control values ​​for physical inputs to the cell culture process. Generating the control values ​​includes predicting future values ​​of the cell culture attributes based on the current values ​​by predicting future values ​​of a first one or more attributes of the cell culture attributes using one or more data-driven models and predicting future values ​​of a second one or more attributes of the cell culture attributes using one or more first principles models. Generating the control values ​​also includes determining the control values ​​by optimizing an objective function according to the predicted future values. The method also includes controlling the physical inputs to the cell culture process using the control values.

Description

[Technical field]

[0001] This application relates generally to cell culture (e.g., in a bioreactor), and more specifically to predicting and controlling cell culture attributes. [Background technology]

[0002] The biopharmaceutical industry is continually striving to improve productivity while ensuring that processes remain highly reliable and cost-effective. With the advent of new digital technologies, higher computing power, better integration flexibility, and possibilities such as artificial intelligence, new means of achieving these objectives are emerging. One of these means is by utilizing process data to improve how processes are controlled. In recent years, many smart factories have attempted to manage different process scenarios and process automation using adaptive models without human intervention. See Catlin et al., A Roadmap for a Digital Transformation, 2017, McKinsey. To achieve this successfully, advanced control of the process in real time is required.

[0003] Due to various challenges such as lack of measurements and process complexity, control of biopharmaceutical processes has rarely progressed beyond simple PID (proportional integral derivative) control of a small set of variables in practice. See Whitby et al., PID Control of Biochemical Reaction Networks, 2019, 2019 IEEE 58th Conference on Decision and Control (CDC), 8372-8379; Sen et al., A Hybrid MPC-PID Control System Design for the Continuous Purification and Processing of Active Pharmaceutical Ingredients, 2014, Processes, 2, 392-418. In such processes, traditional control methods aim to manipulate the extracellular environment to control intracellular reactions of the culture. See Boudreau et al., New Directions in Bioprocess Modeling and Control: Maximizing Process Analytical Technology Benefits, 2006, ISA, Research Triangle Park, NC. Model predictive control (MPC) is an advanced multi-stage control method that is not only effective for multivariable process control, but can also address constraints imposed by both manipulated variables (inputs) and controlled variables (outputs). See SJQin, A Survey of Industrial Model Predictive Control Technology, 2003, Control Engineering Practice, 11, 733-764. The main component of MPC is a dynamic model of the process that is used to determine the optimal control action that leads faster to an optimized and feasible goal.

[0004] In the literature, there are various first-principles and data-driven models for bioprocesses. See Craven et.al., Process Model Comparison and Transferability Across Bioreactor Scales and Modes of Operation for a Mammalian Cell Bioprocess, 2013, AICHE Journal, 29, 186-196; Tulsyan et al., Advances in Industrial Biopharmaceutical Batch Process Monitoring: Machine-Learning Methods for Small Data Problems, 2018, Biotechnol Bioeng, 115, 1915-1924. First-principles models are mainly obtained based on Monod-type kinetic and enzymatic schemes, which result in nonlinear state models with many unknown free parameters. See Craven et al., Glucose Concentration Control of a Fed-Batch Mammalian Cell Bioprocess Using a Nonlinear Model Predictive Controller, 2014, Journal of Process Control, 24, 344-357. On the other hand, the use of data-driven methods for process monitoring and control purposes has been intensively investigated.See Kiran et al., Control of Continuous Fed-Batch Fermentation Process Using Neural Network Based Model Predictive Controller, 2009, Bioprocess Biosyst Eng, 32, 801-808; Tulsyan et al., Spectroscopic Models for Real-Time Monitoring of Cell Culture Processes Using Spatiotemporal Just-in-Time Gaussian Processes, 2021, AICHE Journal, 67, e17210. The choice of model is important as it affects not only the computational load but also the accuracy and reliability of the control policy. Neural network models have been used in many studies for the purpose of controller design in fed-batch fermentation processes. See Chtourou et al., Control of a Bioreactor Using a Neural Network, 1993, Bioprocess Eng., 8, 251-254; Patnaik, An Integrated Hybrid Neural System for Noise Filtering, Simulation and Control of a Fed-Batch Recombinant Fermentation, 2003, Biochem Eng J., 15, 165-175. Unfortunately, due to the time-varying nature of fed-batch fermentation and the limited amount of training data, the models usually do not have high accuracy.

[0005] As mentioned above, models such as Monod-type kinetics can result in a large number of unknown parameters. However, the discrete feed streams in fed-batch processes can result in insensitivity of the target variable to the feeding strategy. Furthermore, the accuracy of these simplified models can be reduced by the complex multi-step reactions in the process, the rapid adaptability of cells in the process (see Sinclair et al., Fermentation Kinetics and Modelling, 1987, Open University Press, Milton Keynes, 44, xi-113), and the random variability that occurs during batch operations. See Jose et al., Developmental Studies of an Adaptive On-Line Softsensor for Biological Wastewater Treatments, 1999, Can. J. Chem. Eng., 77, 707-717. [Prior art documents] [Non-patent literature]

[0006] [Non-Patent Document 1] Catlin et al.,A Roadmap for a Digital Transformation,2017,McKinsey [Non-Patent Document 2] Whitby et al.,PID Control of Biochemical Reaction Networks,2019,2019 IEEE 58th Conference on Decision and Control (CDC),8372-8379 [Non-Patent Document 3] Sen et al.,A Hybrid MPC-PID Control System Design for the Continuous Purification and Processing of Active Pharmaceutical Ingredients,2014,Processes,2,392-418 [Non-Patent Document 4] Boudreau et al., New Directions in Bioprocess Modeling and Control: Maximizing Process Analytical Technology Benefits, 2006, ISA, Research Triangle Park, NC. [Non-Patent Document 5] SJQin,A Survey of Industrial Model Predictive Control Technology,2003,Control Engineering Practice,11,733-764 [Non-Patent Document 6] Craven et.al., Process Model Comparison and Transferability Across Bioreactor Scales and Modes of Operation for a Mammalian Cell Bioprocess,2013,AICHE Journal,29,186-196 [Non-Patent Document 7] Tulsyan et al.,Advances in Industrial Biopharmaceutical Batch Process Monitoring:Machine-Learning Methods for Small Data Problems,2018,Biotechnol Bioeng,115,1915-1924 [Non-Patent Document 8] Craven et al.,Glucose Concentration Control of a Fed-Batch Mammalian Cell Bioprocess Using a Nonlinear Model Predictive Controller,2014,Journal of Process Control,24,344-357 [Non-Patent Document 9] Kiran et al.,Control of Continuous Fed-Batch Fermentation Process Using Neural Network Based Model Predictive Controller,2009,Bioprocess Biosyst Eng,32,801-808 [Non-Patent Document 10] Tulsyan et al.,Spectroscopic Models for Real-Time Monitoring of Cell Culture Processes Using Spatiotemporal Just-in-Time Gaussian Processes,2021,AICHE Journal,67,e17210 [Non-Patent Document 11] Chtourou et al.,Control of a Bioreactor Using a Neural Network,1993,Bioprocess Eng.,8,251-254 [Non-Patent Document 12] Patnaik, An Integrated Hybrid Neural System for Noise Filtering,Simulation and Control of a Fed-Batch Recombinant Fermentation,2003,Biochem Eng J.,15,165-175 [Non-Patent Document 13] Sinclair et al.,Fermentation Kinetics and Modelling,1987,Open University Press,Milton Keynes,44,xi-113 [Non-Patent Document 14] Jose et al.,Developmental Studies of an Adaptive On-Line Softsensor for Biological Wastewater Treatments,1999,Can.J.Chem.Eng.,77,707-717 Summary of the Invention [Means for solving the problem]

[0007] Bioprocesses can often be characterized by nonlinearity, variability, and complexity resulting from metabolic network pathways within the cells. With acceptable understanding of the process, modern advanced control strategies can be employed to increase the reliability and efficiency of the process. Model predictive control (MPC) uses real-time process models to make predictions by optimizing an objective (cost) function at each time interval while adhering to custom constraints. MPC results in prescriptive control actions by predicting upcoming disturbances and ensuring predictive stability. In the MPC framework, predictions of the process of interest are calculated based on future outcomes as related to the objectives and constraints of the model, and the future behavior of the dynamic model is based on the predictive model. Thus, predictive models play an important role in MPC.

[0008] The systems and methods described herein generally provide a hybrid approach to prediction in MPC systems by using both first principles and data-driven modeling. For example, the systems and methods may use data-driven models (e.g., linear regressors and / or neural networks) trained on historical data from an actual cell culture process to predict future values ​​of certain metabolite concentrations and / or other cell culture attributes (e.g., viable cell density (VCD), osmolality, etc.), while also using first principles (e.g., mass balance) models to predict future values ​​of glucose concentrations, the latter predictions being based on feed rates and data-driven model predictions (e.g., VCD predictions). The use of first principles models mitigates the shortcomings of data-driven models in predicting glucose concentrations (e.g., low model sensitivity to feed rates), while the use of data-driven models mitigates the inability of first principles models (e.g., current mass balance models) to accurately and consistently model the relationship between glucose and other metabolites.

[0009] Overall, the hybrid model can predict future cell culture attributes in the prediction phase of MPC over a desired prediction horizon with higher accuracy and consistency. Then, in the optimization phase of MPC, control values ​​(e.g., glucose feed rate values) over a control horizon can be calculated by solving an optimization problem of an objective function subject to certain constraints (e.g., minimum and maximum feed rates). At any given time interval, the first control value determined by MPC (i.e., the value for the earliest time interval of the control horizon) is used to control the physical input to the cell culture process (e.g., the glucose feed rate provided by the glucose pump), and the prediction and optimization phases are repeated / updated for each time interval (e.g., daily or hourly, etc.).

[0010] The techniques disclosed herein may eliminate the need for manual adjustment of control set points. Moreover, by mitigating shortcomings of both data-driven and first principles models, these techniques may provide improved predictive accuracy compared to other modeling techniques, thereby enabling control actions that lead to better performance of the cell culture process (e.g., superior product quality attributes).

[0011] Those skilled in the art will appreciate that the figures described herein are included for illustrative purposes and are not intended to limit the disclosure. The drawings are not necessarily to scale, emphasis instead being placed on illustrating the principles of the disclosure. It should be understood that in some instances, various aspects of the described embodiments may be shown exaggerated or enlarged to facilitate understanding of the described embodiments. In the drawings, like reference characters generally refer to functionally similar and / or structurally similar components throughout the various views. [Brief description of the drawings]

[0012] [Figure 1]FIG. 1 is a simplified block diagram of an exemplary system that may be used to monitor and control a cell culture process according to the techniques disclosed herein. [Diagram 2] FIG. 2 is a block diagram of an example architecture that may be implemented in the system of FIG. 1. [Diagram 3] 3 illustrates an example operation of a model predictive controller that may be used as the model predictive controller of FIG. 1 and / or FIG. 2. [Figure 4] 3 illustrates an example sequence of predictions made by the predictive model of FIG. 1 and / or FIG. 2. [Diagram 5] 2 illustrates an exemplary neural network that can be used as the data-driven model of FIG. 1. [Figure 6A] 1 is a normalized plot showing predictive performance for various cell culture attributes when using linear regressors with a first principles model for a first cell culture process. [Figure 6B] 1 is a normalized plot showing predictive performance for various cell culture attributes when using linear regressors with a first principles model for a first cell culture process. [Figure 6C] 1 is a normalized plot showing predictive performance for various cell culture attributes when using linear regressors with a first principles model for a first cell culture process. [Figure 7A] 1 is a normalized plot showing model predictive controller performance for various cell culture attributes when using a linear regressor with a first principles model for a first cell culture process. [Figure 7B] 1 is a normalized plot showing model predictive controller performance for various cell culture attributes when using a linear regressor with a first principles model for a first cell culture process. [Figure 7C] 1 is a normalized plot showing model predictive controller performance for various cell culture attributes when using a linear regressor with a first principles model for a first cell culture process. [Figure 8A]1 is a normalized plot showing the predictive performance for various cell culture attributes using a neural network with a first principles model for a first cell culture process. [Figure 8B] 1 is a normalized plot showing the predictive performance for various cell culture attributes using a neural network with a first principles model for a first cell culture process. [Figure 8C] 1 is a normalized plot showing the predictive performance for various cell culture attributes using a neural network with a first principles model for a first cell culture process. [Figure 9A] 11 is a normalized plot showing model predictive controller performance for various cell culture attributes when using a neural network with a first principles model for a first cell culture process. [Figure 9B] 11 is a normalized plot showing model predictive controller performance for various cell culture attributes when using a neural network with a first principles model for a first cell culture process. [Figure 9C] 11 is a normalized plot showing model predictive controller performance for various cell culture attributes when using a neural network with a first principles model for a first cell culture process. [Figure 10A] 13 is a normalized plot comparing the predictive performance for various cell culture attributes using linear or nonlinear data-driven predictive models along with a first principles model for a second cell culture process. [Figure 10B] 13 is a normalized plot comparing the predictive performance for various cell culture attributes using linear or nonlinear data-driven predictive models along with a first principles model for a second cell culture process. [Figure 10C] 13 is a normalized plot comparing the predictive performance for various cell culture attributes using linear or nonlinear data-driven predictive models along with a first principles model for a second cell culture process. [Figure 11A]13 is a normalized plot comparing model predictive controller performance for various cell culture attributes when using linear or nonlinear data-driven predictive models along with a first principles model for a second cell culture process. [Figure 11B] 13 is a normalized plot comparing model predictive controller performance for various cell culture attributes when using linear or nonlinear data-driven predictive models along with a first principles model for a second cell culture process. [Figure 11C] 13 is a normalized plot comparing model predictive controller performance for various cell culture attributes when using linear or nonlinear data-driven predictive models along with a first principles model for a second cell culture process. [Figure 11D] 13 is a normalized plot comparing model predictive controller performance for various cell culture attributes when using linear or nonlinear data-driven predictive models along with a first principles model for a second cell culture process. [Figure 12A] 13 is a normalized plot comparing the predictive performance for various cell culture attributes using linear or nonlinear data-driven predictive models along with a first principles model for a third cell culture process. [Figure 12B] 13 is a normalized plot comparing the predictive performance for various cell culture attributes using linear or nonlinear data-driven predictive models along with a first principles model for a third cell culture process. [Figure 12C] 13 is a normalized plot comparing the predictive performance for various cell culture attributes using linear or nonlinear data-driven predictive models along with a first principles model for a third cell culture process. [Figure 13A] 13 is a normalized plot comparing model predictive controller performance for various cell culture attributes using a linear or nonlinear data-driven predictive model along with a first principles model for a third cell culture process. [Figure 13B]13 is a normalized plot comparing model predictive controller performance for various cell culture attributes using a linear or nonlinear data-driven predictive model along with a first principles model for a third cell culture process. [Figure 13C] 13 is a normalized plot comparing model predictive controller performance for various cell culture attributes using a linear or nonlinear data-driven predictive model along with a first principles model for a third cell culture process. [Figure 13D] 13 is a normalized plot comparing model predictive controller performance for various cell culture attributes using a linear or nonlinear data-driven predictive model along with a first principles model for a third cell culture process. [Figure 14] 1 is a normalized graph comparing glucose feed levels for a process with and without the model predictive control and hybrid predictive modeling techniques disclosed herein. [Figure 15] 1 is a normalized plot comparing viable cell density for a process with and without the model predictive control and hybrid predictive modeling techniques disclosed herein. [Figure 16A] 1 is a normalized plot showing predicted versus measured Raman scan vectors for viable cell density for systems without and with the model predictive control and hybrid predictive modeling techniques disclosed herein, respectively. [Figure 16B] 1 is a normalized plot showing predicted versus measured Raman scan vectors for viable cell density for systems without and with the model predictive control and hybrid predictive modeling techniques disclosed herein, respectively. [Figure 17] 1 is a normalized plot comparing glucose concentrations for a process with and without the model predictive control and hybrid predictive modeling techniques disclosed herein. [Figure 18A]1 is a normalized plot showing predicted versus measured Raman scan vectors for glucose concentration for systems without and with the model predictive control and hybrid predictive modeling techniques disclosed herein, respectively; [Figure 18B] 1 is a normalized plot showing predicted versus measured Raman scan vectors for glucose concentration for systems without and with the model predictive control and hybrid predictive modeling techniques disclosed herein, respectively; [Figure 19] 1 includes normalized plots comparing titer and specific productivity for processes with and without the model predictive control and hybrid predictive modeling techniques disclosed herein. [Figure 20A] 1 is a normalized plot showing predicted versus measured Raman scan vectors for potency for systems without and with the model predictive control and hybrid predictive modeling techniques disclosed herein, respectively. [Figure 20B] 1 is a normalized plot showing predicted versus measured Raman scan vectors for potency for systems without and with the model predictive control and hybrid predictive modeling techniques disclosed herein, respectively. [Figure 21] 1 is a normalized plot comparing glucose feed rates for a process with and without the model predictive control and hybrid predictive modeling techniques disclosed herein using Gaussian process modeling for model predictive control. [Figure 22] 1 is a normalized plot comparing viable cell density for a process with and without model predictive control and hybrid predictive modeling techniques disclosed herein using Gaussian process modeling for model predictive control. [Diagram 23] 1 shows normalized plots comparing total cell density, glucose concentration, viability, and osmolality for a process with and without the model predictive control and hybrid predictive modeling techniques disclosed herein using Gaussian process modeling for model predictive control. [Figure 24] 1 is a normalized plot comparing titers for a process with and without model predictive control and hybrid predictive modeling techniques disclosed herein using Gaussian process modeling for model predictive control. [Diagram 25] FIG. 1 is a flow diagram of an exemplary method for controlling a cell culture process using hybrid predictive modeling in a model predictive controller. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0013] The various concepts introduced above and discussed in more detail below may be implemented in any of numerous ways, and the concepts described are not limited to any particular implementation. Several example implementations are provided for illustrative purposes.

[0014] 1 is a simplified block diagram of an exemplary system 100 that may be used to manually monitor and control a cell culture process. The system 100 includes a bioreactor 102, one or more analytical instruments 104, an input device 106, and a computing system 108.

[0015] The bioreactor 102 may be any suitable vessel, device, or system that supports a cell culture (which may include organisms in a medium and / or substances derived therefrom). The bioreactor 102 may contain recombinant proteins expressed by the cell culture, for example, for research purposes, clinical use, commercial sale or other distribution, etc. Depending on the biopharmaceutical process being monitored, the medium may include a particular fluid (e.g., a "broth") and particular nutrients, as well as have a target pH level or range, a target temperature or temperature range, etc.

[0016] The analytical instruments 104 are communicatively coupled to the computing system 108 and may include one or more any in-line, at-line, and / or offline instruments configured to measure one or more attributes of the cell culture in the bioreactor 102. For example, the analytical instruments 104 may measure one or more media component concentrations, such as metabolite concentrations (e.g., glucose, lactate, sodium, potassium, glutamine, ammonium, etc.). Additionally or alternatively, the analytical instruments 104 may measure osmolality, packed cell volume (PCV), viable cell density (VCD), total cell density (TCD), viability, and / or one or more other cell culture attributes associated with the contents of the bioreactor 102 (e.g., biomass).

[0017] In some embodiments, the analytical instruments 104 may use destructive measurement / analysis techniques, while in other embodiments, one, several, or all of the analytical instruments 104 use non-destructive measurement / analysis techniques based on optical or imaging techniques. For example, the analytical instruments 104 may include a Raman analyzer or near-infrared (NIR) spectroscopy with a spectrometer and one or more probes. The Raman analyzer may include a laser source that sends laser light to the probes via respective fiber optic cables, and may also include a charge-coupled device (CCD) or other suitable camera / recording device that records signals received from the probes via another channel of the respective fiber optic cable. Alternatively, the laser source may be integrated into the probe. Each probe may be an immersion probe, or any other suitable type of probe (e.g., a reflection probe or a transmission probe). The analyzer and the probes may non-destructively scan the relevant cell culture attributes in the bioreactor 102 by exciting, observing, and recording the molecular "fingerprint" of the cell culture process. The molecular fingerprint corresponds to the vibrational, rotational, and / or other low frequency modes of molecules within the biologically active content when the content is excited by the laser light delivered by the probe. As a result of this scanning process, the Raman analyzer generates one or more Raman scan vectors, each of which represents intensity as a function of Raman shift (frequency). The Raman analyzer can then analyze the Raman scan vectors to determine (e.g., infer) the value of a corresponding cell culture attribute (e.g., glucose and / or other metabolite concentration).

[0018] The Raman spectroscopy approach described above may be considered a type of "soft" sensing. In other soft sensing embodiments, one, some, or all of the analytical instruments 104 may include a computational / processing device that uses one or more models to combine different types of analytical data and predict one or more results based on correlations between these types of analytical data. Such results may be directly or indirectly related to the model inputs (i.e., analytical data). Alternatively, the computational system 108 itself, or another computational system or device, may perform some or all of this processing for one or more of the analytical instruments 104.

[0019] The input device 106 is communicatively coupled to the computing system 108, which may be (or may include) any electronically controllable actuator or component that provides a physical input to the contents of the bioreactor 102. For example, the input device 106 may be a distributed control system (DCS) that includes or is coupled to an actuator that provides a direct physical input to the bioreactor 102. As a more specific example, the input device 106 may include a glucose pump that adds a controlled amount or rate of glucose feed to the bioreactor 102, or a device that provides heat and / or cooling to the bioreactor 102 and its contents, and the like. In general, the input device 106 may include pumps, valve actuators, and / or any other suitable type or combination of control elements. The input device 106 may include a proportional-integral-derivative (PID) controller, e.g., receive a set point from the computing system 108 as an input to the PID controller. In some embodiments, the system 100 includes two or more electronically controllable input devices controlled by the computing system 108.

[0020] Computing system 108 may be a server, a desktop computer, a laptop computer, a tablet device, or any other suitable type of computing device. In the example embodiment shown in FIG. 1, computing system 108 includes processing hardware 120, a display device 124, a user input device 126, and a memory 128. However, in some embodiments, computing system 108 includes two or more computers, either co-located or remote from one another, or some combination thereof. In these distributed embodiments, operations described herein relating to processing hardware 120 and / or memory 128 may be divided across multiple processing units and / or memories, respectively.

[0021] The processing hardware 120 includes one or more processors, each of which may be a programmable microprocessor that executes software instructions stored in memory 128 to perform some or all of the functions of the computing system 108 described herein. Alternatively, some of the processors in the processing hardware 120 may be other types of processors (e.g., application specific integrated circuits (ASICs), field programmable gate arrays (FPGAs), etc.), and some of the functions of the computing system 108 described herein may instead be implemented in part or in whole in such hardware. The memory 128 may include one or more physical memory devices or units, including volatile and / or non-volatile memory. Any suitable type of memory may be used, such as a read only memory (ROM), a solid state drive (SSD), a hard disk drive (HDD), etc.

[0022] The display device 124 may use any suitable display technology (e.g., LED, OLED, LCD, etc.) to present information to a user, and the user input device 126 may be a keyboard, mouse, trackpad, graphics / drawing tablet, or other suitable input device. In some embodiments, the display device 124 and the user input device 126 are integrated into a single device (e.g., a touch screen display). In general, the display device 124 and the user input device 126 may collectively enable a user to interact with a graphical user interface (GUI) provided by the computing system 108, such as for purposes of monitoring a cell culture process occurring in the bioreactor 102. However, in some embodiments, the computing system 108 does not include the display device 124 and / or the user input device 126.

[0023] The memory 128 stores instructions for one or more software applications, including a cell culture process control (CCPC) application 130. The CCPC application 130, when executed by the processing hardware 120, is generally configured to communicate with the analytical instruments 104 and the input devices 106 to obtain measurements of cell culture attributes and respectively control one or more inputs to the cell culture process. The time intervals may be of any suitable length (e.g., once a day, once an hour, etc.). Moreover, the time intervals may have a fixed or variable length / duration (e.g., having a set / predetermined length, or rather, having a length determined by manual and / or variable inputs). Furthermore, regardless of whether the time intervals are fixed / predetermined, the time intervals may (1) all have the same length / duration, or (2) include two or more different lengths / durations (e.g., having a first time interval lasting one hour, a second time interval lasting three hours, etc.). To this end, CCPC application 130 includes a measurement unit 140 and a model predictive controller (MPC) 142. It will be appreciated that the various units of CCPC application 130 may be distributed among different software applications and / or the functionality of any one of such units may be divided among different software applications.

[0024] The measurement unit 140 may obtain (e.g., request or otherwise monitor) measurements generated by the analytical instruments 104 once per time interval for any desired number of time intervals. In some embodiments, the measurement unit 140 determines one or more cell culture attribute values ​​by processing values ​​obtained from the analytical instruments 104. For example, the measurement unit 140 may determine an average metabolite concentration once per time interval (e.g., once per day) based on metabolite measurements provided more frequently (e.g., once per 15 minutes, once per hour, etc.) by one of the analytical instruments 104. As another example, the measurement unit 140 may analyze Raman scan vectors provided by a spectrometer of the analytical instruments 104 to determine or infer (as described above) values ​​of one or more cell culture attributes. In general, for ease of explanation, terms such as "measured" and "measurement value" are used broadly herein to refer to physically / directly measured values, soft-sensed values, or values ​​derived from (e.g., calculated using) physically / directly measured or soft-sensed values, unless a more specific meaning is clearly indicated by the context in which they are used.

[0025] MPC 142 may apply the cell culture attribute values ​​acquired by measurement unit 140 as inputs to hybrid prediction unit 144, which predicts future cell culture attribute values ​​for a prediction horizon (e.g., a predetermined number of days or other time interval). Based on these predicted values, optimizer 146 of MPC 142 determines control values ​​for each time interval of the control horizon (e.g., each day), which is generally a number of time intervals greater than or equal to, but not greater than, the prediction horizon. Specifically, optimizer 146 determines control values ​​for each time interval of the control horizon by optimizing (e.g., minimizing) an objective function according to various constraints (e.g., keeping variables between minimum and maximum values) and the predicted attribute values ​​provided by hybrid prediction unit 144. At each time interval, in some embodiments, the CCPC application 130 controls the input device 106 using the first control value in the control horizon (i.e., the control value corresponding to the current time interval) by generating a control signal and sending the control signal to the input device 106. For example, the control signal may conform to a particular protocol understood by the input device 106 and may include the control value in an appropriate field of the protocol message. For example, if the input device 106 is a glucose pump, the CCPC application 130 may generate a control message that specifies a particular glucose delivery rate set point in a particular field of the message.

[0026] The hybrid prediction unit 144 utilizes at least two models to generate predictions. For example, the hybrid prediction unit 144 may utilize a first principles model 150 developed based on a first principles understanding of the cell culture process and a data-driven model 152 trained offline using appropriate historical data. In this example, the hybrid prediction unit 144 uses the first principles model 150 to predict values ​​of one or more cell culture attributes for which first principles modeling is known to work better (e.g., more accurately) than a data-driven approach, and uses the data-driven model 152 to predict values ​​of one or more cell culture attributes for which a data-driven (machine learning) model is known to work better (e.g., more accurately) than the first principles model. In some embodiments, for example, the data-driven model 152 uses past measurements (e.g., past measured metabolite concentrations measured by the analytical instrument 104) to predict future concentrations of specific metabolite concentrations and / or other cell culture attributes over a prediction horizon, and the first principles model 150 predicts future glucose concentrations based on the past measurements, the known glucose feed rate, and one or more outputs from the data-driven model 152.

[0027] Depending on the embodiment, the first principles model 150 may model a single phenomenon or may be a collection of multiple first principles models that model multiple phenomena in the cell culture process. The data-driven model 152 may be a linear model, such as a linear regressor, or a non-linear model, such as a feed-forward neural network. In some embodiments, the data-driven model 152 includes two or more data-driven models. For example, the data-driven model 152 may include a different data-driven model for predicting values ​​for each cell culture attribute of the multiple cell culture attributes, each such model being trained with an appropriate type of historical data. Also, the data-driven model 152 may include two or more different types of models for making predictions. For example, the data-driven model 152 may include a linear regressor for predicting future values ​​for each of the first set of metabolite concentrations and a feed-forward neural network for predicting future values ​​for each of the second set of metabolite concentrations and / or other cell culture attributes (e.g., osmolality, etc.). For ease of explanation, the following description primarily refers to a single first principles model and a single data-driven model. However, it will be appreciated that the principles described below can be extended to the use of multiple first principles models and / or multiple data-driven models.

[0028] In some embodiments, data-driven model 152 predicts a value of a cell culture attribute based on past (measured) values ​​of that attribute and one or more known (past or current) control values. For example, data-driven model 152 may predict a current sodium concentration based solely on past measured sodium concentrations and a known glucose feed rate. Additionally, in some embodiments, data-driven model 152 may predict a value of a cell culture attribute based on past (measured) values ​​of other cell culture attributes. For example, data-driven model 152 may predict a current sodium concentration based on past measured concentrations of multiple metabolites (e.g., sodium, glucose, lactate, etc.) and a known glucose feed rate.

[0029] The data-driven model 152 may have any suitable order (e.g., quadratic, cubic, etc.), with the term "order" as used herein referring to the maximum number of different time intervals reflected in measurements used as model inputs in forming a prediction of one or more future time interval values. Thus, for example, a regression model that operates on metabolite concentrations measured on the current day and the previous day is referred to as a quadratic regression model, while a regression model that operates on metabolite concentrations on the current day, the previous day, and the day before is referred to as a cubic regression model. More generally, a quadratic regression model operates on measurements taken at time intervals i and (ix) for at least one cell culture attribute used as model input, and a cubic regression model operates on measurements taken at time intervals i, (ix), and (iy) for at least one cell culture attribute used as model input (where x is any integer greater than 0 and y is any integer greater than x). The models may be linear or nonlinear, depending on the embodiment.

[0030] Because a cubic regression model requires measurements from two preceding time intervals (e.g., the previous two days), such a model may not be available for the two earlier time intervals (e.g., days 0 and 1). Thus, in some embodiments, the hybrid prediction unit 144 of FIG. 1 initially uses a quadratic regression model (e.g., starting with the second time interval) and then switches to a cubic regression model thereafter (e.g., starting with the third time interval). In other embodiments, the hybrid prediction unit 144 uses other techniques for the first time interval (e.g., simply setting the two "preceding measurements" values ​​equal to the current measurements in the first time interval).

[0031] Configurations of the system 100 other than that shown in Fig. 1 are possible. In some embodiments, for example, the system 100 includes a server (not shown in Fig. 1) that trains and / or updates the data-driven model 152 and / or a server that implements the hybrid prediction unit 144 (and also possibly the optimizer 146) and exchanges data with the computing system 108 as part of a web service model. As another example, the system 100 may include one or more additional electronically controllable input devices similar to the input device 106, but possibly of a different type, and the CCPC application 130 includes multiple MPCs (each MPC similar to the MPC 142, each MPC responsible for control of a different one of the input devices), i.e., a MIMO (multiple input / output) MPC. For example, the MPC 142 may control a glucose pump, while a second MPC of the CCPC application 130 (or a separate similar application stored in the memory 128 or another memory) may control the speed of an impeller. However, for ease of explanation, the following description will focus primarily on an embodiment with a single MPC 142 and a single input device 106 .

[0032] In some embodiments, the CCPC application 130 also provides for the presentation (to a user) of information such as measurements (e.g., values ​​obtained by the measurement unit 140) and / or future values ​​output by the hybrid prediction unit 144 (e.g., to enable concurrent manual monitoring / supervision of the cell culture process). For example, the CCPC application 130 may generate and / or populate a graph showing past, current, and predicted / future values ​​of the cell culture attributes and cause the display device 124 to display the graph. Alternatively or additionally, the CCPC application 130 may cause the display device 124 to display the values ​​in a tabular format and / or in some other suitable format. In yet other embodiments, the CCPC application 130 does not display any information to the user.

[0033] FIG. 2 is a block diagram of an exemplary architecture 200 that may be implemented in the system 100 of FIG. 1. In FIG. 2, a cell culture process 202 is performed in the bioreactor 102 of FIG. 1. Various cell culture measurements 204 (i.e., measured cell culture attribute values) are obtained by the measurement unit 140 using the analytical instrument 104 of FIG. 1. As described above, the cell culture measurements 204 may include concentrations of one, some, or all of a set of metabolites in the cell culture (e.g., glucose, lactate, sodium, potassium, ammonium, and / or glutamine), and in some cases, may include one or more other types of measured cell culture attributes, such as VCD, TCD, viability, osmolality, etc. Data-driven models, such as JIT (Just in Time) or CNN (Convolutional Neural Network), may be used to provide approximations of the cell culture measurements.

[0034] The cell culture measurements 204 are input to a hybrid predictive model 206, which includes the first principles model 150 and the data-driven model 152 of FIG. 1 (either or both of which may include multiple models, as discussed above). In FIG. 2, the delay element (z -1 and z -2 ) is used to indicate that past cell culture measurements 204 are also provided as inputs to the hybrid predictive model 206. Figure 2 illustrates an embodiment of a third order (regression or neural network) model, where at least the data-driven model of the hybrid predictive model 206 operates on values ​​from a current time interval (e.g., the current day, or the current time, etc.) and two preceding time intervals (e.g., the past two days) for all of the cell culture measurements 204. However, in other embodiments, past values ​​are only used for a subset of the cell culture measurements 204 and / or the predictive model is of a different order (e.g., second order, fourth order, etc.).

[0035] At each time interval, the hybrid predictive model 206 processes the inputs (i.e., current and past measurements) using the data-driven model 152 and first principles model 150 as described above to generate predicted values ​​of the cell culture attributes over the finite prediction horizon of the MPC 142 (e.g., the next four time intervals, or the next six time intervals, etc.).

[0036] At each time interval, in an optimization step 208, the optimizer 146 operates based on the predicted future values, and possibly other information, to generate control values ​​(e.g., set points) for the input device 106, for example using predictive batch trajectory optimization. The optimizer 146 (and the MPC 142 as a whole) strives to minimize the difference between the amounts of the cell culture variables and the set points while ensuring that the variables stay within specifications. Thus, the optimization problem over a finite time horizon can be formulated as a constrained optimization problem for all batches.

[0037] The optimizer 146 applies the predicted values ​​(at each time interval of the prediction horizon) as input to an objective function, which determines the control values ​​at each time interval of the control horizon. The optimal control values ​​are those that optimize (e.g., minimize) the objective (cost) function, subject to some constraints on the dependent and / or independent variables. The constraints may include, for example, minimum glucose feed (infusion) rate or metabolite concentration, maximum glucose feed rate, and / or other suitable constraints. The objective function may operate on each cell culture attribute having a desired (set point) value, such as different desired concentrations for different metabolites. The optimizer 146 may then determine the control values ​​(e.g., set points for glucose pump feed rate) to guide the cell culture process to the desired objective.

[0038] In some embodiments, the primary objective is to maximize the productivity of the bioprocess while minimizing by-products (i.e., by manipulating the time, amount, and manner in which glucose is fed to the culture). As a result, desired thresholds may be defined for each variable, and the objective function (to be solved by the optimizer 146) may be developed as the sum of quadratic errors between the variables and their desired set points over a time horizon. minJ(X j [i],feed[i]) (Eq. 1A) st:X j (j=1,…,M),feed Where:

number

number

[0039] Every bioprocess is productive if the cell culture variables vary according to predefined specifications. If the cell culture variables exceed the specifications, the process may deviate from the standard and the product quality may be adversely affected. Moreover, it generally does not make sense for the concentrations of the cell culture variables to be negative. As a result, based on the bioprocess predictions, the normalized values ​​of all bioprocess variables may be limited by the optimizer 146 to stay within certain boundaries (e.g., VCD and TDC are greater than or equal to zero; lactate concentration, glutamine concentration, glutamic acid concentration, ammonium concentration, and potassium concentration are less than or equal to 1; glucose concentration is between 0.2 and 0.8; viability is between 0.4 and 1; sodium concentration is between 0.18 and 1; and osmolality is between 0.33 and 1).

[0040] In some embodiments, the linear and / or nonlinear models implemented by the hybrid prediction unit 144 have only one input: the supply. In embodiments where variables other than the VCD are given nonzero weights (in Equation 1B), this means that the controller is moving multiple variables towards their setpoints with only a single input. Moreover, if the main objective is to maximize the VCD, a high threshold can be used while other variables are constrained so that these variables stay within desired ranges.

[0041] In particular, linear MPC is a convex optimization, while nonlinear MPC is a nonconvex optimization. To solve either convex or nonconvex problems, at each time interval / step, optimizer 146 may iterate gradient descent of the Lagrangian function to optimize the process inputs over the prediction horizon (e.g., as described in Kiran et al., Control of Continuous Fed-Batch Fermentation Process Using Neural Network Based Model Predictive Controller, 2009, Bioprocess Biosyst Eng, 32, 801-808). For convex problems, these iterations end at a global minimum at each time step, while nonconvex problems may never converge. Additionally, optimizer 146 may truncate an iteration in a nonlinear MPC embodiment if the gradient descent does not converge to a global minimum, which may result in erroneous values ​​being reported. Furthermore, the solution of linear MPC is globally optimal if the state constraints are considered soft constraints. If these constraints are hard constraints, the solution of the optimization problem may become infeasible. As a result, the global optimum obtained by the linear model of a linear MPC can be considered as another advantage over the nonlinear model in the MPC problem.

[0042] Returning now to the example of Figure 2, the optimizer 208 provides a control value (e.g., a feed rate, or a feed amount, or a change in the feed rate or amount, etc.) as a set point to the cell culture process 202 (more specifically, the input device 106) and also provides the control value to the hybrid predictive model 206, which in this example uses the control value as one of the model inputs in addition to the cell culture measurements 204.

[0043] 3 illustrates the operation 300 of an example MPC, such as MPC 142 of FIG. 1, in a particular embodiment and scenario. In FIG. 3, the x-axis represents time intervals (i, i+1, etc.) and the y-axis represents the amplitude of various measured, predicted, or control values. The area to the left of the y-axis (i-1, i-2, etc.) represents past time intervals, the area to the right of the y-axis (i+1, i+2, etc.) represents future time intervals, and i represents the current time interval. FIG. 3 illustrates the operation 300 of an example MPC, such as MPC 142 of FIG. 1, in a particular embodiment and scenario. In FIG. 3, the x-axis represents time intervals (i, i+1, i+2, etc.) and the y-axis represents the amplitude of various measured, predicted, or control values. The area to the left of the y-axis (i-1, i-2, etc.) represents past time intervals, the area to the right of the y-axis (i+1, i+2, etc.) represents future time intervals, and i represents the current time interval. FIG. 3 illustrates the operation 300 of an example MPC, such as MPC 142 of FIG. 1, in a particular embodiment and scenario. p Future cell culture attribute values ​​306 predicted by the hybrid predictive model 206 (e.g., by the first principles model 150 or the data-driven model 152) over a control horizon N c 3 shows future control values / set points 308 calculated by the MPC 142 over a period of time. In some embodiments, the CCPC application 130 uses only the first control value 312 in the control horizon to control the input device 106 at time point i, and then the prediction / optimization / control process is repeated for the next time interval (time point i+1 in FIG. 3 becomes time point i, time point i+2 becomes time point i+1, and so on).

[0044] 4 shows an exemplary sequence 400 of predictions that may be made by the hybrid prediction unit 144 (i.e., the first principles model 150 and / or the data-driven model 152) of FIG. 1. In FIG. 4, the parameter i represents the current time interval. Thus, in an example where each time interval is one day, i is the current day, i+1 is the next day, i-1 is the previous day, and so on. The sequence 400 shows the prediction progress of a cubic prediction model (e.g., a neural network or a cubic regression model of the data-driven model 152) for the current time interval i. The boxes with dashed lines represent analytical measurements (e.g., the time intervals during which the analytical instrument 104 makes measurements), while the boxes with solid lines represent values ​​predicted by the cubic prediction model. As seen in this example, analytical measurements of the cell culture attribute for the current (i) and the past two (i-1 and i-2) time intervals (possibly along with measurements of other cell culture attributes) are input into a predictive model that enables the predictive model to predict the value of the cell culture attribute at the next time interval i+1. The predictive model then uses the predicted values ​​for time interval i+1 along with the measurements for i and i-1 to predict the value of the cell culture attribute at the next time interval i+2. The predictive model then uses the predicted values ​​for time intervals i+1 and i+2 along with the measurements for i to predict the value of the cell culture attribute at the next time interval i+3, and so on, in this particular example, up to a prediction horizon of four time intervals (up to i+4).

[0045] It has been found that first principles models show the physical relationship between the feed variables and the cell culture variables. To properly model this relationship, data for each model parameter at each time point generally needs to be available and specified. To specify the model parameters, the parameter data should preferably be collected at equal time intervals. Adding a bolus feed to a fed-batch bioprocess means that at some sample times the added feed level may be zero, which creates a non-uniform feed input to the process, and as a result the model parameters may not be specified properly. That is, sparse and non-uniform feed additions in the feed data set may make the model insensitive to the feed rate, which is undesirable for controller design. However, in embodiments where glucose is the metabolite of interest and the main component of the feed, the complexity of the feed can be simplified and the focus can be on evaluating the mass balance between the feed rate and the glucose level as follows: (For non-volume based datasets)

number

number

[0046] Consumption rate k in equations 2a and 2b s[i] is an internal process variable that is not easily measured. Therefore, the consumption rate can be estimated based on historical values ​​of glucose concentration and delivery rate using Equations 2a and 2b as follows:

number

[0047] consumption rate k s [i] is estimated based on the most recent measurements, since this property usually varies smoothly during the culture. However, the consumption rate k s [i] is the estimate of time i from the beginning of the batch, k, in case of sudden changes. s It can be filtered using a Monte Carlo estimate of [i].

[0048] The first principles model 150 uses Equations 2 and 3 to predict future glucose concentration values ​​for the next time interval, and performs a sequence of iterative predictions (e.g., similar to sequence 400) to predict future glucose concentration values ​​for all time intervals 1, . . . , N in the prediction horizon. p In other embodiments, a different first principles model is used to predict glucose concentration and / or a first principles model is used instead (or in addition) to predict a cell culture attribute other than glucose concentration.

[0049] A data-driven model (e.g., data-driven model 142) may also be subject to sparsity in the feed data set if the feed is used as an input in the model structure. Glucose can also be used as an input in the data-driven model because glucose levels change over time (i.e., are not subject to sparsity) and have a physical relationship to the glucose feed. Thus, a hybrid approach combines a data-driven model with the glucose mass balance model of Equations 2 and 3 to obtain a comprehensive model of the entire bioprocess.

[0050] In some embodiments, as described above, the data-driven model 152 is a linear model, such as a linear regressor. For example, the data-driven model 152 may predict one or more cell culture attribute states as: X j [i+1]=a j X j [i]+b j GLC[i]+c j、 (Formula 4) Where X j [.] is an array with an element for each of j different cell culture attributes (e.g., VCD, metabolites other than glucose, viability, etc.), j , b j , and c j is a suitable constant (or an array of j constants). Alternatively, the data-driven model 152 may use a model similar to Equation 4, but where X j [.] and / or additional terms for one or more past values ​​of GLC[.] (i.e., at time i-1, i-2, etc.). In the exemplary embodiment of Equations 2-4, the VCD at time interval i+1 predicted by data-driven model 152 may be used as an input to first principles model 150 (e.g., as an input to Equations 2 and 3).

[0051] The data-driven model 152 may instead be a feed-forward neural network. Two-layer neural networks have been found to perform better than other neural networks. A simplified example of a feed-forward neural network 500 is shown in FIG. 5. Neural networks are proven general function approximators. That is, neural networks can approximate any non-linear input-output behavior by manipulating the number of layers and the availability of training data, as well as using appropriate training methods. As seen in FIG. 5, the neural network 500 includes several inputs in an input layer 502, internal nodes in each of several intermediate or hidden layers 504-1 to 504-L (L is any suitable integer greater than 0), and several outputs in an output layer 506. In this example, the neural network 500 is an (m+1)th order neural network that operates on inputs from the current day or other time interval (x(i)) as well as from each of the previous time intervals back to (and including) the previous mth time interval x(im) (m is any suitable integer greater than 0). 5 shows n outputs for layer 506, in some embodiments, neural network 500 includes only the prediction at the next time interval (i.e., y(i+1)) at each iteration. A prediction sequence similar to sequence 400 of FIG. 4 may then be used to run multiple iterations of neural network 500, thereby generating additional predictions (e.g., y(i+2), y(i+3), etc.) over the length of a desired prediction horizon.

[0052] The governing equation for neural network 500 is:

number

[0053] In Equation 5, x(i) and

number

number

[0054] In Equation 6, y(i) is the measured output and N is the number of training samples. Various local and global optimization approaches have been proposed to find the network weight parameters by optimizing a training cost function such as the function in Equation 6. Although local optimization approaches are relatively fast, they tend to get trapped in local minima of the optimization problem, which leads to poor generalization performance. In some embodiments, a scaled conjugate gradient approach is used to optimize the training cost function and find the network weight parameters. The "scaled conjugate gradient" is a fast and automated training algorithm that, unlike many other training algorithms, has no user-dependent parameters and is less likely to get trapped in local minima of the optimization problem.

[0055] As mentioned above, in some embodiments, the neural network 500 is trained to predict a cell culture attribute (e.g., metabolite concentration, VCD, osmolality, etc.) at a given time interval i based on inputs in layer 502 including concentration / attribute values ​​at one or more earlier time intervals and glucose concentration values ​​(e.g., measurements) at one or more earlier time intervals. In some embodiments, for example, the neural network function for predicting a cell attribute Xj[.] is: X j [i+1]=NN(X j [i],X j [i-1],X j[i-2],GLC[i],GLC[i-1],GLC[i-2]) (Formula 7) It could be.

[0056] This third-order example is sometimes called a "third-order regressor neural network". j [i+1] can be different outputs of a single neural network or different neural networks operating in parallel. The hybrid prediction unit 144 predicts all time intervals 1, ..., N in the prediction horizon. p To predict the value of {tilde over (x)}, equation 7 may be repeated using a prediction sequence similar to sequence 400 of FIG.

[0057] Training the data-driven model 152, whether a neural network or a regression model, can be difficult given the limited detailed real-world historical data available from the cell culture process. For example, metabolite concentrations may not be measured and recorded daily. Thus, in some embodiments, linear interpolation is used to provide more data points (i.e., "missing" values) to a relatively large training data set, but such interpolation tends to be inaccurate. In some embodiments, the data-driven model 152 is continuously adapted by using the measured and predicted values ​​of the cell culture attributes as labels and inputs, respectively, in subsequent training of the data-driven model 152 (i.e., after the predictive model is initially trained and used). In this way, the prediction accuracy can continue to increase over time.

[0058] 6-20 illustrate the performance of various embodiments of the intelligent control techniques described herein for various embodiments of MPC 142 and for various cell culture processes (eg, different drug products and / or process parameters).

[0059] 6A-6C are normalized plots illustrating the predictive performance of one embodiment of MPC 142 for various cell culture attributes (glucose concentration (GLC), total cell density (TCD), glutamine concentration (GLN), sodium concentration (Na), viable cell density (VCD), viability (VIAB), glutamate concentration (GLU), potassium concentration (K), lactate concentration (LAC), ammonium concentration (NH4), osmolality (OSMO)) when using linear regression on a data-driven model (e.g., data-driven model 152) and a first principles model of Equations 2 and 3 (in this example, a mass balance model) in a first cell culture process. The "Predicted" traces in FIGS. 6A-6C correspond to predictions made by the models, while the "Measured" traces correspond to actual measurements. Also shown in FIG. 6C is the controlled feed rate.

[0060] Figures 7A-7C are normalized plots showing the performance of MPC 142 for the same embodiment and the same cell culture process reflected in Figures 6A-6C. While Figures 6A-6C illustrate how well the hybrid prediction unit 144 predicts various cell culture attributes, Figures 7A-7C instead illustrate how well the system 100 using a linear model performs (in this particular embodiment) as shown by the "measured" trace, compared to the "optimal" trace, which represents the solution to the optimization problem calculated by the MPC.

[0061] 8A-8C are normalized plots showing the predictive performance of another embodiment of MPC 142 for the same cell culture attributes and the same cell culture process as in Figures 6A-6C, but using a feed-forward neural network for a data-driven model (e.g., data-driven model 152) and the first principles model of Equations 2 and 3. Again, the "Predicted" traces correspond to the predictions made by the models, while the "Measured" traces correspond to the actual measurements. Measured feed rates are also shown.

[0062] Figures 9A-9C are normalized plots showing the performance of MPC 142 for the same embodiment and cell culture process reflected in Figures 8A-8C. While Figures 8A-8C illustrate how well MPC 142 (i.e., hybrid prediction unit 144) predicts various cell culture attributes, Figures 9A-9C instead illustrate how well system 100 (in this particular embodiment) performs, as shown by the "measured" trace, compared to the "optimal" trace, which represents the solution to the optimization problem calculated by the MPC.

[0063] The root mean square error (RMSE) for predictions made using the embodiment depicted in Figures 6-7 (using a linear model) and using the embodiment depicted in Figures 8-9 (using a non-linear model, more specifically a neural network) is shown below in Table 1.

[0064] [Table 1]

[0065] Figures 10A-10C are normalized plots showing the predictive performance of various embodiments of MPC 142 for different cell culture processes than Figures 6-9. In particular, Figures 10A-10C show predictive performance for embodiments in which MPC 142 uses a linear regression model, a first-order nonlinear (feed-forward neural network) model, and a third-order nonlinear (feed-forward neural network) model, compared to a system (labeled "offline" in Figures 10A-10C) that did not use these predictive models.

[0066] 11A-11D are normalized plots showing the performance of MPC 142 for the same embodiment and same cell culture process reflected in Figures 10A-10C, again along with the results of an "offline" system for comparison purposes. In Figures 11A-11D (and other Figures discussed below), "LMPC" represents the performance of system 100 when MPC 142 uses the linear regression model of Figures 10A-10C, "NLMPC-1" represents the performance of system 100 when MPC 142 uses the first order feedforward neural network of Figures 10A-10C, and "NLMPC-3" represents the performance of system 100 when MPC 142 uses the third order feedforward neural network of Figures 10A-10C.

[0067] Normalized RMSE values ​​for predictions made using the embodiment and cell culture process depicted in FIGS. 10-11 are shown below in Table 2.

[0068] [Table 2]

[0069] Figures 12A-12C are normalized plots showing the predictive performance of various embodiments of MPC 142 for yet another cell culture process different from the cell culture processes of Figures 6-9 and 10-11. In particular, Figures 12A-12C show the predictive performance for embodiments in which MPC 142 uses a linear regression model, a first-order nonlinear (feed-forward neural network) model, and a third-order nonlinear (feed-forward neural network) model, compared to a system (labeled "offline" in Figures 12A-12C) that did not use these predictive models.

[0070] Figures 13A-13D are normalized plots showing the performance of MPC142 for the same embodiment and the same cell culture process reflected in Figures 12A-12C, again along with the results of an "offline" system for comparison purposes. Normalized RMSE values ​​for predictions made using the embodiment and cell culture process depicted in Figures 12-13 are shown below in Table 3.

[0071] [Table 3]

[0072] Table 4 compares the (normalized) resulting integrated VCDs (iVCDs) for a system that did not use the hybrid predictive model (labeled "offline" in Table 4), a linear regressor (first order), and a feedforward neural network (third order) for the first cell culture process of Figures 6-9, the second cell culture process of Figures 10-11, and the third cell culture process of Figures 12-13.

[0073] [Table 4]

[0074] Overall, for MPC with hybrid predictive models, linear models provided better RMSE performance than nonlinear models. In addition, from an optimization perspective, the simpler structure of linear models results in lower optimal control complexity, providing yet another advantage over nonlinear approaches. Specifically, two regressor (quadratic) linear models were found to provide higher accuracy and lower complexity than other approaches, at least for some cell culture processes.

[0075] To further evaluate the performance of certain embodiments of the system 100, a control experiment using traditional cell culture control methods was compared to an experiment utilizing MPC with a hybrid predictive model for glucose feed rate control. In these experiments, samples / measurements were collected once a day and (for MPC with hybrid predictive model) the MPC calculated a daily glucose feeding strategy and optimized the VCD. An upper limit on the glucose feed rate of 12 g / L and a minimum feed rate of 3 g / L were also set as constraints for the optimization stage, but were not enforced.

[0076] Figures 14 and 15 are normalized graphs comparing glucose feed levels and VCD for these two experiments (labeled "MPC Reactor" for the embodiment of system 100 and "Control Reactor" for the conventional technique), respectively, and Figures 16A and 16B show predicted Raman scan vectors versus measured Raman scan vectors for VCD prediction (for the control reactor and MPC reactor, respectively).

[0077] Figure 17 is a normalized graph comparing glucose for the MPC and control experiments, and Figures 18A and 18B show predicted vs. measured Raman scan vectors for glucose concentration prediction (for the control and MPC reactors, respectively). Figure 19 includes a comparison of titer (by process day, final day titer) and specific productivity for a system implementing one embodiment of the MPC / hybrid predictive modeling techniques disclosed herein and a control system. Figures 20A and 20B show predicted vs. measured Raman scan vectors for titer prediction (for the control and MPC bioreactors, respectively).

[0078] Table 5 compares the normalized SE-HPLC HMW, rCELC+HC, and high mannose for the control bioreactor and the MPC / Hybrid predictive modeling reactor to typical acceptance criteria:

[0079] [Table 5]

[0080] Table 6 compares the normalized acidic peak, base peak3, base peak, and main peak for the control bioreactor and the MPC / Hybrid predictive modeling bioreactor with typical acceptance criteria:

[0081] [Table 6]

[0082] As seen in Table 6, the MPC / Hybrid Predictive Bioreactor System has a higher main peak and a lower base peak 3, which is favorable. For the other parameters shown in Tables 5 and 6, the performance of the MPC / Hybrid Predictive Bioreactor System remained within acceptable ranges. As seen throughout Figures 6-20, the MPC / Hybrid Predictive Bioreactor System incorporated Raman predictions for VCD, glucose, and titer. The linear MPC / Hybrid Predictive Bioreactor System generally results in more producing cells, not more cell production. This is important considering that the linear MPC / Hybrid Predictive Bioreactor System was under-fed with nutrients by about 2%. If adequate amounts of nutrients had been fed, the VCD and therefore titer production could have been higher. The overall trend of the resulting VCD fluctuates over time, and such VCD fluctuations are expected as the cell density in the culture decreases or increases due to large bolus feeds and cell growth. Moreover, the linear MPC / Hybrid Predictive Bioreactor System attempts to maintain glucose at a higher level by recommending a higher feed rate. In fact, in the linear MPC / hybrid predictive bioreactor system, it was recommended to feed approximately 35% more glucose than in the manual condition. However, in the linear MPC / hybrid predictive bioreactor system, glucose was not fed until a later date, which resulted in a decrease in the VCD of the linear MPC / hybrid predictive bioreactor system on the following day. Meanwhile, cell viability remained at the same level throughout the batch. This confirmed that the linear MPC / hybrid predictive bioreactor system was a healthy environment for the cells.

[0083] Further advantages may be obtained by using a Gaussian Process (GP) regression model. As mentioned above, data uncertainty and scarcity may limit the effectiveness of data-driven modeling techniques. Gaussian Process Regression models address the inherent uncertainty of data and can operate well even with small data sets. Therefore, in some embodiments, the data-driven model 152 in the MCP 142 is a GP model. This approach is referred to herein as the "GP-MPC technique" or simply "GP-MPC". The GP-MPC technique may be used to model the cell culture process in the bioreactor 102 and to design and determine the best / optimum control actions for the cell culture process. Using GP-MPC, optimal metabolic pathways that the cells can follow while maintaining process constraints to achieve specific goals such as product quality and yield may be identified and enforced. By combining superior titer production with the product quality advantages mentioned above (for the main peak and base peak 3), costs may be significantly reduced (e.g., 5% or more) in a linear MPC / hybrid predictive bioreactor system.

[0084] GP models provide a probabilistic non-parametric modeling approach for black-box identification of nonlinear dynamical systems. See, for example, C.E. Rasmussen and C.K. Williams, Gaussian Processes for Machine Learning. The MIT Press: Cambridge USA, 2006. GP models can predict the conditional posterior distribution of unseen data points conditioned on observed training points, and calculate the mean of the predicted points as a linear combination of these with the training data, with linear combination weights determined by the kernel distance from the training input. GP models can be trained offline using historical data, as described above for data-driven models 152.

[0085] In some embodiments where the data-driven model 152 is a GP model, one or more predictions of the GP model are passed to the glucose mass balance equation (e.g., the VCD[i+1] value in Equations 2 and 3). Glucose is not a manipulated variable, but rather is the primary component of the feed. The objective is to maximize the VCD while maintaining the glucose concentration within a specified range in the bioreactor 102.

[0086] Combining GP with MPC introduces several challenges, such as a cubed increase in computational load with the number of training data points. This also increases the overall computation required to solve the resulting optimal control problem. The optimization requires using the Jacobian to evaluate the best direction and check the optimum condition. The GP model can act as a black box for the optimization problem without using any explicit mathematical formulas. In some embodiments, the optimization problem (i.e., optimizer 146) calculates the Jacobian using a numerical method such as finite differences. Computing a finite difference approximation may require many function evaluations, which slows down the optimization process. To speed up the computation process, the hybrid prediction unit 144 may evaluate a Jacobian function (matrix) and pass the Jacobian function to the optimization problem (i.e., optimizer 146). As mentioned above, the GP model gives a posterior distribution over the function that maps the input to the output. The Gaussian process can be differentiated to obtain a distribution of gradients. If the covariance function is differentiable, the hybrid prediction unit 144 can calculate the gradient in a closed form. Therefore, the need for finite difference calculations is alleviated. Accordingly, during training and tuning of the GP model, the hybrid prediction unit 144 may use a covariance function that is differentiable (e.g., a squared exponential covariance function or other suitable function).

[0087] The GP-MPC technique can result in different feeding strategies compared to traditional feeding strategies. For example, instead of feeding the bioreactor for only 3 days, the GP-MPC technique can suggest different feeding rates over the entire duration of the cell culture process. FIG. 21 is a normalized plot comparing glucose feed rates for a process with and without the GP-MPC technique ("control data" in FIG. 21). The different feeding strategies lead to slightly higher integrated viable cell densities (iVCDs), as seen in FIG. 22. The final titer concentration is highly correlated with some of the attributes in the process, such as VCD and osmolality. Targets can be set for all of these attributes, and optimizations can be formulated to meet these targets. For example, multiple weights can be assigned to attributes in the objective function to change the controller's driving factors based on the requirements of a given manufacturing site. The reason for choosing a specific metabolite-related attribute instead of titer to define the objective function is that while metabolite-related measurements (e.g., VCDs) are easily accessible for each sampling interval, accurate titer estimates are usually not readily available.

[0088] In addition to VCD, trends of certain other metabolite-related attributes and their comparison with the control data are shown in Figure 23. All of the attributes remain within the desired range with GP-MPC and follow reasonable trends during the process. The potency values ​​for the control data and the GP-MPC technique are compared in Figure 24. Advantageously, the GP-MPC technique results in a 15% higher potency at the end of the process compared to the control data.

[0089] In summary, the GP-MPC technique allows observing and maintaining the cell culture process in a consistent state to achieve various objectives according to the requirements of a given manufacturing site. The designed system can ensure the minimization of variability to meet quality targets while optimizing for higher yield by making necessary adjustments in real time. Gaussian processes can highlight areas of the process with poor prediction quality due to scarcity or complexity of data by showing higher variance around the predicted mean value. This information can be used to modify process constraints and enable handling of non-convexity and non-linearity in certain regions.

[0090] 25 is a flow diagram of an example method 2500 of controlling a cell culture process using hybrid predictive modeling in a model predictive controller. Method 2500 may be performed by a system such as system 100 of FIG. 1 (e.g., by processing hardware 120 executing instructions of CCPC application 130). Method 2500 may be repeated (e.g., in real time) for multiple time intervals (e.g., each of multiple days) during the cell culture process, e.g., once per time interval (e.g., once per day, once per hour, etc.), where the time intervals (1) have a fixed or variable length / duration, and (2) are all the same length / duration or include two or more different lengths / durations.

[0091] In block 2502, current values ​​of cell culture attributes associated with a cell culture (e.g., in a bioreactor such as bioreactor 102) are obtained. Block 2502 may include, for example, receiving current values ​​from another device or system (e.g., from analytical instrument 104), measuring some or all of the values ​​directly (e.g., by analytical instrument 104), and / or inferring or predicting some or all of the values ​​(e.g., based on Raman spectroscopy measurements / scan vectors generated by analytical instrument (104)). The cell culture attributes for which values ​​are obtained may include one or more metabolite concentrations (e.g., glucose, lactate, sodium, ammonium, glutamine, glutamic acid, potassium), VCD, TCD, viability, osmolality, and / or one or more other attributes of the cell culture.

[0092] In block 2504, control values ​​for physical inputs to the cell culture process are generated. The physical input may be, for example, a glucose feed rate provided by a glucose pump, or another type of physical input (e.g., an input provided by a heating or cooling device if temperature is controlled, or an impeller speed, etc.). Block 2504 includes predicting future values ​​of the cell culture attributes in block 2506 based on the current values ​​obtained in block 2502. Block 2506 may include, for example, predicting values ​​for each time interval of the prediction horizon.

[0093] The prediction may be based on the most recent measurements of the cell culture attributes (i.e., the "current" values ​​obtained in block 2502) and possibly one or more earlier measurements for some or all of the attributes. Block 2506 includes predicting future values ​​of a first one or more attributes of the cell culture attributes using one or more data-driven models (e.g., data-driven models 152) and predicting future values ​​of a second one or more attributes of the cell culture attributes using one or more first principles models (e.g., first principles models 150). For example, the first attributes may include VCD, TCD, viability, osmolality, lactate concentration, glutamine concentration, glutamic acid concentration, ammonium concentration, sodium concentration, and / or potassium concentration, and / or the second attribute may include a glucose concentration of the cell culture. In some embodiments, block 2506 includes applying the predicted future values ​​of the first attribute of the first one or more attributes (e.g., future VCD values ​​predicted by one of the data-driven models) as input to at least one of the first principles models. The first principles model may include, for example, a mass balance model such as those represented in Equations 2 and 3. The data-driven model may include any one or more of the data-driven model types described above. For example, the data-driven model may include a linear regression model of any suitable order, a feedforward neural network or other nonlinear model of any suitable order, a stochastic regression model such as a Gaussian process model, etc.

[0094] Block 2504 also includes determining control values ​​in block 2508 by optimizing (e.g., minimizing) an objective function according to the predicted future values ​​and any other constraints (e.g., minimum and maximum glucose delivery values) in block 2506. The objective function may have, for example, the form of Equations 1A and 1B. Block 2508 may include, for example, determining control values ​​for each time interval of the control horizon.

[0095] In block 2510, a physical input to the cell culture process is controlled using a control value (e.g., using a first / earliest control value of a set of control values ​​corresponding to a control horizon). For example, block 2510 may include generating a control signal (e.g., a message conforming to the protocol of the input device 106) and sending the control signal to an appropriate device (e.g., the input device 106). As a more specific example, block 2510 may include controlling a glucose feed rate by generating a control signal (e.g., a message / command specifying a set point) and sending the signal to a glucose pump.

[0096] Additional considerations regarding the present disclosure are now provided.

[0097] Some of the drawings described herein show example block diagrams having one or more functional components. It will be understood that such block diagrams are for illustrative purposes and that the devices described and shown may have more, fewer, or alternative components than those shown. Also, in various embodiments, the components (and the functionality provided by each component) may be associated with or otherwise integrated as part of any suitable component.

[0098] The embodiments of the present disclosure relate to a non-transitory computer-readable storage medium having computer code for performing various computer-implemented operations. The term "computer-readable storage medium" is used herein to include any medium capable of storing or encoding a sequence of instructions or computer code for performing the operations, methods, and techniques described herein. The medium and computer code may be of a type that is specially designed and constructed for the purposes of the embodiments of the present disclosure, or may be of a type known and available to those skilled in the art of computer software technology. Some examples of computer-readable storage media include, but are not limited to, magnetic media such as hard disks, floppy disks, and magnetic tapes, optical media such as CD-ROMs and holographic devices, magneto-optical media such as optical disks, and hardware devices specially configured to store and execute program code, such as ASICs, programmable logic devices ("PLDs"), and ROM and RAM devices.

[0099] Examples of computer code include machine code, e.g., produced by a compiler, and files containing high-level code executed by a computer using an interpreter or compiler. For example, an embodiment of the present disclosure may be implemented using Java, C++, or other object-oriented programming languages ​​and development tools. Additional examples of computer code include encryption and compression code. Furthermore, an embodiment of the present disclosure may be downloaded as a computer program product and transferred from a remote computer (e.g., a server computer) to a requesting computer (e.g., a client computer or another server computer) over a transmission channel. Other embodiments of the present disclosure may be implemented in hardwired circuitry in the alternative to, or in combination with, machine-executable software instructions.

[0100] As used herein, the singular terms "a", "an" and "the" may include plural referents unless the context clearly indicates otherwise. As used herein, the terms "nearly", "substantially", "substantial" and "about" are used to describe and account for small variations. When used in conjunction with an event or circumstance, these terms may refer to instances where the event or circumstance occurs exactly, as well as instances where the event or circumstance occurs approximately close to the actual occurrence. For example, when used in conjunction with a numerical value, these terms may refer to a variation range of ±10% or less of the numerical value, such as ±5% or less, ±4% or less, ±3% or less, ±2% or less, ±1% or less, ±0.5% or less, ±0.1% or less, or ±0.05% or less. For example, two numerical values ​​may be considered "substantially" identical if the difference between the two numerical values ​​is ±10% or less of the mean of the numerical values, such as ±5% or less, ±4% or less, ±3% or less, ±2% or less, ±1% or less, ±0.5% or less, ±0.1% or less, or ±0.05% or less.

[0101] Additionally, amounts, ratios, and other numerical values ​​may be presented herein in a range format. It should be understood that such range formats are used for convenience and brevity and should be understood to be flexible and include not only the numerical values ​​explicitly stated as the limits of a range, but also all individual numerical values ​​or subranges contained within that range as if each numerical value and subrange were expressly stated.

[0102] Although the present disclosure has been described and illustrated with reference to specific embodiments, these descriptions and illustrations are not intended to limit the disclosure. Those skilled in the art will understand that various modifications may be made and equivalents may be substituted without departing from the true spirit and scope of the present disclosure as defined by the appended claims. The drawings are not necessarily drawn to scale. The artistic depictions in the present disclosure may differ from the actual device due to manufacturing processes, tolerances, and / or other reasons. There may be other embodiments of the present disclosure that are not specifically illustrated. The present specification and drawings (other than as claimed) should be considered illustrative rather than restrictive. Changes may be made to adapt a particular situation, material, composition of matter, technique, or process to the objective, concept, and scope of the present disclosure. All such modifications are intended to be within the scope of the claims appended hereto. Although the techniques disclosed herein are described with reference to certain operations performed in a particular order, it will be understood that these operations may be combined, sub-divided, or reordered to form equivalent techniques without departing from the teachings of the present disclosure. Thus, unless specifically indicated herein, the order and grouping of the operations is not intended to be a limitation of the disclosure.

Claims

1. A method for controlling a cell culture process using hybrid predictive modeling in a model predictive controller, wherein for multiple time intervals during the cell culture process, To obtain the current values ​​of cell culture attributes related to the cell culture, The processing hardware generates control values ​​for the physical input to the cell culture process, and the generation of these control values ​​is: At a minimum, the future values ​​of the cell culture attributes are predicted based on the current values ​​by (i) predicting the future values ​​of one or more first attributes of the cell culture attributes using one or more data-driven models, and (ii) predicting the future values ​​of one or more second attributes of the cell culture attributes using one or more first-principles models. The control value is determined by optimizing the objective function according to the predicted future values ​​of the cell culture attributes. Including the above-mentioned generation, The processing hardware and the control values ​​are used to control the physical input to the cell culture process. Methods that include...

2. The physical input to the cell culture process is the glucose supply rate. The second one or more attributes include the glucose concentration of the cell culture, The method according to claim 1, wherein controlling the physical input to the cell culture process includes controlling the glucose supply rate by transmitting a control signal to the glucose pump.

3. The method according to claim 2, wherein the first one or more attributes include live cell density, total cell density, viability, osmolality, lactate concentration, glutamine concentration, glutamic acid concentration, ammonium concentration, sodium concentration, and / or potassium concentration.

4. The method according to claim 1, wherein predicting the future values ​​of the second one or more attributes using the one or more first-principles models comprises applying the predicted future values ​​of the first attribute of the first one or more attributes as input to at least one of the one or more first-principles models.

5. The method according to claim 4, wherein the first attribute is the density of living cells.

6. The method according to any one of claims 1 to 5, wherein the one or more data-driven models include a linear regression model.

7. The method according to any one of claims 1 to 5, wherein the one or more data-driven models include a stochastic regression model.

8. The method according to claim 7, wherein the stochastic regression model is a Gaussian process regression model.

9. The method according to any one of claims 1 to 5, wherein the one or more data-driven models include a nonlinear model.

10. The method according to claim 9, wherein the nonlinear model is a feedforward neural network.

11. The method according to any one of claims 1 to 5, wherein predicting the future value of the cell culture attribute is based on (i) the current value of the cell culture attribute and (ii) one or more earlier values ​​of the cell culture attribute.

12. The method according to any one of claims 1 to 5, wherein predicting the future values ​​of the second one or more attributes using the one or more first-principles models comprises applying one or more preceding control values ​​as inputs to the one or more first-principles models.

13. The method according to any one of claims 1 to 5, wherein the current value of the cell culture attribute is obtained based on measurements from one or more analytical instruments.

14. One or more non-temporary computer-readable media storing instructions, which, when executed by the processing hardware of a computing system and over multiple time intervals during a cell culture process, cause the computing system to perform the method according to any one of claims 1 to 13.

15. It is a system, A bioreactor configured to hold cell cultures during the cell culture process, An electronically controllable input device configured to provide a physical input to the cell culture process, One or more analytical instruments configured to measure one or more cell culture attributes related to the cell culture, A computing system, wherein the computing system is configured to perform the method described in any one of claims 1 to 13 for one or more time intervals in the cell culture process. A system that includes this.

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