(667e) Mechanistic Modeling and Parameter-Adaptive Nonlinear Model Predictive Control of a Microbioreactor

Microbioreactors are a promising innovative technology to accelerate biologic drug development. In aerobic cellular respiration, one potential limit to the productivity of such systems is the transport of oxygen from an external gas to the most oxygen-deficient cells, whereas another limit is the potential for excessive spatially localized dissolved oxygen which can result in cellular damage. In this work, a mechanistic model is constructed for the spatiotemporal transport of oxygen through a gas-permeable membrane to the cells within a microbioreactor. An analytical solution to the partial differential equations for oxygen transport is derived using the Finite Fourier Transform method. A parameter-adaptive extended Kalman filter is shown to produce highly accurate estimates of the oxygen uptake rate of the cells, with some fluctuation in estimates of the specific cell growth rate and the specific oxygen uptake rate. The estimates are fed to a model predictive control formulation that improves the spatial control of dissolved oxygen during cell growth by more than 30% compared to a traditional controller. The rest of this extended abstract describes the opportunities and challenges of microbioreactors, and the objectives addressed in this work, while also providing a review of the most closely related literature.

Conventional bench-scale stirred-tank bioreactors are well established for bioprocess development, but are labor-intensive and expensive, especially when operated in parallel for the optimization of media and the determination of optimal operating protocols during startup and transition to perfusion mode. Microbioreactor systems with embedded sensors for control and automation have been proposed as a more efficient alternative [1,2]. The primary fast dynamics that need to be controlled in a bioreactor in general and microbioreactor in particular are associated with the dissolved oxygen (aka DO) concentration. DO concentration either too high or too low causes cell damage or death [3].

The conventional method of bubble sparging is not feasible for aeration at the small volumes in microbioreactors, where bubbles would cause clogging and flow disruptions. An alternative aeration method that is feasible at small volumes is to select one or more walls of the microbioreactor as a gas-permeable membrane for oxygen to diffuse through from an oxygen source [4,5,6,7]. This surface aeration provides oxygen to the cells but creates an oxygen concentration gradient in the microbioreactor, rather than having perfect mixing. Due to physical limitations with implementing the sensors, the DO concentration is only measured at the bioreactor wall opposite of the gas-permeable membrane. One of the objectives of our work is to derive and validate a distributed parameter model for DO concentration in the microbioreactor.

In industrial practice, the pH, temperature, and DO concentration within bioreactors are typically controlled using Proportional-Integral-Derivative (PID) controllers. Many academic studies have been published on the open- and closed-loop control of bioreactors, which include gain-scheduled, nonlinear-inverse-based, singular, adaptive, and model predictive control systems [8,9]. Nonlinear model predictive control (NMPC) is of interest due to its ability to explicitly address dynamic nonlinearities and constraints. Among NMPC schemes, one of the earlier proposals for bioreactor control employed a nonlinear autoregressive with exogenous input model [10]. Later, an adaptive NMPC strategy was evaluated in simulations for the maximization of productivity of a continuous fermenter [11]. Numerous later studies considered NMPC with state estimation. For example, one study investigated the potential of using NMPC with an unscented Kalman filter to control starvation-induced cell death in Chinese hamster ovary (CHO) cells in the bioreactor [12]. Another study considered NMPC with an extended Kalman filter (EKF) for control of nitrogen and oxygen concentrations for a biological nitrogen-removal process, to make the effluent organic concentrations below regulatory limits [13]. Very recently, an NMPC implementation that includes dynamic flux balance models was investigated for fed-batch fermentation [14]. Also, NMPC has been experimentally implemented in recent years, including a study that demonstrated increased biomass and lipid productivity in a microalgal photobioreactor system [15]. Another objective of our work is to propose and evaluate an NMPC algorithm for the control of DO concentration throughout the cell-containing spatial domain within the microbioreactor. The algorithm employs parameter-adaptive EKF algorithm for simultaneous parameter and state estimation. The spatial variation of the DO within the microbioreactor results in different considerations than reported in the literature for stirred-tank bioreactors.

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