Mechanistic modeling and parameter-adaptive nonlinear model predictive control of a microbioreactor

Abstract

Microbioreactors are a promising technology to accelerate biologic drug development. In aerobic cellular respiration, a potential limit to the productivity of such systems is the transport of oxygen from an external gas to the most oxygen-deficient cells, and the potential for excessive spatially localized dissolved oxygen which can result in cellular damage. This article analytically solves a mechanistic model 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 PID controller.