A Scale-up Methodology for Continuous Bioreactor Systems Utilizing an Optimal Design Under Optimal Control Constraint Framework

Continuous operation is used in bioprocesses to allow for increased cell viability through the mitigation of substrate and product inhibition, thereby increasing the productivity of the desired product. However, the dilution rate, feed substrate composition, and reactor geometry play a key role as parameters affecting the productivity in a continuous bioreactor system. In addition, one of the many challenges found in the pharmaceutical industry is quantifying the effects of scale-up. Often, understanding of a biochemical process is gained through experimentation at the bench scale and it is common that these results cannot be replicated at production scale, where mass transfer becomes a more limiting factor¹. Several heuristic techniques have been developed to try and mimic the bench scale system at the plant scale, including maintaining the fluid dynamics of the reactor via a constant impeller tip speed or Reynolds number or maintaining the mass transfer properties of the system by keeping the mass transfer coefficient k_La or dissolved oxygen level constant^2,3,4. These scale-up methods are highly empirical, however, and more direct and accurate methodologies are needed.

This work proposes a method for the scale-up of continuous pharmaceutical systems utilizing a framework that pairs the optimal design and optimal control of the reactor to guarantee feasibility. The development of reliable bio-kinetic models is extended to the design of a continuous bioreactor that uses a multi-feed configuration allowing for the ability to use flow rate and substrate concentration of the feed stream as independent manipulated variables. The design problem for the bioreactor is formulated as a nonlinear program (NLP) for which the optimal control problem governing the dilution rate and substrate concentration and the transport and consumption of oxygen and nutrients are used as constraints. From this algorithm the optimal bioreactor geometry is determined for any bioreactor volume as well as the optimal control policy necessary to maximize the reactor productivity. A beta-carotene production process with kinetic models describing the glucose consumption and metabolic product formation and depletion in the Saccharomyces cerevisiaestrain mutant SM14 is utilized as a case study for the described algorithm.

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