(385f) Solving the Population Balance Model in Cadet and Application to Continuous Antibody Precipitation Processes

Monoclonal antibodies (mAbs) represent a major class of biopharmaceutical products both in terms of worldwide sales volume and value. The industry has adopted a platform purification process where the first significant purification (capture) step is based on protein A chromatography, an affinity bind-and-elute step for mAbs. However, the use of protein A chromatography has been long criticized for its high cost and inherently batch mode operation. To address these issues, we have developed an alternative, continuous, precipitation-based antibody capture step which selectively precipitates antibodies using polyethylene glycol (PEG 3350) and zinc chloride (ZnCl₂) in tubular precipitation reactors equipped with static mixers. The process is inherently continuous and uses inexpensive equipment. The overall performance of precipitation-based processes, in terms of product purity and yield, is critically dependent on subsequent solid-liquid separations operations, such as microfiltration or settling. The performance of these operations is in turn critically dependent on the morphology of the precipitate phase. The particle size distribution (PSD) is a key morphological descriptor of precipitates and depends on the design and operating conditions of the precipitation reactor. To this end, we have instrumented the precipitation reactor with an in-line microscopic particle imaging system and developed a predictive population balance model (PBM) for the continuous precipitation process as a process development and control tool.

We have formulated a dynamic mass balance equation coupled with a two-dimensional PBM with the particle size as the internal coordinate and an axial position in the tubular reactor as the external coordinate. The PBM considers important mechanisms including the axial convection, axial diffusion, particle nucleation as a critical nucleus or with an intrinsic distribution, size-dependent or -independent particle growth, and growth rate dispersion. Further, the Smoluchowski equation is also solved along with the PBM to account for particle aggregation and fragmentation processes that occur in precipitation. Regarding the solution method, we have applied the Finite Volume Method using the upwind, high-resolution scheme by Koren [1] and two WENO schemes (r=2, 3) [2] as the flux reconstruction method. The implementations of these methods are general and can be used on arbitrary grids. Further, we have also adapted both the Finite Volume Preserving scheme [3] and Volume Conserving and Number Preserving [4] scheme to solve the size-based Smoluchowski equation. All algorithms are implemented in a modular, free and open-source process modelling software package, CADET [5]. CADET uses an implicit time stepping scheme, BDF, which is extremely stable for large and stiff ordinary differential equation systems, to solve the discretized PBM. Application of the BDF to the discretized PBM leads to a system of nonlinear algebraic equations that are solved using Newton iteration. An analytical Jacobian we derived for the discretized PBM is also implemented to reduce the runtime compared with an Automatic Differentiation implementation. Thorough numerical analysis and benchmarking have been conducted for seven test cases to validate the implementation and test the solver performance. Furthermore, we also use parallel computing techniques to distribute the computing processes over computing cores for simple or complicated parameter fitting and optimization problems using a genetic optimization algorithm.

We have applied the PBM to the continuous antibody precipitation step. Using hIgG as a mAb mimic, both batch and continuous processes were investigated to study the precipitation kinetics and estimate model parameters. The impact of the precipitants, PEG 3350 and ZnCl₂, were studied separately first and then in combination to probe synergistic effects. The relative importance of the various kinetic processes governing mAb precipitate formation in the PEG 3350 and ZnCl₂ system was assessed and predictions of process performance were made using the PBM tool.

Reference

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3. Forestier-Coste and S Mancini. “A Finite Volume Preserving Scheme on Nonuniform Meshes and for Multidimensional Coalescence”. In: SIAM J. Sci. Comput. 34.6 (2012), B840-B860. issn: 1064-8275. doi: 10.1137/110847998.url:http://epubs.siam.org/doi/10.1137/110847998.
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Acknowledgement

This study was supported by the U.S. Food and Drug Administration, Contract No. 75F40121C00111. Any opinions, findings, conclusions, or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the financial sponsor.