Mechanistic Modeling of Hollow Fiber Fouling and Sieving Predictions for Continuous Bioprocessing

Tangential flow filtration (TFF) is common in bioprocess development for scalable in-line solid/liquid separation, particularly for Chinese Hamster Ovary (CHO) cell retention within perfusion-scale cultures. However, filter fouling from high-density cell cultures and cellular debris progressively reduces product recovery through increased retention and yield loss. We present a comprehensive first-principles mechanistic model that integrates cell growth and death kinetics with fluid mechanics, fouling behavior, and sieving dynamics to predict and understand membrane performance in perfusion bioprocesses. This predictive framework demonstrates how operational parameters, filter geometry, and cell culture performance influence product sieving profiles during extended perfusion runs, while providing insights into key fouling mechanisms, membrane efficiency, and flux distributions. This model estimates particle production rate by considering historical cell density and viability data and particle-size distribution, enabling a priori predictions of sieving profiles across scales without requiring additional data sets. Our analysis demonstrates that Starling flow-the localized reversal of flux where permeate flows back into the fiber lumen (back-filtration) due to axial variations in transmembrane pressure - represents a major contributor to membrane fouling and product retention. The extent of Starling flow intensifies flux gradients along individual fibers, accelerating fouling and reducing effective membrane utilization. In addition to the fouling model, we introduce a dimensionless scaling parameter, the back-flow ratio, which quantifies the extent of Starling flow in membrane systems. This ratio, defined as the flow exiting fibers relative to net permeate flow, serves as both a membrane evaluation heuristic and a TFF scaling parameter. Per the presented analysis, the back-flow ratio-and therefore fouling rate-scales positively with membrane length, permeability, and shear rate. It scales inversely with net permeate flux and lumen diameter, providing fundamental principles for membrane design optimization.