Theoretical analysis of the ultrafiltration behavior of highly concentrated protein solutions

Ultrafiltration is currently used for the concentration and formulation of monoclonal antibody solutions with target protein concentrations of up to 200. g/L or higher. The filtrate flux and maximum achievable antibody concentration in these systems is strongly influenced by the intermolecular interactions and non-ideal behavior in these highly concentrated protein solutions. The objective of this work was to develop a theoretical framework for analyzing the ultrafiltration of highly concentrated protein solutions accounting for the complex thermodynamic and hydrodynamic behavior in these systems. A modified polarization model was developed to describe the bulk mass transfer characteristics. In addition, the model accounts for the back-filtration phenomenon that occurs at very high protein concentrations due to the large pressure drop through the module associated with the high viscosity of the antibody solutions. Model parameters were evaluated from independent data for the protein osmotic pressure, osmotic virial coefficients, and viscosity. Model calculations demonstrate the importance of back-filtration, with numerical results in good agreement with experimental data for both the filtrate flux and maximum achievable antibody concentration obtained in a Pellicon 3 tangential flow filtration module. These results provide important insights into the key factors controlling the ultrafiltration behavior of highly concentrated protein solutions as well as a framework for the design and optimization of these ultrafiltration processes.