Computational fluid dynamic modeling of alternating tangential flow filtration for perfusion cell culture

Abstract Alternating tangential flow (ATF) filtration has been successfully adopted as a low shear cell separation device in many perfusion‐based processes. The reverse flow per cycle is used to minimize fouling compared with tangential flow filtration. Currently, modeling of the ATF system is based on empirically derived formulas, leading to oversimplification of model parameters. In this study, an experimentally validated porous computational fluid dynamic (CFD) model was used to predict localized fluid behavior and pressure profiles in the ATF membrane for both water and supernatant solutions. The results provided numerical evidence of Starling flow phenomena that has been theorized but not previously proven for the current operating parameters. Additionally, feed cross flow velocity was shown to significantly impact the localized flux distribution; higher feed cross flow rates lead to an increased localized permeate flux as well as irreversible and reversible fouling resistance. Further, the small average permeate flux values of 2 L·m−2·h−1 traditionally used in perfusion bioreactor membranes lead to approximately 50% of the membrane length utilized for permeate flow during each pressure and exhaust phase, leading to a full membrane utilization during one ATF cycle. Our preliminary CFD results demonstrate that local flux and resistance distribution further elucidate the dynamics of ATF membrane fouling in a perfusion‐based system.

fresh media is added to replace the spent media. The ATF system (Repligen, Waltham, MA) is unique in that a diaphragm pump and control system serve to generate alternating flow through the hollow fiber module, instead of unidirectional flow as operated in the TFF system. During the pressure phase, the air chamber of the diaphragm is pressurized and pushes liquid through the hollow fibers, into the reactor. This is followed by an exhaust phase where air leaves the chamber though the means of a vacuum pump, pushing the liquid back into the diaphragm liquid chamber (Chotteau, 2015).
However, often because of membrane fouling, retention of the protein product over time increases in the retentate stream leading to loss of process control and potentially loss of product quality.
Concentration polarization and membrane fouling determinately affect product retention. The former is a reversible, caused by protein build-up at the membrane surface. The latter is irreversible and is generally associated with the build-up of cells, cell debris, particulate, and extracellular material at the membrane surface and/ or within its pores (Belfort, Davis, & Zydney, 1994;Field, 2010).
A lot of research has been focused on characterization of the ATF system performance as a cell retention device and comparisons to the TFF have demonstrated superiority of ATF in terms of low shear and reduced fouling and retention of the product (Clincke, Mölleryd, Samani, et al., 2013;Karst, Serra, et al., 2016;Wang et al., 2017). In the exhaust cycle of the ATF system, there is the potential for reverse flow across the membrane, which is thought to minimize fouling, possibly due to flow back into the lumen near the exit fiber. This is known as Starling recirculation phenomenon and is thought to be responsible for the removal of deposited material (Zydney, 2016).
Multiple models are available to describe irreversible membrane fouling leading to flux decline. These include resistance in series models based on protein adsorption, pore plugging, and surface deposition models. However, only a few researchers have focused on characterization of fouling in the ATF system (Kelly et al., 2014).
Additionally, in each case proper validation of the model requires detailed information about structural properties of the membrane including its thickness, pore size, size distribution, and porosity as well as local flow conditions, including for example, axial and radial flow velocities and pressure drops in the bulk region and close to walls of the lumen. Oftentimes, local flow information is not available leading to gross oversimplification of model parameters. It has also previously been shown that cell culture supernatant contributes to fouling of the membrane, independent of the cell suspension (Wang et al., 2017). This provided the motivation for the work reported in this publication to use computational fluid dynamics (CFD) to study flow of cell culture supernatant through porous membrane in an ATF system. This is the first step toward creating predictive models for membrane fouling and sieving decline to guide process design and optimization of the hollow fiber-based ATF system. Previously, Wang et al. (2017) showed that protein sieving was not impacted after the membranes were exposed to permeate solution that had already passed through a 0.2-μm membrane or solution containing cell pellet resuspended in permeate. However, when cell culture supernatant containing primarily particles in the 100-nm size range was introduced to a new hollow fiber membrane, product sieving was severe and almost instantaneous.   The hydraulic filtration resistances were measured based on established methods (Hwang & Sz, 2011;Stressmann & Moresoli, 2008) and calculated using Darcy's equation below:

| Experimental studies
where J is permeate flux (m/s), TMP is transmembrane pressure (kg/m s 2 ), μ is filtrate viscosity (kg/m s), R t (m −1 ) is total membrane resistance during operation, R rm (m −1 ) is intrinsic membrane resistance, R rev (m −1 ) is reversible fouling resistance, and R irev (m −1 ) is irreversible fouling resistance. The clean membrane resistance, R m , was obtained by flowing deionized water through the membrane at a set TMP value. The obtained R m value was used as an input parameter for CFD simulations using water. For supernatant experiments, total membrane resistance, R t , during the last hour of operation (6 hr) was calculated and used as an input parameter for CFD simulations using supernatant. When an experiment was terminated, the supernatant feed was switched to deionized water.
The filtration resistance caused by reversible fouling, R rev , was obtained from the difference between the total filtration resistance before and after feed switch. The resistance caused by irreversible membrane fouling, R irr , was then calculated by subtracting the other resistances from the total filtration resistance. R rev and R irr values were used to compare the impact of different operating conditions on membrane resistance change.
Switching from process fluid to water for measuring membrane permeability may cause precipitation of dissolved species and result in fouling. We observed membrane fouling only under certain conditions using supernatant solution. However, fouling was not observed when switching to water as a feed after the membranes were exposed to protein solution or media. Therefore, water was used as a fluid switch for measuring hydraulic resistances.

| CFD simulations
All CFD simulations modeled a single porous fiber under the assumption that the inlet and permeate mass flow rate was equally distributed among the fibers. Figure 2 shows a two-dimensional (2D)    (4)  (Table 1).
A time-dependent velocity profile boundary condition was set at the inlet of the fiber. Velocity profile with respect to time was computed from the feed flow rates measured experimentally by a flow meter at the ATF outlet for one cycle (Table 1) (Table 2).  Figure 3b shows the CFD and experimental permeate pressure profile across one cycle. As was observed with the inlet pressure profile predictions, the permeate pressure profile also showed good agreement with the CFD model using water as the fluid. As shown in Figure 3, it can be concluded that the simplified single-fiber CFD model correctly predicts inlet and permeate pressure profiles of hollow fiber cartridge axially and temporally.

| Flow and pressure pattern in the ATF system
The ATF system has several advantages over the TFF system, and has been used in numerous perfusion processes ( (Table 3 and Figure 5d).
As shown by previous studies (Wang et al., 2017), low cell culture viabilities result in an increase in particle size in the 100-nm range that affects membrane permeability and product sieving. These data suggest that operating within moderate feed cross flow velocities 0.11-0.22 m·s −1 might be advantageous in reducing permeate flow gradient, and potentially minimizing the fouling incidence by particles in the 100-nm size range. It is important to note that for these simulations, an average total membrane resistance was assumed.
However, since the permeate flow distribution changes temporally and spatially, it may be the case that fouling distribution also varies.
Several empirical models developed for feed cross flow filtration suggest that bidirectional flow and/or Starling flow contribute to F I G U R E 5 Permeate flow distribution axially and temporally at feed cross flow velocities (CFV) of (a) 0.11 m·s −1 , (b) 0.22 m·s −1 , and (c) 0.7 m·s −1 . Highest and lowest permeate value are depicted in red and blue color, respectively. Membrane volumetric flow rate as a function of position along the lumen for various feed cross flow rates (d). A similar membrane utilization of 50% is seen across both phases and is consistent between the feed cross flow rates examined. CFD inlet boundary condition was expressed as a velocity derived experimentally. Outlet lumen was set to 0 Pa and outlet shell boundary condition was set to a 0.00255 m·s −1 velocity equivalent to 2 L m −2 ·h −1 . CFD: computational fluid dynamic cleaning the membrane surface during operation (Breslau, Testa, Milnes, & Medjanis, 1980;Schulz & Ripperger, 1989). However, our current data show that Starling flow did not minimize membrane fouling as the feed cross flow velocity increased. This may imply that the bidirectional flow behavior is a more important aspect for ATF operation leading to a full membrane utilization per cycle.
In addition to operating conditions and bioreactor environment, F I G U R E 6 Comparison of simulated supernatant permeate pressure profile with experimentally measured profile during one ATF cycle with the experimental data at feed cross flow velocities (CFV) of 0.11, 0.22, and 0.7 m·s −1 . Supernatant solution was obtained from the last day of perfusion cell culture. Total resistance was calculated at the last hour of operation was used for supernatant CFD simulations. Permeate flow rate was kept constant at 0.000255 m·s −1 which is equivalent to a permeate flux of 2 L·m −2 ·h −1 . ATF: alternating tangential flow; CFD: computational fluid dynamic F I G U R E 7 Comparison of different filtration resistances of hollow fiber membrane in ATF system under different feed cross flow velocities. R m is intrinsic membrane resistance, R rev is reversible fouling resistance, and R irev is irreversible fouling resistance. Higher feed cross flow velocity conditions increase R rev and R irev resistances compared with lower feed cross flow velocities. ATF: alternating tangential flow