Mathematical and experimental analyses of antibody transport in hollow-fiber-based specific antibody filters.

We are developing hollow fiber-based specific antibody filters (SAFs) that selectively remove antibodies of a given specificity directly from whole blood, without separation of the plasma and cellular blood components and with minimal removal of plasma proteins other than the targeted pathogenic antibodies. A principal goal of our research is to identify the primary mechanisms that control antibody transport within the SAF and to use this information to guide the choice of design and operational parameters that maximize the SAF-based antibody removal rate. In this study, we formulated a simple mathematical model of SAF-based antibody removal and performed in vitro antibody removal experiments to test key predictions of the model. Our model revealed three antibody transport regimes, defined by the magnitude of the Damköhler number Da (characteristic antibody-binding rate/characteristic antibody diffusion rate): reaction-limited (Da </= 0.1), intermediate (0.1 < Da < 10), and diffusion-limited (Da >/= 10). For a given SAF geometry, blood flow rate, and antibody diffusivity, the highest antibody removal rate was predicted for diffusion-limited antibody transport. Additionally, for diffusion-limited antibody transport the predicted antibody removal rate was independent of the antibody-binding rate and hence was the same for any antibody-antigen system and for any patient within one antibody-antigen system. Using SAF prototypes containing immobilized bovine serum albumin (BSA), we measured anti-BSA removal rates consistent with transport in the intermediate regime (Da approximately 3). We concluded that initial SAF development work should focus on achieving diffusion-limited antibody transport by maximizing the SAF antibody-binding capacity (hence maximizing the characteristic antibody-binding rate). If diffusion-limited antibody transport is achieved, the antibody removal rate may be raised further by increasing the number and length of the SAF fibers and by increasing the blood flow rate through the SAF.