Modelling Immunomagnetic Cell Capture in CFD

The separation of cells from a complex sample by immunomagnetic capture has become a standard technique in the last decade and has also obtained increased attention for microfluidic applications. We present a model that incorporates binding kinetics for the formation of cell-bead complexes, which can easily be integrated into a computational fluid dynamics (CFD) code. The model relies on the three equation types: Navier-Stokes equations governing the fluid dynamics, convection-diffusion equations for non-magnetic cells and a Nernst-Planck type equation governing the temporal evolution of cell-bead complex concentrations. The latter two equations are augmented by appropriate ‘reaction’ terms governing the binding kinetics which is formulated as a population rate balance between creation and annihilation of cell-bead complexes. First, the simulation results show, that by means of the developed approach appropriate parameter sets can be identified which allow for a continuous separation of tagged cells (cell/bead complexes) from non-magnetic particles such as non-target cells entering with the target cells. Moreover tagged cells can be, to a certain extend, separated from unbound beads. Second, the computed concentrations at the outlet show a drastic drop for higher cell/bead complexes beyond a certain number of beads per cell. We show that a critical number of beads per cells exists where the binding is considerably reduced or the reaction cascade ceases completely. This occurs when cell/bead complex have a similar magnetic mobility as the free magnetic beads. The presented CFD model has been applied to the simulation of a generic continuous cell separation system showing that the method facilitates the design of magnetophoretic systems.