Direct Simulation of the Migration of Leukocytes in Pressure Driven Flow

We use the direct numerical simulation (DNS) approach to study the motion and deformation of leukocytes in pressure driven flows in a parallel plate channel in the case where there is an adhesion force between the leukocytes and the channel wall and when the adhesion force is absent. Two composite fluid models, consisting of a membrane, cytoplasm and a nucleus, are used to describe leukocytes. The first is the composite-drop model in which the cytoplasm and the nucleus are modeled as fluids, and the second is the drop-rigid-particle model in which the cytoplasm is modeled as a fluid and the nucleus as a rigid particle. The cytoplasm is modeled as a Newtonian fluid. The nucleus in the first model is assumed to be a viscoelastic liquid. The adhesion force is computed using two adhesion force models. In the first model, the adhesion force is given by a potential that varies as the fourth power of the distance between the cell and the adhesive wall. In the second model, the adhesion force is given by the Dembo’s kinetic adhesion model. The numerical code is based on the finite element method and the level-set method is used to track the cell membrane position. In the absence of the adhesion force, the equilibrium location of a freely suspended leukocyte in a pressure driven flow in a channel is shown to depend on the ratio of the cell to plasma viscosities. In presence of the adhesion force, the leukocyte is attracted to the layer of endothelial cells and, as it gets closer, it also deforms to get flatter under the shear forces. This deformation, in turn, further increases the adhesion force.