Theoretical and experimental analysis of cellular adhesion to polymer surfaces

An exact discrete numerical solution to the Grabowski model for predicting cell adhesion to polymer surfaces is discussed. The solution technique allows the possibility of taking into account cell-cell interactions within the flow situation and the multistep process involved in thrombus formation. The proposed solution also allows modification of the wall reaction rate model into a two species reaction rate which distinguishes between the kinetics of contact adhesion and irreversible adhesion. The solution allows determination of effective diffusivity (De) and surface reaction rate (k) constants. Use of the model to examine available experimental data results in the following conclusions: (1) static or dynamic cell adhesion cannot be considered to be diffusion limited; (2) for flow conditions De is a monotonically increasing function of shear rate; (3) under static, i.e., zero flow conditions, De appears to be markedly larger than for flow conditions.