A model of thrombin inactivation in heparinized and nonheparinized tubes with consequences for thrombus formation

The role of flow and mass transport in determining procoagulant concentration at the wall of synthetic and natural cylindrical blood vessels is analyzed theoretically. The model assumes steady laminar flow and considers, in addition to the fluid dynamic parameters, three rate-determining steps: production of procoagulant (thrombin) and its inactivation at the wall, as well as inactivation in the fluid bulk. The ratio of thrombin wall concentration to production rate Cw/N emerges as a critical parameter in characterizing the behavior of the tube wall. With a wall-inactivation rate typical of heparinized materials, Cw/N = 11.1 s/cm, independent of flow (shear rate) and axial position. This is significantly less than the range of Cw/N (50-500 s/cm) for which the thrombin concentration is high enough to result in significant fibrin formation and thrombosis. Hence little fibrin formation and a high degree of thromboresistance is expected for heparinized materials. Nonheparinized materials have Cw/N values above this range, which are only weakly dependent on shear rate and diameter, suggesting that flow-induced dispersion of thrombin (or other procoagulants) has limited impact on the thrombin wall concentration. These latter results appear to refute the conventional wisdom that attributes the relative patency of large-diameter vessels and differences between venous and arterial thrombi to such flow effects. It is likely that additional factors such as flow pulsatility and wall geometry must be considered to account for these observations.