Relationship between release rate and surface concentration for heparinized materials

Mathematical models are used to predict surface concentrations that result from the release of heparin into flowing blood and stagnant or well-mixed plasma. Two release rates--4 X 10(-2) and 3 X 10(-5) micrograms/cm2 min--are considered, which describe elution from an ionically heparinized material and from an immobilized heparin-PVA hydrogel, respectively. When heparin is released at the higher rate into blood flowing in cylindrical tubes with dimensions characteristic of the vasculature, or annular tubes representative of catheter experiments, a minimum surface concentration of 0.5 micrograms/mL is attained virtually at the tube inlet. Release at the lower rate requires tube lengths of several thousand meters to attain the same critical value. Similarly, heparin released from a suspension of beads at the higher rate leads to critical surface concentrations of 0.2 micrograms/mL within a fraction of a second in stagnant plasma, or ca. 5 s in a well-mixed environment. At the lower release rate, 45 or 100 min must elapse before the same level is achieved. These results support the validity of 4 X 10(-2) micrograms/cm2 min as a reasonable minimum release rate to produce a heparin microenvironment sufficient to prevent thrombosis. The lower rate is shown to be insufficient to generate a critical concentration, thus supporting the argument that heparin-PVA does not owe its biological activity to a heparin microenvironment. The model equations can be applied to the release of any material to determine surface concentrations.