The Influence of Transport Parameters and Enzyme Kinetics of the Fibrinolytic System on Thrombolysis: Mathematical Modelling of Two Idealised Cases

Summary

Experimental data obtained by magnetic resonance imaging and photographing clot dissolution in vitro have shown that whole blood clots dissolve almost two orders of magnitude faster when urokinase is introduced into the clot by pressure induced permeation than when its access is limited to diffusion. In view of these findings, two mathematical models have been developed that quantitatively link the enzymatic and transport properties of the fibrinolytic system to the velocity of thrombolysis. Without a pressure gradient across the thrombus, the plasminogen activator molecules diffuse into the thrombus through the blood-thrombus boundary plane. The blood-thrombus boundary slowly moves inwards due to thrombolysis that is spatially restricted to a relatively narrow zone. The velocity of thrombolysis is primarily limited by the diffusion constants of the plasminogen activator and plasmin. In contrast, when plasminogen activator is rapidly distributed along the thrombus by pressure induced bulk flow, lysis occurs at each segment of the thrombus after a lag period that is due to plasmin activation and sufficient fibrin degradation. The lag time is determined primarily by the catalytical properties of the plasminogen activator and plasmin. The mathematical models with the observations of the clot boundaries during lysis permit the characterization of plasmin action on the fibrin network.

• References

• 1 Collen D. Identification and some properties of a new fast-reacting plasmin inhibitor in human plasma. Eur J Biochem 1976; 69: 209-216
• 2 Wiman B, Collen D. On the role of α₂-antiplasmin in the regulation of fibrinolysis. In: The Physiological Inhibitors of Blood Coagulation and Fibrinolysis Collen D, Wiman B, Verstraete M. (eds) Elsevier/North Holland Biomedical Press; Amsterdam: 1979. pp. 177-185
• 3 Takada Y, Takada A. The influence of fibrin and fibrinogen on the activation of plasminogen by urokinase. Thromb Haemostas 1981 46. 210 (Abstr)
• 4 Lijnen HR, Collen D. Alpha–2–antiplasmin. In: Protease Inhibitors in Human Plasma Biochemistry and Pathophysiology Murano G. (ed). PJD Publications Limited; New York: 1986. pp 225-244
• 5 Bookstein JJ, Saldinger E. Accelerated thrombolysis in vitro evaluation of agents and methods of administration. Invest Radiol 1985; 20: 731-735
• 6 Blinc R, Jarh O, Zidanšek A, Blinc A. NMR determination of the fractal geometry of gels around the collapse transition. Z Naturforsch 1989; 44a: 163-164
• 7 Blinc A, Planinšič G, Keber D, Jarh O, Lahajnar G, Zidanšek A, Demsar E. Dependence of blood clot lysis on the mode of transport of urokinase into the clot - a magnetic resonance study in vitro. Thromb Haemostas 1991; 65: 549-552
• 8 Lijnen HR, Collen D. Mechanisms of plasminogen activation by mammalian plasminogen actiyators. Enzyme 1988; 4O: 90-96
• 9 Stewart UA, Bradley MS, Johnson CS. Transport of probe molecules through fibrin gels as observed by means of holographic relaxation methods. Biopolymers 1988; 27: 173-145
• 10 Weinstin B, Doolitle RE. Differential specificities of thrombin, plasmin and trypsin with regard to synthetic and natural substrates and inhibitors. Biochim Biophys Acta 1972; 258: 577-590
• 11 Šabovič M, Lijnen HR, Keber D, Collen D. Effect of retraction on the lysis of human clots with fibrin specific and non-fibrin specific plasminogen activators. Thromb Haemostas 1989; 62: 1083-1087