Modelling of blood coagulation in cerebral aneurysms

Abstract

A fatal subarachnoid haemorrhage occurs when an intracranial aneurysm ruptures and there are no guidelines for rupture risk assessment with perfect reliability. Thrombus formation in stagnant flow condition has been said to play an important role in rupture. However, there are, at present, no mathematical models that allow us to simulate the whole process of thrombus formation in aneurysms. In this study, the authors proposed a mathematical model of intraaneurysmal coagulation so that the amount of fibrin generated in the aneurysm can be calculated. It is known that coagulation is initiated by erythroelastase-IX (EE-IX) in stagnant flow condition. This process is different from contact and tissue factor pathways. In the present coagulation model, the reaction rate constant of factor IX activation by EE-IX was determined. A group of reactions in which anticoagulants are involved are treated as a whole so as to reduce computational cost, and a quantity for the combined reaction rate constant is also determined. It is demonstrated that the present coagulation model can reproduce the rate of fibrin generation in a reference experiment at a reasonable computational cost.