A MATHEMATICAL-MODEL FOR THE FORMATION OF CEREBRAL ANEURYSMS

Cerebral aneurysms are hypothesized to be acquired lesions resulting from a loss of static equilibrium in the apical region of the bifurcation, which causes the opening angle of the bifurcation to change during the cardiac cycle. Repeated dynamic cycling may disrupt wall elements in a manner analogous to a wire breaking with repeated bending and result in the formation of an aneurysm. A mathematical model that predicts the geometry of arterial bifurcations is proposed. The model predicts that the transmural pressure in the smaller branch is greater than or equal to that in the larger branch and that the larger branch makes a smaller angle with the direction of the parent artery. Bifurcations with smaller area ratios (the sum of the luminal areas of the branches divided by the luminal area of the parent artery) have smaller opening angles. When the area ratio is 1.0, the opening angle is about 90-degrees. The model concludes that the opening angle is constant during the cardiac cycle if the fractional change in the radii of the daughter and parent arteries is the same for any increase in blood pressure and if the ratio of transmural pressures in the parent and daughter branches does not change during the cardiac cycle. Otherwise, the bifurcation is considered predisposed to the development of an aneurysm.