Abstract
BackgroundConclusions from studies evaluating vessel dimensions and their deviations from values resulting from the principle of minimum work (PMW) on the formation of intracranial aneurysms (IAs) are still inconclusive. Our study aimed to perform a morphometric analysis of cerebral arterial bifurcations harbouring aneurysms.MethodsThe study comprised 147 patients with basilar artery (BA) and middle cerebral artery (MCA) aneurysms and 106 patients constituting the control group. The following morphometric parameters were evaluated: the radii of vessels forming the bifurcation, the junction exponent, the values of the bifurcation angles (Φ1 and Φ2 angles between the parent vessel trunk axis and the larger or smaller branches, respectively; α angle, the total bifurcation angle) and the difference between the predicted optimal and observed branch angles.ResultsThe analysed parameters for internal carotid artery (ICA) bifurcations were not significantly different among the groups. The MCA and BA bifurcation angles and the radii of the parent MCA and BA vessels with aneurysms were significantly higher than those of the control group. The differences between the predicted optimal and observed branch angles were significantly higher for BA and MCA bifurcations with aneurysms compared to the control group. The mean junction exponent for bifurcations in the circle of Willis (i.e., ICA and BA bifurcations, respectively) and MCA bifurcations with aneurysms was significantly lower than the theoretical optimum and did not significantly differ among the groups. In a multilevel multivariate logistic regression analysis, the branch angles and the radius from the parent vessel were significant independent predictors of the presence of an IA. The ROC analysis indicated that the α angle was the best performer in discriminating between aneurysmal and nonaneurysmal bifurcations.ConclusionsThe dimensions of the arteries forming the circle of Willis do not follow the PMW. Deviation from the energetically optimum geometry for bifurcations beyond the circle of Willis (particularly, a larger radius of the parent artery and a wider total bifurcation angle) may lead to the formation of IAs. Further studies are warranted to investigate the significance of vessel dimensions and the bifurcation angle on the magnitude of shear stress in the walls of arterial bifurcations.
Highlights
Conclusions from studies evaluating vessel dimensions and their deviations from values resulting from the principle of minimum work (PMW) on the formation of intracranial aneurysms (IAs) are still inconclusive
One hundred fifteen patients presented with an unruptured middle cerebral artery (MCA) aneurysm (22 men, 93 women, aged 28 to 79 years [58 ± 10; mean ± standard deviation (SD)]), and 32 patients presented with an unruptured basilar artery (BA) aneurysm (11 men, 22 women, aged 33 to 77 years [60 ± 11; mean ± SD]), which was confirmed by three-dimensional computed tomography angiography (3D Computed tomography angiography (CTA))
Assessment of the statistical significance of the differences among the mean values of the morphometric variables for the internal carotid artery (ICA) in the study groups Table 1 shows a comparison of the morphometric variables, that is, the α, Φ1, and Φ2 angles, the differences between the predicted and observed values for the above angles, the radii (r0, r1, r2), the asymmetry ratio, the area ratio, and the junction exponent for the ICA among the patient groups
Summary
Conclusions from studies evaluating vessel dimensions and their deviations from values resulting from the principle of minimum work (PMW) on the formation of intracranial aneurysms (IAs) are still inconclusive. Our study aimed to perform a morphometric analysis of cerebral arterial bifurcations harbouring aneurysms. The WSS experienced at a bifurcation is dependent on its geometry, including the radii of all vessels involved and the bifurcation angle [11,12,13]. WSS is minimised when the relation between the vessel diameter and the bifurcation angle follows the optimality principle of minimum work (PMW) [14]
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