this study analyzed morphometric and hemodynamic parameters of aneurysmal and non-aneurysmal middle cerebral artery (McA) bifurcations and their relationship with optimal values derived from the principle of minimum work (PMW). The study included 96 patients with MCA aneurysm and 94 controls. Aneurysm patients presented with significantly higher values of the radius and cross-sectional area of the McA trunk, angle between the post-bifurcation branches (α angle) and volume flow rate (VFR) and had significantly lower values of junction exponent and pulsatility index than the controls. The Φ 1 and Φ 2 angles (angles between the MCA trunk axis and the larger and smaller branch, respectively) and α angle in all groups were significantly larger than the optimal PMW-derived angles. The most important independent predictors of MCA aneurysm were junction exponent (odds ratio, OR = 0.42), α angle (oR = 1.07) and VFR (OR = 2.36). Development of cerebral aneurysms might be an independent effect of abnormalities in hemodynamic and morphometric factors. The risk of aneurysm increased proportionally to the deviation of morphometric parameters of the bifurcation from their optimal pMWderived values. The role of bifurcation angle in aneurysm development needs to be explained in future research as the values of this parameter in both aneurysm patients and non-aneurysmal controls in were scattered considerably around the pMW-derived optimum.

Intracranial aneurysms (IAs) are persistent, localised dilatations of the arterial wall that are found in approximately 3% of the general population. The most severe complication of IAs is rupture, which results in devastating consequences such as subarachnoid haemorrhage and brain damage with serious neurological sequelae. Numerous studies have characterised the mechanisms underlying IA development and growth and identified a number of environmental modifiable (smoking, hypertension) and nonmodifiable risk factors (related to the histology of cerebral arteries and genetic factors) in its pathogenesis. Haemodynamic stress also likely plays a crucial role in the formation of IAs and is conditioned by the geometry and morphology of the vessel tree, but its role in the natural history of unruptured IAs remains poorly understood; it is believed that changes in blood flow might generate the haemodynamic forces that are responsible for damage to the vascular wall and vessel remodelling that lead to IA formation. This review summarises the most relevant data on the current theories on the formation of IAs, with particular emphasis on the roles of special conditions resulting from the microscopic anatomy of intracranial arteries, haemodynamic factors, bifurcation morphometry, inflammatory pathways, and the genetic factors involved in IA formation.

Background 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. Methods The 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. Results The 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. Conclusions The 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.

Background Conclusions from studies evaluating vessel dimensions and their deviations from the values resulting from the principle of minimum work (PMW) on the formation of intracranial aneurysms (IAs) are still inconclusive. The aim of our study was the morphometric analysis of cerebral arterial bifurcations harbouring aneurysms. Methods The 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, total bifurcation angle) and the difference between the predicted optimal and observed branch angles. Results The analysed parameters for internal carotid artery (ICA) bifurcations were not significantly different among the groups. MCA and BA bifurcation angles and the radii of the parent MCA and BA vessels with aneurysms were significantly higher compared to 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 not significantly different 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 IAs. The ROC analysis indicated that the α angle was the best performer in discriminating between aneurysmal and non-aneurysmal bifurcations. Conclusions The dimensions of the arteries forming the circle of Willis do not follow the PMW. The deviation from optimum bifurcation geometry for bifurcations beyond the circle of Willis (particularly a wider 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 the shear stress in the walls of arterial bifurcations.