This study is a step towards a new biomechanical-based measurement of the patient specific risk of rupture of cerebral aneurysms. Following a previous experimental investigation suggesting a correlation between the risk of rupture and the material properties of cerebral aneurysms, fluid-structure interaction simulations are performed to compare the deformations of a patient-specific aneurysm when using degraded or undegraded materials. Results show that material properties have a major impact on the magnitude of systolic/diastolic aneurysmal volume variations along the cardiac cycle. Changes in terms of aneurysmal volume variations depending on the tissue characteristics are shown to be measurable by medical imaging. A one-at-a-time data uncertainty analysis is also presented and shows the robustness of this result to input data uncertainties. The study thus suggests that aneurysmal volume variations may be used as the basis of a biomechanical index of rupture risk.