A growth model of saccular aneurysms based on hemodynamic and morphologic discriminant parameters for risk of rupture

The aim of this study was to derive a model describing the evolution of bifurcation type cerebral aneurysms based on morphological and hemodynamic parameters. Idealized bifurcation models were constructed based on the two morphological parameters of aspect ratio (AR) and size ratio (SR). Aneurysm development was investigated according to the following four patterns: R1, increasing SR with constant AR; R2, increasing AR with constant SR; R3, increasing SR and increasing AR; R4, increasing AR with constant parent artery diameter. Relationships were obtained between energy loss (EL) and morphological parameters (EL-SR and EL-AR curves). The curves were validated by mapping the growth of a ruptured patient-specific bifurcation aneurysm at three stages of follow-up. EL increased in parallel with growth patterns R1 and R3, whereas growth pattern R2 showed a decrease in EL. No significant changes were observed in EL when the growth of the aneurysm was associated only with changes in aneurysm size and independent of changes in parent artery diameter and main flow (R4). Changes in parent artery diameter of bifurcation aneurysms resulted in significant variation in EL. Mapping the growth of a follow-up aneurysm onto the EL-AR curve demonstrated that aneurysms with increasing EL during the observation period are at higher risk of rupture than aneurysms with decreasing EL. Based on the proposed growth model, assessment of morphological (AR and SR) and hemodynamic (EL) parameters may provide quantifiable information on the risk of bifurcation aneurysm rupture during clinical patient follow-up.