Quantifying the large-scale hemodynamics of intracranial aneurysms

Abstract

Background and purpose: Hemodynamics play an important role in the mechanisms that govern the initiation, growth, and possible rupture of intracranial aneurysms. The purpose of this study was to objectively characterize these dynamics, classify them, and connect them to aneurysm rupture.

Materials and methods: Image-based computational fluid dynamic simulations were used to re-create the hemodynamics of 210 patient-specific intracranial aneurysm geometries. The hemodynamics were then classified according to their spatial complexity and temporal stability by using quantities derived from vortex core lines and proper orthogonal decomposition.

Results: The quantitative classification was compared with a previous qualitative classification performed by visual inspection. Receiver operating characteristic curves provided area-under-the-curve estimates for spatial complexity (0.905) and temporal stability (0.85) to show that the 2 classifications were in agreement. Statistically significant differences were observed in the quantities describing the hemodynamics of ruptured and unruptured intracranial aneurysms. Specifically, ruptured aneurysms had more complex and more unstable flow patterns than unruptured aneurysms. Spatial complexity was more strongly associated with rupture than temporal stability.

Conclusions: Complex-unstable blood flow dynamics characterized by longer core line length and higher entropy could induce biologic processes that predispose an aneurysm for rupture.

Fig 1.

Qualitative assessments of spatial flow complexity were made by visually inspecting streamline plots. Top left: This flow formed a single vortex and was classified as simple. Bottom left: This flow formed multiple vortices and was classified as complex. Center column: Streamline trajectories around the vortex core lines help to distinguish the individual vortices. Right column: Core lines are also known as vortex skeletons because they provide simplified representations of the large-scale flow structure.

Fig 2.

The temporal coefficients accounting for 99% of the total energy are plotted for stable (top) and unstable (bottom) flows. Vortex core lines (yellow) and neighboring streamline trajectories (red) are used to visualize the spatial structure of the flow at 2 instants during the cardiac cycle. The stable flow retains its spatial structure during the cardiac cycle. Very little energy is transferred between the temporal coefficients resulting in an entropy of S = 0.0713. The unstable flow undergoes large fluctuations and changes its spatial structure. Large amounts of energy are transferred between the temporal coefficients resulting in an entropy of S = 0.674.

Fig 3.

ROC curves summarizing the ability of our flow variables to correctly identify spatially simple (left) and temporally stable (right) hemodynamic flows in our aneurysm data base. The ROC curves were generated by comparing the quantitative classification against qualitative classification.

Fig 4.

ROC curves summarizing the ability of our flow variables to discriminate between ruptured and unruptured aneurysms. The average core line length 〈L〉 measured the flow complexity and the entropy S measured flow stability. A logistic regression was used to combine these 2 variables into a third variable that was tested for enhanced predictive power.