Article Figures & Data
Figures
- 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.
Tables
- Table 1:
Summary and performance statistics of the variables used to quantify spatial flow complexity and temporal flow stability
Category Mean Core Line Length Category Mean Entropy Simple 0.4564 Stable 0.1224 Complex 3.2094 Unstable 0.2458 P value <2.12 × 10−22 P value <8.4 × 10−19 AUC 0.905 AUC 0.86 - Table 2:
Summary and performance statistics of the variables used to quantify spatial flow complexity and temporal flow stability in ruptured and unruptured aneurysms
Category Mean Core Line Length Mean Entropy Combined Unruptured 1.4551 0.181 – Ruptured 3.407 0.2275 – P value <7.6 × 10−8 <0.0002 – AUC 0.72 0.648 0.716
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