Fig 1.
Rationale for our novel formulation (left) and exemplary visualization of its estimation (right).
The probability of rupture, , is calculated as the volume of the probability distribution
within the triangular-shaped area marked in red.
Table 1.
Invasive properties represent key vessel wall characteristics for a biomechanical rupture risk assessment.
Table 2.
Non-invasive properties overview.
Table 3.
Leave-one-out-cross-validation (LOOCV) results for the three probabilistic models.
Fig 2.
AAA Pat17 as seen via CT imaging (I), a 3D rendering of the segmentation result (II), the generated finite element mesh (III) and a visualization of the von Mises stress field corresponding to the mean μlogΘ of the predictive distribution p(logΘ) for that AAA (IV).
Table 4.
Non-invasive properties ξ for AAA Pat17 as well as cohort means and standard deviations (based on all 113 patients in ) for comparison.
Fig 3.
Visualization of the predictive distribution p(logΘ) transformed to the physical parameter range for AAA Pat17.
Plots (I)-(VI) show 2D marginal distributions over all possible parameter combinations between t, α, β and σγ. Highest correlations are observed between t and σγ (), β and σγ (
), t and β (ρt,β = −0.1966) as well as α and β (ρα,β = 0.1413).
Table 5.
Predicted means and standard deviations for the invasive properties of AAA Pat17 along with cohort values over all ndata = 251 samples for comparison.
Fig 4.
Left: Decrease of the objective function over the number of training iterations, where the first training iteration corresponds to the Kriging surrogate after ninit = 8 model evaluations. 11 model evaluations were used for the surrogate creation. Right: Estimated Kriging-based distribution along with a Monte Carlo reference. All densities were calculated using kernel density estimation with Gaussian kernels based on 10, 000 samples of the maximum von Mises stress
.
Fig 5.
Visualization of for all AAAs in group 1.
Table 6.
Overview: Selection process for the diameter matched groups.
Fig 6.
Visualization of for all AAAs in group 2.
Table 7.
Group 1 (asymptomatic, 18 ♂, 0 ♀) overview and obtained results for , RPI, PRRI and
.
Table 8.
Group 2 (symptomatic/ruptured, 13♂, 5 ♀) overview and obtained results for , RPI, PRRI and
.
Fig 7.
Boxplots comparing dmax, , RPI, PRRI and
for the asymptomatic and symptomatic/ruptured group.
The plots illustrate the interquartile range (green and red color) including the sample median as well as the first and third quartiles. Whiskers indicate minimum and maximum values and black dots represent all values from the respective group.
Table 9.
Relative mean and median differences (in %) of dmax, , RPI, PRRI and
between the asymptomatic and the symptomatic/ruptured group.
Fig 8.
Receiver operating characteristic (ROC) curves showing true positive rates (TPR) over false positive rates (FPR) and area under the ROC curve (AUC) scores for dmax, , RPI, PRRI and
.