Biomechanical rupture risk assessment of abdominal aortic aneurysms using clinical data: A patient-specific, probabilistic framework and comparative case-control study

Figures

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  Fig 1. Rationale for our novel formulation (left) and exemplary visualization of its estimation (right). The probability of rupture, ℙrupt, is calculated as the volume of the probability distribution p(σvmmax,σγ) within the triangular-shaped area marked in red.

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  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).

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  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 (ρt,σγ=−0.3214), β and σγ (ρβ,σγ=0.2274), t and β (ρt,β = −0.1966) as well as α and β (ρα,β = 0.1413).

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  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 p(σmaxvm) 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 σmaxvm.

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  Fig 5. Visualization of ℙrupt for all AAAs in group 1.

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  Fig 6. Visualization of ℙrupt for all AAAs in group 2.

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  Fig 7. Boxplots comparing dmax, σmaxvm, RPI, PRRI and ℙrupt 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.

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  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, σmaxvm, RPI, PRRI and ℙrupt.