Biomechanical rupture risk assessment of abdominal aortic aneurysms based on a novel probabilistic rupture risk index

Abstract

A rupture risk assessment is critical to the clinical treatment of abdominal aortic aneurysm (AAA) patients. The biomechanical AAA rupture risk assessment quantitatively integrates many known AAA rupture risk factors but the variability of risk predictions due to model input uncertainties remains a challenging limitation. This study derives a probabilistic rupture risk index (PRRI). Specifically, the uncertainties in AAA wall thickness and wall strength were considered, and wall stress was predicted with a state-of-the-art deterministic biomechanical model. The discriminative power of PRRI was tested in a diameter-matched cohort of ruptured (n = 7) and intact (n = 7) AAAs and compared to alternative risk assessment methods. Computed PRRI at 1.5 mean arterial pressure was significantly (p = 0.041) higher in ruptured AAAs (20.21(s.d. 14.15%)) than in intact AAAs (3.71(s.d. 5.77)%). PRRI showed a high sensitivity and specificity (discriminative power of 0.837) to discriminate between ruptured and intact AAA cases. The underlying statistical representation of stochastic data of wall thickness, wall strength and peak wall stress had only negligible effects on PRRI computations. Uncertainties in AAA wall stress predictions, the wide range of reported wall strength and the stochastic nature of failure motivate a probabilistic rupture risk assessment. Advanced AAA biomechanical modelling paired with a probabilistic rupture index definition as known from engineering risk assessment seems to be superior to a purely deterministic approach.

Keywords: abdominal aortic aneurysm; failure; model finite element; uncertainty; wall stress.

© 2015 The Author(s).

Figures

Figure 1.

Typical FE mesh with hexahedral and tetrahedral elements in the AAA wall and the ILT, respectively.

Figure 2.

Rupture risk definition for a deterministic PWS that is paired with probabilistic wall strength. Dashed area defines the probability that wall strength is lower than a deterministic PWS value. (Online version in colour.)

Figure 3.

Typical first principal Cauchy stress distribution in the wall of a ruptured AAA case. The model used a wall thickness of 2 mm and was inflated at MAP (a,b) and at 1.5 MAP (c,d), respectively. Panels (a,c) are cut to expose the inner surface of the AAA wall, while panels (b,d) show the corresponding outer wall surface. While at MAP wall stress is almost homogeneous across the wall thickness (compare (a) and (b)), some stress gradient across the thickness is seen at 1.5 MAP (compare (c) and (d)). As an example the positions of the PWS are indicated by arrows.

Figure 4.

PWS probability density distributions ρPWS for typical intact and ruptured AAA cases superimposed on mean population wall strength distribution ρΥ for intact (a) and ruptured (b) AAA cases. Ruptured cases show higher mode of PWS and/or larger dispersion which results in significantly larger probabilistic rupture risk index. (Online version in colour.)

Figure 5.

Distribution of rupture risk indices for diameter-matched and MAP-matched ruptured and intact AAAs. (a) A4clinics Research Edition PWRI shows considerable overlap between both groups and did not reach statistical significance (p = 0.328). (b) Proposed PRRI shows less overlap between both groups and reached statistical significance (p = 0.041). Boxes and whiskers cover 50% and all data, respectively. The line inside the box denotes the median.

Figure 6.

ROC curves for PRRI, A4clinics Research Edition PWRI and maximum diameter illustrating the relation between the false positive rate (1−specificity) and the true positive rate (sensitivity) of these predictors.