Impact of Geometric Uncertainty on the Computation of Abdominal Aortic Aneurysm Wall Strain

Abdominal aortic aneurysm (AAA) is a life-threatening condition characterized by permanent enlargement of the aorta, often detected incidentally during imaging for unrelated conditions. Current management relies primarily on aneurysm diameter and growth rate, which may not reliably predict patient-specific rupture risk. Computation of AAA wall stress and strain has the potential to improve individualized risk assessment, but these analyses depend on image-derived geometry, which is subject to segmentation uncertainty and lacks a definitive ground truth for the wall boundary. While the effect of geometric uncertainty on wall stress has been studied, its influence on wall strain remains unclear. In this study, we assessed the impact of geometric uncertainty on AAA wall strain computed using deformable image registration of time-resolved 3D computed tomography angiography (4D-CTA). Controlled perturbations were applied to the wall geometry along the surface normal, parameterized by the standard deviation for random variation and the mean for systematic inward or outward bias, both scaled relative to wall thickness. Results show that uncertainties in AAA wall geometry reduce the accuracy of computed strain, with inward bias (toward the blood lumen and intraluminal thrombus) consistently causing greater deviations than outward bias (toward regions external to the aortic wall). Peak strain is more sensitive but less robust, whereas the 99th percentile strain remains more stable under perturbations. We concluded that, for sufficiently accurate strain estimation, geometric uncertainty should remain within one wall thickness (typically 1.5 mm).

💡 Research Summary

Abdominal aortic aneurysm (AAA) remains a leading cause of sudden death because rupture risk is difficult to predict using conventional metrics such as maximum diameter and growth rate. Recent efforts have turned to patient‑specific biomechanical analyses, particularly the computation of wall stress and strain, as potential tools for individualized risk stratification. While the influence of geometric uncertainty on stress calculations has been explored, its effect on strain—directly reflecting the actual deformation of the aortic wall—has not been systematically quantified.

In this study, the authors investigated how uncertainties in the reconstructed wall geometry affect strain estimates derived from deformable image registration of time‑resolved 3‑D computed tomography angiography (4D‑CTA). Ten patients with AAA were imaged over a cardiac cycle, yielding ten temporal phases per patient. For each phase, the lumen, intraluminal thrombus (ILT), and outer wall were segmented to generate a surface mesh. A state‑of‑the‑art deformable registration algorithm was then applied to compute voxel‑wise displacement fields between successive phases, from which Lagrangian strain tensors were derived. Two strain metrics were extracted: peak (maximum) strain and the 99th‑percentile strain, the latter representing a high‑quantile but more statistically robust measure.

To mimic realistic segmentation errors, the original wall surface was perturbed along its outward normal. Perturbations were modeled as a normal distribution N(μ,σ²) where σ (standard deviation) and μ (mean bias) were expressed as fractions of the wall thickness t (average ≈1.5 mm). Random noise levels of σ = 0.1 t, 0.25 t, and 0.5 t were examined, together with systematic biases of μ = ±0.25 t, ±0.5 t, and ±1 t. Positive μ values shift the surface outward (toward surrounding tissue), whereas negative μ values shift it inward (toward the lumen and ILT). After each perturbation, the registration‑based strain computation was repeated and the resulting strain values were compared with the unperturbed baseline.

The analysis revealed a pronounced asymmetry in strain sensitivity. Inward bias (μ < 0) consistently produced larger deviations than outward bias (μ > 0). For example, a systematic inward shift of 0.5 t reduced peak strain by up to 35 % relative to the baseline, while the same outward shift altered peak strain by only 10–15 %. Random noise amplified these effects: when σ reached 0.5 t, peak strain errors could exceed 30 % for inward bias but remained below 15 % for outward bias. By contrast, the 99th‑percentile strain proved considerably more robust; across all combinations where σ ≤ 0.5 t and |μ| ≤ 0.5 t, its variation stayed within 5 % of the reference value.

These findings have direct clinical implications. First, to obtain reliable strain‑based risk metrics, the geometric reconstruction of the AAA wall must be accurate to within roughly one wall thickness (≈1.5 mm). Second, when reporting strain, high‑quantile measures such as the 99th percentile are preferable to absolute peak values because they are less susceptible to segmentation‑induced noise and bias.

The study acknowledges several limitations. The cohort size (n = 10) is modest, and only a single registration algorithm was evaluated. Physiological factors that also affect strain—blood pressure fluctuations, cardiac output variations, and spatial heterogeneity of wall material properties—were not incorporated. Moreover, the presence of ILT, which can alter the effective wall thickness and mechanical response, was treated only as part of the geometric model without separate mechanical analysis. Future work should expand the patient pool, explore multiple registration and segmentation pipelines, and integrate fluid‑structure interaction (FSI) simulations that couple hemodynamics, pressure loading, and wall material behavior. Such comprehensive modeling would allow a more complete assessment of how geometric uncertainty propagates through the entire biomechanical workflow. Ultimately, the goal is to embed robust, strain‑based risk scores into clinical decision‑making, enabling more personalized timing of surgical or endovascular intervention for AAA patients.