On the Appropriateness of Linear Stress Recovery in Biomechanical Analysis of Abdominal Aortic Aneurysm

Abdominal aortic aneurysm (AAA) wall stress is a candidate rupture risk marker but is typically computed from single-phase images without known cardiac phase. Linear stress recovery methods, which solve a single geometrically linear equilibrium problem on the imaged, already-loaded geometry, have been validated for static stress estimation, but their robustness to unknown imaging phase remains unexplored. We investigated whether imaging phase materially biases 99th percentile stress recovered linearly, and whether linear recovery agrees with non-linear analysis under matched loads. Two patient-specific AAAs from a public 4D-CTA cohort (Case 1: 5.5% strain; Case 2: 4.5% strain) were analyzed. For each, we analyzed diastolic and synthetic systolic geometry, the latter generated by warping the diastolic mesh via displacements from non-linear hyperelastic analysis. Linear stresses were recovered on both geometries under systolic pressure and compared via 99th-percentile maximum principal stress, stress distributions, and 3D stress differential contours. Linear stresses under pulse pressure were compared against non-linear stresses. 99th-percentile stresses from linear recovery on diastolic vs synthetic systolic geometries under systolic pressure differed by 8.6% (Case 1) and 3.5% (Case 2), within segmentation uncertainty. 99th-percentile stresses from linear recovery and non-linear analysis under pulse pressure agreed closely: 0% difference (Case 1) and 1.1% (Case 2), with nearly identical distributions. These findings support linear stress recovery for patient-specific AAA analysis in clinical settings with static single-phase imaging, offering a computationally efficient alternative without compromising accuracy or requiring patient-specific wall properties.