Validation of a Mathematical Model for Rupture Status of Spherical Intracranial Aneurysms

An accurate mathematical model of intracranial aneurysm (IA) mechanics is of great value for its potential utility in assessing probability of IA rupture. Such a model for spherical IAs has been developed which predicts a wall-thickness-to-IA-radius ratio (WTR) of 6.1 × 10^-3 at which IAs rupture. To our knowledge, no further work has been done to validate this model with clinical data. We aim to assess the accuracy and utility of this model of spherical IA rupture mechanics.

Aneurysm height, width, neck diameter, and vessel radius were measured on radiologic images of IAs of the basilar terminus, anterior communicating, and posterior communicating arteries. Geometric modeling was used to approximate IA wall thickness. Calculations were performed with and without accounting for changes in IA morphology which have been shown to occur post-rupture. Receiver operating characteristic (ROC) curves and positive likelihood ratios (LR) were produced for WTR, aspect ratio (AR), bottleneck factor (BF), and size ratio (SR). Logistic regression analysis was performed to determine the WTR where there is a 50% chance of presentation as a ruptured aneurysm in our cohort.

52 unruptured and 28 ruptured spherical IAs were included. ROC curve analysis revealed similar areas under the curve for WTR, AR, BF, and SR, ranging from 0.636 to 0.773 with overlapping confidence intervals. LRs ranged from 1.34 (95% CI 1.09-1.65) for AR calculated with post-rupture dimensional adjustments to 2.14 (95% CI 1.45-3.14) for WTR and BF calculated without post-rupture adjustments. Logistic regression revealed a strong association between decreased WTR and rupture status. The point at which there is a 50% chance of presentation as ruptured was found to be WTR = 7.9 × 10^-3 when calculated without post-rupture adjustments and WTR' = 6.2 × 10^-3 when calculated with post-rupture adjustments, from which the proposed 6.1 × 10^-3 differs by 23% and 1.4%, respectively.

The model for IA rupture mechanics assessed in this study agrees reasonably well with clinical data and could serve as a foundation for further investigation. It additionally performs well in discriminating between ruptured and unruptured aneurysms, though its performance in this dataset is similar to more conventional, simpler parameters. Most importantly, this study demonstrates that biomathematical models can provide valuable insight into the nature of aneurysmal lesions despite their simplifying assumptions.