Wall Stress and Geometry Measures in Electively Repaired Abdominal Aortic Aneurysms

A review on the biomechanical behaviour of the aorta

Large aortic aneurysm and acute and chronic aortic dissection are pathologies of the aorta requiring surgery. Recent advances in medical intervention have improved patient outcomes; however, a clear understanding of the mechanisms leading to aortic failure and, hence, a better understanding of failure risk, is still missing. Biomechanical analysis of the aorta could provide insights into the development and progression of aortic abnormalities, giving clinicians a powerful tool in risk stratification. The complexity of the aortic system presents significant challenges for a biomechanical study and requires various approaches to analyse the aorta. To address this, here we present a holistic review of the biomechanical studies of the aorta by categorising articles into four broad approaches, namely theoretical, in vivo, experimental and combined investigations. Experimental studies that focus on identifying mechanical properties of the aortic tissue are also included. By reviewing the literature and discussing drawbacks, limitations and future challenges in each area, we hope to present a more complete picture of the state-of-the-art of aortic biomechanics to stimulate research on critical topics. Combining experimental modalities and computational approaches could lead to more comprehensive results in risk prediction for the aortic system.

An Objective and Repeatable Sac Isolation Technique for Comparing Biomechanical Metrics in Abdominal Aortic Aneurysms

(1) Abdominal aortic aneurysm (AAA) biomechanics-based metrics often reported may be over/under-estimated by including non-aneurysmal regions in the analyses, which is typical, rather than isolating the dilated sac region. We demonstrate the utility of a novel sac-isolation algorithm by comparing peak/mean wall stress (PWS, MWS), with/without sac isolation, for AAA that were categorized as stable or unstable in 245 patient CT image sets. (2) 245 patient computed tomography images were collected, segmented, meshed, and had subsequent finite element analysis performed in preparation of our novel sac isolation technique. Sac isolation was initiated by rotating 3D surfaces incrementally, extracting 2D projections, curve fitting a Fourier series, and taking the local extrema as superior/inferior boundaries for the aneurysmal sac. The PWS/MWS were compared pairwise using the entire aneurysm and the isolated sac alone. (3) MWS, not PWS, was significantly different between the sac alone and the entire aneurysm. We found no statistically significant difference in wall stress measures between stable (n = 222) and unstable (n = 23) groups using the entire aneurysm. However, using sac-isolation, PWS (24.6 ± 7.06 vs. 20.5 ± 8.04 N/cm2; p = 0.003) and MWS (12.0 ± 3.63 vs. 10.5 ± 4.11 N/cm2; p = 0.022) were both significantly higher in unstable vs. stable groups. (4) Our results suggest that evaluating only the AAA sac can influence wall stress metrics and may reveal differences in stable and unstable groups of aneurysms that may not otherwise be detected when the entire aneurysm is used.

A Predictive Analysis of Wall Stress in Abdominal Aortic Aneurysms Using a Neural Network Model

Rupture risk assessment of abdominal aortic aneurysms (AAAs) by means of quantifying wall stress is a common biomechanical strategy. However, the clinical translation of this approach has been greatly limited due to the complexity associated with the computational tools required for its implementation. Thus, being able to estimate wall stress using nonbiomechanical markers that can be quantified as a direct outcome of clinical image segmentation would be advantageous in improving the potential implementation of said strategy. In the present work, we investigated the use of geometric indices to predict patient-specific AAA wall stress by means of a novel neural network (NN) modeling approach. We conducted a retrospective review of existing clinical images of two patient groups: 98 asymptomatic and 50 symptomatic AAAs. The images were subject to a protocol consisting of image segmentation, processing, volume meshing, finite element modeling, and geometry quantification, from which 53 geometric indices and the spatially averaged wall stress (SAWS) were calculated. SAWS estimated from finite element analysis was considered the gold standard for the predictions. We developed feed-forward NN models composed of an input layer, two dense layers, and an output layer using Keras, a deep learning library in python. The NN models were trained, tested, and validated independently for both AAA groups using all geometric indices, as well as a reduced set of indices resulting from a variable reduction procedure. We compared the performance of the NN models with two standard machine learning algorithms (MARS: multivariate adaptive regression splines and GAM: generalized additive model) and a linear regression model (GLM: generalized linear model). With the reduced sets of indices, the NN-based approach exhibited the highest mean goodness-of-fit (for the symptomatic group 0.71 and for the asymptomatic group 0.79) and lowest mean relative error (17% for both groups). In contrast, MARS yielded a mean goodness-of-fit of 0.59 for the symptomatic group and 0.77 for the asymptomatic group, with relative errors of 17% for the symptomatic group and 22% for the asymptomatic group. GAM had a mean goodness-of-fit of 0.70 for the symptomatic group and 0.80 for the asymptomatic group, with relative errors of 16% for the symptomatic group and 20% for the asymptomatic group. GLM did not perform as well as the other algorithms, with a mean goodness-of-fit of 0.53 for the symptomatic group and 0.70 for the asymptomatic group, with relative errors of 19% for the symptomatic group and 23% for the asymptomatic group. Nevertheless, the NN models required a reduced set of 15 and 13 geometric indices to predict SAWS for the symptomatic and asymptomatic AAA groups, respectively. This was in contrast to the reduced set of nine and eight geometric indices required to predict SAWS with the MARS and GAM algorithms for each AAA group, respectively. The use of NN modeling represents a promising alternative methodology for the estimation of AAA wall stress using geometric indices as surrogates, in lieu of finite element modeling. The performance metrics of NN models are expected to improve with significantly larger group sizes, given the suitability of NN modeling for "big data" applications.

The Association Between Curvature and Rupture in a Murine Model of Abdominal Aortic Aneurysm and Dissection

BACKGROUND

Mouse models of abdominal aortic aneurysm (AAA) and dissection have proven to be invaluable in the advancement of diagnostics and therapeutics by providing a platform to decipher response variables that are elusive in human populations. One such model involves systemic Angiotensin II (Ang-II) infusion into low density-lipoprotein receptor-deficient (LDLr-/-) mice leading to intramural thrombus formation, inflammation, matrix degradation, dilation, and dissection. Despite its effectiveness, considerable experimental variability has been observed in AAAs taken from our Ang-II infused LDLr-/- mice (n=12) with obvious dissection occurring in 3 samples, outer bulge radii ranging from 0.73 to 2.12 mm, burst pressures ranging from 155 to 540 mmHg, and rupture location occurring 0.05 to 2.53 mm from the peak bulge location.

OBJECTIVE

We hypothesized that surface curvature, a fundamental measure of shape, could serve as a useful predictor of AAA failure at supra-physiological inflation pressures.

METHODS

To test this hypothesis, we fit well-known biquadratic surface patches to 360° micro-mechanical test data and used Spearman's rank correlation (rho) to identify relationships between failure metrics and curvature indices.

RESULTS

We found the strongest associations between burst pressure and the maximum value of the first principal curvature (rho=-0.591, p-val=0.061), the maximum value of Mean curvature (rho=-0.545, p-val=0.087), and local values of Mean curvature at the burst location (rho=-0.864, p-val=0.001) with only the latter significant after Bonferroni correction. Additionally, the surface profile at failure was predominantly convex and hyperbolic (saddle-shaped) as indicated by a negative sign in the Gaussian curvature. Findings reiterate the importance of shape in experimental models of AAA.

A Comparative Study of Biomechanical and Geometrical Attributes of Abdominal Aortic Aneurysms in the Asian and Caucasian Populations

In this work, we provide a quantitative assessment of the biomechanical and geometric features that characterize abdominal aortic aneurysm (AAA) models generated from 19 Asian and 19 Caucasian diameter-matched AAA patients. 3D patient-specific finite element models were generated and used to compute peak wall stress (PWS), 99th percentile wall stress (99th WS), and spatially averaged wall stress (AWS) for each AAA. In addition, 51 global geometric indices were calculated, which quantify the wall thickness, shape, and curvature of each AAA. The indices were correlated with 99th WS (the only biomechanical metric that exhibited significant association with geometric indices) using Spearman's correlation and subsequently with multivariate linear regression using backward elimination. For the Asian AAA group, 99th WS was highly correlated (R2 = 0.77) with three geometric indices, namely tortuosity, intraluminal thrombus volume, and area-averaged Gaussian curvature. Similarly, 99th WS in the Caucasian AAA group was highly correlated (R2 = 0.87) with six geometric indices, namely maximum AAA diameter, distal neck diameter, diameter-height ratio, minimum wall thickness variance, mode of the wall thickness variance, and area-averaged Gaussian curvature. Significant differences were found between the two groups for ten geometric indices; however, no differences were found for any of their respective biomechanical attributes. Assuming maximum AAA diameter as the most predictive metric for wall stress was found to be imprecise: 24% and 28% accuracy for the Asian and Caucasian groups, respectively. This investigation reveals that geometric indices other than maximum AAA diameter can serve as predictors of wall stress, and potentially for assessment of aneurysm rupture risk, in the Asian and Caucasian AAA populations.

A machine leaning approach for abdominal aortic aneurysm severity assessment using geometric, biomechanical, and patient-specific historical clinical features

Recent studies monitoring severity of abdominal aortic aneurysm (AAA) suggested that reliance on only the maximum transverse diameter ( D _max ) may be insufficient to predict AAA rupture risk. Moreover, geometric indices, biomechanical parameters, material properties, and patient-specific historical data affect AAA morphology, indicating the need for an integrative approach that incorporates all factors for more accurate estimation of AAA severity. We implemented a machine learning algorithm using 45 features extracted from 66 patients. The model was generated using the J48 decision tree algorithm with the aim of maximizing model accuracy. Three different feature sets were used to assess the prediction rate: i) using D _max as a single-feature set, ii) using a set of all features, and, lastly iii) using a feature set selected via the BestFirst feature selection algorithm. Our results indicate that BestFirst feature selection yielded the highest prediction accuracy. These results indicate that a combination of several specific parameters that comprehensively capture AAA behavior may enable a suitable assessment of AAA severity, suggesting the potential benefit of machine learning for this application.