Correction to: Decision Tree Based Classification of Abdominal Aortic Aneurysms Using Geometry Quantification Measures.

This erratum is to correct the variable name on the left hand side of Eq. (2). The correct variable name is "Diameter" rather than the stated "Area."

Decision Tree Based Classification of Abdominal Aortic Aneurysms Using Geometry Quantification Measures.

Abdominal aortic aneurysm (AAA) is an asymptomatic aortic disease with a survival rate of 20% after rupture. It is a vascular degenerative condition different from occlusive arterial diseases. The size of the aneurysm is the most important determining factor in its clinical management. However, other measures of the AAA geometry that are currently not used clinically may also influence its rupture risk. With this in mind, the objectives of this work are to develop an algorithm to calculate the AAA wall thickness and abdominal aortic diameter at planes orthogonal to the vessel centerline, and to quantify the effect of geometric indices derived from this algorithm on the overall classification accuracy of AAA based on whether they were electively or emergently repaired. Such quantification was performed based on a retrospective review of existing medical records of 150 AAA patients (75 electively repaired and 75 emergently repaired). Using an algorithm implemented within the MATLAB computing environment, 10 diameter- and wall thickness-related indices had a significant difference in their means when calculated relative to the AAA centerline compared to calculating them relative to the medial axis. Of these 10 indices, nine were wall thickness-related while the remaining one was the maximum diameter (Dmax). Dmax calculated with respect to the medial axis is over-estimated for both electively and emergently repaired AAA compared to its counterpart with respect to the centerline. C5.0 decision trees, a machine learning classification algorithm implemented in the R environment, were used to construct a statistical classifier. The decision trees were built by splitting the data into 70% for training and 30% for testing, and the properties of the classifier were estimated based on 1000 random combinations of the 70/30 data split. The ensuing model had average and maximum classification accuracies of 81.0 and 95.6%, respectively, and revealed that the three most significant indices in classifying AAA are, in order of importance: AAA centerline length, L2-norm of the Gaussian curvature, and AAA wall surface area. Therefore, we infer that the aforementioned three geometric indices could be used in a clinical setting to assess the risk of AAA rupture by means of a decision tree classifier. This work provides support for calculating cross-sectional diameters and wall thicknesses relative to the AAA centerline and using size and surface curvature based indices in classification studies of AAA.

The Association Between Geometry and Wall Stress in Emergently Repaired Abdominal Aortic Aneurysms.

Abdominal aortic aneurysm (AAA) is a prevalent cardiovascular disease characterized by the focal dilation of the aorta, which supplies blood to all the organs and tissues in the systemic circulation. With the AAA increasing in diameter over time, the risk of aneurysm rupture is generally associated with the size of the aneurysm. If diagnosed on time, intervention is recommended to prevent AAA rupture. The criterion to decide on surgical intervention is determined by measuring the maximum diameter of the aneurysm relative to the critical value of 5.5 cm. However, a more reliable approach could be based on understanding the biomechanical behavior of the aneurysmal wall. In addition, geometric features that are proven to be significant predictors of the AAA wall mechanics could be used as surrogates of the AAA biomechanical behavior and, subsequently, of the aneurysm's risk of rupture. The aim of this work is to identify those geometric indices that have a high correlation with AAA wall stress in the population of patients who received an emergent repair of their aneurysm. In-house segmentation and meshing algorithms were used to model 75 AAAs followed by estimation of the spatially distributed wall stress by performing finite element analysis. Fifty-two shape and size geometric indices were calculated for the same models using MATLAB scripting. Hypotheses testing were carried out to identify the indices significantly correlated with wall stress by constructing a Pearson's correlation coefficient matrix. The analyses revealed that 12 indices displayed high correlation with the wall stress, amongst which wall thickness and curvature-based indices exhibited the highest correlations. Stepwise regression analysis of these correlated indices indicated that wall stress can be predicted by the following four indices with an accuracy of 76%: maximum aneurysm diameter, aneurysm sac length, average wall thickness at the maximum diameter cross-section, and the median of the wall thickness variance. The primary outcome of this work emphasizes the use of global measures of size and wall thickness as geometric surrogates of wall stress for emergently repaired AAAs.