A Statistical Shape Model of the Morphological Variation of the Infrarenal Abdominal Aortic Aneurysm Neck

Abstract

Hostile aortic neck characteristics, such as short length and large diameter, have been associated with type Ia endoleaks and reintervention after endovascular aneurysm repair (EVAR). However, such characteristics partially describe the complex aortic neck morphology. A more comprehensive quantitative description of 3D neck shape might lead to new insights into the relationship between aortic neck morphology and EVAR outcomes in individual patients. This study identifies the 3D morphological shape components that describe the infrarenal aortic neck through a statistical shape model (SSM). Pre-EVAR CT scans of 97 patients were used to develop the SSM. Parameterization of the morphology was based on the center lumen line reconstruction, a triangular surface mesh of the aortic lumen, 3D coordinates of the renal arteries, and the distal end of the aortic neck. A principal component analysis of the parametrization of the aortic neck coordinates was used as input for the SSM. The SSM consisted of 96 principal components (PCs) that each described a unique shape feature. The first five PCs represented 95% of the total morphological variation in the dataset. The SSM is an objective model that provides a quantitative description of the neck morphology of an individual patient.

Keywords: abdominal; analysis; aneurysm neck morphology; aortic aneurysm; endovascular aneurysm repair; principal component; statistical shape model.

Figure A1

Graph of the generalization ability of the statistical shape model (SSM) by means of the leave-one-out method. The blue dots represent the root mean square error (RMSE, mm) of the reconstructed and actual shapes of n − 1 patients for a given number of principal components (PCs). The open, black dots represent the boundaries of the 95% confidence interval. The mean generalization of the SSM with five PCs is 3.6 (95% CI: 3.2–3.9) mm.

Figure A2

Graph of the specificity of the statistical shape model (SSM); mean specificity and the 95% confidence intervals are given. The mean specificity for five principal components (PCs) is 4.8 (95% CI: 4.7–4.8) mm.

Figure A3

Histograms of the first five principal components (PCs). (a) The first principal component (PC) is not normally distributed; values < −1.5 standard deviation (SD) are not present in the given dataset. Values < −1.5 SD represent a negative neck length, which is anatomically not feasible. Therefore, only −1 SD to +3 SD deviations are shown for PC 1. (b–e) The distributions of PCs 2–5.

Figure 1

Visualization of the parameterization of one patient. The surface of the aortic lumen is visible in light red, and the surface of the aortic neck is visible in dark red. (a) The CLL (black line), ten equidistantly spaced contour points on the CLL (red dots), and the point on the CLL that corresponds to the projection of the origin of the lowest renal artery coordinate (blue dot); (b) for the first CLL coordinate, 36 normal vectors are displayed; (c) the 360 intersections of the normal vectors with the mesh are displayed as red dots. Ten coordinates (light blue dots) at the same orientation were longitudinally rearranged at equal distance (light blue line).

Figure 2

Workflow of the process from a CT scan to the principal component analysis (PCA) and statistical shape model (SSM) results. The first step is to segment the aortic neck lumen in the CT scan (red segmentation). Nine random samples, taken from the dataset consisting of 97 patients, are displayed in the second box to show the anatomical variation. The third box represents the mathematical procedures applied to perform a PCA and obtain the SSM. On the right, three visualizations, corresponding to the first three PCs, with the results of the SSM, are shown.

Figure 3

Compactness curve of the statistical shape model (SSM) that shows the cumulative morphological variation that is described by the principal components (PCs). The blue dot indicates 95% of the total variation by the first five PCs; the red dot indicates 98% of the total variation described by the first nine PCs.

Figure 4

Visualization of shape variation of the abdominal aortic neck for the first five principal components (PCs). PC 1 describes 51% of the total shape variation, which mainly is variation in neck length, with −1SD representing the shortest neck in the dataset and +3SD the longest neck. PC 2 describes 30% of the total variation, which is mainly deflection to the left and right. Deflection in the right direction is oriented more anteriorly compared to deflection to the left. PC 3 describes 12% of the total variation, mainly deflection in the anterior direction. PC 4 describes 2% of the total variation but is an important component, as it describes mainly the neck diameter. PC 5 also describes 2% of the total variation, which is mainly deflection of the distal neck end.

Figure 5

Example of a patient’s original shape (brown mesh) and the reconstructed shape (red mesh), starting with the mean shape as the reconstructed shape (a). In each of the subplots (b–j), the number of included principal components (PCs) in the statistical shape model (SSM) is increased by one. The root mean square error (RMSE) of principal component (PC) 1 is 6.5 mm, whereas the mean RMSE of PCs 1 to 9 is reduced to 2.5 mm.