On growth measurements of abdominal aortic aneurysms using maximally inscribed spheres.

The maximum diameter, total volume of the abdominal aorta, and its growth rate are usually regarded as key factors for making a decision on the therapeutic operation time for an abdominal aortic aneurysm (AAA) patient. There is, however, a debate on what is the best standard method to measure the diameter. Currently, two dominant methods for measuring the maximum diameter are used. One is measured on the planes perpendicular to the aneurism's central line (orthogonal diameter) and the other one is measured on the axial planes (axial diameter). In this paper, another method called 'inscribed-spherical diameter' is proposed to measure the diameter. The main idea is to find the diameter of the largest sphere that fits within the aorta. An algorithm is employed to establish a centerline for the AAA geometries obtained from a set of longitudinal scans obtained from South Korea. This centerline, besides being the base of the inscribed spherical method, is used for the determination of orthogonal and axial diameter. The growth rate parameters are calculated in different diameters and the total volume and the correlations between them are studied. Furthermore, an exponential growth pattern is sought for the maximum diameters over time to examine a nonlinear growth pattern of AAA expansion both globally and locally. The results present the similarities and discrepancies of these three methods. We report the shortcomings and the advantages of each method and its performance in the quantification of expansion rates. While the orthogonal diameter measurement has an ability of capturing a realistic diameter, it fluctuated. On the other hand, the inscribed sphere diameter method tends to underestimate the diameter measurement but the growth rate can be bounded in a narrow region for aiding prediction capability. Moreover, expansion rate parameters derived from this measurement exhibit good correlation with each other and with growth rate of volume. In conclusion, although the orthogonal method remains the main method of measuring the diameter of an abdominal aorta, employing the idea of maximally inscribed spheres provides both a tool for generation of the centerline, and an additional parameter for quantification of aneurysmal growth rates.