On growth measurements of abdominal aortic aneurysms using maximally inscribed spheres

Abstract

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.

Association of Intraluminal Thrombus, Hemodynamic Forces, and Abdominal Aortic Aneurysm Expansion Using Longitudinal CT Images

“…For the maximum diameter calculation, the method of inscribed spheres 19 , which consist of calculating diameters of maximally inscribed spheres along the centerline, was used. Therefore, the largest value of the diameter along the centerline was defined as the maximum diameter.…”

Computational Growth and Remodeling of Abdominal Aortic Aneurysms Constrained by the Spine

“…Figure 12(b) shows the computed range of maximum diameter's rate compared with that of the clinical data analysis performed in Ref. [47]. Watton et al [25] were the first to study the effects of the spine (as a rigid plane) in an idealized model of evolving aneurysms.…”

“…The longitudinal CT data from 14 patients are used in Ref. [47]. Table 2 The average amount (calculated over the whole AAA surface) of von Mises stress VMS, longitudinal stretch k 1 , circumferential stretch k 2 , collagen content per reference area M c , collagen content per current area m c , smooth muscle content per reference area M m , and smooth muscle content per current area m m .…”

Computational Biomechanics for Medicine

“…Recently, Doyle et al [4] used CFD and longitudinal CT data (from four time points) to show ILT development and expansion in AAA. In addition, Zambrano et al [33] reported in a study from patients longitudinal CT studies that ILT accumulation rate would relate in a linear manner with the AAA expansion rate. They calculated these rates by measuring the changes in volume between two consecutive CT scans of ILT and AAA, respectively.…”

“…These rates were defined as the changes of volumes between two consecutive scans over that time interval. Each color refers to longitudinal CT data of a different patient [33]. (c) The changes of active proteolytic enzymes in the ILT's depth.…”