Predicting the growth of aortic aneurysms: a comparison of linear vs exponential models

The aim of the present study was to determine whether the growth curve of aortic aneurysms had a predictable pattern, specifically whether the growth pattern was better defined by a linear or exponential rate of growth. A twelve-year retrospective review was undertaken. The authors studied 59 patients with aortic aneurysm who have been followed up nonoperatively for more than three years with sequential computed tomographic (CT) scans. There was a total of 74 aortic aneurysms (thoracic aortic aneurysm [TAA]: 30, abdominal aortic aneurysm [AAA]: 44). The diameter of the aortic aneurysm was normalized by dividing by the initial diameter. Exponential (y = A exp [Bt]) and linear (y = C+Dt) regression curves of growth of aneurysmal diameters were calculated, where y is the normalized diameter and t is the time after first CT examination in months. In regression analysis, the values fit well to the exponential growth curves, giving high regression coefficients. Exponential regression equations of TAA and AAA were y = 1.0192 exp (0.0032t), r = 0.720 and y = 1.0129 exp (0.0045t), r = 0.789, respectively. The results in favor of the exponential curve analysis were slightly higher than those favoring the linear curve. This is the first study that showed the growth curves of aortic aneurysms. Aortic aneurysms may grow exponentially rather than linearly with time, and the growth curves might be useful for estimating the natural history or predicting the timing of surgery.