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The diameter-cube hypothesis: a new biophysical model of aneurysm rupture
Phillip Dickey1, Purushothaman Kailasnath
1Department of Neurosurgery, Yale University School of Medicine, New Haven, Connecticut, USA.
Background:
Recent discussions on the relationship between intracranial aneurysm diameter and rupture probability have focused on the presence of an apparent critical diameter of 10 mm for aneurysm rupture. Despite the fact that many investigators have argued against the existence of this critical diameter, no one has yet proposed a viable alternative concept. In this report we present a scientifically rigorous alternative concept, that the size-specific rupture probability (RP) of an aneurysm varies as the third power of the aneurysm diameter.
Methods:
We utilized a new biophysical model of aneurysm rupture that predicts the relationship between the size-specific rupture probability of an aneurysm and the diameter (D) to be RP = kD(3). We tested this hypothesis against data from two autopsy studies and one large clinical aneurysm study. Subsequently, using this D(3) hypothesis and the different size distributions of aneurysms in the study populations, we predicted the variation of cumulative rupture probability (CRP) with diameter for each population.
Results:
Data from the autopsy studies supported the diameter-cube hypothesis, with the log-log plots of size-specific rupture probability versus aneurysm diameter from the two autopsy series yielding lines with slopes 3.54 (R(2) = 0.61, p < 0.12) and 3.05 (R(2) = 0.98, p << 0.001). Plots of cumulative rupture probability versus diameter were determined to be sensitive to the size distributions of the unruptured aneurysms in the population. Furthermore, none of the CRP plots showed evidence of a critical diameter for aneurysm rupture.
Conclusions:
RP varies as the third power of aneurysm diameter, a relationship that predicts a continuous increase in RP with increasing size rather than the existence of a threshold diameter that separates low- from high-risk aneurysms. Accordingly, all aneurysms have finite risk for rupture and deserve consideration for treatment. Much of the current controversy regarding the relationship between rupture rates and diameter is a result of different size distributions in study populations rather than differences in aneurysm biology.