Abstract
BackgroundUnderstanding aneurysm growth rate allows us to predict not only the current rupture risk, but also accumulated rupture risk in the future. However, determining growth rate of unruptured intracranial aneurysms often requires follow-up of patients for a long period of time so that significant growth can be observed and measured. We investigate a relationship between growth rate and rupture rate and develop a theoretical model that can predict average behavior of unruptured intracranial aneurysms based on existing clinical data.MethodsA mathematical model is developed that links growth rate and rupture rate. This model assumes a stable aneurysm size distribution so the number of aneurysm ruptures is balanced by the growth of aneurysms. Annual growth rates and growth profiles are calculated from a hypothetical size distribution and data from a previous clinical study.ResultsOur model predicts a growth rate of 0.34–1.63 mm/yr for three different growth models when the rupture rate at 10 mm is 1%. The growth rate is 0.56–0.65 mm/yr if annual rupture rate averaged over all aneurysm sizes is assumed to be 2%. The peak of aneurysm size distribution coincides with a period of slow growth between 5 mm and 8 mm.ConclusionThis mathematical model can be used to predict aneurysm growth rate, and the results are consistent with previous clinical studies. Predictions from both hypothetical and clinical cases agree very well. This model explains why some aneurysms may grow into a stable size and remain so without rupture.
Highlights
Understanding aneurysm growth rate allows us to predict the current rupture risk, and accumulated rupture risk in the future
Our model basically provides a link between growth rate and rupture rate; the aneurysm size distribution is a pre-requisite to the calculation of growth rate
We assume a profile for the aneurysm size distribution: N(r) = ar/(1+kr2)2
Summary
Understanding aneurysm growth rate allows us to predict the current rupture risk, and accumulated rupture risk in the future. We investigate a relationship between growth rate and rupture rate and develop a theoretical model that can predict average behavior of unruptured intracranial aneurysms based on existing clinical data. Natural history of intracranial aneurysms can help us to understand the course of aneurysm development and allow proper assessment of aneurysm rupture risk. A large clinical study on unruptured intracranial aneurysms, the International Study of Unruptured Intracranial Aneurysms (ISUIA), has studied more than 4000 aneurysm patients and raised serious interests on risk factors and rupture rate of unruptured aneurysms [1,2]. They (page number not for citation purposes)
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