Comparison of Two Markov Models for a 30-Year Simulation of the Natural History of Intracranial Aneurysms

Abstract

Objective: There are several Markov models which simulate long-term aneurysm growth and rupture. By comparing multiple models, we cannot only find a way to accurately simulate the growth and rupture behavior of untreated aneurysms in our database, but also find he best model to simulate aneurysm behavior for other studies. This will let us identify which aneurysms require invasive treatment. Methods: We analyzed 290 aneurysms in 29 males and 177 females. The mean diameter was 4.5 ± 3.45 mm, and the mean age was 61 ± 13.22 years. We tested Markov Model I and Markov Model II to simulate growth and rupture over 30 years, and growth and rupture were functions of aneurysm volume. At five-year intervals, we calculated the odds ratio and used the One-Way ANOVA and Independent T-Test to test the effects of aneurysm diameter and growth on the rupture rate. Results: After 30 years, the mean aneurysm sizes were 9.18 ± 2.37 mm and 7.80 ± 6.44 mm for Markov Models I and II, respectively. The mean rupture rate was 13.93% ± 12.89% for Markov Model I and 14.15% ± 21.96% for Markov Model II. There was a significantly higher rupture rate and significant odds ratio for larger aneurysms and “Significant Growth” aneurysms at most five-year intervals. Conclusion: Aneurysms larger than 9.5 mm need immediate surgical treatment. For aneurysms between 3.5 - 9.5 mm, early intervention is recommended if the growth rate exceeds 0.36 mm/year. Markov Model I is the optimal model for our database due to the unrealistically large aneurysms produced by Markov Model II.