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


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.

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Patel, S. and Chien, A. (2014) Comparison of Two Markov Models for a 30-Year Simulation of the Natural History of Intracranial Aneurysms. Open Journal of Radiology, 4, 220-234. doi: 10.4236/ojrad.2014.42030.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Dhar, S., Tremmel, M., Mocco, J., Kim, M., Yamamoto, J., Siddiqui, A.H., et al. (2008) Morphology Parameters for Intracranial Aneurysm Rupture Risk Assessment. Neurosurgery, 63, 185-197.
[2] Hoi, Y., Meng, H., Woodward, S.H., Bendok, B.R., Hanel, R.A., Guterman, L.R., et al. (2004) Effects of Arterial Geometry on Aneurysm Growth: Three-Dimensional Computational Fluid Dynamics Study. Journal of Neurosurgery, 101, 676-681.
[3] Jou, L. and Mawad, M.E. (2009) Growth Rate and Rupture Rate of Unruptured Intracranial Aneurysms: A Population Approach. Biomedical Engineering Online, 8, 1-9.
[4] Juvela, S., Kristiina, P. and Porras, M. (2001) Factors Affecting Formation and Growth of Intracranial Aneurysms: A Long-Term Follow-Up Study. Stroke, 32, 485-491.
[5] Juvela, S., Porras, M. and Heiskanen, O. (1993) Natural History of Unruptured Intracranial Aneurysms: A Long-Term Follow-Up Study. Journal of Neurosurgery, 79, 174-182.
[6] Kassell, N.F. and Drake, C.G. (1982) Timing of Aneurysm Surgery. Neurosurgery, 10, 514-519.
[7] Lall, R.R., Eddleman, C.S., Bendok, B.R. and Batjer, H.H. (2009) Unruptured Intracranial Aneurysms and the Assessment of Rupture Risk Based on Anatomical and Morphological Factors: Sifting Through the Sands of Data. Neurosurgical Focus, 26, 1-7.
[8] Matsubara, S., Hadeishi, H., Suzuki, A., Yasui, N. and Nishimura, H. (2004) Incidence and Risk Factors for the Growth of Unruptured Cerebral Aneurysms: Observation Using Serial Computerized Tomography Angiography. Journal of Neurosurgery, 101, 908-914.
[9] Prestigiacomo, C.J., He, W., Catrambone, J., Chung, S., Kasper, L., Pasupuleti, L., et al. (2009) Predicting Aneurysm Rupture Probabilities through the Application of a Computed Tomography Angiography-Derived Binary Logistic Regression Model. Journal of Neurosurgery, 110, 1-6.
[10] Allcock, J.M. and Canham, P.B. (1976) Angiographic Study of the Growth of Intracranial Aneurysms. Journal of Neurosurgery, 45, 617-621.
[11] Dell, S. (1982) Asymptomatic Cerebral Aneurysm: Assessment of Its Risk of Rupture. Neurosurgery, 10, 162-166.
[12] He, W., Hauptman, J., Pasupuleti, L., Setton, A., Farrow, M.G., Kasper, L., et al. (2010) True Posterior Communicating Artery Aneurysms: Are They More Prone to Rupture? A Biomorphometric Analysis. Journal of Neurosurgery, 112, 611-615.
[13] Chmayssani, M., Rebeiz, J.G., Rebeiz, T.J., Batjer, H.H. and Bendok, B.R. (2011) Relationship of Growth to Aneurysm Rupture in Asymptomatic Aneurysms ≤ 7 mm: A Systematic Analysis of the Literature. Neurosurgery, 68, 1164-1171.
[14] Koffijberg, H., Buskens, E., Algra, A., Wermer, M.J. and Rinkel, G.J. (2008) Growth Rates of Intracranial Aneurysms: Exploring Constancy. Journal of Neurosurgery, 109, 176-185.
[15] Chang, H.S. (2006) Simulation of the Natural History of Cerebral Aneurysms Based on Data from the International Study of Unruptured Intracranial Aneurysms. Journal of Neurosurgery, 104, 188-194.
[16] Yoshimoto, Y. (2006) A Mathematical Model of the Natural History of Intracranial Aneurysms: Quantification of the Benefit of Prophylactic Treatment. Journal of Neurosurgery, 104, 195-200.
[17] Greenburg, I.M. (1984) Cerebral Aneurysm Rupture during Neurosurgery. Neurosurgery, 15, 243-245.
[18] Weir, B., Disney, L. and Karrison, T. (2002) Sizes of Ruptured and Unruptured Aneurysms in Relation to Their Sites and the Ages of Patients. Journal of Neurosurgery, 96, 64-70.
[19] Qureshi, A.I., Sung, G.Y., Suri, M.F., Straw, R.N., Guterman, L.R. and Hopkins, L.N. (2000) Factors Associated with Aneurysm Size in Patients with Subarachnoid Hemorrhage: Effect of Smoking and Aneurysm Location. Neurosurgery, 46, 44-50.
[20] Fernandez Zubillaga, A., Guglielmi, G., Vinuela, F. and Duckwiler, G.R. (1994) Endovascular Occlusion of Intracranial Aneurysms with Electrically Detachable Coils: Correlation of Aneurysm Neck Size and Treatment Results. American Journal of Neuroradiology, 15, 815-820.
[21] Hademenos, G.J., Massoud, T.F., Turjman, F. and Sayre, J.W. (1998) Anatomical and Morphological Factors Correlating with Rupture of Intracranial Aneurysms in Patients Referred for Endovascular Treatment. Neuroradiology, 40, 755-760.
[22] Rogers, L.A. (1987) Intracranial Aneurysm Size and Potential for Rupture. Journal of Neurosurgery, 67, 475-476.
[23] The International Study of Unruptured Intracranial Aneurysms Investigators (1998) Unruptured Intracranial Aneurysms-Risk of Rupture and Risks of Surgical Intervention. New England Journal of Medicine, 339, 1725-1733.
[24] Batjer, H. and Samson, D. (1986) Intraoperative Aneurysmal Rupture: Incidence, Outcome, and Suggestions for Surgical Management. Neurosurgery, 18, 701-707.
[25] Miyazawa, N., Akiyama, I. and Yamagata, Z. (2006) Risk Factors for Growth of Unruptured Intracranial Aneurysms: Follow-Up Study by Serial 0.5-T Magnetic Resonance Angiography. Neurosurgery, 58, 1047-1053.

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