MATHEMATICAL MODEL OF CEREBRAL DAUGHTER ANEURYSM HEMODYNAMICS AND FORMATION

Introduction. The presence of daughter aneurysms is a factor of increased risk of rupture of the parent aneurysm sac. Increased wall shear stress of the aneurysm, caused by the impact of the blood flow against the aneurysm wall, leads to local damage of the latter and, consequently, to the formation of a daughter sac. A literature search in various scientific databases showed a limited number of studies investigating the above scientific hypothesis.

Aim. To study the hemodynamics and growth of daughter cerebral aneurysms using an individual mathematical model.

Materials and methods. Thirty-eight aneurysms with 50 daughter sacs were studied. The selected aneurysms varied in size and location. The mathematical model is based on the assumption that when an aneurysm reaches a state of imminent rupture, the weakest area of the aneurysm wall passively responds to a surge of intra-aneurysmal pressure by forming a daughter aneurysm that will be the site of the eventual rupture. The daughter and parent aneurysms were assumed to be spherical. Using mathematical modeling, the growth of the daughter aneurysm was observed. To determine the change in tensile stress in the daughter aneurysm wall under conditions of constant pressure and changing geometry, the Law of Laplace was applied to the parent and daughter aneurysms.

Results. Aneurysm rupture occurs at specific combinations of the coefficients λ and μ. The higher the λ (3.2–4.5), the lower the critical μ (0.02–0.05), and vice versa. The highest risk of rupture is characteristic of aneurysms of the middle cerebral artery (p=0.008) and the anterior communicating artery (p=0.014). Aneurysms of the posterior communicating artery and the ophthalmic segment of the internal carotid artery have a significantly lower risk of rupture (p<0.001). During dynamic follow-up, significant aneurysm growth due to the daughter sac occurred only in cases with high λ values (3.4–4.1) and specifically in aneurysms of the middle cerebral and anterior communicating arteries.

Conclusion. The critical values of the aneurysm's orifice coefficient (μ) and aspect ratio (λ) can serve as determining risk factors for rupture and act as crucial guidelines when deciding on the suitability of surgical treatment.

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