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Neuroscience and Neurosurgery

New methods for controlling cerebral aneurysms with Reynolds Number and Shear stress: Literary review

Dr.  Allal Assia,  Mechanical Engineering Departement, National Polytechnic School Maurice Audin , Oran,  Algeria

Dr. Habchi Nawel , National hospital for Neurology and Neurosurgery (NHNN) and University of Victoria London, United Kingdom


An aneurysm is a pathology where a blood vessel dilates abnormally due to a weakness in the vessel's wall. Brain aneurysms result in swelling in the form of a sac, usually in the most fragile arteries. Ruptured brain aneurysms are the most common cause of subarachnoid hemorrhage, a stroke less common than ischemic strokes. This study aims to study the Reynolds number and shear stress for blood flow, as fluid flow is characterized by these parameters. The Reynolds number can identify the region where the flow is laminar, transient, or turbulent, while the shear stress measures the force exerted at the artery wall level.

Blood flow is classified into laminar flow and turbulent flow based on the Reynolds number value. Laminar flow admits symmetrical and parallel current lines, while turbulent flow is characterized by spatiotemporal fluctuations of current lines leading to vortic-like phenomena. The results indicate that blood flow is transient before and after an aneurysm and becomes turbulent inside the aneurysm. Shear stresses are equal to the pressure, which varies little compared to the patient's pressure but increases as blood pressure increases.

Keywords: Brain aneurysm, Reynolds number, Shear stress


An aneurysm is a pathology not always symptomatic in which a blood vessel dilates abnormally. In this sense, it is a situation in which an artery or vein widens abnormally due to a weakness in the wall of the blood vessel in question. A cerebral aneurysm occurs when the wall of an intracranial artery expands abnormally under the influence of various factors. A sac is then created, more fragile than the carrier artery, where blood circulates under pressure, since this sac communicates with the vessel through a collar.


This aneurysm can rupture and cause subarachnoid hemorrhage. The Location, shape, course and mode of discovery of the aneurysm depend on the etiology. The evolution of intercranial aneurysms is towards an increase in their volume under the influence of hemodynamic factors. This increase in volume leads to a weakening of their wall. This is why a ruptured aneurysm is the “The most” frequent and also the most dramatic mode of discovery.


•       One of the preferred sites of intracranial aneurysms is the anterior communicating artery (30 to 37%) it is an anastomotic artery connecting the two anterior cerebral arteries in front of the chiasma. It participates in the constitution of the arterial circle of the brain.

•       It provides: anteromedial central arteries, suprachiasmatic artery, median commissural artery, median callous artery.


2-Purpose of the study

The study of the Reynolds number and the shear stress for a blood flow is very important because any fluid flow is characterized by these parameters. Through the Reynolds number we will be able to identify the region or regions where the flow is laminar, transient or turbulent; The shear stress will allow us to measure the force exerted on the artery wall


3-Mathematical method

Blood flow is considered in anterior communicating artery of length L and radius R, δ is the maximum swelling of the aneurysm. The equation of conservation of mass will be represented by the conservation of the mass flow rate and the continuity equation will be governed by the compressibility of the blood.

The geometrical parameters are usually used to determine the category and characteristic of aneurysms for making treatment decisions. These parameters include aneurysm size, aspect ratio and vessel curvature. Study area are Before, after aneurysm and the region of aneurysm.

This graph shows us that the shear stress increases linearly as a function of arterial pressure and this according to the correlation


5 Conclusion

This work will lead us to early detection of intracranial aneurysm just with the radius and the position of aneurysm and allowed us to use biomechanical parameters in order to apply them to medicine and more specifically to brainaneurysms. The parameters are the Reynolds Re number and the shear stresses

For a low magnification the regime remains transient on the other hand for a magnification of the order of 1.8mm up to 2.5mm the speed becomes turbulent.


The shear stress remains virtually constant along the position but increases linearly depending on the patient's blood pressure.



1.     L. Achab, A. Magnin, J.R. Clermont, S. Benhadid :  Etude numérique d’écoulements du sang dans desdomaines axisymétriques en présence d’une sténose importante avec un modèle de fluide à seuil : 22ème Congrès Français de Mécanique Lyon, 24 au 28 Août 2015

2.     Les 5 types d'anévrismes (causes et symptômes) - Médical - 2022 (




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