[01] Mohammed Musad, Oil and Minerals Faculty, University of Ade, Aden, Yemen.

In this research paper a mathematical models have been developed to study the effect of aneurysm on blood flow. The artery under consideration for the development of model is cylindrical with an axially symmetric aneurysm and fully of blood. The blood assumed to be Newtonian fluid with constant viscosity µ and constant density . The results indicated that the size of aneurysm has directly proportional relation with pressure difference, and inversely proportional relation with velocity. While the size of aneurysm has irregular relation with wall shears stress, shear rate and flow rate of blood, where every one of them has maximum value at R=1.6r.

Symmetrical Aneurysm, Wall Shear Stress, Pressure Difference, Blood Flow

[01] Hershey D, Cho S. J. (1966), Blood flow in rigid, tubes thickness and slip. Velocity of plasma film at the wall. J. Appl. Physiology. Vol. 21, 27-32. [02] Fei D. Y, Thomas J. D and rittgers S. E. (1994), the effect of angle and flow rate upon hemodynamic in distal vascular graft anastomoses: a numerical model study, journal of biomechanical engineering 116: 331-336. [03] Song M. H, Sato M, Ueda Y, (2000), Three dimensional simulation of coronary artery bypass grafting, with the use of computational fluid dynamics, Surg. Today 30: 993-998. [04] Mohammed Musad (2012). Mathematical Modeling of Blood Flow though Stenosed Arteries, ISBN 978-3-8484-3286-8, LAP Lambert Academic Publishing GmbH & Co. KG. [05] Sheard G. J, Ryan K (2008). Wall Shear Stress and Flow Stability in A model Fusiform Aneurysm, ANZIAM. J. 50: C1-C15. [06] Kondo S, Hashimoto N, Kikuchi H, Hazama F, Nagata I, and Kataoka H (1997). Cerebral Aneurysm Arising at Non-branching Site. An experimental study. Stroke: 28: 393-404. [07] Shojima M, Oshima M, Takagi K, Torii R, Hayakawa M, Katada K, Morita A, and Kirino T (2004). Magnitude and Role of Wall Shear Stress on Cerebral Aneurysm Computational Fluid Dynamic Study of 20 Middle Cerebral Aneurysm, Stroke: 35. 2500-2505. [08] Loic Boussel, Vitaliy Rayz, Charles McCulloch, Alastair Martin, Gabriel, Acevedo-Bolton, Michael Lawton, Randall Higashida, Wade S. Smith, William L (2008). Aneurysm Growth Occurs at Region of Low Wall Shear Stress: Patient-Specific Correlation of Hemodynamics and Growth in a Longitudinal Study. Stroke: 3. 2997-3002. [09] Hakon Osterabo (2013). The Effects of Heart Rate on Blood Flow in Intracranial Aneurysm. July. Online http://folk.uio.no/kentand/haakon_thesis.pdf. [10] Vashishath Patel (2011). Impact of Geometry on Blood Flow Patterns in Abdominal Aortic Aneurysm. New Brunswick, New Jersey. [11] Endar A. Fino. Amon. Crastina H (2001). Blood flow in Abdominal Aorta Aneurysm, Pulsatile Flow Hemodynamic. ASME: 123. 474-484. [12] M. R. Levitt, P. M. McGah, A. Aliseda, P. D. Mourad, J. D. Nerva, S. S. Vaidya, R. P. Morton, B. V. Ghodke, and L. J. Kim (2014). Cerebral Aneurysms Treated with Flow-Diverting Stents: Computational Models with Intravascular Blood Flow Measurements. AJNR Am J Neuroradiol 35: 143–148. [13] Chao Wang, ZhongbinTian Jian Liu, Linkai Jing, Nikhil Paliwal, Shengzhang Wang, Ying Zhang, Jianping Xiang, Adnan H. Siddiqui, HuiMeng and Xinjian Yang, (2016). Flow diverter effect of LVIS stent on cerebral aneurysm hemodynamics: a comparison with Enterprise stents and the Pipeline device. Wang et al. J Transl Med: 14: 199. [14] Irving. P. Herman (2007). Physics of the Human Body, Springer Berlin Heidelberg.