Newtonian and non-Newtonian CFD Models of Intracranial Aneurysm: A Review
Volume 12, No. 1, January 2020, Pages 62-86
Samar A. Mahrous1,2,*, Nor Azwadi Che Sidik1,3, Khalid M. Saqr2,4
1 Department of Thermo-fluid Universiti Teknologi Malaysia, 81310 UTM Skudai, Malaysia
2 College of Engineering and Technology, Arab Academy for Science, Technology and Maritime Transport, P.O.BOX 1029 Alexandria, Egypt
3 Malaysia – Japan International Institute of Technology (MJIIT), University Teknologi Malaysia Kuala Lumpur, 54100 Kuala Lumpur, Malaysia
4 Research Center for Computational Neurovascular Biomechanics (RCCNB), Alexandria University Hospital in Smouha, 21554 Alexandria, Egypt
*Corresponding author: firstname.lastname@example.org
Intracranial aneurysms; computational fluid dynamics (CFD); hemodynamics; blood rheology models; patient-specific models
Computational Fluid Dynamics (CFD) has become an essential research tool to investigate the physical, biophysical and pathophysiological processes leading to the formation, growth and rupture of intracranial aneurysms (IAs). The diverse anatomical complexities of IAs dictate a staggering level of sophistication inherited in the CFD modeling process. From medical imaging to wall shear stress mapping on the aneurysm walls, there are numerous physical assumptions related to blood flow and wall dynamics. The majority of such assumptions remain controversial until today. This review is an endeavor to summarize, in a critical and comprehensive manner, the different assumptions used to calculate blood viscosity in CFD models of IA hemodynamics. The tabulated summaries of literature presented herein also highlight the inconsistency of location choice and imaging techniques used to select IA models for CFD studies. This review presents a roadmap for the state-of-the art knowledge about blood viscosity models used with IA CFD models, and suggests future research directions to further characterize the nature of blood flow which contributes to the improvement of diagnosis and management of IAs.
CITE THIS ARTICLE
Samar, A. Mahrous, et al. “Newtonian and non-Newtonian CFD Models of Intracranial Aneurysm: A Review.” CFD Letters 12.1 (2020): 62-86.
Samar, A. M., Nor Azwadi, C. S., & Khalid, M. S.(2020). Newtonian and non-Newtonian CFD Models of Intracranial Aneurysm: A Review. CFD Letters, 12(1), 62-86.
Samar A. Mahrous, Nor Azwadi Che Sidik and Khalid M. Saqr.”Newtonian and non-Newtonian CFD Models of Intracranial Aneurysm: A Review.” CFD Letters. 12, no. 1 (2020): 62-86.
Samar, A.M., Nor Azwadi, C.S., and Khalid, M.S., 2020. Newtonian and non-Newtonian CFD Models of Intracranial Aneurysm: A Review. CFD Letters 12(1), pp. 62-86.
Samar AM, Nor Azwadi CS, Khalid MS. Newtonian and non-Newtonian CFD Models of Intracranial Aneurysm: A Review. CFD Letters. 2020;12(1): 62-86.
REFERENCES Cornejo, Sergio, Amador Guzmán, Alvaro Valencia, Jose Rodríguez, and Ender Finol. “Flow-induced wall mechanics of patient-specific aneurysmal cerebral arteries: Nonlinear isotropic versus anisotropic wall stress.” Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine 228, no. 1 (2014): 37-48.
 Gard, Andrew P. “Every 18 Minutes, A Brain Aneurysm Ruptures.” May 3, (2017).
 Hop, Jeannette W., Gabrie?l JE Rinkel, Ale Algra, and Jan van Gijn. “Case-fatality rates and functional outcome after subarachnoid hemorrhage: a systematic review.” Stroke 28, no. 3 (1997): 660-664.
 Keedy, Alexander. “An overview of intracranial aneurysms.” McGill Journal of Medicine: MJM 9, no. 2 (2006): 141.
 Schievink, Wouter I. “Intracranial aneurysms.” New England Journal of Medicine 336, no. 1 (1997): 28-40.
 Rhoton, Jr AL. “The cerebrum. Anatomy.” Neurosurgery 61, no. 1 Suppl (2007): 37-118.
 Basri, Adi Azriff, Shah Mohammed Abdul Khader, Cherian Johny, Raghuvir Pai, Muhammad Zuber, Kamarul Arifin Ahmad, and Zanuldin Ahmad. “Numerical Study of Haemodynamics Behaviour in Normal and Single Stenosed Renal Artery using Fluid–Structure Interaction.” Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 51, no. 1 (2018): 91-98.
 Sforza, Daniel M., Christopher M. Putman, and Juan Raul Cebral. “Hemodynamics of cerebral aneurysms.” Annual review of fluid mechanics 41 (2009): 91-107.
 Frösen, Juhana, Riikka Tulamo, Anders Paetau, Elisa Laaksamo, Miikka Korja, Aki Laakso, Mika Niemelä, and Juha Hernesniemi. “Saccular intracranial aneurysm: pathology and mechanisms.” Acta neuropathologica 123, no. 6 (2012): 773-786.
 Humphrey, J. D., and P. B. Canham. “Structure, mechanical properties, and mechanics of intracranial saccular aneurysms.” Journal of elasticity and the physical science of solids 61, no. 1-3 (2000): 49-81.
 Jamali, Muhammad Sabaruddin Ahmad, and Zuhaila Ismail. “Simulation of Heat Transfer on Blood Flow through a Stenosed Bifurcated Artery.” Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 60, no. 2 (2019): 310-323.
 Wang, Xiaohong, and Xiaoyang Li. “Biomechanical behaviors of curved artery with flexible wall: A numerical study using fluid–structure interaction method.” Computers in biology and medicine 41, no. 11 (2011): 1014-1021.
 Foutrakis, George N., Howard Yonas, and Robert J. Sclabassi. “Saccular aneurysm formation in curved and bifurcating arteries.” American Journal of Neuroradiology 20, no. 7 (1999): 1309-1317.
 Valencia, Alvaro, and Francisco Solis. “Blood flow dynamics and arterial wall interaction in a saccular aneurysm model of the basilar artery.” Computers & structures 84, no. 21 (2006): 1326-1337.
 Kim, C. H., J. Cervos-Navarro, H. Kikuchi, N. Hashimoto, and F. Hazama. “Degenerative changes in the internal elastic lamina relating to the development of saccular cerebral aneurysms in rats.” Acta neurochirurgica 121, no. 1-2 (1993): 76-81.
 Sadamasa, Nobutake, Kazuhiko Nozaki, and Nobuo Hashimoto. “Disruption of gene for inducible nitric oxide synthase reduces progression of cerebral aneurysms.” Stroke 34, no. 12 (2003): 2980-2984.
 Scanarini, M., S. Mingrino, R. Giordano, and A. Baroni. “Histological and ultrastructural study of intracranial saccular aneurysmal wall.” Acta neurochirurgica 43, no. 3-4 (1978): 171-182.
 Takao, Yamamoto, Otsuka, Suzuki, and Masuda. “Analysis of Cerebral Aneurysms using Computational Fluid Dynamics (CFD)(New Concept in Treatment for Cerebral Aneurysm)”. Japanese Journal of Neurosurgery 21, no. 4 (2012): 298-305.
 Penn, David L., Ricardo J. Komotar, and E. Sander Connolly. “Hemodynamic mechanisms underlying cerebral aneurysm pathogenesis.” Journal of Clinical Neuroscience 18, no. 11 (2011): 1435-1438.
 Lee, Robert MKW. “Morphology of cerebral arteries.” Pharmacology & therapeutics 66, no. 1 (1995): 149-173.
 Dr?ghia, F., ALINA C?T?LINA Dr?ghia, and D. O. I. N. A. Onicescu. “Electron microscopic study of the arterial wall in the cerebral aneurysms.” Rom J Morphol Embryol 49 (2008): 101-103.
 Tamura, Tetsuya, Mohammad A. Jamous, Keiko T. Kitazato, Kenji Yagi, Yoshiteru Tada, Masaaki Uno, and Shinji Nagahiro. “Endothelial damage due to impaired nitric oxide bioavailability triggers cerebral aneurysm formation in female rats.” Journal of hypertension 27, no. 6 (2009): 1284-1292.
 Irie, Keiko, Hitomi Anzai, Masahiko Kojima, Naomi Honjo, Makoto Ohta, Yuichi Hirose, and Makoto Negoro. “Computational fluid dynamic analysis following recurrence of cerebral aneurysm after coil embolization.” Asian journal of neurosurgery 7, no. 3 (2012): 109.
 Chiu, Jeng-Jiann, and Shu Chien. “Effects of disturbed flow on vascular endothelium: pathophysiological basis and clinical perspectives.” Physiological reviews 91, no. 1 (2011): 327-387.
 Sforza, D. M., C. M. Putman, S. Tateshima, F. Vinuela, and J. R. Cebral. “Effects of perianeurysmal environment during the growth of cerebral aneurysms: a case study.” American Journal of Neuroradiology 33, no. 6 (2012): 1115-1120.
 Tanoue, T., S. Tateshima, J. P. Villablanca, F. Viñuela, and K. Tanishita. “Wall shear stress distribution inside growing cerebral aneurysm.” American journal of neuroradiology 32, no. 9 (2011): 1732-1737.
 Jou, Liang-Der, Gregory Wong, Brad Dispensa, Michael T. Lawton, Randall T. Higashida, William L. Young, and David Saloner. “Correlation between lumenal geometry changes and hemodynamics in fusiform intracranial aneurysms.” American journal of neuroradiology 26, no. 9 (2005): 2357-2363.
 Boussel, Loic, Vitaliy Rayz, Charles McCulloch, Alastair Martin, Gabriel Acevedo-Bolton, Michael Lawton, Randall Higashida, Wade S. Smith, William L. Young, and David Saloner. “Aneurysm growth occurs at region of low wall shear stress: patient-specific correlation of hemodynamics and growth in a longitudinal study.” Stroke 39, no. 11 (2008): 2997-3002.
 Sakaki, T., E. Kohmura, T. Kishiguchi, T. Yuguchi, T. Yamashita, and T. Hayakawa. “Loss and apoptosis of smooth muscle cells in intracranial aneurysms studies with in situ DNA end labeling and antibody against single-stranded DNA.” Acta neurochirurgica 139, no. 5 (1997): 469-475.
 Steinman, David A., Jaques S. Milner, Chris J. Norley, Stephen P. Lownie, and David W. Holdsworth. “Image-based computational simulation of flow dynamics in a giant intracranial aneurysm.” American Journal of Neuroradiology 24, no. 4 (2003): 559-566.
 Algabri, Yousif A., Surapong Chatpun, and Ishkrizat Taib. “An Investigation of Pulsatile Blood Flow in An Angulated Neck of Abdominal Aortic Aneurysm Using Computational Fluid Dynamics.” Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 57, no. 2 (2019): 265-274.
 Wang, Sheng-zhang, Jia-liang Chen, Guang-hong Ding, Gang Lu, and Xiao-long Zhang. “Non-newtonian computational hemodynamics in two patient-specific cerebral aneurysms with daughter saccules.” Journal of Hydrodynamics 22, no. 5 (2010): 639-646.
 Ku, David N., Don P. Giddens, Christopher K. Zarins, and Seymour Glagov. “Pulsatile flow and atherosclerosis in the human carotid bifurcation. Positive correlation between plaque location and low oscillating shear stress.” Arteriosclerosis: An Official Journal of the American Heart Association, Inc. 5, no. 3 (1985): 293-302.
 Evju, Øyvind, and Kent-Andre Mardal. “On the assumption of laminar flow in physiological flows: Cerebral aneurysms as an illustrative example.” In Modeling the Heart and the Circulatory System, pp. 177-195. Springer, Cham, 2015.
 Khan, M. O., K. Valen-Sendstad, and D. A. Steinman. “Narrowing the expertise gap for predicting intracranial aneurysm hemodynamics: impact of solver numerics versus mesh and time-step resolution.” American Journal of Neuroradiology 36, no. 7 (2015): 1310-1316.
 Khan, M. O., D. A. Steinman, and K. Valen?Sendstad. “Non?Newtonian versus numerical rheology: Practical impact of shear?thinning on the prediction of stable and unstable flows in intracranial aneurysms.” International journal for numerical methods in biomedical engineering 33, no. 7 (2017): e2836.
 Cebral, Juan R., Marcelo A. Castro, James E. Burgess, Richard S. Pergolizzi, Michael J. Sheridan, and Christopher M. Putman. “Characterization of cerebral aneurysms for assessing risk of rupture by using patient-specific computational hemodynamics models.” American Journal of Neuroradiology 26, no. 10 (2005): 2550-2559.
 Hoi, Yiemeng, Hui Meng, Scott H. Woodward, Bernard R. Bendok, Ricardo A. Hanel, Lee R. Guterman, and L. Nelson Hopkins. “Effects of arterial geometry on aneurysm growth: three-dimensional computational fluid dynamics study.” Journal of neurosurgery 101, no. 4 (2004): 676-681.
 Meng, Hui, Zhijie Wang, Yiemeng Hoi, Ling Gao, Eleni Metaxa, Daniel D. Swartz, and John Kolega. “Complex hemodynamics at the apex of an arterial bifurcation induces vascular remodeling resembling cerebral aneurysm initiation.” Stroke 38, no. 6 (2007): 1924-1931.
 Campo-Deaño, Laura, Mónica SN Oliveira, and Fernando T. Pinho. “A review of computational hemodynamics in middle cerebral aneurysms and rheological models for blood flow.” Applied Mechanics Reviews 67, no. 3 (2015): 030801.
 Frolov, S. V., S. V. Sindeev, D. Liepsch, and A. Balasso. “Experimental and CFD flow studies in an intracranial aneurysm model with Newtonian and non-Newtonian fluids.” Technology and Health Care 24, no. 3 (2016): 317-333.
 Hippelheuser, James E., Alexandra Lauric, Alex D. Cohen, and Adel M. Malek. “Realistic non-Newtonian viscosity modelling highlights hemodynamic differences between intracranial aneurysms with and without surface blebs.” Journal of biomechanics 47, no. 15 (2014): 3695-3703.
 Ieuan Owen, J. G., Marcel Escudier, and Rob Poole. “The importance of the non-Newtonian characteristics of blood in flow modelling studies.” Journal of Applied Fluid Mechanics 2 (2009).
 Morales, Hernán G., Ignacio Larrabide, Arjan J. Geers, Martha L. Aguilar, and Alejandro F. Frangi. “Newtonian and non-Newtonian blood flow in coiled cerebral aneurysms.” Journal of biomechanics 46, no. 13 (2013): 2158-2164.
 Otani, Tomohiro, Satoshi Ii, Masayuki Hirata, and Shigeo Wada. “Computational study of the non-Newtonian effect of blood on flow stagnation in a coiled cerebral aneurysm.” Nihon Reoroji Gakkaishi 45, no. 5 (2017): 243-249.
 Suzuki, Takashi, Hiroyuki Takao, Takamasa Suzuki, Tomoaki Suzuki, Shunsuke Masuda, Chihebeddine Dahmani, Mitsuyoshi Watanabe et al. “Variability of hemodynamic parameters using the common viscosity assumption in a computational fluid dynamics analysis of intracranial aneurysms.” Technology and Health Care 25, no. 1 (2017): 37-47.
 Xiang, Jianping, Markus Tremmel, John Kolega, Elad I. Levy, Sabareesh K. Natarajan, and Hui Meng. “Newtonian viscosity model could overestimate wall shear stress in intracranial aneurysm domes and underestimate rupture risk.” Journal of neurointerventional surgery 4, no. 5 (2012): 351-357.
 Berg, P., S. Saalfeld, S. Voß, T. Redel, B. Preim, G. Janiga, and O. Beuing. “Does the DSA reconstruction kernel affect hemodynamic predictions in intracranial aneurysms? An analysis of geometry and blood flow variations.” Journal of neurointerventional surgery 10, no. 3 (2018): 290-296.
 Geers, Arjan J., Ignacio Larrabide, A. G. Radaelli, Hrvoje Bogunovic, HAF Gratama Van Andel, C. B. Majoie, and Alejandro F. Frangi. “Reproducibility of image-based computational hemodynamics in intracranial aneurysms: comparison of CTA and 3DRA.” In 2009 IEEE International Symposium on Biomedical Imaging: From Nano to Macro, pp. 610-613. IEEE, 2009.
 Schneiders, J. J., H. A. Marquering, L. Antiga, R. Van den Berg, E. VanBavel, and C. B. Majoie. “Intracranial aneurysm neck size overestimation with 3D rotational angiography: the impact on intra-aneurysmal hemodynamics simulated with computational fluid dynamics.” American Journal of Neuroradiology 34, no. 1 (2013): 121-128.
 Robertson, Anne M., Adélia Sequeira, and Marina V. Kameneva. “Hemorheology.” In Hemodynamical flows, pp. 63-120. Birkhäuser Basel, 2008.
 Eckmann, David M., Shelly Bowers, Mark Stecker, and Albert T. Cheung. “Hematocrit, volume expander, temperature, and shear rate effects on blood viscosity.” Anesthesia & Analgesia 91, no. 3 (2000): 539-545.
 Merrill, E. W., E. R. Gilliland, G. Cokelet, H. Shin, A. Britten, and R. E. Wells Jr. “Rheology of blood and flow in the microcirculation.” Journal of applied physiology 18, no. 2 (1963): 255-260.
 Cebral, Juan R., Fernando Mut, Jane Weir, and Christopher Putman. “Quantitative characterization of the hemodynamic environment in ruptured and unruptured brain aneurysms.” American Journal of Neuroradiology 32, no. 1 (2011): 145-151.
 Jou, L-D., Deok Hee Lee, Hesham Morsi, and Michel E. Mawad. “Wall shear stress on ruptured and unruptured intracranial aneurysms at the internal carotid artery.” American Journal of Neuroradiology 29, no. 9 (2008): 1761-1767.
 Cebral, J. R., F. Mut, M. Raschi, E. Scrivano, R. Ceratto, P. Lylyk, and C. M. Putman. “Aneurysm rupture following treatment with flow-diverting stents: computational hemodynamics analysis of treatment.” American journal of neuroradiology 32, no. 1 (2011): 27-33.
 Xiang, Jianping, Sabareesh K. Natarajan, Markus Tremmel, Ding Ma, J. Mocco, L. Nelson Hopkins, Adnan H. Siddiqui, Elad I. Levy, and Hui Meng. “Hemodynamic–morphologic discriminants for intracranial aneurysm rupture.” Stroke 42, no. 1 (2011): 144-152.
 Stuart, John, and Martin W. Kenny. “Blood rheology.” Journal of clinical pathology 33, no. 5 (1980): 417.
 Mejia, Juan, Rosaire Mongrain, and Olivier F. Bertrand. “Accurate prediction of wall shear stress in a stented artery: Newtonian versus non-Newtonian models.” Journal of biomechanical engineering 133, no. 7 (2011): 074501.
 Johnston, Barbara M., Peter R. Johnston, Stuart Corney, and David Kilpatrick. “Non-Newtonian blood flow in human right coronary arteries: transient simulations.” Journal of biomechanics 39, no. 6 (2006): 1116-1128.
 Mallik, B. Basu, Saktipada Nanda, Bhabatosh Das, Debanshu Saha, Debanu Shankar Das, and Koustav Paul. “A non-Newtonian fluid model for blood flow using power-law through an atherosclerotic arterial segment having slip velocity.” International journal of pharmaceutical, chemical and biological sciences 3, no. 3 (2013): 752-760.
 Mandal, Prashanta Kumar. “An unsteady analysis of non-Newtonian blood flow through tapered arteries with a stenosis.” International Journal of Non-Linear Mechanics 40, no. 1 (2005): 151-164.
 Jeong, W. W., and K. Rhee. “Effects of surface geometry and non-newtonian viscosity on the flow field in arterial stenoses.” Journal of mechanical science and technology 23, no. 9 (2009): 2424-2433.
 K Kulcsár, Zsolt Mihály. “Role of hemodynamics in the life cycle of cerebral aneurysm.” Semmelweis University, PhD Thesis (2011).
 Lindekleiv, Haakon M., Kristian Valen-Sendstad, Michael K. Morgan, Kent-Andre Mardal, Kenneth Faulder, Jeanette H. Magnus, Knut Waterloo, Bertil Romner, and Tor Ingebrigtsen. “Sex differences in intracranial arterial bifurcations.” Gender medicine 7, no. 2 (2010): 149-155.
 Anand, M., and K. R. Rajagopal. “A shear-thinning viscoelastic fluid model for describing the flow of blood.” Int. J. Cardiovasc. Med. Sci 4, no. 2 (2004): 59-68.
 Bodnár, T., A. Sequeira, and L. Pirkl. “Numerical Simulations of Blood Flow in a Stenosed Vessel under Different Flow Rates using a Generalized Oldroyd?B Model.” In AIP Conference Proceedings, vol. 1168, no. 1, pp. 645-648. AIP, 2009.
 Kouhi, E., Y. S. Morsi, and S. H. Masood. “Haemodynamic analysis of coronary artery bypass grafting in a non-linear deformable artery and Newtonian pulsatile blood flow.” Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine 222, no. 8 (2008): 1273-1287.
 Lee, K. W., and X. Y. Xu. “Modelling of flow and wall behaviour in a mildly stenosed tube.” Medical engineering & physics 24, no. 9 (2002): 575-586.
 Saqr, Khalid M., Ossama Mansour, Simon Tupin, Tamer Hassan, and Makoto Ohta. “Evidence for non-Newtonian behavior of intracranial blood flow from Doppler ultrasonography measurements.” Medical & biological engineering & computing 57, no. 5 (2019): 1029-1036.
 Stojanovi?, Nebojša, Ivan Stefanovi?, Saša Ran?elovi?, Rade Miti?, Petar Bošnjakovi?, and Dragan Stojanov. “Presence of anatomical variations of the circle of Willis in patients undergoing surgical treatment for ruptured intracranial aneurysms.” Vojnosanitetski pregled 66, no. 9 (2009): 711-717.
 Kayembe, K. N., Masakiyo Sasahara, and Fumitada Hazama. “Cerebral aneurysms and variations in the circle of Willis.” Stroke 15, no. 5 (1984): 846-850.
 Zarins, Christopher K., Don P. Giddens, B. K. Bharadvaj, Vikrom S. Sottiurai, Robert F. Mabon, and Seymour Glagov. “Carotid bifurcation atherosclerosis. Quantitative correlation of plaque localization with flow velocity profiles and wall shear stress.” Circulation research 53, no. 4 (1983): 502-514.
 Castro, M. A., Christopher M. Putman, and J. R. Cebral. “Computational fluid dynamics modeling of intracranial aneurysms: effects of parent artery segmentation on intra-aneurysmal hemodynamics.” American Journal of Neuroradiology 27, no. 8 (2006): 1703-1709.
 Wang, Qing, Wei-zhe Wang, Zhi-min Fei, Ying-zheng Liu, and Zhao-min Cao. “Simulation of blood flow in intracranial ICA-pcoma aneurysm via computational fluid dymamics modeling.” Journal of Hydrodynamics 21, no. 5 (2009): 583-590.
 Alnæs, Martin Sandve, Jørgen Isaksen, Kent-André Mardal, Bertil Romner, Michael K. Morgan, and Tor Ingebrigtsen. “Computation of hemodynamics in the circle of Willis.” Stroke 38, no. 9 (2007): 2500-2505.
 Isaksen, Jørgen Gjernes, Yuri Bazilevs, Trond Kvamsdal, Yongjie Zhang, Jon H. Kaspersen, Knut Waterloo, Bertil Romner, and Tor Ingebrigtsen. “Determination of wall tension in cerebral artery aneurysms by numerical simulation.” Stroke 39, no. 12 (2008): 3172-3178.
 Valen-Sendstad, Kristian, Kent-André Mardal, Mikael Mortensen, Bjørn Anders Pettersson Reif, and Hans Petter Langtangen. “Direct numerical simulation of transitional flow in a patient-specific intracranial aneurysm.” Journal of biomechanics 44, no. 16 (2011): 2826-2832.
 Sforza, D. M., C. M. Putman, E. Scrivano, P. Lylyk, and J. R. Cebral. “Blood-flow characteristics in a terminal basilar tip aneurysm prior to its fatal rupture.” American Journal of Neuroradiology 31, no. 6 (2010): 1127-1131.
 Chien, A., M. A. Castro, S. Tateshima, J. Sayre, J. Cebral, and F. Vinuela. “Quantitative hemodynamic analysis of brain aneurysms at different locations.” American Journal of Neuroradiology 30, no. 8 (2009): 1507-1512.
 Shojima, Masaaki, Marie Oshima, Kiyoshi Takagi, Ryo Torii, Motoharu Hayakawa, Kazuhiro Katada, Akio Morita, and Takaaki Kirino. “Magnitude and role of wall shear stress on cerebral aneurysm: computational fluid dynamic study of 20 middle cerebral artery aneurysms.” Stroke 35, no. 11 (2004): 2500-2505.
 Raschi, Marcelo, Fernando Mut, Greg Byrne, Christopher M. Putman, Satoshi Tateshima, Fernando Viñuela, Tetsuya Tanoue, Kazuo Tanishita, and Juan R. Cebral. “CFD and PIV analysis of hemodynamics in a growing intracranial aneurysm.” International journal for numerical methods in biomedical engineering 28, no. 2 (2012): 214-228.
 Singh, Pankaj K., Alberto Marzo, Bethany Howard, Daniel A. Rufenacht, Philippe Bijlenga, Alejandro F. Frangi, Patricia V. Lawford, Stuart C. Coley, D. Rodney Hose, and Umang J. Patel. “Effects of smoking and hypertension on wall shear stress and oscillatory shear index at the site of intracranial aneurysm formation.” Clinical neurology and neurosurgery 112, no. 4 (2010): 306-313.
 Bowker, T. J., P. N. Watton, P. E. Summers, J. V. Byrne, and Y. Ventikos. “Rest versus exercise hemodynamics for middle cerebral artery aneurysms: a computational study.” American Journal of Neuroradiology 31, no. 2 (2010): 317-323.
 Baek, H., M. V. Jayaraman, P. D. Richardson, and G. E. Karniadakis. “Flow instability and wall shear stress variation in intracranial aneurysms.” Journal of the Royal Society Interface 7, no. 47 (2009): 967-988.
 Jou, Liang-Der, Christopher M. Quick, William L. Young, Michael T. Lawton, Randall Higashida, Alastair Martin, and David Saloner. “Computational approach to quantifying hemodynamic forces in giant cerebral aneurysms.” American Journal of Neuroradiology 24, no. 9 (2003): 1804-1810.
 Hassan, Tamer, Eugene V. Timofeev, Tsutomu Saito, Hiroaki Shimizu, Masayuki Ezura, Yasushi Matsumoto, Kazuyoshi Takayama, Teiji Tominaga, and Akira Takahashi. “A proposed parent vessel geometry—based categorization of saccular intracranial aneurysms: computational flow dynamics analysis of the risk factors for lesion rupture.” Journal of neurosurgery 103, no. 4 (2005): 662-680.
 Ujiie, Hiroshi, Hiroyuki Tachi, Osamu Hiramatsu, Andrew L. Hazel, Takeshi Matsumoto, Yasuo Ogasawara, Hiroshi Nakajima, Tomokatsu Hori, Kintomo Takakura, and Fumihiko Kajiya. “Effects of size and shape (aspect ratio) on the hemodynamics of saccular aneurysms: a possible index for surgical treatment of intracranial aneurysms.” Neurosurgery 45, no. 1 (1999): 119-130.
 Cebral, Juan R., Marcelo Adrián Castro, Sunil Appanaboyina, Christopher M. Putman, Daniel Millan, and Alejandro F. Frangi. “Efficient pipeline for image-based patient-specific analysis of cerebral aneurysm hemodynamics: technique and sensitivity.” IEEE transactions on medical imaging 24, no. 4 (2005): 457-467.
 Beck, J., S. Rohde, M. El Beltagy, M. Zimmermann, J. Berkefeld, V. Seifert, and A. Raabe. “Difference in configuration of ruptured and unruptured intracranial aneurysms determined by biplanar digital subtraction angiography.” Acta neurochirurgica 145, no. 10 (2003): 861-865.
 Forget Jr, Thomas R., Ronald Benitez, Erol Veznedaroglu, Ashwini Sharan, William Mitchell, Marco Silva, and Robert H. Rosenwasser. “A review of size and location of ruptured intracranial aneurysms.” Neurosurgery 49, no. 6 (2001): 1322-1326.
 Raghavan, Madhavan L., Baoshun Ma, and Robert E. Harbaugh. “Quantified aneurysm shape and rupture risk.” Journal of neurosurgery 102, no. 2 (2005): 355-362.
 Rinkel, Gabriel JE, Mamuka Djibuti, Ale Algra, and J. Van Gijn. “Prevalence and risk of rupture of intracranial aneurysms: a systematic review.” Stroke 29, no. 1 (1998): 251-256.
 Weir, Bryce, Lew Disney, and Theodore Karrison. “Sizes of ruptured and unruptured aneurysms in relation to their sites and the ages of patients.” Journal of neurosurgery 96, no. 1 (2002): 64-70.
 ORZ, S. KOBAYASHI, M. OSAWA & Y. TANAKA, Y. “Aneurysm size: a prognostic factor for rupture.” British journal of neurosurgery 11, no. 2 (1997): 144-149.
 Carter, Bob S., Sunil Sheth, Eric Chang, Manish Sethl, and Christopher S. Ogilvy. “Epidemiology of the size distribution of intracranial bifurcation aneurysms: smaller size of distal aneurysms and increasing size of unruptured aneurysms with age.” Neurosurgery 58, no. 2 (2006): 217-223.
 Castro, M. A., C. M. Putman, M. J. Sheridan, and J. R. Cebral. “Hemodynamic patterns of anterior communicating artery aneurysms: a possible association with rupture.” American journal of neuroradiology 30, no. 2 (2009): 297-302.
 Cebral, J. R., M. Sheridan, and C. M. Putman. “Hemodynamics and bleb formation in intracranial aneurysms.” American Journal of Neuroradiology 31, no. 2 (2010): 304-310.
 Molla and Paul, “LES of non-Newtonian physiological blood flow in a model of arterial stenosis”. Medical Engineering & Physics. 34, no. 8 (2012): p. 1079-87.
 Yilmaz, Fuat, and Mehmet Yasar Gundogdu. “A critical review on blood flow in large arteries; relevance to blood rheology, viscosity models, and physiologic conditions.” Korea-Australia Rheology Journal 20, no. 4 (2008): 197-211.
 Husain, I., C. Langdon, and J. Schwark. “Non-Newtonian pulsatile blood flow in a modeled artery with a stenosis and an aneurysm.” Rec. Res. Envi. Geo. Sc: 413-418.
 Fisher, Carolyn, and Jenn Stroud Rossmann. “Effect of non-Newtonian behavior on hemodynamics of cerebral aneurysms.” Journal of biomechanical engineering 131, no. 9 (2009): 091004.
 Perktold, Karl, R. Peter, and Michael Resch. “Pulsatile non-Newtonian blood flow simulation through a bifurcation with an aneurysm.” Biorheology 26, no. 6 (1989): 1011-1030.
 Valencia, Alvaro A., Amador M. Guzmán, Ender A. Finol, and Cristina H. Amon. “Blood flow dynamics in saccular aneurysm models of the basilar artery.” Journal of biomechanical engineering 128, no. 4 (2006): 516-526.
 Steinman, David A. “Assumptions in modelling of large artery hemodynamics.” In Modeling of physiological flows, pp. 1-18. Springer, Milano, 2012.
 Rayz, V. L., L. Boussel, M. T. Lawton, G. Acevedo-Bolton, L. Ge, W. L. Young, R. T. Higashida, and D. Saloner. “Numerical modeling of the flow in intracranial aneurysms: prediction of regions prone to thrombus formation.” Annals of biomedical engineering 36, no. 11 (2008): 1793.
 Arzani, Amirhossein. “Accounting for residence-time in blood rheology models: do we really need non-Newtonian blood flow modelling in large arteries?.” Journal of The Royal Society Interface 15, no. 146 (2018): 20180486.
 Sochi, Taha. “Non-Newtonian rheology in blood circulation.” arXiv preprint arXiv:1306.2067 (2013).
 Sankar, D. S., and Yazariah Yatim. “Comparative analysis of mathematical models for blood flow in tapered constricted arteries.” In Abstract and Applied Analysis, vol. 2012. Hindawi, 2012.
 Madlener, K., B. Frey, and H. K. Ciezki. “Generalized reynolds number for non-newtonian fluids.” Progress in Propulsion Physics 1 (2009): 237-250.
 Passerini, Tiziano, Annalisa Quaini, Umberto Villa, Alessandro Veneziani, and Suncica Canic. “Validation of an open source framework for the simulation of blood flow in rigid and deformable vessels.” International journal for numerical methods in biomedical engineering 29, no. 11 (2013): 1192-1213.
 Mikhal, Julia. “Modeling and simulation of flow in cerebral aneurysms.” University of Twente, Enschede (2012).
 Burleson, Arrmelle C., and Vincent T. Turitto. “Identification of quantifiable hemodynamic factors in the assessment of cerebral aneurysm behavior on behalf of the subcommittee on biorheology of the scientific and standardization committee of the ISTH.” Thrombosis and haemostasis 75, no. 01 (1996): 118-123.
 Gao, Ling, Yiemeng Hoi, Daniel D. Swartz, John Kolega, Adnan Siddiqui, and Hui Meng. “Nascent aneurysm formation at the basilar terminus induced by hemodynamics.” Stroke 39, no. 7 (2008): 2085-2090.
 Morimoto, Masafumi, Susumu Miyamoto, Akira Mizoguchi, Noriaki Kume, Toru Kita, and Nobuo Hashimoto. “Mouse model of cerebral aneurysm: experimental induction by renal hypertension and local hemodynamic changes.” Stroke 33, no. 7 (2002): 1911-1915.
 Shojima, Masaaki, Shigeru Nemoto, Akio Morita, Marie Oshima, Eiju Watanabe, and Nobuhito Saito. “Role of shear stress in the blister formation of cerebral aneurysms.” Neurosurgery 67, no. 5 (2010): 1268-1275.
 Evju, Øyvind, Kristian Valen-Sendstad, and Kent-André Mardal. “A study of wall shear stress in 12 aneurysms with respect to different viscosity models and flow conditions.” Journal of biomechanics 46, no. 16 (2013): 2802-2808.
 Kondo, Soichiro. “Cerebral Aneurysms Arising at Non-branching Sites: An Experimental Study.” Stroke 28, no. 2 (1997): 398.
 Fukuda, Shunichi, Nobuo Hashimoto, Hiroaki Naritomi, Izumi Nagata, Kazuhiko Nozaki, Soichiro Kondo, Michiharu Kurino, and Haruhiko Kikuchi. “Prevention of rat cerebral aneurysm formation by inhibition of nitric oxide synthase.” Circulation 101, no. 21 (2000): 2532-2538.
 Miura, Yoichi, Fujimaro Ishida, Yasuyuki Umeda, Hiroshi Tanemura, Hidenori Suzuki, Satoshi Matsushima, Shinichi Shimosaka, and Waro Taki. “Low wall shear stress is independently associated with the rupture status of middle cerebral artery aneurysms.” Stroke 44, no. 2 (2013): 519-521.
 Meng, H., V. M. Tutino, J. Xiang, and A. Siddiqui. “High WSS or low WSS? Complex interactions of hemodynamics with intracranial aneurysm initiation, growth, and rupture: toward a unifying hypothesis.” American Journal of Neuroradiology 35, no. 7 (2014): 1254-1262.
 Tateshima, S., K. Tanishita, H. Omura, J. P. Villablanca, and F. Vinuela. “Intra-aneurysmal hemodynamics during the growth of an unruptured aneurysm: in vitro study using longitudinal CT angiogram database.” American journal of neuroradiology 28, no. 4 (2007): 622-627.
 Cavazzuti, Marco, Mark Atherton, Michael Collins, and Giovanni Barozzi. “Beyond the virtual intracranial stenting challenge 2007: non-Newtonian and flow pulsatility effects.” Journal of biomechanics 43, no. 13 (2010): 2645-2647.
 Cavazzuti, Marco, M. A. Atherton, M. W. Collins, and Giovanni Sebastiano Barozzi. “Non-Newtonian and flow pulsatility effects in simulation models of a stented intracranial aneurysm.” Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine 225, no. 6 (2011): 597-609.
 Huang, Changsheng, Zhenhua Chai, and Baochang Shi. “Non-newtonian effect on hemodynamic characteristics of blood flow in stented cerebral aneurysm.” Communications in Computational Physics 13, no. 3 (2013): 916-928.
 Bernabeu, Miguel O., Rupert W. Nash, Derek Groen, Hywel B. Carver, James Hetherington, Timm Krüger, and Peter V. Coveney. “Impact of blood rheology on wall shear stress in a model of the middle cerebral artery.” Interface Focus 3, no. 2 (2013): 20120094.
 Carty, Gregory, Surapong Chatpun, and Daniel M. Espino. “Modeling blood flow through intracranial aneurysms: A comparison of Newtonian and non-Newtonian viscosity.” Journal of Medical and Biological Engineering 36, no. 3 (2016): 396-409.
 Bernsdorf, Jörg, and Dinan Wang. “Non-Newtonian blood flow simulation in cerebral aneurysms.” Computers & Mathematics with Applications 58, no. 5 (2009): 1024-1029.
 B Bernsdorf, Jürg, and Dinan Wang. “Blood flow simulation in cerebral aneurysm: A lattice Boltzmann application in medical physics.” In Parallel Computational Fluid Dynamics 2007, pp. 291-296. Springer, Berlin, Heidelberg, 2009.
 Valencia, Alvaro, Alvaro Zarate, Marcelo Galvez, and Lautaro Badilla. “Non?Newtonian blood flow dynamics in a right internal carotid artery with a saccular aneurysm.” International Journal for Numerical Methods in Fluids 50, no. 6 (2006): 751-764.
 Mantha, A., Christof Karmonik, G. Benndorf, C. Strother, and Ralph Metcalfe. “Hemodynamics in a cerebral artery before and after the formation of an aneurysm.” American Journal of Neuroradiology 27, no. 5 (2006): 1113-1118.
 Goodarzi Ardakani, Vahid, Xin Tu, Alberto M. Gambaruto, Iolanda Velho, Jorge Tiago, Adélia Sequeira, and Ricardo Pereira. “Near-Wall Flow in Cerebral Aneurysms.” Fluids 4, no. 2 (2019): 89.
 Gambaruto, Alberto, João Janela, Alexandra Moura, and Adélia Sequeira. “Shear-thinning effects of hemodynamics in patient-specific cerebral aneurysms.” Mathematical biosciences and engineering: MBE 10, no. 3 (2013): 649-665.
 Agrawal, Vishal, Chandan Paul, M. K. Das, and K. Muralidhar. “Effect of coil embolization on blood flow through a saccular cerebral aneurysm.” Sadhana 40, no. 3 (2015): 875-887.
 Schirmer, Clemens M., and Adel M. Malek. “Critical influence of framing coil orientation on intra-aneurysmal and neck region hemodynamics in a sidewall aneurysm model.” Neurosurgery 67, no. 6 (2010): 1692-1702.
 Ahmed, S., I. D. Šutalo, H. Kavnoudias, and A. Madan. “Fluid structure interaction modelling of a patient specific cerebral aneurysm: effect of hypertension and modulus of elasticity.” (2007): 75-81.