{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,14]],"date-time":"2026-02-14T02:27:35Z","timestamp":1771036055122,"version":"3.50.1"},"reference-count":55,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2022,3,7]],"date-time":"2022-03-07T00:00:00Z","timestamp":1646611200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Fluids"],"abstract":"<jats:p>Intracranial aneurysms (IA) are dilations of the cerebral arteries and, in most cases, have no symptoms. However, it is a very serious pathology, with a high mortality rate after rupture. Several studies have been focused only on the hemodynamics of the flow within the IA. However, besides the effect of the flow, the development and rupture of the IA are also associated with a combination of other factors such as the wall mechanical behavior. Thus, the objective of this work was to analyze, in addition to the flow behavior, the biomechanical behavior of the aneurysm wall. For this, CFD simulations were performed for different Reynolds numbers (1, 100, 500 and 1000) and for two different rheological models (Newtonian and Carreau). Subsequently, the pressure values of the fluid simulations were exported to the structural simulations in order to qualitatively observe the deformations, strains, normal stresses and shear stress generated in the channel wall. For the structural simulations, a hyperelastic constitutive model (5-parameter Mooney\u2013Rivlin) was used. The results show that with the increase in the Reynolds number (Re), the recirculation phenomenon is more pronounced, which is not seen for Re = 1. The higher the Re, the higher the strain, displacement, normal and shear stresses values.<\/jats:p>","DOI":"10.3390\/fluids7030100","type":"journal-article","created":{"date-parts":[[2022,3,7]],"date-time":"2022-03-07T10:21:16Z","timestamp":1646648476000},"page":"100","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Fluid Flow and Structural Numerical Analysis of a Cerebral Aneurysm Model"],"prefix":"10.3390","volume":"7","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4415-7267","authenticated-orcid":false,"given":"Maria Sabrina","family":"Souza","sequence":"first","affiliation":[{"name":"Instituto Polit\u00e9cnico de Bragan\u00e7a, ESTiG, C. Sta. Apol\u00f3nia, 5300-253 Bragan\u00e7a, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2414-073X","authenticated-orcid":false,"given":"Andrews","family":"Souza","sequence":"additional","affiliation":[{"name":"Mechanical Engineering and Resource Sustainability Center (MEtRICs), University of Minho, Campus de Azur\u00e9m, 4800-058 Guimar\u00e3es, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9447-4746","authenticated-orcid":false,"given":"Violeta","family":"Carvalho","sequence":"additional","affiliation":[{"name":"Mechanical Engineering and Resource Sustainability Center (MEtRICs), University of Minho, Campus de Azur\u00e9m, 4800-058 Guimar\u00e3es, Portugal"},{"name":"ALGORITMI Research Centre, University of Minho, Campus de Azur\u00e9m, 4800-058 Guimar\u00e3es, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7464-3944","authenticated-orcid":false,"given":"Senhorinha","family":"Teixeira","sequence":"additional","affiliation":[{"name":"ALGORITMI Research Centre, University of Minho, Campus de Azur\u00e9m, 4800-058 Guimar\u00e3es, Portugal"}]},{"given":"Carla S.","family":"Fernandes","sequence":"additional","affiliation":[{"name":"Instituto Polit\u00e9cnico de Bragan\u00e7a, ESTiG, C. Sta. Apol\u00f3nia, 5300-253 Bragan\u00e7a, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3428-637X","authenticated-orcid":false,"given":"Rui","family":"Lima","sequence":"additional","affiliation":[{"name":"Mechanical Engineering and Resource Sustainability Center (MEtRICs), University of Minho, Campus de Azur\u00e9m, 4800-058 Guimar\u00e3es, Portugal"},{"name":"Transport Phenomena Research Center (CEFT), Faculdade de Engenharia da Universidade do Porto (FEUP), R. Dr. Roberto Frias, 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6300-148X","authenticated-orcid":false,"given":"Jo\u00e3o","family":"Ribeiro","sequence":"additional","affiliation":[{"name":"Instituto Polit\u00e9cnico de Bragan\u00e7a, ESTiG, C. Sta. Apol\u00f3nia, 5300-253 Bragan\u00e7a, Portugal"},{"name":"Centro de Investiga\u00e7\u00e3o de Montanha (CIMO), Instituto Polit\u00e9cnico de Bragan\u00e7a, 5300-252 Bragan\u00e7a, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2022,3,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2536","DOI":"10.1161\/01.STR.0000034708.66191.7D","article-title":"Recommendations for the endovascular treatment of intracranial aneurysms: A statement for healthcare professionals from the Committee on Cerebrovascular Imaging of the American Heart Association Council on Cardiovascular Radiology","volume":"33","author":"Johnston","year":"2002","journal-title":"Stroke"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1056\/NEJM199701023360106","article-title":"Intracranial Aneurysms","volume":"336","author":"Schievink","year":"1997","journal-title":"N. Engl. J. Med."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2368","DOI":"10.1161\/STR.0000000000000070","article-title":"Guidelines for the Management of Patients With Unruptured Intracranial Aneurysms: A Guideline for Healthcare Professionals From the American Heart Association\/American Stroke Association","volume":"46","author":"Thompson","year":"2015","journal-title":"Stroke"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"693","DOI":"10.1227\/NEU.0b013e3182354d68","article-title":"Analysis of nonmodifiable risk factors for intracranial aneurysm rupture in a large, retrospective cohort","volume":"70","author":"Amenta","year":"2012","journal-title":"Neurosurgery"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1146\/annurev.fluid.39.050905.110128","article-title":"The Biomechanics of Arterial Aneurysms","volume":"39","author":"Lasheras","year":"2007","journal-title":"Annu. Rev. Fluid Mech."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"597","DOI":"10.3109\/07853890.2014.949299","article-title":"Molecular basis and genetic predisposition to intracranial aneurysm","volume":"46","author":"Tromp","year":"2014","journal-title":"Ann. Med."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"850","DOI":"10.1016\/j.molmed.2017.07.007","article-title":"Molecular Sensors of Blood Flow in Endothelial Cells","volume":"23","author":"Baratchi","year":"2017","journal-title":"Trends Mol. Med."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Hoskins, P.R., Lawford, P.V., and Doyle, B.J. (2017). Cardiovascular Biomechanics, Springer.","DOI":"10.1007\/978-3-319-46407-7"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1366","DOI":"10.1007\/s10439-012-0723-0","article-title":"Suggested connections between risk factors of intracranial aneurysms: A review","volume":"41","author":"Cebral","year":"2013","journal-title":"Ann. Biomed. Eng."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1098\/rsif.2005.0073","article-title":"Hyperelastic modelling of arterial layers with distributed collagen fibre orientations","volume":"3","author":"Gasser","year":"2006","journal-title":"J. R. Soc. Interface"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.24243\/JMEB\/4.1.163","article-title":"Study of PDMS characterization and its applications in biomedicine: A review","volume":"4","author":"Victor","year":"2019","journal-title":"J. Mech. Eng. Biomech."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Ariati, R., Sales, F., Souza, A., Lima, R.A., and Ribeiro, J. (2021). Polydimethylsiloxane Composites Characterization and Its Applications: A Review. Polymers, 13.","DOI":"10.3390\/polym13234258"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1136\/neurintsurg-2018-013921","article-title":"Comparison of intracranial aneurysm flow quantification techniques: Standard PIV vs. stereoscopic PIV vs. tomographic PIV vs. phase-contrast MRI vs. CFD","volume":"11","author":"Roloff","year":"2019","journal-title":"J. Neurointerv. Surg."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"e3207","DOI":"10.1002\/cnm.3207","article-title":"Geometrical effects in the hemodynamics of stenotic and non-stenotic left coronary arteries\u2014numerical and in vitro approaches","volume":"35","author":"Doutel","year":"2019","journal-title":"Int. J. Numer. Method. Biomed. Eng."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"103535","DOI":"10.1016\/j.mechrescom.2020.103535","article-title":"3D manufacturing of intracranial aneurysm biomodels for flow visualizations: Low cost fabrication processes","volume":"107","author":"Souza","year":"2020","journal-title":"Mech. Res. Commun."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3120","DOI":"10.1016\/j.jbiomech.2014.06.025","article-title":"Fluid dynamics of aortic root dilation in Marfan syndrome","volume":"47","author":"Querzoli","year":"2014","journal-title":"J. Biomech."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00348-016-2221-x","article-title":"A laboratory model of the aortic root flow including the coronary arteries","volume":"57","author":"Querzoli","year":"2016","journal-title":"Exp. Fluids"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00348-020-02998-4","article-title":"Effects of wall compliance on multiharmonic pulsatile flow in idealized cerebral aneurysm models: Comparative PIV experiments","volume":"61","author":"Tupin","year":"2020","journal-title":"Exp. Fluids"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1016\/j.measurement.2016.03.045","article-title":"Wall expansion assessment of an intracranial aneurysm model by a 3D Digital Image Correlation System","volume":"88","author":"Rodrigues","year":"2016","journal-title":"Measurement"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"87","DOI":"10.2174\/1874120702014010087","article-title":"In vitro stenotic arteries to perform blood analogues flow visualizations and measurements: A Review","volume":"14","author":"Carvalho","year":"2020","journal-title":"Open Biomed. Eng. J."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Carvalho, V., Gon\u00e7alves, I., Lage, T., Rodrigues, R.O., Minas, G., Teixeira, S.F.C.F., Moita, A.S., Hori, T., Kaji, H., and Lima, R.A. (2021). 3D printing techniques and their applications to organ-on-a-chip platforms: A systematic review. Sensors, 21.","DOI":"10.3390\/s21093304"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"117725","DOI":"10.1016\/j.applthermaleng.2021.117725","article-title":"Recent advances on the thermal properties and applications of nanofluids: From nanomedicine to renewable energies","volume":"201","author":"Souza","year":"2022","journal-title":"Appl. Therm. Eng."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Sadek, S.H., Rubio, M., Lima, R., and Vega, E.J. (2021). Blood particulate analogue fluids: A review. Materials, 14.","DOI":"10.3390\/ma14092451"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Pinho, D., Carvalho, V., Gon\u00e7alves, I.M., Teixeira, S., and Lima, R. (2020). Visualization and measurements of blood cells flowing in microfluidic systems and blood rheology: A personalized medicine perspective. J. Pers. Med., 10.","DOI":"10.3390\/jpm10040249"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Faustino, V., Rodrigues, R.O., Pinho, D., Costa, E., Santos-Silva, A., Miranda, V., Amaral, J.S., and Lima, R. (2019). A microfluidic deformability assessment of pathological red blood cells flowing in a hyperbolic converging microchannel. Micromachines, 10.","DOI":"10.3390\/mi10100645"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1016\/j.mechrescom.2019.103399","article-title":"Flexible PDMS microparticles to mimic RBCs in blood particulate analogue fluids","volume":"100","author":"Pinho","year":"2019","journal-title":"Mech. Res. Commun."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"67","DOI":"10.24840\/2183-6493_001.001_0007","article-title":"Polymer microfluidic devices: An overview of fabrication methods","volume":"1","author":"Rodrigues","year":"2015","journal-title":"U. Porto J. Eng."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Miranda, I., Souza, A., Sousa, P., Ribeiro, J., Castanheira, E.M.S., Lima, R., and Minas, G. (2022). Properties and Applications of PDMS for Biomedical Engineering: A Review. J. Funct. Biomater., 13.","DOI":"10.3390\/jfb13010002"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1805","DOI":"10.1007\/s11548-019-02036-7","article-title":"Flow-splitting-based computation of outlet boundary conditions for improved cerebrovascular simulation in multiple intracranial aneurysms","volume":"14","author":"Saalfeld","year":"2019","journal-title":"Int. J. Comput. Assist. Radiol. Surg."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"676","DOI":"10.3171\/jns.2004.101.4.0676","article-title":"Effects of arterial geometry on aneurysm growth: Three-dimensional computational fluid dynamics study","volume":"101","author":"Hoi","year":"2004","journal-title":"J. Neurosurg."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Carvalho, V., Pinho, D., Lima, R.A., Teixeira, J.C., and Teixeira, S. (2021). Blood Flow Modeling in Coronary Arteries: A Review. Fluids, 6.","DOI":"10.3390\/fluids6020053"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"011011","DOI":"10.1115\/1.4050981","article-title":"Numerical modeling of the wave soldering process and experimental validation","volume":"144","author":"Carvalho","year":"2021","journal-title":"J. Electron. Packag.\u2014ASME"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Carvalho, V., Carneiro, F., Ferreira, A.C., Gama, V., Teixeira, J.C., and Teixeira, S. (2021). Numerical study of the unsteady flow in simplified and realistic iliac bifurcation models. Fluids, 6.","DOI":"10.3390\/fluids6080284"},{"key":"ref_34","first-page":"1998","article-title":"Modeling blood pulsatile turbulent flow in stenotic coronary arteries","volume":"14","author":"Carvalho","year":"2020","journal-title":"Int. J. Biol. Biomed. Eng."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"550","DOI":"10.1016\/j.jbiomech.2008.10.006","article-title":"Can temporal fluctuation in spatial wall shear stress gradient initiate a cerebral aneurysm? A proposed novel hemodynamic index, the gradient oscillatory number (GON)","volume":"42","author":"Shimogonya","year":"2009","journal-title":"J. Biomech."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"723","DOI":"10.3171\/2016.10.JNS161695","article-title":"Impact of bifurcation angle and inflow coefficient on the rupture risk of bifurcation type basilar artery tip aneurysms","volume":"128","author":"Rashad","year":"2018","journal-title":"J. Neurosurg."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1021","DOI":"10.1177\/0271678X19854640","article-title":"What does computational fluid dynamics tell us about intracranial aneurysms? A meta-analysis and critical review","volume":"40","author":"Saqr","year":"2019","journal-title":"J. Cereb. Blood Flow Metab."},{"key":"ref_38","first-page":"63","article-title":"Computational Simulation of Therapeutic Parent Artery Occlusion to Treat Giant Vertebrobasilar Aneurysm","volume":"25","author":"Hassan","year":"2004","journal-title":"AJNR Am. J. Neuroradiol."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1615\/InterJEnerCleanEnv.2018020888","article-title":"Hemodynamics of a cerebral aneurysm under rest and exercise conditions","volume":"19","author":"Usmani","year":"2018","journal-title":"Int. J. Energy Clean Environ."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"109590","DOI":"10.1016\/j.jbiomech.2019.109590","article-title":"A pilot validation of CFD model results against PIV observations of haemodynamics in intracranial aneurysms treated with flow-diverting stents","volume":"100","author":"Li","year":"2019","journal-title":"J. Biomech."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"3846","DOI":"10.1016\/j.jbiomech.2015.09.039","article-title":"An automatic CFD-based flow diverter optimization principle for patient-specific intracranial aneurysms","volume":"48","author":"Janiga","year":"2015","journal-title":"J. Biomech."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Carvalho, V., Rodrigues, N., Lima, R.A., and Teixeira, S. (2020, January 19\u201322). Numerical simulation of blood pulsatile flow in stenotic coronary arteries: The effect of turbulence modeling and non-Newtonian assumptions. Proceedings of the International Conference on Applied Mathematics & Computer Science, Chania, Greece.","DOI":"10.1109\/CSCC49995.2020.00027"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1002\/fld.1590","article-title":"Computational fluid dynamics of stented intracranial aneurysms using adaptive embedded unstructured grids","volume":"57","author":"Appanaboyina","year":"2008","journal-title":"Int. J. Numer. Methods Fluids"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"144","DOI":"10.1161\/STROKEAHA.110.592923","article-title":"Hemodynamic-morphologic discriminants for intracranial aneurysm rupture","volume":"42","author":"Xiang","year":"2011","journal-title":"Stroke"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1411","DOI":"10.1007\/s10439-012-0695-0","article-title":"High wall shear stress and spatial gradients in vascular pathology: A review","volume":"41","author":"Dolan","year":"2013","journal-title":"Ann. Biomed. Eng."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"1949","DOI":"10.1016\/j.jbiomech.2004.09.030","article-title":"Molecular basis of the effects of shear stress on vascular endothelial cells","volume":"38","author":"Li","year":"2005","journal-title":"J. Biomech."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"7827","DOI":"10.1002\/jcp.29436","article-title":"Epigenetic response of endothelial cells to different wall shear stress magnitudes: A report of new mechano-miRNAs","volume":"235","author":"Rashad","year":"2020","journal-title":"J. Cell. Physiol."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"349","DOI":"10.3233\/THC-161135","article-title":"Effect of elasticity on wall shear stress inside cerebral aneurysm at anterior cerebral artery","volume":"24","author":"Xu","year":"2016","journal-title":"Technol. Heal. Care."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"582","DOI":"10.1063\/1.1712836","article-title":"A theory of large elastic deformation","volume":"11","author":"Mooney","year":"1940","journal-title":"J. Appl. Phys."},{"key":"ref_50","unstructured":"Lawrence, K.L. (2012). ANSYS Workbench Tutorial Release 14, SDC Publications."},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Chen, X., and Liu, Y. (2014). Finite Element Modeling and Simulation with ANSYS Workbench, CRC Press.","DOI":"10.1201\/b17284"},{"key":"ref_52","first-page":"1079","article-title":"An Analysis of the Geometry of Saccular Intracranial Aneurysms","volume":"20","author":"Parlea","year":"1999","journal-title":"AJNR Am. J. Neuroradiol"},{"key":"ref_53","unstructured":"Bird, R.B., Armstrong, R.C., and Hassager, O. (1987). Dynamic of Polymeric Liquids, John Willey & Sons."},{"key":"ref_54","unstructured":"\u00c7engel, Y.A., and Ghajar, A.J. (2012). Heat and Mass Transfer, Mc. Graw Hill. [4th ed.]."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1016\/j.mechrescom.2018.04.007","article-title":"Biomechanical analysis of PDMS channels using different hyperelastic numerical constitutive models","volume":"90","author":"Cardoso","year":"2018","journal-title":"Mech. Res. Commun."}],"container-title":["Fluids"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2311-5521\/7\/3\/100\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:33:33Z","timestamp":1760135613000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2311-5521\/7\/3\/100"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,3,7]]},"references-count":55,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2022,3]]}},"alternative-id":["fluids7030100"],"URL":"https:\/\/doi.org\/10.3390\/fluids7030100","relation":{},"ISSN":["2311-5521"],"issn-type":[{"value":"2311-5521","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,3,7]]}}}