{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,8]],"date-time":"2026-10-08T06:26:38Z","timestamp":1791440798316,"version":"4.3.3"},"reference-count":45,"publisher":"Public Library of Science (PLoS)","issue":"4","license":[{"start":{"date-parts":[[2025,4,8]],"date-time":"2025-04-08T00:00:00Z","timestamp":1744070400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.plosone.org"],"crossmark-restriction":false},"short-container-title":["PLoS ONE"],"abstract":"<jats:p>This study investigates the influence of varying degrees of stenosis on blood flow within elliptic arteries, emphasizing the critical role of artery shape in clinical evaluations as opposed to the commonly studied circular arteries. Unlike prior work, this research offers a precise definition of stenosis by incorporating the measured length, height, and position of the narrowing. Employing the non-Newtonian Williamson fluid model, we conducted comprehensive numerical simulations to examine blood flow through four distinct stenosis formations. The novelty of this work lies in its accurate modeling of stenosis and use of advanced mesh generation, combined with commercial software and the finite volume method, to capture detailed hemodynamic behavior. Visualized results, including pressure profiles, velocity line graphs, and streamlines, further underscore the distinctive flow dynamics shaped by the elliptic geometry. Key findings of the obtained results reveal that blood velocity peaks near the stenosis and drops significantly post-stenosis, with notable variations in flow patterns, energy loss, and pressure distribution across different stenosis types. Further, higher velocity of blood flow is observed in elliptic arteries in comparison with circular ones. In the area of the high corners of stenotic segments, the pressure profile reaches high values. As a result of the narrowing of the arterial cross-section, the varied time shows that the post-stenotic segment of the artery has a higher pressure than the pre-stenotic section. The varied time suggests that an axially symmetric profile will eventually be the norm for the flow within the arterial portion. These insights have profound implications for improving clinical diagnosis and treatment strategies for conditions related to stenosed elliptic arteries.<\/jats:p>","DOI":"10.1371\/journal.pone.0317989","type":"journal-article","created":{"date-parts":[[2025,4,8]],"date-time":"2025-04-08T14:34:41Z","timestamp":1744122881000},"page":"e0317989","update-policy":"https:\/\/doi.org\/10.1371\/journal.pone.corrections_policy","source":"Crossref","is-referenced-by-count":14,"title":["Modeling and simulation of blood flow in unhealthy elliptic arteries with computational fluid dynamics approach"],"prefix":"10.1371","volume":"20","author":[{"given":"Abdul","family":"Wahab","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Muhammad Imran","family":"Asjad","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Muhammad Bilal","family":"Riaz","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7008-8576","authenticated-orcid":true,"given":"Jamil Abbas","family":"Haider","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"340","published-online":{"date-parts":[[2025,4,8]]},"reference":[{"issue":"4","key":"pone.0317989.ref001","doi-asserted-by":"crossref","first-page":"B61","DOI":"10.1115\/1.1483340","article-title":"Fundamentals of computational fluid dynamics","volume":"55","author":"H Lomax","year":"2002","journal-title":"Appl Mech Rev."},{"issue":"1","key":"pone.0317989.ref002","doi-asserted-by":"crossref","first-page":"010803","DOI":"10.1115\/1.4042820","article-title":"Discrete energy-conservation properties in the numerical simulation of the Navier\u2013Stokes equations","volume":"71","author":"G Coppola","year":"2019","journal-title":"Appl Mech Rev."},{"key":"pone.0317989.ref003","first-page":"1","article-title":"Governing equations in computational fluid dynamics: derivations and a recent review","volume":"1","author":"WY Tey","year":"2017","journal-title":"Prog Energy Environ."},{"issue":"2","key":"pone.0317989.ref004","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1080\/10407799608914980","article-title":"Incompressible computational fluid dynamics and the continuity constraint method for the three-dimensional navier-stokes equations","volume":"29","author":"PT Williams","year":"1996","journal-title":"Numer Heat Transf Part B: Fundament"},{"issue":"5\u20136","key":"pone.0317989.ref005","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1016\/S0376-0421(00)00005-1","article-title":"Elements of computational fluid dynamics on block structured grids using implicit solvers","volume":"36","author":"KJ Badcock","year":"2000","journal-title":"Prog Aerosp Sci."},{"issue":"1","key":"pone.0317989.ref006","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0021-9991(91)90291-R","article-title":"A locally refined rectangular grid finite element method: application to computational fluid dynamics and computational physics","volume":"92","author":"DP Young","year":"1991","journal-title":"J Comput Phys"},{"key":"pone.0317989.ref007","doi-asserted-by":"crossref","first-page":"218","DOI":"10.1016\/j.compfluid.2014.09.031","article-title":"Velocity-distribution in pressurized pipe flow using CFD: accuracy and mesh analysis","volume":"105","author":"NMC Martins","year":"2014","journal-title":"Comput Fluids"},{"issue":"11","key":"pone.0317989.ref008","doi-asserted-by":"crossref","first-page":"2996","DOI":"10.1002\/aic.11301","article-title":"A computational model for temperature and sterility distributions in a pilot\u2010scale high\u2010pressure high\u2010temperature process","volume":"53","author":"K Knoerzer","year":"2007","journal-title":"AIChE J"},{"issue":"23\u201324","key":"pone.0317989.ref009","doi-asserted-by":"crossref","first-page":"4883","DOI":"10.1016\/j.ijheatmasstransfer.2007.01.062","article-title":"Influence of pulsatile blood flow and heating scheme on the temperature distribution during hyperthermia treatment","volume":"50","author":"K Khanafer","year":"2007","journal-title":"Int J Heat Mass Transf."},{"issue":"1","key":"pone.0317989.ref010","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1146\/annurev-fluid-120720-124800","article-title":"A perspective on the state of aerospace computational fluid dynamics technology","volume":"55","author":"M Mani","year":"2023","journal-title":"Annu Rev Fluid Mech"},{"issue":"8","key":"pone.0317989.ref011","doi-asserted-by":"crossref","first-page":"423","DOI":"10.4070\/kcj.2011.41.8.423","article-title":"Computational fluid dynamics in cardiovascular disease","volume":"41","author":"B-K Lee","year":"2011","journal-title":"Korean Circ J"},{"key":"pone.0317989.ref012","doi-asserted-by":"crossref","first-page":"104099","DOI":"10.1016\/j.compbiomed.2020.104099","article-title":"The effect of airway motion and breathing phase during imaging on CFD simulations of respiratory airflow","volume":"127","author":"CC Gunatilaka","year":"2020","journal-title":"Comput Biol Med"},{"issue":"2","key":"pone.0317989.ref013","first-page":"547","article-title":"Numerical modeling and optimization of respirational emergency drug delivery device using computational fluid dynamics and response surface method","volume":"34","author":"M Yousefi","year":"2021","journal-title":"Int J Eng."},{"issue":"10","key":"pone.0317989.ref014","doi-asserted-by":"crossref","first-page":"1235","DOI":"10.1016\/j.medengphy.2009.08.001","article-title":"Mesh morphing for finite element analysis of implant positioning in cementless total hip replacements","volume":"31","author":"MT Bah","year":"2009","journal-title":"Med Eng Phys"},{"issue":"4","key":"pone.0317989.ref015","doi-asserted-by":"crossref","first-page":"1370","DOI":"10.1109\/TBME.2020.3030316","article-title":"CFD assisted evaluation of in vitro experiments on bearingless blood pumps","volume":"68","author":"P Puentener","year":"2021","journal-title":"IEEE Trans Biomed Eng"},{"key":"pone.0317989.ref016","author":"CC Botar"},{"issue":"2","key":"pone.0317989.ref017","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1109\/TBME.2006.886853","article-title":"Cerebrospinal fluid flow in the normal and hydrocephalic human brain","volume":"54","author":"AA Linninger","year":"2007","journal-title":"IEEE Trans Biomed Eng"},{"issue":"1","key":"pone.0317989.ref018","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1080\/02656736.2018.1506164","article-title":"Clinical validation of a novel thermophysical bladder model designed to improve the accuracy of hyperthermia treatment planning in the pelvic region","volume":"35","author":"G Schooneveldt","year":"2018","journal-title":"Int J Hyperthermia"},{"issue":"6","key":"pone.0317989.ref019","doi-asserted-by":"crossref","first-page":"1532","DOI":"10.1109\/TBME.2012.2187448","article-title":"Phantom model of physiologic intracranial pressure and cerebrospinal fluid dynamics","volume":"59","author":"S Bottan","year":"2012","journal-title":"IEEE Trans Biomed Eng"},{"key":"pone.0317989.ref020","article-title":"Quantitative analysis of hemodynamic state and muscle atrophy of residual limb after trans-femoral amputation","author":"R Dong","year":"2018"},{"key":"pone.0317989.ref021","doi-asserted-by":"crossref","first-page":"106650","DOI":"10.1016\/j.ijmecsci.2021.106650","article-title":"Analysis of finite element and finite volume methods for fluid-structure interaction simulation of blood flow in a real stenosed artery","volume":"207","author":"D Lopes","year":"2021","journal-title":"Int J Mech Sci"},{"issue":"12","key":"pone.0317989.ref022","doi-asserted-by":"crossref","first-page":"2098","DOI":"10.1063\/1.1693841","article-title":"Numerical solution of the Navier-Stokes equations by the finite element method","volume":"15","author":"RT Cheng","year":"1972","journal-title":"Phys Fluids"},{"issue":"4","key":"pone.0317989.ref023","first-page":"434","article-title":"Fast virtual fractional flow reserve based upon steady-state computational fluid dynamics analysis: results from the VIRTU-Fast study","volume":"2","author":"PD Morris","year":"2017","journal-title":"Basic Transl Sci."},{"issue":"15","key":"pone.0317989.ref024","doi-asserted-by":"crossref","first-page":"1578","DOI":"10.1177\/2047487316645469","article-title":"Translational and emerging clinical applications of metabolomics in cardiovascular disease diagnosis and treatment","volume":"23","author":"AC Dona","year":"2016","journal-title":"Eur J Prev Cardiol"},{"issue":"2","key":"pone.0317989.ref025","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1136\/hrt.45.2.157","article-title":"Non-invasive estimation of pulmonary artery systolic pressure with Doppler ultrasound","volume":"45","author":"L Hatle","year":"1981","journal-title":"Br Heart J"},{"issue":"1","key":"pone.0317989.ref026","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1053\/j.tvir.2014.12.002","article-title":"Computed tomography angiography and magnetic resonance angiography imaging of the mesenteric vasculature","volume":"18","author":"KD Hagspiel","year":"2015","journal-title":"Tech Vasc Interv Radiol"},{"key":"pone.0317989.ref027"},{"issue":"11","key":"pone.0317989.ref028","first-page":"740","article-title":"Stent placement compared with balloon angioplasty for obstructed coronary bypass grafts","volume":"337","author":"MP Savage","year":"1997","journal-title":"Saphenous Vein De Novo Trial Investigators. N Engl J Med"},{"key":"pone.0317989.ref029","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1016\/j.aej.2024.06.037","article-title":"Numerical simulations of energy storage performance in a close configuration: a Galerkin finite element-based computation","volume":"104","author":"AH Majeed","year":"2024","journal-title":"Alexandria Eng J"},{"issue":"26","key":"pone.0317989.ref030","doi-asserted-by":"crossref","first-page":"2450248","DOI":"10.1142\/S0217984924502488","article-title":"Finite element simulations of Herschel\u2013Bulkley visco-plastic materials over a cylinder: drag and lift correlation analysis","volume":"38","author":"AH Majeed","year":"2024","journal-title":"Mod Phys Lett B"},{"issue":"15","key":"pone.0317989.ref031","doi-asserted-by":"crossref","first-page":"2450184","DOI":"10.1142\/S0217979224501844","article-title":"Numerical study of hydrodynamic forces of nonlinear fluid flow in a channel-driven cavity: finite element-based simulation","volume":"38","author":"R Mahmood","year":"2024","journal-title":"Int J Mod Phys B."},{"issue":"3","key":"pone.0317989.ref032","doi-asserted-by":"crossref","DOI":"10.1063\/5.0189237","article-title":"Finite element simulations of double diffusion in a staggered cavity filled with a power-law fluid","volume":"36","author":"AH Majeed","year":"2024","journal-title":"Phys Fluids"},{"key":"pone.0317989.ref033","doi-asserted-by":"crossref","first-page":"103827","DOI":"10.1016\/j.csite.2023.103827","article-title":"Flow and heat transfer analysis over a pair of heated bluff bodies in a channel: characteristics of non-linear rheological models","volume":"53","author":"AH Majeed","year":"2024","journal-title":"Case Stud Thermal Eng"},{"issue":"2","key":"pone.0317989.ref034","first-page":"47","article-title":"Dynamic response of heat and mass transfer in blood flow through stenosed bifurcated arteries","volume":"17","author":"S Chakravarty","year":"2005","journal-title":"Korea-Australia Rheol J."},{"issue":"5","key":"pone.0317989.ref035","doi-asserted-by":"crossref","first-page":"760","DOI":"10.1093\/ndt\/gfz053","article-title":"Cardiovascular disease in the kidney transplant recipient: epidemiology, diagnosis and management strategies","volume":"34","author":"J Rangaswami","year":"2019","journal-title":"Nephrol Dial Transplant"},{"key":"pone.0317989.ref036","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1016\/j.aej.2023.02.005","article-title":"Numerical computations of blood flow through stenosed arteries via CFD tool OpenFOAM","volume":"69","author":"S Nadeem","year":"2023","journal-title":"Alexandria Eng J"},{"key":"pone.0317989.ref037","doi-asserted-by":"crossref","first-page":"113550","DOI":"10.1016\/j.molliq.2020.113550","article-title":"Numerical investigation of hematocrit variation effect on blood flow in an arterial segment with variable stenosis degree","volume":"313","author":"A Elhanafy","year":"2020","journal-title":"J Molecul Liquids"},{"key":"pone.0317989.ref038","doi-asserted-by":"crossref","first-page":"105434","DOI":"10.1016\/j.cmpb.2020.105434","article-title":"Numerical investigation of non-Newtonian blood flow within an artery with cone shape of stenosis in various stenosis angles","volume":"192","author":"S-R Yan","year":"2020","journal-title":"Comput Methods Programs Biomed"},{"key":"pone.0317989.ref039"},{"key":"pone.0317989.ref040"},{"key":"pone.0317989.ref041"},{"issue":"2","key":"pone.0317989.ref042","doi-asserted-by":"crossref","first-page":"368504231180092","DOI":"10.1177\/00368504231180092","article-title":"CFD analysis on blood flow inside a symmetric stenosed artery: physiology of a coronary artery disease","volume":"106","author":"S Akhtar","year":"2023","journal-title":"Sci Prog"},{"key":"pone.0317989.ref043","doi-asserted-by":"crossref","first-page":"991","DOI":"10.1016\/j.jmmm.2015.11.022","article-title":"MHD flow of Cattanneo\u2013Christov heat flux model for Williamson fluid over a stretching sheet with variable thickness: using numerical approach","volume":"401","author":"T Salahuddin","year":"2016","journal-title":"J Magnetism Magnet Mater"},{"issue":"8","key":"pone.0317989.ref044","doi-asserted-by":"crossref","first-page":"1005","DOI":"10.1007\/s13204-013-0282-1","article-title":"Flow and heat transfer analysis of Williamson nanofluid","volume":"4","author":"S Nadeem","year":"2013","journal-title":"Appl Nanosci"},{"issue":"3","key":"pone.0317989.ref045","doi-asserted-by":"crossref","first-page":"172","DOI":"10.37934\/arfmts.87.3.172183","article-title":"Effect of different types of stenosis on generalized power law model of blood flow in a bifurcated artery","volume":"87","author":"MSA Jamali","year":"2021","journal-title":"ARFMTS"}],"container-title":["PLOS ONE"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pone.0317989","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,8]],"date-time":"2025-04-08T14:35:54Z","timestamp":1744122954000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pone.0317989"}},"subtitle":[],"editor":[{"given":"Mohsen","family":"Mehrabi","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"editor"}]}],"short-title":[],"issued":{"date-parts":[[2025,4,8]]},"references-count":45,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2025,4,8]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pone.0317989","relation":{},"ISSN":["1932-6203"],"issn-type":[{"value":"1932-6203","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,4,8]]}}}