Numerical Simulation and Visualization of Newtonian and Non-Newtonian Hemodynamics in a Stenotic Blood Vessel

Document Type : Research Paper

Authors

1 MPESG, Corrosion Lab, 3-08, Aeronautical and Mechanical Engineering Division, University of Salford, M5 4WT, UK

2 Engineering Mechanics Research, Israfil House, Dickenson Rd., Manchester, M13, UK

3 Department of Physics, College of Science, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul 02841, Republic of Korea

4 Material Science Innovation and Modelling (MaSIM) Research Focus Area, North-West University (Mafikeng Campus), Private Bag X2046, Mmabatho 2735, South Africa

Abstract

Cardiovascular disease (CVD) remains the leading cause of mortality worldwide, with atherosclerosis-driven stenoses significantly altering haemodynamic and influencing potential nanoparticle drug delivery outcomes. This study applies computational fluid dynamics (CFD) via ANSYS FLUENT finite volume software, to two-dimensional stenosed arteries of varying severities (30%, 50%, 70%) and shoulder lengths (2, 4, 6 mm). Two regimes have been compared: a steady Newtonian baseline, where viscosity and velocity remain constant and a physiologically realistic pulsatile non-Newtonian Carreau regime incorporating shear-thinning viscosity and cardiac-cycle effects. In the steady Newtonian simulations, velocity plots showed that increasing stenosis severity amplified throat jet velocities and extended recirculation zones, while shoulder length governed the sharpness and spatial extent of disturbed flow. The pulsatile Carreau model revealed systolic acceleration and diastolic deceleration in velocity contour plots, greater pressure drops with stenosis severity. It also showed wall shear stress (WSS) distributions characterised by high shear at stenotic throats and low or oscillatory shear effects downstream. These disturbed, low-WSS regions were identified as potential nanoparticle deposition sites for pharmacodynamics treatments, aligning with prior findings on plaque-prone haemodynamics. The results demonstrate that stenosis severity amplifies haemodynamic disturbances, while shoulder length shapes their distribution, together influencing the likelihood of nanoparticle residence and deposition. These findings are consistent with published literature, supporting CFD as a predictive tool for assessing hemodynamics. Future research could integrate deformable arterial walls through fluid–structure interaction (FSI), patient-specific geometries, and explicit nanoparticle transport for drug delivery in clinical translation.

Keywords

Main Subjects

[1]          W. H. Organization. Cardiovascular diseases (CVDs), Accessed; https://www.who.int/news-room/fact-sheets/detail/cardiovascular-diseases-(cvds). English
[2]          J. Frostegård, Immunity, atherosclerosis and cardiovascular disease, BMC medicine, Vol. 11, No. 1, pp. 117, 2013.
[3]          D. P. Ramji, A. Ismail, J. Chen, F. Alradi, S. Al Alawi, Survey of in vitro model systems for investigation of key cellular processes associated with atherosclerosis,  in: Atherosclerosis: Methods and Protocols, Eds., pp. 39-56: Springer, 2022.
[4]          G. Franck, G. Even, A. Gautier, M. Salinas, A. Loste, E. Procopio, A.-T. Gaston, M. Morvan, S. Dupont, C. Deschildre, Haemodynamic stress-induced breaches of the arterial intima trigger inflammation and drive atherogenesis, European heart journal, Vol. 40, No. 11, pp. 928-937, 2019.
[5]          M. Owais, A. Y. Usmani, K. Muralidhar, Pulsatile flow hemodynamics in stenosed arterial curvatures, Physical Review Fluids, Vol. 10, No. 6, pp. 063101, 2025.
[6]          S. Berger, L.-D. Jou, Flows in stenotic vessels, Annual review of fluid mechanics, Vol. 32, No. 1, pp. 347-382, 2000.
[7]          W. W. Nichols, M. O'Rourke, E. R. Edelman, C. Vlachopoulos, 2022, McDonald’s blood flow in arteries: theoretical, experimental and clinical principles, CRC press,
[8]          D. N. Ku, D. P. Giddens, C. K. Zarins, S. 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., Vol. 5, No. 3, pp. 293-302, 1985.
[9]          S. S. Shibeshi, W. E. Collins, The rheology of blood flow in a branched arterial system, Applied rheology (Lappersdorf, Germany: Online), Vol. 15, No. 6, pp. 398, 2005.
[10]        B. M. Johnston, P. R. Johnston, S. Corney, D. Kilpatrick, Non-Newtonian blood flow in human right coronary arteries: steady state simulations, Journal of biomechanics, Vol. 37, No. 5, pp. 709-720, 2004.
[11]        P. Ballyk, D. Steinman, C. Ethier, Simulation of non-Newtonian blood flow in an end-to-side anastomosis, Biorheology, Vol. 31, No. 5, pp. 565-586, 1994.
[12]        U. Morbiducci, D. Gallo, D. Massai, R. Ponzini, M. A. Deriu, L. Antiga, A. Redaelli, F. M. Montevecchi, On the importance of blood rheology for bulk flow in hemodynamic models of the carotid bifurcation, Journal of biomechanics, Vol. 44, No. 13, pp. 2427-2438, 2011.
[13]        A. Zaman, N. Ali, O. Anwar Bég, Numerical simulation of unsteady micropolar hemodynamics in a tapered catheterized artery with a combination of stenosis and aneurysm, Medical & biological engineering & computing, Vol. 54, No. 9, pp. 1423-1436, 2016.
[14]        B. Vasu, A. Dubey, O. A. Bég, R. S. R. Gorla, Micropolar pulsatile blood flow conveying nanoparticles in a stenotic tapered artery: Non-Newtonian pharmacodynamic simulation, Computers in Biology and Medicine, Vol. 126, pp. 104025, 2020.
[15]        Y. I. Cho, K. R. Kensey, Effects of the non-Newtonian viscosity of blood on flows in a diseased arterial vessel. Part 1: Steady flows, Biorheology, Vol. 28, No. 3-4, pp. 241-262, 1991.
[16]        E. Nader, S. Skinner, M. Romana, R. Fort, N. Lemonne, N. Guillot, A. Gauthier, S. Antoine-Jonville, C. Renoux, M.-D. Hardy-Dessources, Blood rheology: key parameters, impact on blood flow, role in sickle cell disease and effects of exercise, Frontiers in physiology, Vol. 10, pp. 493606, 2019.
[17]        P. K. Mandal, An unsteady analysis of non-Newtonian blood flow through tapered arteries with a stenosis, International journal of non-linear mechanics, Vol. 40, No. 1, pp. 151-164, 2005.
[18]        S. Karimi, M. Dabagh, P. Vasava, M. Dadvar, B. Dabir, P. Jalali, Effect of rheological models on the hemodynamics within human aorta: CFD study on CT image-based geometry, Journal of Non-Newtonian Fluid Mechanics, Vol. 207, pp. 42-52, 2014.
[19]        R. B. Bird, W. E. Stewai, E. N. Lightfoot, Phenomena Second Edition, 2002.
[20]        F. M. White, Fluid mechanics Power, 2011.
[21]        A. FLUENT, ANSYS FLUENT CFD Theory Manual, Theory Guide, 2025.
[22]        M. Khan, H. Sardar, M. M. Gulzar, A. S. Alshomrani, On multiple solutions of non-Newtonian Carreau fluid flow over an inclined shrinking sheet, Results in physics, Vol. 8, pp. 926-932, 2018.
[23]        J. V. Soulis, T. M. Farmakis, G. D. Giannoglou, G. E. Louridas, Wall shear stress in normal left coronary artery tree, Journal of biomechanics, Vol. 39, No. 4, pp. 742-749, 2006.
[24]        M. E. GENDY, O. A. Bég, A. Kadir, M. Islam, D. Tripathi, Computational fluid dynamics simulation and visualization of Newtonian and non-Newtonian transport in a peristaltic micro-pump, Journal of Mechanics in Medicine and Biology, Vol. 21, No. 08, pp. 2150058, 2021.
[25]        N. Ali, Z. Asghar, M. Sajid, O. Anwar Bég, Biological interactions between Carreau fluid and microswimmers in a complex wavy canal with MHD effects, Journal of the Brazilian Society of Mechanical Sciences and Engineering, Vol. 41, No. 10, pp. 446, 2019.
[26]        K. Mamun, M. M. Rahman, M. N. Akhter, M. Ali, Physiological non-Newtonian blood flow through single stenosed artery, in Proceeding of, AIP Publishing LLC, pp. 040001.
[27]        A. M. Gambaruto, J. Janela, A. Moura, A. Sequeira, Shear-thinning effects of hemodynamics in patient-specific cerebral aneurysms, Mathematical biosciences and engineering, Vol. 10, No. 3, pp. 649-665, 2013.
[28]        G. De Nisco, M. L. Rizzini, R. Verardi, C. Chiastra, A. Candreva, G. De Ferrari, F. D'Ascenzo, D. Gallo, U. Morbiducci, Modelling blood flow in coronary arteries: Newtonian or shear-thinning non-Newtonian rheology?, Computer Methods and Programs in Biomedicine, Vol. 242, pp. 107823, 2023.
[29]        A. Sequeira, J. Janela, An overview of some mathematical models of blood rheology, A Portrait of State-of-the-Art Research at the Technical University of Lisbon, pp. 65-87, 2007.
[30]        V. Carvalho, D. Lopes, J. Silva, H. Puga, R. A. Lima, J. C. Teixeira, S. Teixeira, Comparison of CFD and FSI simulations of blood flow in stenotic coronary arteries,  in: Applications of computational fluid dynamics simulation and modeling, Eds.: IntechOpen, 2022.
[31]        S. Kuharat, M. Chaudhry, O. A. Beg, T. A. Bég, Computational hemodynamic simulation of non-Newtonian fluid-structure interaction in a curved stenotic artery, European Mechanical Science, Vol. 8, No. 4, pp. 226-256, 2024.
[32]        R. L. Hewlin Jr, M. Smith, J. P. Kizito, Computational assessment of unsteady flow effects on magnetic nanoparticle targeting efficiency in a magnetic stented carotid bifurcation artery, Cardiovascular Engineering and Technology, Vol. 14, No. 5, pp. 694-712, 2023.
[33]        T. Matoba, J.-i. Koga, K. Nakano, K. Egashira, H. Tsutsui, Nanoparticle-mediated drug delivery system for atherosclerotic cardiovascular disease, Journal of cardiology, Vol. 70, No. 3, pp. 206-211, 2017.
[34]        J. Tan, A. Thomas, Y. Liu, Influence of red blood cells on nanoparticle targeted delivery in microcirculation, Soft matter, Vol. 8, No. 6, pp. 1934-1946, 2012.
[35]        F. Yilmaz, M. Y. Gundogdu, A critical review on blood flow in large arteries; relevance to blood rheology, viscosity models, and physiologic conditions, Korea-Australia Rheology Journal, Vol. 20, No. 4, pp. 197-211, 2008.
[36]        C. G. Caro, 2012, The mechanics of the circulation, Cambridge University Press,
[37]        P. Decuzzi, S. Lee, B. Bhushan, M. Ferrari, A theoretical model for the margination of particles within blood vessels, Annals of biomedical engineering, Vol. 33, No. 2, pp. 179-190, 2005.
[38]        J. Boyd, J. M. Buick, S. Green, Analysis of the Casson and Carreau-Yasuda non-Newtonian blood models in steady and oscillatory flows using the lattice Boltzmann method, Physics of Fluids, Vol. 19, No. 9, 2007.
[39]        G. A. Holzapfel, R. W. Ogden, 2003, Biomechanics of soft tissue in cardiovascular systems, Springer Science & Business Media,
[40]        J. Tripathi, B. Vasu, O. A. Bég, R. S. R. Gorla, Unsteady hybrid nanoparticle-mediated magneto-hemodynamics and heat transfer through an overlapped stenotic artery: Biomedical drug delivery simulation, Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine, Vol. 235, No. 10, pp. 1175-1196, 2021.
[41]        A. Dubey, B. Vasu, O. Anwar Bég, R. S. Gorla, A. Kadir, Computational fluid dynamic simulation of two-fluid non-Newtonian nanohemodynamics through a diseased artery with a stenosis and aneurysm, Computer Methods in Biomechanics and Biomedical Engineering, Vol. 23, No. 8, pp. 345-371, 2020.
[42]        J. Tripathi, B. Vasu, O. A. Bég, Computational simulations of hybrid mediated nano-hemodynamics (Ag-Au/Blood) through an irregular symmetric stenosis, Computers in Biology and Medicine, Vol. 130, pp. 104213, 2021.
Volume 57, Issue 3
July 2026
Pages 443-472
  • Receive Date: 08 April 2026
  • Revise Date: 14 April 2026
  • Accept Date: 16 April 2026