Influence of Wall Compliance on Flow Dynamics in Stenosed Channels: An Immersed Boundary Method Study

Document Type : Research Paper

Authors
A. Fahim 1
S. Anish 1
R. Maniyeri 2
1 Advanced Fluid Mechanics Laboratory, Department of Mechanical Engineering, National Institute of Technology Karnataka (NITK), Surathkal, Mangalore-575025, Karnataka, India
2 Biophysics Laboratory, Department of Mechanical Engineering, National Institute of Technology Karnataka (NITK), Surathkal, Mangalore-575025, Karnataka, India
10.22055/jacm.2025.48540.5311
Abstract
Understanding the hemodynamics of stenosed arteries is essential for evaluating cardiovascular function and informing clinical interventions. This study investigates pulsatile flow through two-sided collapsible channels simulating arterial stenosis using a fluid–structure interaction (FSI) framework. A finite volume solver based on the immersed boundary method is employed to capture the coupled dynamics between pulsatile flow and compliant channel walls under physiologically realistic conditions. Simulations are conducted for stenosis severities of 25%, 50%, and 75%, across heart rates of 60, 100, and 150 beats per minute (BPM), with comparative analysis between rigid and flexible wall configurations. In the compliant models, wall displacement is most pronounced at the stenosis throat due to pulsatile pressure loading, leading to dynamic lumen reshaping. This deformation produces broader, flattened velocity jets compared to the narrow, high-speed jets observed in rigid-wall cases. Notably, flexible wall configurations exhibit pre-stenotic flow reversal during the diastolic phase, resulting in early recirculation zones that are absent in their rigid counterparts. In rigid models, the peak time-averaged wall shear stress (TAWSS) arises sharply just upstream of the stenosis, whereas in flexible walls, it shifts slightly downstream and is reduced due to the presence of persistent vortices and moderated velocity gradients. The oscillatory shear index (OSI) demonstrates a wider spatial distribution in compliant arteries, driven by prolonged and asymmetric recirculation. Additionally, a distinct phase lag between wall displacement and the driving pressure wave reveals viscoelastic behaviour of the arterial wall. These findings highlight the pivotal role of wall elasticity in modulating hemodynamic stresses and flow structures, emphasising the importance of FSI-based modelling for accurate prediction of blood flow in stenosed arteries.
Keywords
Flexible channel
Immersed boundary method
Stenosis
Hemodynamic indicators
Subjects

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[1] Falk, E., Pathogenesis of Atherosclerosis, Journal of the American College of Cardiology, 47, 2006, C7-C12.
[2] Rafieian-Kopaei, M., Setorki, M., Doudi, M., Baradaran, A., Nasri, A., Atherosclerosis: Process, Indicators, Risk Factors and New Hopes, International Journal of Preventive Medicine, 5, 2014, 927.
[3] Varghese, S.S., Frankel, S.H., Fischer, P.F., Direct numerical simulation of stenotic flows. Part 1. Steady flow, Journal of Fluid Mechanics, 582, 2007, 253–280.
[4] Ahmed, S.A., Giddens, D.P., Pulsatile poststenotic flow studies with laser Doppler anemometry, Journal of Biomechanics, 17(9), 1984, 695–705.
[5] Ding, G., Choi, K.S., Ma, B., Kato, T., Yuan, W., Transitional pulsatile flows with stenosis in a two-dimensional channel, Physics of Fluids, 33(3), 2021, 034115.
[6] Bathe, M., Kamm, R.D., A Fluid-Structure Interaction Finite Element Analysis of Pulsatile Blood Flow Through a Compliant Stenotic Artery, Journal of Biomechanical Engineering, 121(4), 1999, 361-369.
[7] Kamm, R.D., Pedley, T.J., Flow in Collapsible Tubes: A Brief Review, Journal of Biomechanical Engineering, 111(3), 1989, 177–179.
[8] Shapiro, A.H., Steady Flow in Collapsible Tubes, Journal of Biomechanical Engineering, 99(3), 1977, 126–147.
[9] Tang, D., Yang, J., Yang, C., Ku, D.N., A Nonlinear Axisymmetric Mode with Fluid-Wall Interactions for Steady Viscous Flow in Stenotic Elastic Tubes, Journal of Biomechanical Engineering, 121(5), 1999, 494-501.
[10] Hazel, A.L., Heil, M., Steady finite-Reynolds-number flows in three-dimensional collapsible tubes, Journal of Fluid Mechanics, 486, 2003, 79–103.
[11] Huang, Q., Tian, F.B., Young, J., Lai, J.C.S., Transition to chaos in a two-sided collapsible channel flow, Journal of Fluid Mechanics, 926, 2021, A15.
[12] Huang, Q., Ji, X., Ma, J., Wang, L., Young, J., Lai, J.C.S., Self-excited oscillations of three-dimensional collapsible tubes conveying both laminar and turbulent flows, Physics of Fluids, 36, 2024, 121920.
[13] Wang, D.Y., Luo, X.Y., Stewart, P.S., Energetics of collapsible channel flow with a nonlinear fluid-beam model, Journal of Fluid Mechanics, 926, 2021, A2.
[14] Wang, D., Luo, X., Liu, Z., Stewart, P.S., Flow-induced surface instabilities in a flexible-walled channel with a heavy wall, Journal of Fluid Mechanics, 956, 2023, A1.
[15] Peskin, C.S., Numerical Analysis of Blood Flow in the Heart, Journal of Computational Physics, 25, 1977, 220-252.
[16] Mittal, R., Iaccarino, G., Immersed boundary methods, Annual Review of Fluid Mechanics, 37, 2005, 239–261.
[17] Goldstein, D., Handler, R., Sirovich, L., Modeling a No-Slip Flow Boundary with an External Force Field, Journal of Computational Physics, 105(2), 1993, 354–366.
[18] Maniyeri, R., Suh, Y.K., Kang, S., Kim, M.J., Numerical study on the propulsion of a bacterial flagellum in a viscous fluid using an immersed boundary method, Computers & Fluids, 62, 2012, 13–24.
[19] Kanchan, M., Maniyeri, R., Numerical analysis of the buckling and recuperation dynamics of flexible filament using an immersed boundary framework, International Journal of Heat and Fluid Flow, 77, 2019, 256–277.
[20] Kanchan, M., Maniyeri, R., Numerical simulation of buckling and asymmetric behavior of flexible filament using temporal second-order immersed boundary method, International Journal of Numerical Methods for Heat & Fluid Flow, 30(3), 2020, 1047–1095.
[21] Jensen, O.E., Heil, M., High-frequency self-excited oscillations in a collapsible-channel flow, Journal of Fluid Mechanics, 481, 2003, 235–268.
[22] Luo, X.Y., Pedley, T.J., A numerical simulation of unsteady flow in a two-dimensional collapsible channel, Journal of Fluid Mechanics, 314, 1996, 191–225.
[23] Tang, C., Zhu, L., Akingba, G., Lu, X.Y., Viscous flow past a collapsible channel as a model for self-excited oscillation of blood vessels, Journal of Biomechanics, 48(10), 2015, 1922–1929.
[24] Ku, D.N., Blood flow in arteries, Annual Review of Fluid Mechanics, 29(1), 1997, 399–434.
[25] Albadawi, M., Abuouf, Y., Ahmed, M., Influence of Arterial Wall Elasticity on Blood Flow Dynamic Factors of Stenotic Carotid Artery, ASME International Mechanical Engineering Congress and Exposition. Vol. 85598. American Society of Mechanical Engineers, 2021.
[26] Valencia, A., Villanueva, M., Unsteady flow and mass transfer in models of stenotic arteries considering fluid-structure interaction, International Communications in Heat and Mass Transfer, 33(8), 2006, 966–975.
[27] Giannoglou, G.D., Chatzizisis, Y.S., Zamboulis, C., Parcharidis, G.E., Mikhailidis, D.P., Louridas, G.E., Elevated heart rate and atherosclerosis: An overview of the pathogenetic mechanisms, International Journal of Cardiology, 126(3), 2008, 302–312.
[28] Rauramaa, R., Halonen, P., Väisänen, S.B., Lakka, T.A., Schmidt-Trucksäss, A., Berg, A., Penttilä, I.M., Rankinen, T., Bouchard, C., Effects of Aerobic Physical Exercise on Inflammation and Atherosclerosis in Men: The DNASCO Study, Annals of Internal Medicine, 140(12), 2004, 1007–1014.
[29] Song, J., Kouidri, S., Bakir, F., Numerical study on flow topology and hemodynamics in tortuous coronary artery with symmetrical and asymmetrical stenosis, Biocybernetics and Biomedical Engineering, 41(1), 2021, 142–155.
[30] Griffith, B.E., Patankar, N.A., Immersed Methods for Fluid–Structure Interaction, Annual Review of Fluid Mechanics, 52(1), 2020, 421–448.
[31] Zhu, L., Peskin, C.S., Simulation of a flapping flexible filament in a flowing soap film by the immersed boundary method, Journal of Computational Physics, 179(2), 2002, 452–468.
[32] Leathers, B.J., Guy, R.D., Immersed Boundary Double Layer method: An introduction of methodology on the Helmholtz equation, Journal of Computational Physics, 506, 2024, 112922.
[33] Lai, M.C., Peskin, C.S., An immersed boundary method with formal second-order accuracy and reduced numerical viscosity, Journal of Computational Physics, 160(2), 2000, 705–719.
[34] Beyer, R.P., LeVeque, R.J., Analysis of a One-Dimensional Model for the Immersed Boundary Method, SIAM Journal on Numerical Analysis, 29(2), 1992, 332–364.
[35] Gong, Z.X., Lu, C.J., Huang, H.X., Effect of regularized delta function on accuracy of immersed boundary method, Applied Mathematics and Mechanics (English Edition), 33(11), 2012, 1453–1466.
[36] Sood, T., Roy, S., Pathak, M., Effect of pulse rate variation on blood flow through axisymmetric and asymmetric stenotic artery models, Mathematical Biosciences, 298, 2018, 1–18.
[37] Klarhö Fer, M., Csapo, B., Balassy, C., Szeles, J.C., Moser, E., High-Resolution Blood Flow Velocity Measurements in the Human Finger, Magnetic Resonance in Medicine: An Official Journal of the International Society for Magnetic Resonance in Medicine, 45(4), 2001, 716-719.
[38] Khan, P.M., Sharma, S.D., Chakraborty, S., Roy, S., Effect of heart rate on the hemodynamics in healthy and stenosed carotid arteries, Physics of Fluids, 35(6), 2023, 061906.
[39] Kershaw, D.S., The Incomplete Cholesky-Conjugate Gradient Method for the Iterative Solution of Systems of Linear Equations, Journal of Computational Physics, 26, 1978, 43-65.
[40] Layek, G.C., Midya, C., Effect of constriction height on flow separation in a two-dimensional channel, Communications in Nonlinear Science and Numerical Simulation, 12(5), 2007, 745–759.
[41] Vahidkhah, K., Abdollahi, V., Numerical simulation of a flexible fiber deformation in a viscous flow by the immersed boundary–lattice Boltzmann method, Communications in Nonlinear Science and Numerical Simulation, 17, 2012, 1475–1484.
[42] Chhai, P., Rhee, K., Computational study on phase lag of arterial-wall motion for assessment of plaque vulnerability, Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine, 234(5), 2020, 517–526.
[43] Wild, N.C., Bulusu, K.V., Plesniak, M.W., Vortical Structures Promote Atheroprotective Wall Shear Stress Distributions in a Carotid Artery Bifurcation Model, Bioengineering, 10(9), 2023, 1036.
[44] Razavi, A., Shirani, E., Sadeghi, M.R., Numerical simulation of blood pulsatile flow in a stenosed carotid artery using different rheological models, Journal of Biomechanics, 44(11), 2011, 2021–2030.
Journal of Applied and Computational Mechanics
Volume 12, Issue 3
Summer 2026
Pages 799-814