In this paper, the authors extend their study of wall mechanics given in Part 1 to the overall problem of fluid-solid interactions in arterial flows. Fluid-solid coupling has become a specific topic in computational methods and applied mechanics. In this review, firstly, the effects of elasticity of blood vessels on wave propagation and local flow patterns in large arteries are discussed. Then, numerical techniques are reviewed together with the alternative coupled methods available in fluid—wall models. Finally, a novel numerical algorithm combining two commercial codes for coupled solid/fluid problems is presented. As a consequence of the present studies, wall effects are now able to be included in predictions of haemodynamics in a clinical context.
XuX. Y.CollinsM. W.A review of the numerical analysis of blood flow in arterial bifurcation. Proc. Instn Mech. Engrs, Part H, Journal of Engineering in Medicine, 1990, 204, 205–216.
2.
XuX. Y.CollinsM. W.Studies of blood flow in arterial bifurcation using a numerical simulation method. Proc. Instn Mech. Engrs, Part H, Journal of Engineering in Medicine, 1994, 208, 163–175.
3.
CaroC. G.PedleyT. J.SchroterR. C.SeedW. A.The Mechanics of the Circulation, 1978 (Oxford University Press, Oxford).
4.
TozerenA.Elastic properties of arteries and their influence on the cardiovascular system. Trans. ASME, J. Biomech. Engng, 1984, 106, 182–185.
5.
MoodieT. B.HaddowJ. B.Waves in thin walled elastic tubes containing an incompressible inviscid fluid. Int. J. Non-linear Mechanics, 1977, 12, 223–231.
6.
BergelD. H.The static elastic properties of the arterial wall. J. Physiol., 1961, 156, 445–457.
7.
MirskyI.Ventricular and arterial wall stress based on large deformation analysis. Biophys. J., 1973, 13, 1141–1159.
8.
FungY. C.FronekK.PatitucciP.Pseudoelasticity of arteries and the choice of its mathematical expression. Am. J. Physiol, 1979, 237, H620–H631.
9.
DemirayH.Pulse velocities in initially stressed arteries. J. Biomechanics, 1988, 21, 55–58.
10.
DemirayH.A note on the elasticity of soft biological tissues. J. Biomechanics, 1972, 5, 309–311.
11.
AtabekH. B.LewH. S.Wave propagation through a viscous incompressible fluid contained in an initially stressed elastic tube. Biophys. J., 1966, 7, 480–503.
12.
WitzigK.Uber erzwungene wellenbewegungen zaher, incompressibler flussigkeiten in elastischen rohren. PhD dissertation, University of Bern, 1914.
13.
O'RourkeM. F.TaylorM. G.Input impedance of the systemic circulation. Circulation Res., 1967, 20, 365.
14.
WomersleyJ. R.The mathematical analysis of the arterial circulation in a state of oscillatory motion, WADC-TR56–614, Wright Air Development Centre, 1957.
15.
WangD. M.TarbellJ. M.Nonlinear analysis of flow in an elastic tube (artery): Steady streaming effects. J. Fluid Mechanics, 1992, 239, 341–358.
16.
DuttaA.WangD. M.TarbellJ. M.Numerical analysis of flow in an elastic artery model. Trans. ASME. J. Biomech. Engng, 1992, 114, 26–33.
17.
LiepschD.MoravecS.Pulsatile flow of non-newtonian fluid in distensible models of human arteries. Biorheology, 1984, 21, 571–586.
18.
FriedmanM. H.BargeronC. B.DetersO. J.HutchinsG. M.MarkF. F.Correlation between wall shear and intimal thickness at a coronary artery branch. Atherosclerosis, 1987, 68, 27–33.
19.
NeremR. M.CornhillJ. F.The role of fluid mechanics in atherogenesis. Trans. ASME, J. Biomech. Engng, 1980, 102, 181–189.
20.
CaroC. G.Fitz-GeraldJ. M.SchroterR. C.Atheroma and arterial wall shear: Observation, correlation and proposal of a shear dependent mass transfer mechanism for atherogenesis. Proc. R. Soc. Lond., 1971, 177, 109–159.
21.
DuncanD. D.BargeronC. B.BrochardtS. E.DetersO. J.GearhartS. A.MarkF. F.FriedmanM. H.The effect of compliance on wall shear in casts of a human aortic bifurcation. Trans. ASME, J. Biomech. Engng, 1990, 112, 183–188.
22.
AnayiotosA. S.JonesS. A.GiddensD. P.GlagovS.ZarinsC. K.Shear stress at a compliant model of the human carotid bifurcation. Trans. ASME, J. Biomech. Engng, 1994, 116, 98–106.
23.
HorstenJ. B.A.M.van SteenhovenA. A.van DongenM. E. H.Linear propagation of pulsatile waves in visco-elastic tubes. J. Biomechanics, 1989, 22, 477–484.
24.
LouZ.YangW. J.A computer simulation of the blood flow at the aortic bifurcation with flexible walls. Trans. ASME, J. Biomech. Engng, 1993, 115, 306–315.
25.
ReuderinkP. J.Analysis of the flow in a 3-D distensible model of the carotid artery bifurcation. PhD thesis, Department of Mechanical Engineering, University of Technology, Eindhoven, 1991.
26.
PerktoldK.RappitschG.Computer simulation of local blood flow and vessel mechanics in a compliant carotid artery bifurcation model. J. Biomechanics, 1995, 28, 845–856.
27.
RaoS. S.The Finite Element Method in Engineering, 1989 (Pergamon Press, Oxford).
28.
TurnerM. J.CloughR. W.MartinH. C.ToppL. J.Stiffness and deflection analysis of complex structures. J. Aeronaut. Sci., 1956, 23, 805–824.
29.
FungY. C.Biomechanics—Mechanical Properties of Living Tissues, 1981 (Springer-Verlag, New York).
30.
SteinmanD. A.EthierC. R.The effect of wall distensibility on flow in a two-dimensional end-to-side anastomosis. Trans. ASME, J. Biomech. Engng, 1994, 116, 294–301.
31.
XuX. Y.CollinsM. W.Numerical modelling of blood flow in compliant arteries and arterial bifurcation. In Biofluid Mechanics (Ed. PowerH.), 1995, pp. 55–94 (Computational Mechanics Publications, Southampton, Boston).
32.
LanT. H.XuX. Y.HuttonA.CollinsM. W.A numerical algorithm for solving coupled solid/fluid interaction problems. In Numerical Methods in Laminar and Turbulent Flows (Ed. TaylorC.), 1995, Vol. IX, Part 2, pp. 1539–1550 (Pineridge Press, Swansea).
33.
RastM. P.Simultaneous solution of Navier-Stokes and elastic membrane equations by finite element method. Int. J. Numer. Meth. Fluids, 1994, 19, 1115–1135.
34.
HenryF. S.CollinsM. W.A novel predictive model with compliance for arterial flow. In 1993 Advances in Bioengineering, ASME Vol. BED 26, 1993, pp. 131–135 (American Society of Mechanical Engineers, New York).
35.
PerktoldK.RappitschG.Numerical analysis of arterial wall mechanics and local blood flow phenomena. In 1993 Advances in Bioengineering, ASME Vol. BED 26, 1993, pp. 127–130 (American Society of Mechanical Engineers, New York).
36.
HoferM.RappitschG.PerktoldK.TrubelW.SchimaH.Numerical study of wall mechanics and fluid dynamics in end-to-side anastomoses and correlation to intimal hyperplasia. J. Biomechanics, 1996, 29, 1297–1308.
ReuderinkP. J.WillemsP. J. B.SchreursP. J.G.van SteenhovenA. A.Fluid flow through distensible models of the carotid artery bifurcation. In Biofluid Mechanics, Blood Flow in Large Vessels (Ed. LiepschD.), 1989, pp. 329–334 (Springer, Berlin).
39.
EngelR.Analysis of fluid-structure interaction problems in nuclear reactor engineering. Int. J. Comput. Appl. Technol., 1994, 7, 193–205.
40.
CFX4: User Guide, 1995 (Harwell Laboratory, UK, AEA Industrial Technology).
OsenbergH. P.Simulation des arteriellen bluflusses-ein allgemeines modell mit anwendung auf das menschliche hirngefaβsystem. Dissertation, ETH-Zurich, Zurich, 1991.
