Arterial bifurcation flow has been of special interest for some years because of its important role in the formation of atherosclerotic plaques and thrombi. To investigate the flow phenomena analytically, four major factors need to be accommodated—the three-dimensionality of a general bifurcation, the pulsatile nature of the laminar flow, the distensibility of the arterial wall and the non- Newtonian character of the blood. In this review, both engineering and medical aspects of each factor are carefully surveyed. It is demonstrated that the latest generation of computational fluid dynamics codes can treat this problem area and that it is both feasible and desirable to investigate the effects of each independent factor.
Get full access to this article
View all access options for this article.
References
1.
FryD. L.Haemodynamic forces in atherogenesis. In Cerebrovascular disease, 1976, pp. 77–95 (Raven Press, New York).
2.
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. Land., 1971, B171, 109–159.
3.
CaroC. G.Arterial fluid mechanics and atherogenesis. Recent Advances in Cardiovascular Disease, 1981, 2, 6–11.
4.
FernandezR. C.WittK. J.BotainM. R.Pulsatile flow through a bifurcation with applications to arterial disease. J. Biomech, 1976, 9, 575–580.
5.
KuD. N.GiddensD. P.ZarinsC. K.GlagovS.Pulsatile flow and atherosclerosis in the human carotid bifurcation. Arteriosclerosis, 1985, 5(3), 293–302.
6.
StehbensW. E.Flow in glass models of arterial bifurcations and berry aneurysm at low Reynolds numbers. Q. J. Expl. Physiol., 1975, 60, 181–192.
7.
BharadvajB. K.MabonR. F.GiddensD. P.Steady flow in a model of the human carotid bifurcation. Part I—Flow visualisation. J. Biomech., 1982, 15, 349–362.
8.
KuD. N.GiddensD. P.Pulsatile flow in a model carotid bifurcation. Arteriosclerosis, 1983, 3(1), 31–39.
9.
KarinoT.KwongH. M.GoldsmithH. L.Particle flow behaviour in models of branching vessels; I. Vortices in 90° T-junctions. Biorheol., 1979, 16, 231–248.
10.
BharadvajB. K.MabonR. F.GiddensD. P.Steady flow in a model of the human carotid bifurcation. Part II—Laser-Doppler anemometer measurements. J. Biomech., 1982, 15, 363–378.
11.
LutzR. T.HsuL.MenamatA.ZrubekJ.EdwardsK.Comparison of steady and pulsatile flow in a double branching arterial model. J. Biomech., 1984, 18, 753–759.
12.
KuD. N.GiddensD. P.Haemodynamics of the normal human carotid bifurcation: in vitro and in vivo studies. Ultrasound in Med. Biol., 1985, 11(1), 13–26.
13.
JonesC. J. H.LeverM. J.OgasawaraY.ParkerK. H.TsujiokaK.HiramatsuO.CaroC. G.KajiyaF.Velocity profiles at an arterial bifurcation: measurement using high frequency multichannel Doppler ultrasound (to be published).
14.
PedleyT. J.The fluid mechanics of large blood vessels, 1980 (Cambridge University Press).
15.
LippertH.PabstR.Arterial variations in man, 1985, (J. F. Bergmann Verlag, Munchen).
16.
RenemanR. S.MerodeT.VanH. P.HoeksA. P. G.Flow velocity patterns in and distensibility of the carotid artery bulb in subjects of various ages. Circulation, 1985, 71, 500–509.
17.
RenamanR. S.MerodesT.VanH. P.HoeksA. P. G.Cardiovascular applications of multi-gate pulsed Doppler systems. Ultrasound in Med. Biol., 1986, 12, 357–370.
18.
ForsterF. K.ChikosP. M.FrazierJ. S.Geometric modelling of the carotid bifurcation in humans: Implications in ultrasonic Doppler and radiologic investigations. J. Clin. Ultrasound, 1985, 13, 385–390.
19.
ThompsonJ. F.WarsiZ. U. A.MastinC. W.Boundary-fitted coordinate systems for numerical solution of partial difference equations—a review. J. Comput. Physics, 1982, 47, 1–108.
HauserJ.TaylorC.Numerical grid generation in computational fluid dynamics. Proceedings of the International Conference held at Landshut, 1986, Germany.
EisemanP. R.EriebacherG.Grid generation for the solution of partial differential equations. NASA contractor report 178365, 1987.
24.
GordonW. J.ThielL. C.Transfinite mapping and their applications to grid generation. In Numerical grid generation (Ed. ThompsonJ. F.), 1982 (North-Holland).
25.
UsabW. J.MurmanE. M.Embedded mesh solution of the Euler equations using a multiple-grid method. AIAA papers, 1983.
26.
EriksonL. E.Generation of boundary-conforming grids around wing-body configurations using transfinite interpolation. AIAA J., 1982, 20(10), 1313–1320.
27.
ThompsonJ. F.ThamesF. C.MastinC. W.Automatic numerical generation of body-fitted curvilinear system for field containing any number of arbitrary two-dimensional bodies. J. Comput. Physics, 1974, 15, 299–319.
28.
MastinC. W.ThompsonJ. F.Transformation of three-dimensional regions onto rectangular regions by elliptic systems. Numer. Math., 1978, 29, 397–407.
29.
PeraireJ.MorganK.PeiroJ.Unstructured mesh methods for CFD. Von Karman Institute for Fluid Dynamics ‘Numerical grid generation’ lecture note, 1990.
30.
MikiK.TakagiT.A domain decomposition and overlapping method for the generation of three-dimensional boundary-fitted coordinate systems. J. Comput. Physics, 1984, 53, 319–330.
31.
SteinhoffJ.Blending method for grid generation. J. Comput. Physics, 1986, 65, 370–385.
32.
ThompsonJ. F.ThamesF. C.MastinC. W.TOMCAT—a code for numerical generation of boundary-fitted curvilinear coordinate systems on fields containing any number of arbitrary two-dimensional bodies. J. Comput. Physics, 1977, 24, 274–302.
33.
WintersK. H.JacksonC. P.A guide to finite-element grid generation using TGIN (release 1). AERE-R 11530, 1984.
34.
BrienV.EhrlichL. W.FriendmanM. H.Unsteady flow in a branch. J. Fluid Mech., 1976, 75, 315–336.
35.
BrienV.EhrlichL. M.Simulation of unsteady flow at renal branches. J. Biomech., 1977, 10, 623–631.
36.
LiepschD.MoravecS.Measurement and calculations of laminar flow in a ninety degree bifurcation, J. Biomech., 1982, 15, 473–585.
37.
PerktoldK.HilberitD.Numerical simulation of pulsatile flow in a carotid bifurcation model. J. Biomech., 1986, 8, 193–199.
38.
RindtC. C. M.VosseF. N. N. V. D.SteenhovenA. A. V.JanssenJ. D.A numerical and experimental analysis of the flow in a two-dimensional model of the human carotid bifurcation. J. Biomech., 1987, 20, 499–509.
39.
KhodadadiJ. M.VlachosN. S.LiepschD.MoravecS.LDA measurements and numerical prediction of pulsatile laminar flow in a plane 90-degree bifurcation. J. Biomech. Engng., 1988, 110, 129–136.
40.
WilleS. O.Numerical simulation of steady flow inside a three-dimensional aortic bifurcation model. J. Biomed. Engng, 1984, 6, 49–55.
41.
DinnarU.EndenG.IsraeliM.A numerical study of flow in a three dimensional bifurcation. Cardiovascular Systems Dynamics Society Meeting, 1988, Canada.
42.
RindtC. C. M.Analysis of the three-dimensional flow field in the carotid artery bifurcation. PhD thesis, 1989, Eindhoven University of Technology, The Netherlands.
43.
PerktoldK.PeterR.Numerical 3D-simulation of pulsatile wall shear stress in an arterial T-bifurcation model. J. Biomed. Engng, 1990, 12, 2–12.
44.
ReynoldsO.On the dynamical theory of incompressible viscous fluids and the determination of the criterion. Phil. Trans. Proc. R. Soc., 1895, A186, 123–164.
45.
CollinsM. W.AllenP. H. G.SzpiroO.Computational methods for entry length heat transfer by combined laminar convection in vertical tubes. Proc. Instn. Mech. Engrs, 1977, 191, 19–30.
46.
AllenP. H. G.CollinsM. W.SzpiroO.The influence of temperature dependence of thermophysical properties on the prediction accuracy in laminar mixed-convection heat transfer in vertical tubes. Proceedings of Sixth International Conference on Heat transfer, Toronto, 1978.
47.
CollinsM. W.A finite difference analysis of non-Newtonian fluids in circular tubes. Proceedings of Third International Conference on Numerical methods in thermal problems, Seattle, 1983, pp. 540–550.
48.
GosmanA. D.KhalileE.WhiterlawJ. H.The calculation of two-dimensional turbulent recirculating flows. Proceedings of Symposium on Turbulent shear flows, Pennsylvania State University, Pa., 1977.
GrotzbachG.Simulation of turbulent flow and heat transfer for selected problems of nuclear thermal-hydraulics. International Conference on Supercomputing in nuclear applications, Mito, Japan, March 1990.
52.
VokeP. R.CollinsM. W.Large-eddy simulations of turbulent flow in plain and distorted channels. AERE Harwell Report HTFS RS 551, 1984, Annual Research Symposium, University of Warwick.
53.
CollinsM. W.CiofaloM.Computational fluid dynamics and its application to transport processes (submitted to Journal of Chemical Technology and Biotechnology).
54.
GreshoP.A modified finite element method for solving the time-dependent incompressible Navier-Stokes equations. Part I: TheoryInt. J. Numer. Math. in Fluids, 1984, 4, 557–598.
55.
PatankarS. V.Numerical heat transfer and fluid flow, 1983 (Hemisphere).
56.
Van DoormalJ. P.RaithbyG. D.Enhancement of the SIMPLE method for predicting incompressible fluid flows. Numer. Heat Transfer, 1984, 7, 147–163.
57.
IssaR. I.Solution of the implicitly discretised fluid flow equations by operator-splitting. J. Comput. Physics, 1986, 62, 40–65.
58.
KightleyJ. R.The conjugate gradient method applied to turbulent flow calculations. Proceedings of the Sixth GAMM Conference on Numerical methods in fluid mechanics, Gottingen, 1985.
BurnsA. D.WilkesN. S. A.Finite difference method for the computation of fluid flows in complex 3D geometries. UKAEA report, 1987 (AERE, Harwell).
61.
CiofaloM.CollinsM. W.Time-dependent numerical simulation of the starting flow of an incompressible fluid past a downstream facing step. Proceedings of AGARD Conference on Validation of computing fluid dynamics, NATO, Lisbon, 1988.
62.
LonsdaleR.An algorithm for solving thermal-hydraulic equations in complex geometry. The ASTEC Code, UKAEA report, 1988 (Dounreay).
63.
RhieC. M.ChowW. L.A numerical study of the turbulent flow past an airfoil with trailing edge separation. AIAA J., 1983, 21, 1525–1532.
64.
CollinsM. W.XuX. Y.A predictive scheme for flow in arterial bifurcations: Comparison with laboratory measurements. In Biomechanical transport processes, NATO workshop, Corsica, 1989.
65.
KuD.LiepschD.The effects of non-Newtonian visco-elasticity and wall elasticity on flow at a 90 degree bifurcation. Biorheol., 1986, 23, 359–370.
66.
WomersleyJ. R.Oscillatory flow in arteries: The constrained elastic tube as a model of arterial flow and pulse transmission. Physics in Med. Biol., 1958, 2, 178–187.
67.
McDonaldD. A.Blood flow in arteries, 1960 (Williams and Wilkins, Baltimore).
68.
AnliketM.RockwellR. L.OgdenE.Nonlinear analysis of flow pulses and shock waves in arteries. Part I: Derivation and properties of mathematical model. Part II: Parameters study related to clinical problems. J. Appl. Math. Phys. (ZAMO), 1971, 22, 217–246 (Part I), 563–581 (Part II).
69.
LiepschD.Note on wave propagation in a thin elastic tube containing a viscous fluid. J. Biomech., 1985, 18, 685–694.
70.
MoravecS.LiepschD.Flow investigation in a model of a three-dimensional human artery with Newtonian and non-Newtonian fluids. Part I. Biorheol., 1983, 20, 745–759.
71.
CollinsM. W.XuX. Y.Flow studies in canine artery bifurcation using a numerical simulation method (submitted to ASME Journal of Biomechanical Engineering, 1990).
72.
XuX. Y.CollinsM. W.The problem of numerical analysis of blood flow in arterial bifurcation—a review. Internal report, The City University, 1989.
