The structural response of a large artery is characteristically complex and includes the highly non-linear, history-dependent response of a nonhomogeneous anisotropic structure undergoing finite deformations. The mechanics of the arterial wall has been studied for nearly two centuries. The goals of such research range from the desire to have a basic knowledge and understanding of the mechanics and physiology of this complex structure to the need for data and methods for the design of arterial prostheses. In this paper, the models for arterial wall behaviour are critically reviewed. Firstly, the structure and general characteristics of the arterial wall are discussed. This is followed by a comprehensive review of the constitutive laws. Finally, structural analyses of the arterial wall by mathematical and numerical methods are discussed. Predictions using the authors' preferred models give focus to important issues, and in Part 2 the review and predictions are extended to the fluid-solid coupled situation.
HumphreyJ. D.Mechanics of the arterial wall: Review and directions. Critical Rev. Biomed. Engng, 1995, 30, 1–138.
2.
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.
3.
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.
CoxR. H.Regional variation of series elasticity in canine arterial smooth muscle. Am. J. Physiol., 1978, 234, 542–551.
6.
PatelD. J.JanickiJ. S.VaishnavR. N.YongJ. T.Dynamic anisotropic viscoelastic properties of the aorta in living dogs. Circulation Res., 1973, 32, 93–107.
7.
VaishnavR. N.YongJ. T.JanickiJ. S.PatelD. J.Nonlinear anisotropic elastic properties of the canine aorta. Biophys. J., 1972, 12, 1008–1027.
8.
YoungJ. T.VaishnavR. N.PatelD. J.Nonlinear anisotropic viscoelastic properties of canine arterial segments. J. Biomechanics, 1977, 10, 549–559.
9.
CarewT. E.VaishnavR. N.PatelD. J.Compressibility of the arterial wall. Circulation Res., 1968, 23, 61–68.
10.
ChuongC. J.FungY. C.Compressibility and constitutive relation of arterial wall in radial compression experiments. J. Biomechanics, 1984, 17, 35–40.
11.
CoxR. H.Anisotropic properties of the canine carotid artery in-vitro. J. Biomechanics, 1975, 8, 293–300.
12.
DobrinP. B.Biaxial anisotropy of dog carotid artery: Estimation of circumferential elastic modulus. J. Biomechanics, 1986, 19, 351–358.
13.
GentileB. J.ChuongC. J.OrdwayG. A.Regional volume distensibility of canine thoracic aorta during moderate treadmill exercise. Circulation Res., 1988, 63, 1012–1019.
14.
PapageorgiouG. L.JonesN. B.Circumferential and longitudinal viscoelasticity of human iliac arterial segments in-vitro. J. Biomed. Engng, 1988, 10, 82–90.
15.
TanakaT. J.FungY. C.Elastic and inelastic properties of the canine aorta and their variation along the aortic tree. J. Biomechanics, 1974, 7, 357–370.
16.
PatelD. J.FryD. L.Elastic symmetry of arterial segments in dogs. Circulation Res., 1969, 24, 1–18.
17.
WeizsackerH. W.PintoJ. G.Isotropy and anisotropy of the arterial wall. J. Biomechanics, 1988, 21, 477–487.
18.
BurtonA. C.Relation of structure to function of the tissues of the blood vessels. Physiol. Rev., 1954, 34, 619–642.
19.
von MaltzahnW. W.BesdoD.WiemerW.Elastic properties of arteries: A nonlinear two-layer cylindrical model. J. Biomechanics, 1981, 14, 389–397.
20.
DemirayH.VitoR. P.A layered cylindrical shell model for an aorta. Int. J. Engng Sci., 1991, 29, 47–54.
21.
KangT.HumphreyJ. D.Finite deformation of an inverted artery. In 1991 ASME Advances in Bioengineering (Ed. VanderbyR.), 1991 (American Society of Mechanical Engineers, New York).
22.
XieJ.FungY. C.Bending of blood vessel wall: Stress-strain laws of the intima-media and adventitial layers. Trans. ASME. J. Biomech. Engng, 1995, 117, 136–145.
23.
von MaltzahnW. W.WarriyarR. G.KeitzerW. F.Experimental measurements of elastic properties of media and adventitia of bovine carotid arteries. J. Biomechanics, 1984, 17, 839–847.
24.
FungY. C.FronekK.PatitucciP.Pseudoelasticity of arteries and the choice of its mathematical expression. Am. J. Physiol., 1979, 237, H620–H631.
25.
HallI. H.Deformation of Solids, 1968 (The Universities Press Limited, Northern Ireland).
26.
ViidikA.Biomechanics and functional adaptation of tendons and joint ligaments. In Studies on the Anatomy and Function of Bone and Joints (Ed. EvansF. G.), 1966, pp. 17–39 (Springer-Verlag, New York).
27.
FungY. C.Biomechanics—Mechanical Properties of Living Tissues, 1981 (Springer-Verlag, New York).
28.
CollinsR.HuW. C. L.Dynamic deformation experiments on aortic tissue. J. Biomechanics, 1972, 5, 333–337.
29.
MohanD.MelvinJ. W.Failure properties of passive human aortic tissue. I—Uniaxial tension tests. J. Biomechanics, 1982, 15, 887–902.
30.
MohanD.MelvinJ. W.Failure properties of passive human aortic tissue. II—Biaxial tension tests. J. Biomechanics, 1983, 16, 31–44.
31.
VaishnavR. N.VossoughiJ.Incremental formulations in vascular mechanics. Trans. ASME, J. Biomech. Engng, 1984, 106, 105–111.
32.
VossoughiJ.VaishnavR. N.Uniaxial mechanical properties of blood vessels. In Proceedings of the 7th Brazilian Conference onBiomedical Engineering, 1981, pp. 125–130.
33.
HayashiK.WashizuT.KiralyR. J.NoseY.Mechanical properties of aortas and pulmonary arteries of calves implanted with cardiac prostheses. J. Biomechanics, 1981, 14, 173–182.
34.
VaishnavR. N.YoungJ. T.PatelD. J.Distribution of stress and strain-energy density through the wall thickness in a canine aortic segment. Circulation Res., 1973, 32, 577–583.
35.
ChuongC. J.FungY. C.Three-dimensional stress distribution in arteries. Trans. ASME, J. Biomech. Engng, 1983, 105, 268–274.
36.
von MaltzahnW. W.Parameter sensitivity analysis and improvement of a two-layer arterial wall model. Trans. ASME, J. Biomech. Engng, 1983, 105, 389–392.
37.
HudetzA. G.MonosE.Characterisation of anisotropic elastic properties of the arteries by exponential and polynomial strain energy functions. Acta Physiol. Acad. Scientiarum Hung., 1981, 57, 111–122.
38.
DengS. X.TomiokaJ.DehesJ. C.FungY. C.New experiments on shear modulus of elasticity of arteries. Am. J. Physiol., 1994, 266, H1–10.
39.
TakamizawaK.HayashiK.Strain energy density function and uniform strain hypothesis for arterial mechanics. J. Biomechanics, 1987, 20, 7–17.
40.
Kas'yanovV. A.RachevA. I.Deformation of blood vessels upon stretching, intramural pressure and torsion. Mech. Comp. Mater., 1980, 16, 76–80.
41.
HayashiK.Experimental approaches on measuring the mechanical properties and constitute laws of arterial walls. Trans. ASME. J. Biomech. Engng, 1993, 115, 481–488.
42.
ManakJ. J.The two dimensional in-vitro passive stress-strain elasticity relationships for steer thoracic aorta blood vessel tissue. J. Biomechanics, 1980, 13, 637–646.
43.
EladD.FouxA.KivityY.A model for the nonlinear elastic response of large arteries. Trans. ASME, J. Biomech. Engng, 1988, 110, 185–189.
44.
HumphreyJ. D.StrumpfR. K.YinF. C. P.A theoretically based experimental approach for identifying vascular constitute relations. Biorheology, 1989, 26, 687–702.
GowB. S.TaylorM. G.Measurement of viscoelastic properties of arteries in the living dogs. Circulation Res., 1968, 23, 111–122.
47.
HayashiK.HandaH.NagasawaS.OkumuraA.MoritakeK.Stiffness and elastic behaviour of human intracranial and extracranial arteries. J. Biomechanics, 1980, 13, 175–184.
48.
TozerenA.Elastic properties of arteries and their influence on the cardiovascular system. Trans. ASME, J. Biomech. Engng, 1984, 106, 182–185.
49.
LangewoutersG. L.WesselingK. H.GoedhardW. J. A.The elastic properties of 45 human thoracic and 20 abdominal aortas in vitro and the parameters of a new model. J. Biomechanics, 1984, 17, 425–435.
50.
DemirayH.Incremental elastic modulus for isotropic elastic bodies with application to arteries. Trans. ASME, J. Biomech. Engng, 1983, 105, 308–309.
51.
DemirayH.WeizsackerH. W.PascaleK.ErbayH. A.A stress-strain relation for a rat abdominal aorta. J. Biomechanics, 1988, 21, 369–374.
52.
AnlikerM.MoritzW. E.OgdenE.Transmission characteristics of axial waves in blood vessels. J. Biomechanics, 1968, 1, 235–246.
53.
PatelD. J.VaishnavR. N.Basic Haemodynamics and Its Role in Disease Process, 1980 (University Park Press, Baltimore).
54.
FungY. C.Inversion of a class of nonlinear stress-strain relationship of biological soft tissues. Trans. ASME, J. Biomech. Engng, 1979, 101, 23–27.
55.
ArndtJ. O.StegallH. F.WickerH. J.Mechanics of the aorta in vivo: Radiographic approach. Circulation Res., 1971, 28, 693–704.
56.
FryD. L.Certain chemorheologic considerations regarding the blood vascular interface with particular reference to coronary artery disease. Circulation, 1969, 29 (Suppl. IV), IV38–59.
57.
SimonB. R.KobayashiA. S.StrandnessD. E.WiederhielmC. A.Large deformation analysis of the arterial cross section. J. Basic Engng, 1971, 93, 138–146.
FungY. C.Biodynamics: Circulation, 1984 (Springer, New York).
60.
ChuongC. J.FungY. C.On residual stress in arteries. Trans. ASME, J. Biomech. Engng, 1986, 108, 189–192.
61.
ChaudhryH. R.BukietB.DavisA.RitterA. B.FindleyT.Residual stresses in oscillating thoracic arteries reduce circumferential stresses and stress gradients. J. Biomechanics, 1997, 30, 57–62.
62.
SimonB. R.KobayashiA. S.WiederhielmC. A.StrandnessD. E.Deformation of the arterial vasa vasorum at normal and hypertensive arterial pressures. J. Biomechanics, 1973, 6, 349–359.
63.
AyorindeO. A.KobayashiA. S.MeratiJ. K.Finite elasticity analysis of unanesthetised and anesthetised aorta. Trans. ASME, J. Appl. Mechanics, 1975, 42, 547–551.
64.
VitoR. P.WhangM. C.GlagovS.AokiT.Distribution of strains and stresses in the arterial cross section. In 1991 Advances in Bioengineering (Ed. VanderbyR.), ASME Vol. BED 20, 1991, pp. 639–642 (American Society of Mechanical Engineers, New York).
65.
ThubrikarM. J.RoskelleyS. K.EppinkR. T.Study of stress concentration in the walls of the bovine coronary arterial branch. J. Biomechanics, 1990, 23, 15–26.
66.
KenyonD. E.A mathematical model of water flux through aortic tissue. Bull. Math. Biol., 1979, 41, 79–90.
67.
JainR.JayaramanG.Theoretical model for water flux through the artery wall. Trans. ASME, J. Biomech. Engng, 1987, 109, 311–317.
68.
SimonB. R.GaballaM. A.Poroelastic finite element models for large arteries. In 1986 Advances in Bioengineering, ASME Vol. BED 2, 1986, pp. 140–141 (American Society of Mechanical Engineers, New York).
69.
YuanY.SimonB. R.Constraint relations for orthotropic porohyperelastic constitute laws and finite element formulations for soft tissues. In 1992 Advances in Bioengineering, ASME Vol. BED 22, 1992, pp. 203–206 (American Society of Mechanical Engineers, New York).
70.
SimonB. R.Multiphase poroelastic finite element models for soft tissue structures. Appl. Mech. Rev., 1992, 45, 191–218.
71.
FryD. L.VaishnavR. N.Mass transport in the arterial wall. In Basic Haemodynamics and Its Role in Disease Process (Eds PatelD. J.VaishnavR. N.), 1980, Ch. 10, pp. 425–482 (University Park Press, Baltimore, Maryland).
72.
SimonB. R.KaufmannM. V.McAfeeM. A.BaldwinA. L.Finite element models for arterial wall mechanics. Trans. ASME, J. Biomech. Engng, 1993, 115, 489–496.
73.
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.
