Understanding how transmural distributions of stress relate to the mechanisms of vascular growth, remodeling, and disease necessitates computations that are based on a constitutive relation for the arterial wall. Although a number of candidate relations are in the literature, they have not been compared in detail. In this note, three commonly used descriptors of the passive behavior of common carotid arteries are compared using simple “thought experiments.” It is shown that two of the three relations are inherently limited in the degree of anisotropy they allow, that each predicts a different anisotropy, and that one yields physically unrealistic predictions given many of the published values of the material parameters. Based on this comparison, it appears that the relation proposed by Chuong and Fung is the best available, though there may be a need to search for an alternate form, particularly for muscular arteries. The methods presented herein are offered as a guide to help the experimentalist identify alternate forms of pseudostrain-energy functions for arteries.

1.
Chaudhry
H. R.
,
Bukiet
B.
,
Davis
A.
,
Ritter
A. B.
, and
Findley
T.
,
1997
, “
Residual stresses in oscillating thoracic arteries reduce circumferential stresses and stress gradients
,”
J. Biomech.
, Vol.
30
, pp.
57
62
.
2.
Chuong
C. J.
, and
Fung
Y. C.
,
1986
, “
On residual stress in arteries
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
108
, pp.
189
192
.
3.
Humphrey
J. D.
, and
Yin
F. C. P.
,
1986
, “
Fiber-induced material behavior in composites
,”
Mech. Res. Comn.
, Vol.
13
, pp.
277
283
.
4.
Humphrey
J. D.
,
Strumpf
R. K.
, and
Yin
F. C. P.
,
1990
, “
Determination of a constitutive relation for passive myocardium: I. A new functional form
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
112
, pp.
333
339
.
5.
Humphrey
J. D.
,
1995
, “
Arterial wall mechanics: Review and directions
,”
Crit. Rev. Biomed. Engr.
, Vol.
23
, pp.
1
162
.
6.
Rachev
A.
,
Steriopulos
N.
, and
Meister
J.-J.
,
1998
, “
A model for geometric and mechanical adaptation of arteries to sustained hypertension
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
120
, pp.
9
17
.
7.
Simon
B. R.
,
Kobayashi
A. S.
,
Strandness
D. E.
, and
Wiederhielm
C. A.
,
1971
, “
Large deformation analysis of the arterial cross section
,”
ASME Journal of Basic Engineering
, Vol.
93
, pp.
138
146
.
8.
Taber
L. A.
, and
Eggers
D. W.
,
1996
, “
Theoretical study of stress-modulated growth in the aorta
,”
J. Theor. Biol.
, Vol.
180
, pp.
343
357
.
9.
Takamizawa
K.
, and
Hayashi
K.
,
1987
, “
Strain energy density function and uniform strain hypothesis for arterial mechanics
,”
J. Biomech.
, Vol.
20
, pp.
7
17
.
10.
von Maltzahn
W. W.
,
Warriyar
R. G.
, and
Keitzer
W. F.
,
1984
, “
Experimental measurements of elastic properties of media and adventitia of bovine carotid arteries
,”
J. Biomech.
, Vol.
17
, pp.
839
847
.
This content is only available via PDF.
You do not currently have access to this content.