Few multiaxial constitutive laws under the vasoactive condition have been proposed as compared with those under the passive condition. The biaxial isometric properties of vasoactive rabbit arteries were studied, although the constitutive law was not proposed. The purpose of the present study is also to describe the multiaxial active mechanical properties of arteries. A novel strain energy function for the active stress has been proposed. This function is simple and may describe the multiaxial characteristics of constricted vessels. Although this study used mean stress and mean stretch ratio to determine the mechanical properties of vessels, a triaxial constitutive law of constricted vessels may be developed. There remains the subject of residual strains under active condition. If this problem will be solved, the accurate stress analysis under vasoactive conditions is possible.

References

1.
Herlihy
,
J. T.
, and
Murphy
,
R. A.
,
1973
, “
Length–Tension Relationship of Smooth Muscle of the Hog Carotid Artery
,”
Circ. Res.
,
33
(
3
), pp.
275
283
.10.1161/01.RES.33.3.275
2.
Herlihy
,
J. T.
,
1980
, “
Helically Cut Vascular Strip Preparation: Geometrical Considerations
,”
Am. J. Physiol. Heart Circ. Physiol.
,
238
(
1
), pp.
H107
H109
.
3.
Ohhashi
,
T.
, and
Azuma
,
T.
,
1980
, “
Paradoxical Relaxation of Strips Induced by Vasoconstrictive Agents
,”
Blood Vessels
,
17
(
1
), pp.
16
26
.
4.
Dobrin
,
P. B.
,
1973
, “
Isometric and Isobaric Contraction of Carotid Arterial Smooth Muscle
,”
Am. J. Physiol.
,
225
(
3
), pp.
659
663
.
5.
Cox
,
R. H.
,
1978
, “
Comparison of Carotid Artery Mechanics in the Rat, Rabbit, and Dog
,”
Am. J. Physiol. Heart Circ. Physiol.
,
234
(
3
), pp.
H280
H288
.
6.
Vaishnav
,
R. N.
,
Young
,
J. T.
, and
Patel
,
D. J.
,
1973
, “
Distribution of Stresses and of Strain–Energy Density Through the Wall Thickness in a Canine Aortic Segment
,”
Circ. Res.
,
32
(
5
), pp.
577
587
.10.1161/01.RES.32.5.577
7.
Fung
,
Y. C.
,
Fronek
,
K.
, and
Patitucci
,
P.
,
1979
, “
Pseudoelasticity of Arteries and Choice of its Mathematical Expression
,”
Am. J. Physiol. Heart Circ. Physiol.
,
237
(
5
), pp.
H620
H631
.
8.
Holzapfel
,
G. A.
,
Gasser
,
G. A.
, and
Ogden
,
R. W.
,
2000
, “
A New Constitutive Framework for Arterial Wall Mechanics and a Comparative Study of Material Models
,”
J. Elasticity
,
61
(
1–3
), pp.
1
48
.10.1023/A:1010835316564
9.
Humphrey
,
D. J.
,
2002
,
Cardiovascular Solid Mechanics: Cells, Tissues, and Organs
,
Springer-Verlag
,
NY
.
10.
Huo
,
Y.
,
Cheng
,
Y.
,
Zhao
,
X.
,
Lu
,
X.
, and
Kassab
,
G. A.
,
2012
, “
Biaxial Vasoactivity of Porcine Coronary Artery
,”
Am. J. Physiol. Heart Circ. Physiol.
,
302
(
10
), pp.
H2058
H2063
.10.1152/ajpheart.00758.2011
11.
Muratada
,
S. C.
,
Kroon
,
M.
, and
Holzapfel
,
G. A.
,
2010
, “
A Calcium-Driven Mechanochemical Model for Prediction of Force Generation in Smooth Muscle
,”
Biomech. Modell. Mechanobiol.
,
9
(
6
), pp.
749
762
.10.1007/s10237-010-0211-0
12.
Muratada
,
S. C.
,
Arner
,
A.
, and
Holzapfel
,
G. A.
,
2012
, “
Experiments and Mechanochemical Modeling of Smooth Muscle Contraction: Significance of Filament Overlap
,”
J. Theor. Biol.
,
297
(3), pp.
176
186
.10.1016/j.jtbi.2011.11.012
13.
Böl
,
M.
, and
Schmitz
,
A.
,
2013
, “
A Coupled Chemomechanical Model for Smooth Muscle Contraction
,”
Computer Models in Biomechanics. From Nano to Macro
,
G. A.
Holzapfel
, and
E.
Kuhl
, eds.,
Springer
,
Amsterdam, The Netherlands
, pp.
63
75
.
14.
Takamizawa
,
K.
,
Hayashi
,
K.
, and
Matsuda
,
T.
,
1992
, “
Isometric Biaxial Tension of Smooth Muscle in Isolated Cylindrical Segments of Rabbit Arteries
,”
Am. J. Physiol. Heart Circ. Physiol.
,
263
(
1
), pp.
H30
H34
.
15.
Holzapfel
,
G. A.
,
Sommer
,
G.
,
Gasser
,
C. T.
, and
Regitnig
,
P.
,
2005
, “
Determination of Layer-Specific Mechanical Properties of Human Coronary Arteries With Nonatherosclerotic Intimal Thickening and Related Constitutive Modeling
,”
Am. J. Physiol. Heart Circ. Physiol.
,
289
(
5
), pp.
H2048
H2058
.10.1152/ajpheart.00934.2004
16.
Takamizawa
,
K.
, and
Hayashi
,
K.
,
1987
, “
Strain Energy Density Function and Uniform Strain Hypothesis for Arterial Mechanics
,”
J. Biomech.
,
20
(
1
), pp.
7
17
.10.1016/0021-9290(87)90262-4
17.
Carew
,
T. E.
,
Vaishnav
,
R. N.
, and
Patel
,
D. J.
,
1968
, “
Compressibility of the Arterial Wall
,”
Circ. Res.
,
23
(
1
), pp.
61
68
.10.1161/01.RES.23.1.61
18.
Patel
,
D. J.
, and
Fry
,
D. L.
,
1969
, “
The Elastic Symmetry of Arterial Segments in Dogs
,”
Circ. Res.
,
24
(
1
), pp.
1
8
.10.1161/01.RES.24.1.1
19.
Holzapfel
,
G. A.
,
Gasser
,
T. C.
, and
Stadler
,
M.
,
2002
, “
A Structural Model for Viscoelastic Behavior of Arterial Walls: Continuum Formulation and Finite Analysis
,”
Eur. J. Mech. A/Solids
,
21
(
3
), pp.
441
463
.10.1016/S0997-7538(01)01206-2
20.
Arner
,
A.
, and
Uvelius
,
B.
,
1982
, “
Force–Velocity Characteristics and Active Tension in Relation to Content and Orientation of Smooth Muscle Cells in Aortas from Normotensive and Spontaneous Hypertensive Rats
,”
Circ. Res.
,
50
(
6
), pp.
812
821
.10.1161/01.RES.50.6.812
21.
Todd
,
M. E.
,
Laye
,
C. G.
, and
Osborne
,
D. N.
,
1983
, “
The Dimensional Characteristics of Smooth Muscle in Rat Blood Vessels. A Computer-Assisted Analysis
,”
Circ. Res.
,
53
(
3
), pp.
319
331
.10.1161/01.RES.53.3.319
22.
Rachev
,
A.
, and
Hayashi
,
K.
,
1999
, “
Theoretical Study of the Effects of Vascular Smooth Muscle Contraction on Strain and Stress Distributions in Arteries
,”
Ann. Biomed. Eng.
,
27
(
4
), pp.
459
468
.10.1114/1.191
23.
Zulliger
,
M. A.
,
Rachev
,
A.
, and
Stergiopulos
,
N.
,
2004
, “
A Constitutive Formulation of Arterial Mechanics Including Vascular Smooth Muscle Tone
,”
Am. J. Physiol. Heart Circ. Physiol.
,
287
(
3
), pp.
H1335
H1343
.10.1152/ajpheart.00094.2004
24.
Wagner
,
H. P.
, and
Humphrey
,
D. J.
,
2011
, “
Differential Passive and Active Biaxial Mechanical Behavior of Muscular and Elastic Arteries: Basilar Versus Common Carotid
,”
ASME J. Biomech. Eng.
,
133
(
5
), p.
051009
.10.1115/1.4003873
25.
Huo
,
Y.
,
Zhao
,
X.
,
Cheng
,
X.
,
Lu
,
X.
, and
Kassab
,
G. S.
,
2013
, “
Two-Layer Model of Coronary Artery Vasoactivity
,”
J. Appl. Physiol.
,
114
(
10
), pp.
1451
1459
.10.1152/japplphysiol.01237.2012
You do not currently have access to this content.