Abstract
The purpose of this paper is to present a simple new method for calculating the opening angle produced by a given residual stress field in a soft biological tissue. The method uses minimization of potential energy, and is therefore named the MPE method. The accuracy of the MPE method is evaluated by comparing the opening angle it predicts to results from a finite element model of the opening angle experiment. We show that the MPE method provides good predictions of the opening angle, and that it is significantly more accurate than two other methods previously used in the literature.
Issue Section:
Technical Papers
1.
Chuong, C. J., and Fung, Y. C., 1986, “Residual Stress in Arteries,”
Frontiers in Biomechanics, G. W. Schmid-Schonbein, S. L.-Y.
Woo and B. W. Zweifach, eds., Springer, New York, pp. 117–129.
2.
Chuong
, C.
J.
, and
Fung
, Y.
C.
, 1986
,
“On Residual Stresses in Arteries
,”
J. Biomech. Eng.
, 108
, pp.
189
–192
.3.
Guccione
, J.
M.
,
McCulloch
, A.
D.
, and
Waldman
, L.
K.
, 1991
,
“Passive Material Properties of Intact Ventricular Myocardium
Determined from a Cylindrical Model
,” J. Biomech.
Eng.
, 113
, pp.
42
–55
.4.
Takamizawa
,
K.
, and
Hayashi
,
K.
,
1987
, “Strain Energy Density Function and
Uniform Strain Hypotesis for Arterial Mechanics
,” J.
Biomech. Eng.
, 20
, pp.
7
–17
.5.
Vaishnav, R. N., and Vossoughi, J., 1983, “Estimation of Residual
Strains in Aortic Segments,” Biomedical Engineering II. Recent
Developments, C. W. Hall, ed., Pergamon, New York, pp.
330–333.
6.
Vaishnav
, R.
N.
, and
Vossoughi
,
J.
,
1987
, “Residual Stress and Strain in Aortic
Segments
,” J. Biomech. Eng.
,
20
, pp.
235
–239
.7.
Omens
, J.
H.
, and
Fung
, Y.
C.
, 1990
,
“Residual Strain in Rat Left Ventricle
,”
Circ. Res.
, 66
, pp.
37
–45
.8.
Taber
, L.
A.
, Hu
,
N.
,
Pexieder
,
T.
,
Clark
, E.
B.
, and
Keller
, B.
B.
, 1992
,
“Residual Strain the Ventricle of the Stage 16–24 Chick
Embryo
,” Circ. Res.
, 72
,
pp. 455
–462
.9.
Fung
, Y.
C.
, and
Liu
, S.
Q.
, 1989
,
“Change of Residual Strains in Arteries Due to Hypertrophy
Caused by Aortic Constriction
,” Circ. Res.
,
65
, pp.
1340
–1349
.10.
Fung
, Y.
C.
, and
Liu
, S.
Q.
, 1991
,
“Changes of the Zero-stress State of Rat Pulmonary Arteries
in Hypoxic Hypertension
,” J. Appl.
Physiol.
, 70
, pp.
2455
–2470
.11.
Greenwald
, S.
E.
,
Moore
, J.
E.
,
Rachev
,
A.
,
Kane
, T. P.
C.
, and
Meister
, J.
J.
, 1997
,
“Experimental Investigation of the Distribution of Residual
Strains in the Artery Wall
,” J. Biomech.
Eng.
, 119
, pp.
438
–444
.12.
Han
, H.
C.
, and
Fung
, Y.
C.
, 1991
,
“Species Difference of the Zero-stress State of Aorta: Pig
vs. Rat
,” J. Biomech. Eng.
,
113
, pp.
446
–451
.13.
Liu
, S.
Q.
, and
Fung
, Y.
C.
, 1988
,
“Zero-stress State of Arteries
,” J.
Biomech. Eng.
, 110
, pp.
82
–84
.14.
Liu
, S.
Q.
, and
Fung
, Y.
C.
, 1989
,
“Relationship Between Hypertension, Hypertrophy, and Opening
Angle of Zero-stress State of Arteries Following Aortic
Constriction
,” J. Biomech. Eng.
,
111
, pp.
325
–335
.15.
Vossoughi, J., Hedjazi, Z., and Borris II, F. S., 1993, “Intimal
Residual Stress and Strain in Large Arteries,” Proceedings of the Summer
Bioengineering Conference, N. A. Langrana, M. H. Friedman, and E.
S. Grood, eds., ASME, New York, pp. 434–437.
16.
Fung
, Y.
C.
, and
Liu
, S.
Q.
, 1992
,
“Strain Distribution in Small Blood Vessels With Zero-stress
State Taken into Consideration
,” Am. J.
Physiol.
, 31
, pp.
H544–H552
H544–H552
.17.
Xie
, J.
P.
, Liu
,
S. Q.
,
Yang
, R.
F.
, and
Fung
, Y.
C.
, 1991
,
“The Zero-stress State of Rat Veins and Vena
Cava.
,” J. Biomech. Eng.
,
113
, pp.
36
–41
.18.
Han
, H.
C.
, and
Fung
, Y.
C.
, 1991
,
“Residual Strains in Porcine and Canine
Trachea
,” J. Biomech.
, 24
,
pp. 307
–315
.19.
Taber
, L.
A.
, and
Eggers
, D.
W.
, 1996
,
“Theoretical Study of Stress-modulated Growth in the
Aorta
,” J. Theor. Biol.
,
180
, pp.
343
–357
.20.
Taber
, L.
A.
, 1998
,
“A Model for Aortic Growth Based on Fluid Shear and Fiber
Stresses
,” J. Biomech. Eng.
,
120
, pp.
348
–354
.21.
Van Dyke, T. J., and Hoger, A., 2000, “A Finite Element
Investigation of Opening Angle Experiments,” in preparation.
22.
Johnson
, B.
E.
, and
Hoger
,
A.
,
1995
, “The Use of a Virtual Configuration in
Formulating Constitutive Equations for Residually Stressed Elastic
Materials
,” J. Elast.
, 41
,
pp. 177
–215
.23.
Hoger
,
A.
,
1997
, “Virtual Configurations and Constitutive
Equations for Residually Stressed Bodies with Material
Symmetry
,” J. Elast.
, 48
,
pp. 125
–144
.24.
Bathe, K.-J., 1996, Finite Element Procedures.
Prentice-Hall. Englewood Cliffs, New Jersey.
25.
Holzapfel
, G.
A.
, and
Weizsa¨cker
, H.
W.
, 1998
,
“Biomechanical Behavior of the Arterial Wall and its
Numerical Characterization
,” Comput. Biol.
Med.
, 28
, pp.
377
–392
.26.
Crisfield, M. A., 1997, Non-linear Finite Element Analysis
of Solids and Structures, Volume 2: Advanced Topics. John Wiley
& Sons. Chichester, England.
Copyright © 2002
by ASME
You do not currently have access to this content.