A rational methodology is developed for optimal design of biaxial stretch tests intended for estimating material parameters of flat tissues. It is applied to a structural model with a variety of constitutive equations and test protocols, and for a wide range of parameter levels. The results show nearly identical optimal designs under all circumstances. Optimality is obtained with two uniaxial stretch tests at mutually normal directions inclined by 22.5 deg to the axes of material symmetry. Protocols which include additional equibiaxial tests provide superior estimation with lower variance of estimates. Tests performed at angles 0, 45, and 90 deg to the axes of material symmetry provide unreliable estimates. The optimal sampling is variable and depends on the protocols and model parameters. In conclusion, the results indicate that biaxial tests can be improved over presently common procedures and show that this conclusion applies for a variety of circumstances.

1.
Alexander
H.
, and
Cook
T. H.
,
1977
, “
Accounting for Natural Tension in the Mechanical Testing of Human Skin
,”
J. Invest. Dermatol.
, Vol.
69
, pp.
310
314
.
2.
Bard, Y., 1974, Nonlinear Parameter Estimation, Academic Press, N.Y.
3.
Beck, J. V., and Arnold, K. J., 1977, Parameter Estimation in Engineering Science, Wiley, N.Y.
4.
Box, G. E. P., and Draper, N. R., 1987, Empirical Model-Building and Response Surfaces, Wiley, N.Y.
5.
Choi
H. S.
, and
Vito
R. P.
,
1990
, “
Two-Dimensional Stress-Strain Relationship for Canine Pericardium
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
112
, pp.
153
159
.
6.
Dennis
J. E.
,
Gay
D. H.
, and
Welsch
R. E.
,
1981
, “
An Adaptive Nonlinear Least-squares Algorithm
,”
ACM Trans. Math. Software
, Vol.
7
, pp.
348
368
.
7.
Distefano
J. J.
,
1979
, “
Matching the Model and the Experiment to the Goals: Data Limitations, Complexity and Optimal Biochemical Signals
,”
J. Cybern. Info. Sci.
, Vol.
2
, pp.
6
20
.
8.
Endrenyi, L., 1981, Kinetic Data Analysis, Plenum, N.Y., pp. 137–167.
9.
Fung, Y. C., 1972, “Stress-Strain-History Relations of Soft Tissues in Simple Elongation,” Biomechanics—Its Foundations and Objectives, Fung, Y. C., Perrone, N., and Anliker, M., eds., pp. 181–208, Prentice-Hall, N.J.
10.
Hukins, D. W. L., 1988, “Disc Structure and Function,” Biology of the Intervertebral Disc, Ghosh, P., ed., pp. 1–37, CRC Press, Boca Raton, FL.
11.
Humphrey
J. D.
,
Strumpf
R. K.
, and
Yin
F. C. P.
,
1990
, “
Determination of Constitutive Relation for Passive Myocardium: I. A New Functional Form
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
112
, pp.
333
339
.
12.
Lanir
Y.
,
1983
, “
Constitutive Equation for Fibrous Connective Tissues
,”
J. Biomechanics
, Vol.
16
, pp.
1
12
.
13.
Lanir
Y.
, and
Fung
Y. C.
,
1974
a, “
Two-Dimensional Mechanical Properties of Rabbit Skin. I. Experimental System
,”
J. Biomechanics
, Vol.
7
, pp.
29
34
.
14.
Lanir
Y.
, and
Fung
Y. C.
,
1974
b, “
Two-Dimensional Mechanical Properties of Rabbit Skin. II. Experimental Results
,”
J. Biomechanics
, Vol.
7
, pp.
171
182
.
15.
Lee
M. C.
,
Fung
Y. C.
,
Shabetai
R.
, and
LeWinter
M. M.
,
1987
, “
Biaxial Mechanical Properties of Human Pericardium and Canine Comparisons
,”
Amer. J. Physiol.
, Vol.
253
, pp.
H75–H82
H75–H82
.
16.
Lutchen, K. R., and Saidel, G. M., 1982, “Sensitivity Analysis and Experimen
17.
Nathanson
M. H.
, and
Saidel
G. M.
,
1985
, “
Mutiple-Objective Criteria for Optimal Experimental Design: Application to Ferrokinetics
,”
Amer. J. Physiol.
, Vol.
248
, pp.
378
386
.
18.
Sacks
M. S.
, and
Chuong
C. J.
,
1992
, “
Characterization of Collagen Fiber Architecture in the Canine Diaphragmatic Central Tendon
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
114
, pp.
183
190
.
19.
Slinker
B. K.
, and
Glantz
S. A.
,
1985
, “
Multiple Regression for Physiological Data Analysis: The Problem of Multicolinearity
,”
Amer. J. Physiol.
, Vol.
249
, pp.
R1–R12
R1–R12
.
20.
Smaill, B., and Hunter, P. J., 1991, “Structure and Function of the Diastolic Heart: Material Properties of Passive Myocardium,” Theory of the Heart, Glass, L., Hunter, P., and McCulloch, A., eds., Sprinter-Verlag, N.Y.
21.
Vawter
D. L.
,
Fung
Y. C.
, and
West
J. B.
,
1978
, “
Elasticity of Excised Dog’s Lung Tissue
,”
J. Appl. Physiol.
, Vol.
45
, pp.
261
269
.
22.
Yin
F. C. P.
,
Strumpf
R. K.
,
Chew
P. H.
, and
Zeger
S. L.
,
1987
, “
Quantification of the Mechanical Properties of Non-contracting Canine Myocardium under Simultaneous Biaxial Loading
,”
J. Biomechanics
, Vol.
20
, pp.
577
589
.
This content is only available via PDF.
You do not currently have access to this content.