Simulations of soft tissues require accurate and robust constitutive models, whose form is derived from carefully designed experimental studies. For such investigations of membranes or thin specimens, planar biaxial systems have been used extensively. Yet, all such systems remain limited in their ability to: (1) fully prescribe in-plane deformation gradient tensor F2D, (2) ensure homogeneity of the applied deformation, and (3) be able to accommodate sufficiently small specimens to ensure a reasonable degree of material homogeneity. To address these issues, we have developed a novel planar biaxial testing device that overcomes these difficulties and is capable of full control of the in-plane deformation gradient tensor F2D and of testing specimens as small as ∼4 mm × ∼4 mm. Individual actuation of the specimen attachment points, combined with a robust real-time feedback control, enabled the device to enforce any arbitrary F2D with a high degree of accuracy and homogeneity. Results from extensive device validation trials and example tissues illustrated the ability of the device to perform as designed and gather data needed for developing and validating constitutive models. Examples included the murine aortic tissues, allowing for investigators to take advantage of the genetic manipulation of murine disease models. These capabilities highlight the potential of the device to serve as a platform for informing and verifying the results of inverse models and for conducting robust, controlled investigation into the biomechanics of very local behaviors of soft tissues and membrane biomaterials.

References

1.
Fung
,
Y. C.
,
1993
,
Biomechanics: Mechanical Properties of Living Tissues
, 2nd ed.,
Springer-Verlag
,
New York
.
2.
Sacks
,
M.
,
2000
, “
Biaxial Mechanical Evaluation of Planar Biological Materials
,”
J. Elasticity
,
61
, pp.
199
246
.
3.
Zhang
,
W.
,
Feng
,
Y.
,
Lee
,
C. H.
,
Billiar
,
K. L.
, and
Sacks
,
M. S.
,
2015
, “
A Generalized Method for the Analysis of Planar Biaxial Mechanical Data Using Tethered Testing Configurations
,”
ASME J. Biomech. Eng.
,
137
(
6
), p.
064501
.
4.
Grashow
,
J. S.
,
Yoganathan
,
A. P.
, and
Sacks
,
M. S.
,
2006
, “
Biaxial Stress-Stretch Behavior of the Mitral Valve Anterior Leaflet at Physiologic Strain Rates
,”
Ann. Biomed. Eng.
,
34
(
2
), pp.
315
325
.
5.
Sacks
,
M. S.
,
1999
, “
A Method for Planar Biaxial Mechanical Testing That Includes In-Plane Shear
,”
ASME J. Biomech. Eng.
,
121
(
5
), pp.
551
555
.
6.
Raghupathy
,
R.
, and
Barocas
,
V. H.
,
2010
, “
Generalized Anisotropic Inverse Mechanics for Soft Tissues
,”
ASME J. Biomech. Eng.
,
132
(
8
), p.
081006
.
7.
Aggarwal
,
A.
, and
Sacks
,
M. S.
,
2015
, “
An Inverse Modeling Approach for Semilunar Heart Valve Leaflet Mechanics: Exploitation of Tissue Structure
,”
Biomech. Model. Mechanobiol.
,
15
(4), pp.
1
24
.
8.
Lee
,
C. H.
,
Amini
,
R.
,
Gorman
,
R. C.
,
Gorman
,
J. H.
, 3rd
., and
Sacks
,
M. S.
,
2014
, “
An Inverse Modeling Approach for Stress Estimation in Mitral Valve Anterior Leaflet Valvuloplasty for In-Vivo Valvular Biomaterial Assessment
,”
J. Biomech.
,
47
(
9
), pp.
2055
2063
.
9.
Ferruzzi
,
J.
,
Bersi
,
M. R.
, and
Humphrey
,
J. D.
,
2013
, “
Biomechanical Phenotyping of Central Arteries in Health and Disease: Advantages of and Methods for Murine Models
,”
Ann. Biomed. Eng.
,
41
(
7
), pp.
1311
1130
.
10.
Billiar
,
K. L.
, and
Sacks
,
M. S.
,
1997
, “
A Method to Quantify the Fiber Kinematics of Planar Tissues Under Biaxial Stretch
,”
J. Biomech.
,
30
(
7
), pp.
753
756
.
11.
Nielsen
,
P. M.
,
Hunter
,
P. J.
, and
Smaill
,
B. H.
,
1991
, “
Biaxial Testing of Membrane Biomaterials: Testing Equipment and Procedures
,”
ASME J. Biomech. Eng.
,
113
(
3
), pp.
295
300
.
12.
Sun
,
W.
,
Sacks
,
M. S.
, and
Scott
,
M. J.
,
2005
, “
Effects of Boundary Conditions on the Estimation of the Planar Biaxial Mechanical Properties of Soft Tissues
,”
ASME J. Biomech. Eng.
,
127
(
4
), pp.
709
715
.
13.
Rivlin
,
R. S.
, and
Saunders
,
D. W.
,
1951
, “
Large Elastic Deformations of Isotropic Materials—7: Experiments on the Deformation of Rubber
,”
Philos. Trans. R. Soc. London Ser. A
,
243
(
865
), pp.
251
288
.
14.
Billiar
,
K. L.
, and
Sacks
,
M. S.
,
2000
, “
Biaxial Mechanical Properties of the Natural and Glutaraldehyde Treated Aortic Valve Cusp—Part I: Experimental Results
,”
ASME J. Biomech. Eng.
,
122
(
1
), pp.
23
30
.
15.
Eilaghi
,
A.
,
Flanagan
,
J. G.
,
Brodland
,
G. W.
, and
Ethier
,
C. R.
,
2009
, “
Strain Uniformity in Biaxial Specimens Is Highly Sensitive to Attachment Details
,”
ASME J. Biomech. Eng.
,
131
(
9
), p.
091003
.
16.
Jacobs
,
N. T.
,
Cortes
,
D. H.
,
Vresilovic
,
E. J.
, and
Elliott
,
D. M.
,
2013
, “
Biaxial Tension of Fibrous Tissue: Using Finite Element Methods to Address Experimental Challenges Arising From Boundary Conditions and Anisotropy
,”
ASME J. Biomech. Eng.
,
135
(
2
), p.
021004
.
17.
Utkin
,
V.
,
1977
, “
Variable Structure Systems With Sliding Modes
,”
IEEE Trans. Autom. Control
,
22
(
2
), pp.
212
222
.
18.
DeCarlo
,
R.
,
Zak
,
S.
, and
Matthews
,
G.
,
1988
, “
Variable Structure Control of Nonlinear Multivariable Systems: A Tutorial
,”
Proc. IEEE
,
76
(
3
), pp.
212
232
.
19.
Fan
,
R.
, and
Sacks
,
M. S.
,
2014
, “
Simulation of Planar Soft Tissues Using a Structural Constitutive Model: Finite Element Implementation and Validation
,”
J. Biomech.
,
47
(
9
), pp.
2043
2054
.
20.
Sacks
,
M. S.
, and
Chuong
,
C. J.
,
1998
, “
Orthotropic Mechanical Properties of Chemically Treated Bovine Pericardium
,”
Ann. Biomed. Eng.
,
26
(
5
), pp.
892
902
.
21.
Collins
,
M.
,
Eberth
,
J. F.
,
Wilson
,
E.
, and
Humphrey
,
J.
,
2012
, “
Acute Mechanical Effects of Elastase on the Infrarenal Mouse Aorta: Implications for Models of Aneurysms
,”
J. Biomech.
,
45
(
4
), pp.
660
665
.
22.
Eberth
,
J. F.
,
Popovic
,
N.
,
Gresham
,
V. C.
,
Wilson
,
E.
, and
Humphrey
,
J. D.
,
2010
, “
Time Course of Carotid Artery Growth and Remodeling in Response to Altered Pulsatility
,”
Am. J. Physiol. Heart Circ. Physiol.
,
299
(
6
), pp.
H1875
H1883
.
23.
Chen
,
K.
,
Fata
,
B.
, and
Einstein
,
D. R.
,
2008
, “
Characterization of the Highly Nonlinear and Anisotropic Vascular Tissues From Experimental Inflation Data: A Validation Study Toward the Use of Clinical Data for In-Vivo Modeling and Analysis
,”
Ann. Biomed. Eng.
,
36
(
10
), pp.
1668
1680
.
24.
Rausch
,
M. K.
,
Famaey
,
N.
,
Shultz
,
T. O.
,
Bothe
,
W.
,
Miller
,
D. C.
, and
Kuhl
,
E.
,
2013
, “
Mechanics of the Mitral Valve: A Critical Review, an In Vivo Parameter Identification, and the Effect of Prestrain
,”
Biomech. Model. Mechanobiol.
,
12
(
5
), pp.
1053
1071
.
25.
Billiar
,
K. L.
, and
Sacks
,
M. S.
,
2000
, “
Biaxial Mechanical Properties of the Native and Glutaraldehyde-Treated Aortic Valve Cusp—Part II: A Structural Constitutive Model
,”
ASME J. Biomech. Eng.
,
122
(
4
), pp.
327
335
.
26.
Humphrey
,
J. D.
,
Strumpf
,
R. K.
, and
Yin
,
F. C.
,
1990
, “
Determination of a Constitutive Relation for Passive Myocardium—I: A New Functional Form
,”
ASME J. Biomech. Eng.
,
112
(
3
), pp.
333
339
.
27.
Humphrey
,
J. D.
,
Strumpf
,
R. K.
, and
Yin
,
F. C.
,
1990
, “
Determination of a Constitutive Relation for Passive Myocardium—II: Parameter Estimation
,”
ASME J. Biomech. Eng.
,
112
(
3
), pp.
340
346
.
28.
Lee
,
C. H.
,
Feaver
,
K.
,
Zhang
,
W.
,
Gorman
,
R. C.
,
Gorman
,
J. H.
, and
Sacks
, M. S.,
2016
, “Inverse Modeling Based Estimation of In-Vivo Stresses and Their Relation to Simulated Layer-Specific Interstitial Cell Deformations in the Mitral Valve,” Summer Biomechanics, Bioengineering and Biotransport Conference (SB3C), National Harbor, MD, June 29–July 2.
29.
Wagenseil
,
J. E.
,
Nerurkar
,
N. L.
,
Knutsen
,
R. H.
,
Okamoto
,
R. J.
,
Li
,
D. Y.
, and
Mecham
,
R. P.
,
2005
, “
Effects of Elastin Haploinsufficiency on the Mechanical Behavior of Mouse Arteries
,”
Am. J. Physiol. Heart Circ. Physiol.
,
289
(
3
), pp.
1209
1217
.
30.
Chai
,
S.
,
Chai
,
Q.
,
Danielsen
,
C. C.
,
Hjorth
,
P.
,
Nyengaard
,
J. R.
,
Ledet
,
T.
,
Yamaguchi
,
Y.
,
Rasmussen
,
L. M.
, and
Wogensen
,
L.
,
2005
, “
Overexpression of Hyaluronan in the Tunica Media Promotes the Development of Atherosclerosis
,”
Circ. Res.
,
96
(
5
), pp.
583
591
.
31.
Slotine
,
J.-J. E.
, and
Li
,
W.
,
1991
,
Applied Nonlinear Control
,
Prentice Hall
, Englewood Cliffs, NJ.
32.
Edwards
,
C.
, and
Spurgeon
,
S.
,
1998
,
Sliding Mode Control: Theory and Applications
,
CRC Press
, Boca Raton, FL.
33.
Kuo
,
T.-C.
,
Huang
,
Y.-J.
, and
Chang
,
S.-H.
,
2008
, “
Sliding Mode Control With Self-Tuning Law for Uncertain Nonlinear Systems
,”
ISA Trans.
,
47
(
2
), pp.
171
178
.
You do not currently have access to this content.