This study shows how a probabilistic microstructural model for fibrous connective tissue behavior can be used to objectively describe soft tissue low-load behavior. More specifically, methods to determine tissue reference length and the transition from the strain-stiffening “toe-region” to the more linear region of the stress-strain curve of fibrous connective tissues are presented. According to a microstructural model for uniaxially loaded collagenous tissues, increasingly more fibers are recruited and bear load with increased tissue elongation. Fiber recruitment is represented statistically according to a Weibull probability density function (PDF). The Weibull PDF location parameter in this formulation corresponds to the stretch at which the first fibers begin to bear load and provides a convenient method of determining reference length. The toe-to-linear region transition is defined by utilizing the Weibull cumulative distribution function (CDF) which relates the fraction of loaded fibers to the tissue elongation. These techniques are illustrated using representative tendon and ligament data from the literature, and are shown to be applicable retrospectively to data from specimens that are not heavily preloaded. The reference length resulting from this technique provides an objective datum from which to calculate stretch, strain, and tangent modulus, while the Weibull CDF provides an objective parameter with which to characterize the limits of low-load behavior.

1.
Lam
,
T. C.
,
Shrive
,
N. G.
, and
Frank
,
C. B.
,
1995
, “
Variations in Rupture Site and Surface Strains at Failure in the Maturing Rabbit Medial Collateral Ligament
,”
ASME J. Biomech. Eng.
,
117
(
4
), pp.
455
461
.
2.
Chimich
,
D.
,
Frank
,
C.
,
Shrive
,
N.
,
Dougall
,
H.
, and
Bray
,
R.
,
1991
, “
The Effects of Initial End Contact on Medial Collateral Ligament Healing: A Morphological and Biomechanical Study in a Rabbit Model
,”
J. Orthop. Res.
,
9
(
1
), pp.
37
47
.
3.
Przybylski
,
G. J.
,
Carlin
,
G. J.
,
Patel
,
P. R.
, and
Woo
,
S. L.
,
1996
, “
Human Anterior and Posterior Cervical Longitudinal Ligaments Possess Similar Tensile Properties
,”
J. Orthop. Res.
,
14
(
6
), pp.
1005
1008
.
4.
Sabiston
,
P.
,
Frank
,
C.
,
Lam
,
T.
, and
Shrive
,
N.
,
1990
, “
Transplantation of the Rabbit Medial Collateral Ligament. I. Biomechanical Evaluation of Fresh Autografts
,”
J. Orthop. Res.
,
8
(
1
), pp.
35
45
.
5.
Woo
,
S. L.
,
Gomez
,
M. A.
,
Inoue
,
M.
, and
Akeson
,
W. H.
,
1987
, “
New Experimental Procedures to Evaluate the Biomechanical Properties of Healing Canine Medial Collateral Ligaments
,”
J. Orthop. Res.
,
5
(
3
), pp.
425
432
.
1.
Hull
,
M. L.
,
Berns
,
G. S.
,
Varma
,
H.
, and
Patterson
,
H. A.
,
1996
, “
Strain in the Medial Collateral Ligament of the Human Knee Under Single and Combined Loads,” [erratum appears in
J. Biomech
,
29
(
8
), pp.
1115
1115
];
2.
Hull
,
M. L.
,
Berns
,
G. S.
,
Varma
,
H.
, and
Patterson
,
H. A.
J. Biomech., 29(2), pp. 199–206.
1.
Fleming
,
B. C.
,
Beynnon
,
B. D.
,
Tohyama
,
H.
,
Johnson
,
R. J.
,
Nichols
,
C. E.
,
Renstrom
,
P.
, and
Pope
,
M. H.
,
1994
, “
Determination of a Zero Strain Reference for the Anteromedial Band of the Anterior Cruciate Ligament
,”
J. Orthop. Res.
,
12
(
6
), pp.
789
795
.
2.
Belkoff
,
S. M.
, and
Haut
,
R. C.
,
1991
, “
A Structural Model Used to Evaluate the Changing Microstructure of Maturing Rat Skin
,”
J. Biomech.
,
24
(
8
), pp.
711
720
.
3.
Belkoff
,
S. M.
, and
Haut
,
R. C.
,
1992
, “
Microstructurally Based Model Analysis of Gamma-Irradiated Tendon Allografts
,”
J. Orthop. Res.
,
10
(
3
), pp.
461
464
.
4.
Kastelic
,
J.
,
Palley
,
I.
, and
Baer
,
E.
,
1980
, “
A Structural Mechanical Model for Tendon Crimping
,”
J. Biomech.
,
13
(
10
), pp.
887
893
.
5.
Hurschler
,
C.
,
Loitz-Ramage
,
B.
, and
Vanderby
, Jr.,
R.
,
1997
, “
A Structurally Based Stress-Stretch Relationship for Tendon and Ligament
,”
ASME J. Biomech. Eng.
,
119
(
4
), pp.
392
399
.
6.
Lanir
,
Y.
,
1979
, “
A Structural Theory for the Homogeneous Biaxial Stress-Strain Relationships in Flat Collagenous Tissues
,”
J. Biomech.
,
12
(
6
), pp.
423
436
.
7.
Lanir
,
Y.
,
1963
, “
Constitutive Equations for Fibrous Connective Tissues
,”
J. Biomech.
,
16
(
1
), pp.
1
12
.
8.
Kwan
,
M. K.
, and
Woo
,
S. L.
,
1989
, “
A Structural Model to Describe the Nonlinear Stress-Strain Behavior for Parallel-Fibered Collagenous Tissues
,”
ASME J. Biomech. Eng.
,
111
(
4
), pp.
361
363
.
9.
Viidik
,
A.
,
1972
, “
Simultaneous Mechanical and Light Microscopic Studies of Collagen Fibers
,”
Z. Anat. Entwicklungsgesch
,
136
(
2
), pp.
204
212
.
10.
Sacks, M. S., 2001, “A Structural Constitutive Model for Planar Collagenous Tissues That Integrates Sals-Derived Fiber Orientation Data,” Advances in Bioengineering, 51, ASME, New York.
11.
Hurschler
,
C.
,
Provenzano
,
P. P.
,
Vanderby
, Jr.,
R.
,
1998
, “
Scanning Electron Microscopic Investigation of Healing and Normal Rat Medial Collateral Ligaments Fixed Under Slack and Loaded Conditions
,”
Trans. Orthop. Res. Soc.
,
23
, pp.
1032
1032
.
12.
Panjabi
,
M. M.
,
Yoldas
,
E.
,
Oxland
,
T. R.
, and
Crisco
, 3rd,
J. J.
,
1996
, “
Subfailure Injury of the Rabbit Anterior Cruciate Ligament
,”
J. Orthop. Res.
,
14
(
2
), pp.
216
227
.
13.
Weibull
,
W.
,
1951
, “
A Statistical Distribution Function of Wide Applicability
,”
ASME J. Appl. Mech.
,
18
(
3
), pp.
293
297
.
14.
Hines, W. W., and Montgomery, D. C., 1980, Probability and Statistics in Engineering and Management Science, John Wiley and Sons, New York.
15.
Abrahams
,
M.
,
1967
, “
Mechanical Behavior of Tendon in Vitro: A Preliminary Report
,”
Med. Biol. Eng.
,
5
, pp.
433
443
.
16.
Provenzano
,
P. P.
,
Heisey
,
D.
,
Haysashi
,
K.
,
Lakes
,
R. S.
, and
Vanderby
, Jr.,
R.
,
2002
, “
Sub-Failure Damage in Ligament: A Structural and Cellular Evaluation
,”
J. Appl. Physiol.
, (
1
), pp.
362
371
.
17.
Hansen
,
K. A.
,
Weiss
,
J. A.
, and
Barton
,
J. K.
,
2002
, “
Recruitment of Tendon Crimp With Applied Tensile Strain
,”
ASME J. Biomech. Eng.
,
124
(
1
), pp.
72
77
.
18.
Kato
,
Y. P.
,
Christiansen
,
D. L.
,
Hahn
,
R. A.
,
Shieh
,
S.-J.
,
Goldstein
,
J. D.
, and
Silver
,
F. H.
,
1989
, “
Mechanical Properties of Collagen Fibers: A Comparison of Reconstituted and Rat Tail Tendon Fibers
,”
Biomaterials
,
10
, pp.
38
42
.
19.
Sasaki
,
N.
, and
Odajima
,
S.
,
1996
, “
Elongation Mechanism of Collagen Fibrils and Force-Strain Relations of Tendon at Each Level of Structural Hierarchy
,”
J. Biomech.
,
29
(
9
), pp.
1131
1136
.
20.
Sasaki
,
N.
, and
Odajima
,
S.
,
1996
, “
Stress-Strain Curve and Young’s Modulus of a Collagen Molecule as Determined by The X-Ray Diffraction Technique
,”
J. Biomech.
,
29
(
5
), pp.
655
658
.
You do not currently have access to this content.