Viscoelastic relaxation and recovery of tendon.

Abstract

Tendons exhibit complex viscoelastic behaviors during relaxation and recovery. Recovery is critical to predicting behavior in subsequent loading, yet is not well studied. Our goal is to explore time-dependent recovery of these tendons after loading. As a prerequisite, their strain-dependent viscoelastic behaviors during relaxation were also characterized. The porcine digital flexor tendon was used as a model of tendon behavior. Strain-dependent relaxation was observed in tests at 1, 2, 3, 4, 5, and 6% strain. Recovery behavior of the tendon was examined by performing relaxation tests at 6%, then dropping to a low but nonzero strain level. Results show that the rate of relaxation in tendon is indeed a function of strain. Unlike previously reported tests on the medial collateral ligament (MCL), the relaxation rate of tendons increased with increased levels of strain. This strain-dependent relaxation contrasts with quasilinear viscoelasticity (QLV), which predicts equal time dependence across various strains. Also, the tendons did not recover to predicted levels by nonlinear superposition models or QLV, though they did recover partially. This recovery behavior and behavior during subsequent loadings will then become problematic for both quasilinear and nonlinear models to correctly predict.

Full text

Page 1

Viscoelastic Relaxation and Recovery of Tendon
SARAH E. DUENWALD,1RAY VANDERBY JR.,1,2and RODERIC S. LAKES1,3
1Department of Biomedical Engineering, University of Wisconsin-Madison, Madison, WI 53706-1687, USA;2Department of
Orthopedics and Rehabilitation, University of Wisconsin-Madison, Madison, WI 53706-1687, USA; and3Department of
Engineering Physics, University of Wisconsin-Madison, 1500 Engineering Drive, 541, Madison, WI 53706-1687, USA
(Received 7 July 2008; accepted 27 March 2009; published online 8 April 2009)
Abstract—Tendons exhibit complex viscoelastic behaviors
during relaxation and recovery. Recovery is critical to
predicting behavior in subsequent loading, yet is not well
studied. Our goal is to explore time-dependent recovery of
these tendons after loading. As a prerequisite, their strain-
dependent viscoelastic behaviors during relaxation were also
characterized. The porcine digital flexor tendon was used as a
model of tendon behavior. Strain-dependent relaxation was
observed in tests at 1, 2, 3, 4, 5, and 6% strain. Recovery
behavior of the tendon was examined by performing relax-
ation tests at 6%, then dropping to a low but nonzero strain
level. Results show that the rate of relaxation in tendon is
indeed a function of strain. Unlike previously reported tests
on the medial collateral ligament (MCL), the relaxation rate
of tendons increased with increased levels of strain. This
strain-dependent relaxation contrasts with quasilinear visco-
elasticity (QLV), which predicts equal time dependence
across various strains. Also, the tendons did not recover to
predicted levels by nonlinear superposition models or QLV,
though they did recover partially. This recovery behavior and
behavior during subsequent loadings will then become
problematic for both quasilinear and nonlinear models to
correctly predict.
Keywords—Quasilinear
superposition, Tendon.
viscoelasticity(QLV), Nonlinear
INTRODUCTION
Like many tissues in the body, tendons exhibit vis-
coelastic, or time-dependent, behavior. When the tissue
is held at a constant strain level, the stress in the tissue
decreases, a phenomenon called stress relaxation.
Conversely, when held at a constant stress level, strain
in the tissue increases, known as creep. This visco-
elasticity is thought to be a function of the main
mechanical component, collagen, as well as other
constituents of the extracellular matrix such as prote-
oglycans, glycoproteins, and water. Tendon collagen
consists mainly of type I collagen fibers which are
predominantly oriented parallel to the direction of
load, or the long axis of the tendon.9,28
It is important to understand the viscoelasticity of
tendon to accurately understand the behavior of a
tendon. Creep and stress relaxation must be well de-
fined in order to accurately predict how a tendon will
behave under transient loadings, but a robust model of
the tendon also requires an understanding of recovery
behavior following removal of the load. Post-load
recovery is not only important for understanding the
unloaded tendon; it is also critical to tendon behavior
under subsequent loadings. Failure to accurately
account for the time-dependent recovery during un-
loaded periods will be a source of error when pre-
dicting behavior in response to future loads, especially
if the unloaded period is short, and achieving repro-
ducible data during serial testing. Although stress
relaxation and creep behaviors of many tissues have
been studied, including rat MCL,29sheep digital ten-
don,33bovine cornea,3and the stapedial tendon in the
middle ear,4relatively few studies investigate the
recovery periods following creep or stress relaxation
testing. This omission leads to incomplete data to
understand and model post-loading behavior in ten-
don.
The main research concerning the recovery period
following loading is regarding the recovery of the spine
and its discs following creep experiments. McGill and
Brown performed creep testing on human subjects for
20 min and monitored the recovery after the removal
of the load for 20 min.21Likewise, Eckstrom et al.
induced creep in the porcine spine over 1 h, and
observed its recovery for an hour following the re-
moval of load.8Gedalia et al. performed similar testing
in lumbar structures, loading them for 50 min and
monitoring recovery after 50 min.10Finally, Solomo-
now et al. subjected cat spines to cyclic loading for
Address correspondence to Roderic S. Lakes, Department of
Engineering Physics, University of Wisconsin-Madison, 1500 Engi-
neering Drive, 541, Madison, WI 53706-1687, USA. Electronic mail:
duenwald@wisc.edu, lakes@engr.wisc.edu
Annals of Biomedical Engineering, Vol. 37, No. 6, June 2009 (? 2009) pp. 1131–1140
DOI: 10.1007/s10439-009-9687-0
0090-6964/09/0600-1131/0 ? 2009 Biomedical Engineering Society
1131

Page 2

50 min, and observed the recovery for 7 h.32Interest-
ingly, each of these studies found that the recovery of
creep in the spine requires more time than the duration
over which the load was applied. However, with the
different structure and function of the tendon, it is
crucial to perform experiments on tendon itself rather
than draw conclusions from spine behavior.
Surgical applications have also sparked research
regarding tendon viscoelasticity. Graf et al. found that
recovery from 10-min stress relaxation testing was not
complete after 30 min.11Understanding creep and
recovery of a tendon graft is important to ensure
proper joint kinematics and maximize success in joint
reconstructions.
Knowledge of the biomechanical behavior of the
tendonsandligaments
understanding, quantifying, and treating injuries in
these tissues. Their behaviors are important when
considering the wide use of grafts, whether in an
autograft, synthetic graft, or allograft, as any such
graft should ideally match the properties of the pre-
damaged tendon or ligament for optimal function.
Increased laxity could allow abnormal and extreme
movement of the joint, leading to injury of surround-
ing tissue. Insufficient laxity could limit movement and
result in tearing of the graft under normal movement
conditions. A distinction between tendon and ligament
behavior is also important when considering grafts.
Though often viewed as surgically interchangeable,
tendons and ligaments serve different biomechanical
functions and have unique behaviors. Even subtle
differences may be important for grafting and tissue
engineering applications. The goal of this study
therefore is to use the porcine digital flexor tendon as a
model to characterize stress relaxation over a range of
strains, comparing its behavior to that found in other
tendon and ligament studies, and examine the time-
dependent recovery behavior of the tendon following
the removal of a step load.
isalsoimportantfor
MATERIALS AND METHODS
Forty-three digital flexor tendons were carefully
dissected from porcine legs obtained from a local
abattoir. Ten were allocated to each experiment (as
described in the following paragraphs), and three were
used for a repeatability study (described later). The
tendon was removed from the muscle belly, but re-
mained attached to the bone at the distal insertion site.
All excess tissue, including muscle tissue and the ten-
don sheath, was carefully removed from the tendon.
The bone was potted in lightweight filler hardened with
a cream hardener for gripping in the test machine. The
tendons were kept hydrated with PBS saline solution
throughout harvesting and processing. Tendons were
then wrapped in saline-soaked gauze, covered with
aluminum foil, and sealed in plastic bags to be stored
in a ?30 ?C freezer until time of testing. Investigators
report that such careful freezing procedures have little
effect on the biomechanical properties of collagenous
tissues such as tendon and ligament.14,22
All experiments were performed using a servohy-
draulic mechanical test system (Bionix 858; MTS,
Minneapolis, MN) in conjunction with a computer to
collect data. The load frame was equipped with a lower
block designed to hold the potted bone and an upper
soft tissue grip designed to hold the tendon. The upper
grip utilized a holder for dry ice to provide a secure
grip on the tendon fibers, and is denoted a ‘‘cryogrip.’’
This cryogrip was connected to a 50 lb load cell (Eaton
Corporation) with data collected on a PC. The lower
block remained stationary during test runs, while the
cryogrip moved to the specified displacement. All
strain was measured as the grip-to-grip elongation di-
vided by the undeformed length of the specimen. The
lower block and tendon were contained in a bath so
that throughout testing the tendon was submerged in
physiologic buffer solution at ambient room tempera-
ture.
All testing began with a preload of 1 N to remove
slack in the tendon and a preconditioning protocol in
which the tendon was stretched to 2% strain in a
sinusoidal wave for 20 s with a period of 2 s. After
preconditioning, the specimen was allowed to recover
for 5 min before being again stretched to 2% strain
and held for 100 s (see Fig. 1), after which it was un-
FIGURE 1.
without observed recovery. This waveform was performed at
1, 2, 3, 4, 5, and 6% strains (only 6% strain input shown here)
for the relaxation at various strains experiments and at 2%
strain during preconditioning.
Input waveform for single relaxation analysis
DUENWALD et al.1132

Page 3

loaded for 1000 s, or 10 times the length of relaxation,
prior to further testing. Strain was treated as a step
rather than a ramp, with the zero time point assigned
halfway through the rise time, and data collection
beginning at t = 2.5tr, or about 0.1 s, where tris the
rise time of the machine. This experimental design
follows Lakes’ example for creep.15
The cross-sectional area of the tendon was assumed
to be elliptical, and was calculated (prior to testing)
from micrometer measurements of the long and short
axes when the tendon was under preload.
Stress in the tissue was computed as:
rðtÞ ¼ FðtÞ=A0;
ð1Þ
where F(t) is the force as a function of time, and A0is
the cross-sectional area of the tendon. The relaxation
function was calculated via:
EðtÞ ¼ rðtÞ=e;
ð2Þ
where r(t) is the stress defined in Eq. (1), and e is the
constant strain level to which the tendon is pulled.
The basic form of the nonlinear superposition is:
Z
where E(t,e) is the relaxation function (defined in
Eq. 2). With the use of the discrete step strain function,
the nonlinear superposition prediction becomes:
rðe;tÞ ¼
E½t ? s;eðsÞ?deðsÞ
ds
ds;
ð3Þ
rðtÞ ¼ e1Eðt;e1Þ ? ðe1? e2ÞEðt ? t1;e2Þ;
where t is the time from the start of stress relaxation at
strain level e1and t1is the time at which recovery at
strain level e2begins.
The basic equation for stress in QLV is:
Zt
where E(t,e) has been separated into the product of a
time-dependent modulus, Et(t), and g(e), which repre-
sents the nonlinear strain dependence (independent of
time).
Since we are using a discrete step strain function, we
utilize the form:
ð4Þ
rðtÞ ¼
0
Etðt ? sÞgðeÞdr
de
deðsÞ
ds
ds:
ð5Þ
rðtÞ ¼ ðe1ÞEtðtÞgðe1Þ ? ðe1? e2ÞEtðt ? t1Þgðe2Þ
to describe the stress behavior predicted by QLV.
ð6Þ
Relaxation at Various Strains
Ten porcine flexor tendons were tested in this por-
tion of the experiment to examine the stress relaxation
behavior that occurs as the tendon is tested over a
range of strains. The tendons were tested at 1, 2, 3, 4, 5,
and 6% strain in randomized order to ensure that the
trends were due to differences in strain, not the testing
order. Each relaxation test involved the tendon being
stretched to the prescribed strain (1, 2, 3, 4, 5, or 6%)
and held for 100 s prior to being released to the pre-
load level to rest for 1000 s before the next test was run
(see Fig. 1 for representative waveform). The tendon
was then stretched to the next prescribed strain and
released, in the same manner as just described, until all
six strain levels (1–6%) had been tested. Force data
were recorded throughout the entire relaxation and
recovery period on the PC simultaneously with time
and strain recording. At the conclusion of the sixth
test, data were exported for analysis.
Relaxation and Recovery Comparison
Ten porcine flexor tendons were tested to examine
the recovery behavior during the period immediately
following stress relaxation. Tendons were stretched to
2% strain, at which they were held for 100 s, and then
dropped to preload at which they rested for 1000 s.
They were then stretched to 6% strain for 100 s of
relaxation, after which the strain was lowered to 2%
for a 100 s period in which recovery could be observed
(see Fig. 2 for waveform). The recovery was recorded
at a low strain rather than zero strain, as zero strain
would cause the tendon to become slack, preventing
observation of recovery behavior with the load cell.
The maximum strain of 6% was chosen as it would be
high enough to allow adequate recovery at a nonzero
FIGURE 2.
analysis. During such analysis, relaxation always took place
at 6% strain, but the recovery portion was performed at 1, 2,
and 3% strain.
Input waveform for relaxation and recovery
Viscoelastic Relaxation and Recovery of Tendon1133

Page 4

strain while still being low enough to avoid damage to
or failure of the tissue.
After the recovery period, the specimen was released
to its preload and allowed to rest for 1000 s before
repeating the waveform. This was done until a total of
three waveforms were completed on the tissue (to en-
sure a good data set from each specimen), and repeated
for each of the 10 specimens. Force data were recorded
throughout the entire relaxation and recovery period
on the PC simultaneously with time and strain
recording. E(t) was calculated from the stress relaxa-
tion data at 6% and 2% strain, and curve fits of the
E(t) were calculated in order to make model predic-
tions of the relaxation and recovery. Nonlinear
superposition and QLV equations were then plotted
with and compared to experimental data.
This procedure was repeated for 10 tendons for
recovery at 3% strain and 10 tendons for recovery at
1% strain (with the relaxation performed at 6% strain
as before) for a total of 30 tendons (including the
previous 10 in this section), where all previously
mentioned components of 2% strain were replaced
with 3% and 1% strain. This was done to determine
whether the nonzero strain (1, 2, or 3%) level deter-
mined the rate of recovery.
Repeatability and Statistics
In order to evaluate the repeatability of experiments
on a particular specimen, three specimens underwent
the relaxation (at 6% strain) and recovery (at 2%
strain) procedures outlined in the previous section a
total of five times. Load data were recorded over 100 s
of relaxation and over 100 s of recovery. Load values
at 0.1, 1, 10, and 100 s were averaged between the
relaxation runs for each tendon, and the standard
deviation at each time point was measured; the process
was then repeated for each of the recovery runs. This
process allowed a quantification of repeatability not
achievable through graphical representation alone; by
analyzing the time points in each run it is possible to
compare the similarity of each curve (small standard
deviations ensure that the curves follow the same
general path).
The deviation between different specimens was also
of interest. Variations between stress relaxation curves
and recovery curves from data collected from all 43
specimens (not just from the three involved in this
study) were measured to get the full range of specimen-
to-specimen variation. The average and standard
deviation between the curves of these specimens were
measured and recorded in a table. Student t-tests were
conducted on A and n values to determine statistical
significant differences (where a value of p £ 0.05 is
considered statistically significant).
RESULTS
Data from each of the various tests were graphed so
that behavioral trends could be examined. Information
from each tendon tested was collected and graphed,
then categorized into subgroups based on the test(s)
performed on the tissue.
Relaxation at Various Strains
Two types of graphs were constructed from the data
collected for each tendon tested at various strains.
First, a graph showing load vs. time (Fig. 3) was pro-
duced to describe the relative behavior at various
strains. Next, the data were used to create a set of
FIGURE 3.
tissue at various strains, displaying the increasing time
dependency with increasing strain. (a) All six strain levels,
showing the converging nature of the curves. (b) 2, 4, and 6%
strain curves, each data set fitted with the curve fit of the 2%
strain.
Load vs. time during relaxation of the tendon
DUENWALD et al. 1134

Page 5

isochronal stress vs. strain curves to display the strain-
stiffening behavior of the tendon (Fig. 4).
Figure 3a shows that the rate of relaxation (dem-
onstrated by the slope of the log-log plot) increases
with increasing strain. Thus, the tendon displays more
viscoelastic behavior at the higher strains and more
elastic behavior at lower strains. This trend is further
displayed in Fig. 3b as the curve fit of the 2% strain is
plotted with the 4% and 6% strain data. This figure
also displays that QLV is inadequate to model the
relaxation behavior; QLV predicts that the rate of
relaxation is independent of strain,27which differs
from our observed relaxation behavior.
The isochronal curves in Fig. 4 show that despite
the higher rates of relaxation at higher strains, the
tendon displays strain-stiffening behavior at all times
(with an increase in strain on the tendon, the tendon
becomes increasingly stiff), manifested by the concave-
up slope of the curve.16
Relaxation and Recovery Analysis
Force vs. time information from the 6% strain and
the 2% strain tests, as well as the force vs. time data
gathered during the recovery period (when strain is
reduced from 6% to 2%), normalized for strain level
(i.e., divided by their relative strain level), were plotted
on a graph, and fitted with a power law equation (this
was also performed for experiments using 6% and 3%
or 6% and 1% strain). When plotted on a log-log scale
(see Fig. 5), the results follow straight line trends,
indicating that both relaxation and recovery curves can
be approximated by the power law equation:
r
e0¼ Atn;
ð7Þ
where A has units of Pa and t has units of seconds. The
slopes of the straight lines of the relaxation data on
these plots indicate the power, or n value, of the data,
and thus the magnitude of n indicates how rapidly
relaxation or recovery occurs in time. In agreement
with the previous results of relaxation at various
strains, the absolute value of the power of the 6%
strain relaxation curve (in this example, n = 0.115) was
higher than that of the 2% strain relaxation curve (in
this example, n = 0.060). Interestingly, the absolute
value of the power of the recovery curve (in this
example, n = 0.017) was much smaller than either of
the relaxation curves. This indicates that the recovery
occurs at a much slower rate than relaxation, even the
relaxation at the lower strains. Relative rates at dif-
ferent strain levels will be discussed further in the next
section.
Figure 6 contains both the nonlinear superposition
prediction and the QLV prediction based on relaxation
curves performed at 6% and 3% strain. Neither non-
linear superposition nor QLV accurately predict the
recovery behavior. Nonlinear superposition over-pre-
dicted the recovery(at
218.6 ± 58.6%, and QLV over-predicted the recovery
(at the highest stress) by 266.9 ± 50.9%.
While recovery during the 100 s period immediately
following stress relaxation was slow and did not come
to completion during the 100-s period, it was observed
that, following the 1000 s of unloading between suc-
cessive tests, the tendon recovered to within 0.5 N of
the original preload in all cases.
the highest stress)by
FIGURE 4.
strain level for designated time point, displaying the strain-
stiffening behavior of the tendon.
Isochronal curves showing the stress at each
FIGURE 5.
plete test of the tendon, showing the increased slope of the
relaxation curve compared to the recovery curve.
Relaxation and recovery results from one com-
Viscoelastic Relaxation and Recovery of Tendon1135

Page 6

Repeatability and Statistics
It was observed that the relaxation (Fig. 7a) and
recovery (Fig. 7b) tests run on a single specimen were
quite repeatable, with small deviations between either
recovery curves or relaxation curves (Tables 1 and 2).
There was, however, a larger amount of variability
between different tendons, leading to larger standard
deviations in both the A and n values (Table 3). Even
with the larger standard deviations, many of the A and
n values were significantly different between strain
levels. A values, which represent the initial stress
magnitude for a given strain level, were significantly
higher for stress relaxation curves at 6% strain than for
relaxation at 3% strain (p = 0.0418) and at 2% strain
(p = 0.0003), and were also significantly higher for
relaxation at 3% strain vs. 2% strain (p = 0.050). A
values were significantly lower for recovery curves at
1%strainvs.both3%
(p<0.0001) strains, but were not significantly higher
for 3% strain compared to 2% (p = 0.3121). The n
values, which represent the rate of relaxation or
recovery at a given strain level, were significantly
(p = 0.0048) and2%
FIGURE 6.
position and QLV models. The baseline is denoted by ‘‘B’’ and
the relaxed 3% asymptote (lowest level reached during
relaxation) is denoted by ‘‘RA.’’ (a) Relaxation and recovery
curves based on experimental data, nonlinear superposition
model, and QLV model. (b) Recovery portion of the data,
demonstrating that neither QLV nor nonlinear superposition
are accurate predictions of recovery behavior, and QLV is the
worse fit of the two.
Experimental data compared to nonlinear super-
FIGURE 7.
specimen. The relaxation and especially the recovery are very
repeatable between test runs on a single specimen.
Relaxation (a) and recovery (b) curves on a single
TABLE 1.Repeatability statistics on five relaxation tests for
a single specimen.
Relaxation
Loads (N) at time points
0.1 s1 s10 s100 s
Averages (N)
Standard deviation (N)
% of average
84.64
7.483
8.840
72.02
4.548
6.315
61.22
4.003
6.539
46.62
3.028
6.495
DUENWALD et al. 1136

Page 7

higher for relaxation at 6% strain than at 3% strain
(p<0.0001) and 2% strain (p<0.0001). The n values
were also significantly higher for relaxation at 3%
strain than at 2% strain (p = 0.0291). The rates of
recovery (n values) were not significantly higher at 3%
strain than at 2% strain (p = 0.1115), but were sig-
nificantly higher at 3% than at 1% strain (p = 0.0059);
they were also significantly higher at 2% strain than at
1% strain (p = 0.0008). The rate of relaxation at 6%
strain was significantly higher than the rate of recovery
at 1, 2, or 3% strain (p<0.0001 in all three cases).
DISCUSSION
Our experimental results show that both relaxation
and recovery of the porcine digital flexor tendon over
100 s of loaded behavior can be well approximated by
a power law in time, but the recovery is not predicted
by a simple nonlinear superposition equation or by the
more complex QLV theory. The experimental recovery
proceeds at a much slower rate than relaxation, and
much slower than predicted by nonlinear superposition
or QLV. Also deviating from the theory of QLV was
the presence of a strain-dependent relaxation rate, as
demonstrated by Figs. 3a and 3b. The strain-stiffening
tendency of the isochronal stress-strain curves (Fig. 4)
suggest that the observed increased relaxation at
higher strain levels was not due to slippage of the
tendon in the grips. Such behavior would result in
strain-softening (marked by a concave-down slope of
the line) behavior at higher strains.
Our study is not the first to demonstrate the limi-
tations of QLV in soft tissues. A major limitation no-
ted by others is the assumption of a linear material
response,34manifesting itself in a single reduced
relaxation function over a range of strain levels26or
constant amplitude of viscous effects over a range of
frequencies.17The QLV model was inaccurate at high
strain rates during experiments performed by Woo
et al.,35and has also been shown by investigators to
under-predict hysteresis25,36and early stress relaxa-
tion.7
Physiologic strain ranges up to 8% in vivo,20so it
was assumed that a grip-to-grip strain of 6% would be
below the damage threshold, and thus would allow
recovery of the tissue. It has been suggested by Mag-
nusson et al. that tendon is less likely to deform than
the muscle–tendon unit during loading.20In fact, Lie-
ber et al. noted that while passive stretch in the phys-
iologic range can be up to 8% strain, only 2% of that
strain occurs in the tendon.18This indicates that, in
vivo, tendon may experience lower strains than used in
this study (up to 6%), and perhaps recovers more
slowly from such strains. The isochronal curves in
Fig. 4 indicate that tendon is still in the pre-damage
‘‘toe’’ region of the load–strain curve, and the stresses
induced at 6% strain were much lower than the ulti-
mate stress of the tendon, which is 80–90 MPa31
(Fig. 6 displays a maximum stress of less than 1 MPa).
Possible explanation for the low rate of recovery in-
clude incomplete recovery of water lost during loading,
a phenomenon discussed by Han et al.,12or failure of
proteoglycan–collagen interactions, which may be
capable of storing some energy elastically.23,24The
ability of tendon to nearly recover to preload in every
instance indicates that there is little or no plasticity.
The relaxations at various strains demonstrate a
higher rate of relaxation at higher strains, and a lower
rate of relaxation at lower strains. This behavior is
similar to results found for sheep digital tendons,33
porcine digital flexor tendon,5mouse tail tendons,9and
TABLE 3.A and n values for relaxation and recovery curves for all specimens.
Strain level (%)
RelaxationRecovery
A (MPa)nA (MPa)n
6
3
2
1
83.3 ± 50.5
59.7 ± 47.5
38.3 ± 31.2
–
?0.113 ± 0.026
?0.078 ± 0.031
?0.051 ± 0.027
–
––
13.2 ± 11.3
11.5 ± 4.46
2.70 ± 1.79
0.044 ± 0.044
0.027 ± 0.019
0.005 ± 0.002
Respective number of specimens for each category: relaxation at 6% (n = 43), relaxation at 3% (n = 20),
relaxation at 2% (n = 20), recovery at 3% (n = 10), recovery at 2% (n = 13), and recovery at 1% (n = 10).
TABLE 2. Repeatability statistics on five recovery tests for a
single specimen.
Recovery
Load (N) at time points
0.1 s1 s 10 s100 s
Average load (N)
Standard deviation (N)
% of average
1.988
0.0576
2.900
2.051
0.0536
2.615
2.108
0.0640
3.035
2.206
0.0483
2.188
Viscoelastic Relaxation and Recovery of Tendon 1137

Page 8

bovine cornea.3This behavior is opposite, however, to
results found for the MCL of rabbit,13human,2and
rat.29While some differences may be due to gripping
differences (tendons have a soft-tissue grip, while lig-
ament involve two bone grips), different insertion sites
(ligament testing incorporates two insertion sites, ten-
don only one), or strain measurement differences (grip-
to-grip measurement vs. strain tracking using optical
markers), such results hint at biomechanical differ-
ences between tendons and ligaments, which should be
pursued further in the future. There are also large
differences between tendons that serve different func-
tions. Batson et al. discovered significant material and
structural differences between the superficial digital
flexor tendon and the common digital extensor tendon
of the horse, including differences in water content,
ultimate strain, and both glycosaminoglycan and
chondroitin contents.1Rumian et al. found differences
in the extracellular matrix between an assortment of
tendons and ligaments in sheep, finding differences not
only between the tendon and ligament groups, but also
between the various ligaments and tendons themselves,
including fibril diameter distributions, water content,
and glycosaminoglycan content.30These findings show
that tendon and ligament properties vary with position
and function in the body. Whether these variations are
due to site-specific mechanical adaptation or are pre-
determined genetically remains unknown.
The recovery behaviors following creep and/or
relaxation testing in other biological tissues, particu-
larly the spine, show a similarly slow rate. Not only did
the spines fail to recover during an unloading period
equal in length to the loading period,8,21most still had
not completely recovered in unloaded periods double
or more the length of time of loading. Gedalia et al.
observed that the lumbar structures failed to recover
after more than double the amount of time allotted for
creep testing.10Likewise, Solomonow et al. observed
only 92% recovery after a full 7 h of recovery follow-
ing 50 min of cyclic loading in the cat spine.32Fol-
lowing 1-h creep tests in wrist ligaments, Crisco et al.
observed that after 2 h of unloading the ligaments had
not yet fully recovered. However, after 24 h of
unloading, the wrist ligaments had fully recovered
from creep, suggesting that other biological tissues
(including tendon) can fully recover if given adequate
time.6
An interesting behavior was also discovered in
microtubule networks by Lin et al. An experiment
found that following creep testing, the extent of the
recovery of the microtubule network was dependent on
the nature of the network. They found that the cross-
linked microtubule network recovered completely,
where the physically entangled microtubule network
had a residual strain of 0.12 (after creeping to a strain
of
intriguing to investigators, as it suggests that the
microstructure of the tendon may be a factor influ-
encing its recovery, an idea that could be pursued
further in future experiments.
Studies of nonbiological viscoelastic polymers can
help give insight into the behavior of biological poly-
meric components such as collagen. A study by Zhang
and Moore investigated the creep and relaxation
behavior of high density polyethylene, as well as the
recovery of the polymer following the removal of
load.37Like tendon, the polyethylene exhibited non-
linear behavior during both uniaxial loading and
unloading. Also similar to the tendon, following re-
moval of load, the polyethylene recovered continu-
ously, but at a rate slower than that of relaxation or
creep. Previous studies on basic polymers such as
polyethylene loaded in the same way as tendon may
then provide insight into behaviors of which can be
related to biological polymers like collagen, the major
mechanical component of tendon, and provide input
into future models of tendon behavior.
The understanding of viscoelastic properties of tis-
sues is crucial to understanding their biomechanical
function in the body. In vivo, the time-dependent
properties of tendon affect their ability to convert
muscle contraction into skeletal movement as well as
positional stability of the body. The recovery behavior
of tendon elucidates this effect. Slow recovery of ten-
don after loading means it will likely not achieve full
recovery prior to subsequent loading, and it will de-
form more (from its original length) under similar
loads (in creep scenarios); failure to recover completely
from a stress relaxation scenario results in a slightly
longer tendon, reducing the efficiency of the muscle–
tendon contraction.
This study examined the viscoelastic behavior of the
porcine digital flexor tendon, investigating the strain
dependency of stress relaxation and focusing on the
largely unexamined recovery that follows unloading.
We observed that the rate of stress relaxation is
dependent on strain level, which does not follow the
QLV model. We also found that the strain-dependence
of stress relaxation in our tendon model, as well as
those found in the literature (increasing rate with
increasing strain), has a trend opposite that of ligament
studies found in the literature (decreasing rate with
increasing strain). By recording the recovery from load
at a low but nonzero strain level, we were able to
monitor an entire recovery curve over 100 s. This
allowed for analysis of the recovery behavior of ten-
don, which progresses at a rate slower than relaxation
and is not well predicted with current viscoelastic
modelsfor tendon. This
understanding of tendon behavior, provides data for
approximately0.55).19
Thisphenomenonis
studyexpandsour
DUENWALD et al.1138

Page 9

more robust models of tendon behavior, and demon-
strates the complex biomechanical challenges for
replacement tissues.
ACKNOWLEDGMENTS
This work was funded by NSF award 0553016. The
authors thank Ron McCabe for his technical assis-
tance.
REFERENCES
1Batson, E. L., R. J. Paramour, T. J. Smith, H. L. Birch, J.
C. Patterson-Kane, and A. E. Goodship. Are the material
properties and matrix composition of equine flexor and
extensor tendons determined by their functions? Equine
Vet.J.35(3):314–318,2003.
776148327.
2Bonifasi-Lista, C., S. P. Lake, M. S. Small, and J. A. Weiss.
Viscoelastic properties of the human medial collateral lig-
ament under longitudinal, transverse, and shear loading. J.
Orthop. Res. 23:67–76, 2005. doi:10.1016/j.orthres.2004.
06.002.
3Boyce, B. L., R. E. Jones, T. D. Nguyen, and J. M. Gra-
zier. Stress-controlled viscoelastic tensile response of bo-
vine cornea. J. Biomech. 40:2367–2376, 2007. doi:10.1016/
j.jbiomech.2006.12.001.
4Cheng, T., and R. Z. Gan. Mechanical properties of sta-
pedial tendon in human middle ear. J. Biomech. Eng.
129:913–918, 2007. doi:10.1115/1.2800837.
5Ciarletta, P., S. Micera, D. Accoto, and P. Dario. A novel
microstructural approach in tendon viscoelastic modeling
at the fibrillar level. J. Biomech. 39:2034–2042, 2006.
doi:10.1016/j.jbiomech.2005.06.025.
6Crisco, J., S. Chelikani, R. Brown, and S. Wolfe. The effect
of exercise on ligamentous stiffness of the wrist. J. Hand
Surg. 22A:44–48, 1997.
7Doehring, T. C., A. D. Freed, E. O. Carew, and I. Vesely.
Fractional order viscoelasticity of the aortic valve cusp: An
alternative to quasilinear viscoelasticity. J. Biomech. Eng.
127(4):700–708, 2005. doi:10.1115/1.1933900.
8Eckstrom, L., A. Kaigle, E. Hult, S. Holm, M. Rostgat,
and T. Hansson. Intervertebral disc response to cyclic
loading: An animal model. Proc. Inst. Mech. Eng. 210:249–
258, 1996. doi:10.1243/PIME_PROC_1996_210_421_02.
9Elliot, D. M., P. S. Robinson, J. A. Gimbel, J. J. Sarver, J.
A. Abboud, R. V. Iozzo, and L. J. Soslowsky. Effect of
altered matrix proteins on quasilinear viscoelastic proper-
ties in transgenic mouse tail tendons. Ann. Biomed. Eng.
31:599–605, 2003. doi:10.1114/1.1567282.
10Gedalia, U., M. Solomonow, B. Zhou, R. Baratta, Y. Lu,
and M. Harris. Biomechanics of increased exposure to
lumbar injury caused by cyclic loading II: Recovery of
reflexive muscular stability with rest. Spine 24(23):2461–
2467, 1999. doi:10.1097/00007632-199912010-00007.
11Graf, B. K., R. Vanderby, M. J. Ulm, R. P. Rogalski, and
R. J. Thielke. Effect of preconditioning on the viscoelastic
response of primate patellar tendon. Arthroscopy 10(1):90–
96, 1994.
doi:10.2746/042516403
12Han, S., S. J. Gemmell, K. G. Helmer, P. Grigg, J. W.
Wellen, A. H. Hoffman, and C. H. Sotak. Changes in ADC
caused by tensile loading of rabbit achilles tendon: Evi-
dence for water transport. J. Mag. Reson. 144:217–227,
2000. doi:10.1006/jmre.2000.2075.
13Hingorani, R. V., P. P. Provenzano, R. S. Lakes, A. Es-
carcega, and R. Vanderby. Nonlinear viscoelasticity in
rabbit medical collateral ligament. Ann. Biomed. Eng.
32(2):306–312, 2004.doi:10.1023/B:ABME.0000012751.
31686.70.
14Hirpara, K. M., P. J. Sullivan, and M. E. O’Sullivan. The
effects of freezing on the tensile properties of repaired
porcine flexor tendon. J. Hand Surg. 33A:353–358, 2008.
doi:10.1016/j.jhsa.2007.12.011.
15Lakes, R. S. Viscoelastic Materials. Cambridge: Cambridge
University Press, 2009.
16Lakes, R. S., and R. Vanderby. Interrelation of creep and
relaxation: A modeling approach for ligaments. J. Biomech.
Eng. 121:612–615, 1999. doi:10.1115/1.2800861.
17Ledoux, W. R., D. F. Meaney, and H. J. Hillstrom. A quasi-
linear,viscoelastic,structuralmodeloftheplantarsofttissue
with frequency-sensitive damping properties. J. Biomech.
Eng. 126(6):831–837, 2004. doi:10.1115/1.1824133.
18Lieber, R. L., M. E. Leonard, C. G. Brown, and C. L.
Trestik. Frog semitendinosis tendon load-strain and stress-
strain properties during passive loading. Am. J. Phys.
261:C86–C92, 1991.
19Lin, Y., G. H. Koenderink, F. C. MacKintosh, and D. A.
Weitz. Viscoelastic properties of microtubules. Macromol-
ecules 40(21):7714–7720, 2007. doi:10.1021/ma070862l.
20Magnusson, S. P., P. Aagaard, and J. J. Nielson. Passive
energy return after repeated stretches of the hamstring
muscle-tendon unit. Med. Sci. Sports Exerc. 32(6):1160–
1164, 2002. doi:10.1097/00005768-200006000-00020.
21McGill, S., and S. Brown. Creep response of lumbar spine
to prolonged full flexion. Clin. Biomech. 7:43–46, 1992.
doi:10.1016/0268-0033(92)90007-Q.
22Moon, D. K., S. L. Woo, Y. Takakura, M. T. Gabriel, and
S. D. Abramowitch. The effects of refreezing on the vis-
coelastic and tensile properties of ligaments. J. Biomech.
39:1153–1157, 2006. doi:10.1016/j.jbiomech.2005.02.012.
23Mow, V. C., A. F. Mak, W. M. Lai, L. C. Rosenberg, and
L. H. Tang. Viscoelastic properties of proteoglycan sub-
units and aggregates in varying solution concentrations. J.
Biomech. 17(5):325–338, 1984. doi:10.1016/0021-9290(84)
90027-7.
24Mow, V. C., W. Zhu, W. M. Lai, T. E. Hardingham, C.
Hughes, and H. Muir. The influence of link protein sta-
bilization on the viscometric properties of proteoglycan
aggregate solutions. Biochim. Biophys. Acta 992(2):201–
208, 1989.
25Navajas, D., G. N. Maksym, and J. H. T. Bates. Dynamic
viscoelastic nonlinearity of lung parenchymal tissue.
J. Appl. Physiol. 79(1):348–356, 1995.
26Nekouzadeh, A., K. M. Pryse, E. L. Elson, and G. M.
Genin. A simplified approach to quasilinear viscoelastic
modeling. J. Biomech. 40(14):3070–3078, 2007. doi:10.1016/
j.jbiomech.2007.03.019.
27Oza, A., R. Vanderby, and R. S. Lakes. Interrelation of
creep and relaxation for nonlinearly viscoelastic materials:
Application to ligament and metal. Rheol. Acta 42:557–568,
2003. doi:10.1007/s00397-003-0312-0.
28Provenzano, P., D. Heisey, K. Hayashi, R. Lakes, and R.
Vanderby. Subfailure damage in ligament: A structural and
cellular evaluation. J. Appl. Phys. 92:362–371, 2002.
Viscoelastic Relaxation and Recovery of Tendon1139

Page 10

29Provenzano, P., R. Lakes, T. Keenan, and R. Vanderby.
Nonlinear ligament viscoelasticity. Ann. Biomed. Eng.
29:908–914, 2001. doi:10.1114/1.1408926.
30Rumian, A. P., A. L. Wallace, and H. L. Birch. Tendons
and ligaments are anatomically distinct but overlap in
molecular and morphological features—A comparative
study in an ovine model. J. Orthop. Res. 25(4):458–464,
2007. doi:10.1002/jor.20218.
31Shadwick, R. E. Elastic energy storage in tendons:
Mechanical differences related to function and age. J. Appl.
Physiol. 68(3):1033–1040, 1990. doi:10.1063/1.346741.
32Solomonow, M., B. H. Zhou, R. V. Baratta, Y. Lu, M.
Zhu, and M. Harris. Biexponential recovery model of
lumbar viscoelasticity and reflexive muscular activity after
prolonged cyclic loading. Clin. Biomech. 15:167–175, 2000.
doi:10.1016/S0268-0033(99)00062-5.
33Sverdlik, A., and Y. Lanir. Time-dependent mechanical
behavior of sheep digital tendons, including the effects
of preconditioning. J. Biomech. Eng. 124:78–84, 2002.
doi:10.1115/1.1427699.
34van Dommelen, J. A. W., M. M. Jolandan, B. J. Ivarsson, S.
A. Millington, M. Raut, J. R. Kerrigan, J. R. Crandall, and
D. R. Diduch. Nonlinear viscoelastic behavior of human
knee ligaments subjected to complex loading histories. Ann.
Biomed. Eng. 34(6):1008–1018, 2006. doi:10.1007/s10439-
006-9100-1.
35Woo, S. L.-Y., M. A. Gomez, and W. H. Akeson. The time
and history dependent viscoelastic properties of the canine
medial collateral ligament. J. Biomech. Eng. 103:293–298,
1981.
36Yang, W., T. C. Fung, K. S. Chian, and C. K. Chong.
Viscoelasticity of esophageal tissue and application of QLV
model. J. Biomech. Eng. 128(6):909–916, 2006. doi:10.1115/
1.2372473.
37Zhang, C., and I. D. Moore. Nonlinear mechanical
response of high density polyethylene. Part 1: Experimental
investigation and model evaluation. Polym. Eng. Sci.
37(2):404–413, 1997. doi:10.1002/pen.11683.
DUENWALD et al.1140