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Rinnakkaistallenteet Luonnontieteiden ja metsätieteiden tiedekunta
2018
Comparison of elastic, viscoelastic and failure tensile material properties of
knee ligaments and patellar tendon
Ristaniemi, Aapo
Elsevier BV
Tieteelliset aikakauslehtiartikkelit
© Elsevier Ltd
CC BY-NC-ND https://creativecommons.org/licenses/by-nc-nd/4.0/
http://dx.doi.org/10.1016/j.jbiomech.2018.07.031
https://erepo.uef.fi/handle/123456789/7108
Downloaded from University of Eastern Finland's eRepository
1 Comparison of elastic, viscoelastic and failure tensile material properties of knee ligaments 1
and patellar tendon 2
A. Ristaniemi*, L. Stenroth, S. Mikkonen, R.K. Korhonen 3
Department of Applied Physics, University of Eastern Finland, Kuopio, FI-70211, Finland 4
5
Original article 6
7
* Address for correspondence:
8
Aapo Ristaniemi 9
Department of Applied Physics, University of Eastern Finland 10
Yliopistonranta 1F, POB 1627 11
Kuopio, Finland, FI-70211 12
Tel. +358400815152 13
E-mail: aapo.ristaniemi@uef.fi 14
15
Keywords: material properties, viscoelastic, ligament, patellar tendon, knee joint 16
Word count: 3985 17
18
2 Abstract
19
The knee ligaments and patellar tendon function in concert with each other and other joint tissues, 20
and are adapted to their specific physiological function via geometry and material properties.
21
However, it is not well known how the viscoelastic and quasi-static material properties compare 22
between the ligaments. The purpose of this study was to characterize and compare these material 23
properties between the knee ligaments and patellar tendon.
24
Dumbbell-shaped tensile test samples were cut from bovine knee ligaments (ACL, LCL, MCL, 25
PCL) and patellar tendon (PT) and subjected to tensile testing (n=10 per ligament type). A 26
sinusoidal loading test was performed at 8 % strain with 0.5 % strain amplitude using 0.1, 0.5 and 27
1 Hz frequencies. Subsequently, an ultimate tensile test was performed to investigate the stress- 28
strain characteristics.
29
At 0.1 Hz, the phase difference between stress and strain was higher in LCL compared with ACL, 30
PCL and PT (p<0.05), and at 0.5 Hz higher in LCL compared with all other ligaments and PT 31
(p<0.05). PT had the longest toe-region strain (p<0.05 compared with PCL and MCL) and MCL 32
had the highest linear and strain-dependent modulus, and toughness (p<0.05 compared with ACL, 33
LCL and PT).
34
The results indicate that LCL is more viscous than other ligaments at low-frequency loads. MCL 35
was the stiffest and toughest, and its modulus increased most steeply at the toe-region, possibly 36
implying a greater amount of collagen. This study improves the knowledge about elastic, 37
viscoelastic and failure properties of the knee ligaments and PT.
38 39
3 Introduction
40
Ligaments are soft tissues in the musculoskeletal system that connect bone to bone. Their main 41
functions are to transmit forces, restrict and guide joint movement, stabilize joints and act as 42
mechanical dampers (Birch, 2013; Reynolds et al., 2017). In the knee joint, they function in concert 43
with each other and other joint tissues, such as articular cartilage and meniscus (Butler et al., 1980;
44
Ellis and Weiss, 2015). They are composed mainly of water (65 to 70 % of total weight), type I 45
collagen (70 to 80 % of dry weight), elastin (few percent), and proteoglycans (few percent) (Woo 46
et al., 2005, 1999). Similar to tendons, ligaments exhibit a hierarchical structure with highly 47
oriented fascicles, formed from fibers, and lower levels of hierarchy at fibril and collagen molecule 48
scale (Ellis and Weiss, 2015).
49 50
Adequate mechanical properties of ligaments are essential for the physiological function of the 51
knee joint. Ligaments function primarily in tension in the direction of the collagen fibers and thus 52
tensile properties in that direction are of special interest. Shear, transverse and compressive loads 53
also exist in ligaments (Ellis and Weiss, 2015; Gardiner et al., 2001), but they are less significant 54
during normal joint function. Different ligaments are adapted to their specific function via their 55
geometry and material properties (Birch, 2013). However, time-dependent and failure properties 56
of ligaments at the mesoscopic level are not well known. These properties, such as the Young’s 57
modulus and ultimate strength, represent the intrinsic material properties, as opposed to the 58
structural properties of the entire ligaments, and are essential in understanding the structure- 59
function relationships.
60 61
4 During normal locomotion, ligaments and tendons experience dynamic loads. The resulting 62
response of these tissues is time-dependent and affected by their viscoelastic properties. However, 63
studies comparing time-dependent properties of different ligaments have been concentrating on 64
varying strain rates in ultimate tensile testing (Pioletti et al., 1999; van Dommelen et al., 2005), 65
although a sinusoidal test mimics better normal knee function and repeated ligament loading.
66
Sinusoidal test results have been previously reported for human medial collateral ligament 67
(Bonifasi-Lista et al., 2005; Lujan et al., 2009), and, to our knowledge, there are no studies which 68
compare the sinusoidal test results of anterior cruciate ligament (ACL), posterior cruciate ligament 69
(PCL), medial collateral ligament (MCL), lateral collateral ligament (LCL) and patellar tendon 70
(PT) from the same set of skeletally mature knees.
71 72
Only a few studies have compared stress-strain characteristics of knee ligaments within the same 73
set of knees. Eleswarapu et al. (2011) compared the Young’s modulus and ultimate strength of 74
immature (one-week-old) bovine ligaments and found that PT had the highest modulus and 75
strength (27.5 ± 2.8 and 15.7 ± 3.3 MPa), while ACL had the lowest values (2.1 ± 1.0 and 1.4 ± 76
0.6 MPa), but the low absolute values clearly show the immaturity of the tissues. Butler et. al.
77
(1986) compared bone-fascicle-bone units of ACL, PCL, LCL and PT (MCL not compared) of 78
three cadavers, and discovered that ACL, PCL and LCL had no significant differences in the 79
Young’s modulus, strength or toughness, while PT had significantly higher values in all those 80
parameters. They observed similar failure strains for ligaments and PT; uniform failure strains 81
have also been suggested for different tendons (LaCroix et al., 2013). Smeets et al. (2017) 82
compared MCL and LCL and observed significantly higher Young’s modulus for MCL, and 83
significantly higher failure strain and toughness for LCL. To our knowledge, there are no studies 84
5 to compare the linear, non-linear and failure material properties of ACL, PCL, MCL, LCL and PT 85
from the same set of skeletally mature knees.
86 87
The purpose of the study was to comprehensively characterize and compare the viscoelastic and 88
quasi-static tensile material properties of knee joint ligaments and patellar tendon at the 89
mesoscopic level. Tensile properties were determined experimentally using a sinusoidal loading 90
test and ultimate test until tissue failure using dumbbell-shaped samples of bovine ligaments. In 91
the absence of previous comparative studies of ligament viscoelasticity, but significantly lower 92
water content observed in PT compared to knee ligaments (Rumian et al., 2007), we hypothesized 93
that viscous properties are similar between the ligaments, but lower in PT. Regarding stress-strain 94
characteristics, we hypothesized that collateral ligaments and patellar tendon exhibit higher linear 95
and strain-dependent Young’s modulus than cruciate ligaments (Butler et al., 1986; Eleswarapu et 96
al., 2011; Smeets et al., 2017), while toe, yield and failure strains are similar between ligaments 97
(Butler et al., 1986; LaCroix et al., 2013). The results of this study aid in understanding the 98
differences in the elastic and viscoelastic material properties of knee joint ligaments and PT, and 99
their structure-function relationships.
100 101
Methods 102
Sample preparation 103
Anterior cruciate ligament (ACL), posterior cruciate ligament (PCL), medial collateral ligament 104
(MCL), lateral collateral ligament (LCL) and patellar tendon (PT) were carefully dissected from 105
10 skeletally mature bovine stifle joints. The measurements were conducted using dumbbell- 106
shaped samples, approximately 10 mm in length and 1.8 and 2 mm in thickness and width (Figure 107
6 1a and 1b) (Bonifasi-Lista et al., 2005; Chokhandre et al., 2015; Eleswarapu et al., 2011;
108
Henninger et al., 2013; Quapp and Weiss, 1998; Stabile et al., 2004). Detailed information on 109
sample preparation can be found in the supplementary material.
110 111
Mechanical testing 112
Mechanical testing was carried out using a uniaxial material testing system. Detailed information 113
on the device and the used preconditioning can be found in the supplementary material. The 114
samples were immersed in a phosphate-buffered saline solution (PBS) during the measurement.
115
After a four-step stress-relaxation test (results not reported here), with the tissue relaxed at 8 % 116
nominal strain for 30 minutes, a sinusoidal test was performed with 0.5 % nominal strain amplitude 117
at 0.1 Hz, 0.5 Hz and 1 Hz frequencies for 20 cycles at each frequency. The strain level and 118
amplitude were chosen based on pilot measurements and physiological levels. Those 119
measurements showed 8 % to be in the linear region, which would make the test condition as 120
similar as possible to all ligaments, and it can occur for example during walking (Bates et al., 2015;
121
Gardiner et al., 2001; Roldán et al., 2017; Taylor et al., 2013). The strain amplitude of 0.5 % was 122
chosen to retain consistency between ligaments, and to keep the test in the linear region. Strains in 123
ACL during walking can vary much more (Roldán et al., 2017; Taylor et al., 2013), but in similar 124
experiments a smaller amplitude of 0.125 % was used (Bonifasi-Lista et al., 2005; Lujan et al., 125
2009). 20 cycles was used to ensure a stable response. The specimen was allowed to recover at 0 126
% strain for 60 minutes before starting the ultimate tensile test until tissue failure with a velocity 127
of 0.005 mm/s. A slow speed was chosen to obtain the quasi-static response of the tissue, with no 128
or only minor effect of strain rate stiffening (van Dommelen et al., 2005).
129 130
7 Data analysis
131
All analyses, except statistical analyses, were conducted using a custom MATLAB code 132
(MATLAB R2016b, The MathWorks, Inc., Natick, MA, USA). During data analysis, the axial 133
strain was defined as logarithmic, 𝜀𝜀= ln𝐿𝐿𝐿𝐿
0, where 𝐿𝐿 is the current length of the sample and 𝐿𝐿0 the 134
initial length of the sample. Logarithmic strain was chosen as the strain measure, since strains were 135
relatively high and comparison with other experimental studies is easily possible. Assuming 136
constant volume (incompressible material), the stress was defined as true stress, 𝜎𝜎= 𝐴𝐴𝐹𝐹
0 𝐿𝐿
𝐿𝐿0, where 137
𝐹𝐹 is the measured tensile force and 𝐴𝐴0 the initial cross-sectional area.
138 139
Sinusoidal data was analyzed by fitting a sinusoidal function to the stress and strain data (Bonifasi- 140
Lista et al., 2005) (Figure 1c) 141
𝑧𝑧=𝐴𝐴 𝑠𝑠𝑠𝑠𝑠𝑠(2𝜋𝜋𝜋𝜋𝜋𝜋+𝜑𝜑) +𝑧𝑧0 (1)
142
where 𝑧𝑧 is the value of the stress or strain, 𝐴𝐴 is the amplitude, 𝜋𝜋 is the frequency, 𝜋𝜋 is the time, 𝜑𝜑 143
is the phase angle and 𝑧𝑧0 is the constant term. From these, the dynamic modulus, 𝐸𝐸𝑑𝑑𝑑𝑑𝑑𝑑 = 𝐴𝐴𝐴𝐴𝜎𝜎
𝜀𝜀, and 144
phase difference between stress and strain, 𝛾𝛾 = 𝜑𝜑𝜎𝜎 − 𝜑𝜑𝜀𝜀, were determined.
145 146
Figure 1d presents the determination of the material properties from the ultimate tensile testing.
147
The test was considered to be initiated when the stress reached 0.2 MPa and the results were 148
analyzed from that stress onwards, in order not to include slack in the data analysis. The Young’s 149
modulus was determined by the maximum tangent modulus (Screen et al., 2004) that was present 150
in the stress-strain curve. It was obtained by linear fittings to the stress-strain data with a strain 151
range of 8 % and going through all the points in the curve. Toe region end point (𝜀𝜀𝑡𝑡𝑡𝑡𝑡𝑡,𝜎𝜎𝑡𝑡𝑡𝑡𝑡𝑡) and 152
8 yield point (𝜀𝜀𝑑𝑑𝑦𝑦𝑡𝑡𝑦𝑦𝑑𝑑,𝜎𝜎𝑑𝑑𝑦𝑦𝑡𝑡𝑦𝑦𝑑𝑑) were defined when the strain difference between the stress-strain curve 153
and linear fit was 0.6 % (Danso et al., 2014). Ultimate strength (𝜀𝜀𝑢𝑢𝑦𝑦𝑡𝑡,𝜎𝜎𝑢𝑢𝑦𝑦𝑡𝑡) was the maximum stress 154
reached during the experiment. Linear region length was determined as 𝜀𝜀𝑦𝑦𝑦𝑦𝑑𝑑𝑡𝑡𝑙𝑙𝑙𝑙 =𝜀𝜀𝑑𝑑𝑦𝑦𝑡𝑡𝑦𝑦𝑑𝑑− 𝜀𝜀𝑡𝑡𝑡𝑡𝑡𝑡. 155
Toughness, 𝐾𝐾 (energy density), was calculated up to the yield and ultimate strain (Figure 1d) as 156
the integral over the stress-strain curve:
157
𝐾𝐾𝑑𝑑𝑦𝑦𝑡𝑡𝑦𝑦𝑑𝑑/𝑢𝑢𝑦𝑦𝑡𝑡 = ∫𝜀𝜀𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦/𝑢𝑢𝑦𝑦𝑢𝑢𝜎𝜎 𝑑𝑑𝜀𝜀
0 . (2)
158
In order to characterize ligament nonlinearities more comprehensively, the toe region of the stress- 159
strain curve, 0 <𝜀𝜀 <𝜀𝜀𝑡𝑡𝑡𝑡𝑡𝑡, was characterized by fitting a second order formula (Danso et al., 2014) 160
to the data 161
𝜎𝜎=𝐴𝐴𝜀𝜀2+𝐵𝐵𝜀𝜀+𝐶𝐶, (3)
162
where A, B and C are constants. When taking a derivative over strain, Eq. 3 becomes 163
𝑑𝑑𝜎𝜎
𝑑𝑑𝜀𝜀 = 2𝐴𝐴𝜀𝜀+𝐵𝐵= 𝐸𝐸𝜀𝜀𝜀𝜀+𝐸𝐸0, (4) 164
where 𝐸𝐸𝜀𝜀 and 𝐸𝐸0 are the strain-dependent and initial modulus. Alternatively, the toe region was 165
characterized with a traditional exponential formula (Fung, 1967) 166
𝜎𝜎=𝐷𝐷(𝑒𝑒𝐹𝐹𝜀𝜀−1), (5)
167
where D and F are constants.
168 169
Statistical analyses 170
All statistical analyses were carried out using IBM SPSS Statistics 23.0.0.2 (SPSS Inc., IBM 171
Company, Armonk, NY, USA). In the tables and figures, the data is presented as mean ± standard 172
deviation, since nearly all data was normally distributed (Shapiro-Wilk test), and the few 173
parameters that were not, showed only a minor deviation from normal distribution. Statistical 174
comparisons in the mechanical parameters between ligament types were made using a linear mixed 175
9 model (McCulloch et al., 2008), which takes into account that the ligament samples come from 176
the same set of knees. Each mechanical parameter was analyzed with the ligament type (ACL, 177
LCL, MCL, PCL, and PT) as a fixed variable and the knee as a random subject variable with knee- 178
specific random intercepts.
179 180
Results 181
The results of the sinusoidal testing are presented in Figure 2 (phase difference 𝛾𝛾) and Table 1 182
(dynamic modulus 𝐸𝐸𝑑𝑑𝑑𝑑𝑑𝑑). At 0.1 Hz loading frequency, the phase difference was significantly 183
higher in LCL compared with ACL, PCL and PT (p<0.01). A significant difference was also found 184
between MCL and PCL (p<0.05). At 0.5 Hz, the phase difference was significantly higher in LCL 185
compared with all other ligaments and PT (p<0.01 when compared with PCL and PT, p<0.05 when 186
compared with ACL and MCL), while other ligaments did not differ significantly from each other.
187
At 1 Hz, no significant differences were found in the phase difference between the ligaments. The 188
dynamic modulus was significantly higher in MCL compared with ACL, LCL (p<0.05) and PT 189
(p<0.01) at all loading frequencies. At 0.1 Hz, the dynamic modulus was higher in PCL compared 190
with PT (p<0.05).
191 192
The results of the ultimate tensile testing are presented in Table 2 and Figures 3, 4 and 5.
193
Significant differences in the toe region second-order fit parameter A (Eqs. 3, 4), related to the 194
strain-dependent modulus, was observed in MCL compared with ACL, LCL (p<0.05) and PT 195
(p<0.01), and between PCL and PT (p<0.05). The toe region fit parameter F (Eq. 5) was higher in 196
MCL compared with LCL and PT (p<0.05). No other significant differences were found between 197
the ligaments in the other toe region fit parameters.
198
10 199
Strain at the toe region end (𝜀𝜀𝑡𝑡𝑡𝑡𝑡𝑡) was significantly higher in PT compared with PCL (p<0.01) and 200
MCL (p<0.05), and significantly higher in LCL compared with PCL (p<0.05). No significant 201
differences in the stress at this strain (𝜎𝜎𝑡𝑡𝑡𝑡𝑡𝑡) between the ligaments were found (Figure 4). The yield 202
stress was significantly higher in MCL than in ACL and PT (p<0.05), while the yield strain showed 203
no significant differences between the ligaments (Figure 4). The ultimate strain was significantly 204
higher in LCL and PT compared with ACL (p<0.05) (Figure 4). The ultimate strength was 205
significantly higher in MCL compared with PT (p<0.01) and ACL (p<0.05). The Young’s modulus 206
was higher in MCL than in ACL and PT (p<0.05). Toughness up to the yield strain (𝐾𝐾𝑑𝑑𝑦𝑦𝑡𝑡𝑦𝑦𝑑𝑑) was 207
higher in MCL than in PT (p<0.05) and toughness up to the failure strain (𝐾𝐾𝑢𝑢𝑦𝑦𝑡𝑡) was higher in 208
MCL compared with PT and ACL (p<0.05).
209 210
Discussion 211
In this study, we determined experimentally viscoelastic, and quasi-static nonlinear, linear and 212
failure tensile material properties of bovine stifle joint ligaments and patellar tendon. The main 213
results were that 1) LCL is the most viscous at low-frequency loads, and 2) MCL is the stiffest and 214
has the highest strain-dependent modulus and toughness. Furthermore, PT was surprisingly soft 215
and was shown to have many parameters comparable with ACL and PCL, such as the Young’s 216
modulus and toughness. This study provides novel information of the mechanical material 217
properties of bovine knee joint ligaments at the mesoscopic level. This information is also useful 218
in determination of structure-function relationships.
219 220
11 Based on the phase difference results, LCL seems to be more viscous than the other ligaments at 221
low-frequency loading. It is well known that all tissues are adapted to their specific loading 222
environment. Therefore, it may be that for normal joint function at low speeds or close to static 223
loads the viscous component of the tissue might be beneficial, providing damping effect and 224
stabilizing the joint (Birch, 2013; Reynolds et al., 2017). Since the LCL resists varus rotation, the 225
more viscous behavior of LCL could be an adaptation to frontal plane sway movement, which 226
occurs at frequencies comparable to the ones used in the current study (Giemza et al., 2013). Cattle 227
stand 40 to 50 % of time (Rajapaksha et al., 2015) and thus loading caused by sway may occur in 228
large amounts. To our knowledge, the literature lacks similar comparison of this parameter 229
between knee ligaments. However, the magnitudes of phase differences obtained in this study were 230
comparable to the values reported for human MCL (Bonifasi-Lista et al., 2005; Lujan et al., 2009).
231
The observed behavior could originate from differences in water content (Rumian et al., 2007), as 232
fluid flow affects tissue viscoelasticity, though its effect is more emphasized in compression (Li 233
et al., 2005). Another explanation could be higher collagen content in LCL (Hanada et al., 2014), 234
as collagen viscoelasticity was shown to highly affect the time-dependent behavior of cartilage in 235
tension (Li et al., 2005). Additionally, collateral ligaments have been shown to contain more small- 236
diameter fibrils than ACL, PCL and PT (Rumian et al., 2007), resulting in larger interaction areas 237
between fibrils and other extracellular matrix constituents, which may affect viscoelasticity at the 238
mesoscopic level. Finally, possibly lower elastin content compared to cruciate ligaments (Kharaz 239
et al., 2018) might increase LCL viscosity, as elastin has been thought to be an elastic stabilizer 240
restoring tissue back to its original shape.
241 242
12 MCL had the highest strain-dependent modulus (Eq. 3, 4), 𝐹𝐹 (Eq. 5, describing also strain 243
dependency in the toe-region (Criscenti et al., 2015)), dynamic modulus, Young’s modulus, yield 244
stress, ultimate strength, toughness at yield and toughness at failure. This means that MCL was the 245
stiffest, strongest and required the most energy prior to yield and rupture among the ligaments and 246
PT. Higher Young’s modulus of MCL compared with ACL is consistent with earlier studies 247
(Butler et al., 1992; Chandrashekar et al., 2006; Chawla et al., 2009; Noyes and Grood, 1976;
248
Pioletti et al., 1999; Quapp and Weiss, 1998) but higher Young’s modulus compared with PT was 249
not (Butler et al., 1986; Eleswarapu et al., 2011; Johnson et al., 1994). The reason for higher values 250
of these material properties of MCL could be its adaptation to the loading environment and 251
surrounding structures. For efficient operation of the knee, the shape and size of MCL is restricted, 252
but the force transmit capability and stiffness are required to control valgus rotation. The results 253
might be explained by the higher collagen content in collateral ligaments (Hanada et al., 2014) and 254
possibly more oriented collagen fibrils along the direction of the loading. Additionally, higher 255
elastin (Kharaz et al., 2018) and GAG (Kharaz 2018, Rumian 2007) contents in cruciate ligaments 256
might explain their differences to MCL, as presumably higher elastin and GAG contents lower the 257
relative amount of collagen. Elastin has been shown to contribute only slightly to the stress-strain 258
behavior outside the toe-region (Henninger et al., 2013) and the role of GAGs is more emphasized 259
in compression (Korhonen and Jurvelin, 2010).
260 261
Rumian et. al (2007) studied the collagen fibril diameters of different ligaments and PT in an ovine 262
model, and found out that the fibril diameter distribution histogram, showing the amount of 263
collagen fibrils with small, medium and large diameters, in PT was more similar with ACL and 264
PCL (bimodal, more high-diameter fibrils) than with MCL and LCL (more small-diameter fibrils).
265
13 This could partly explain why PT had the Young’s modulus and toughness values closer to cruciate 266
ligaments than collateral ligaments.
267 268
PT had the longest toe region strain, suggesting that it could have larger crimp angles compared 269
with collateral and cruciate ligaments. This was manifested by small strain dependent modulus in 270
the toe region, with significant differences compared to PCL and MCL. The long toe region strain 271
might be needed in normal bovine PT operation, to provide a large operating strain range at rest, 272
standing and walking. Interestingly, patellar tendon did not have larger Young’s modulus 273
compared with ligaments, as could be expected based on the Young’s moduli obtained in earlier 274
measurements on dumbbell-shaped samples (Eleswarapu et al., 2011), bone-ligament-bone 275
complexes (Blevins et al., 1994; Chandrashekar et al., 2012; Flahiff et al., 1995; Haut and 276
Powlison, 1990; Johnson et al., 1994; Stäubli et al., 1999), fascicles (Butler et al., 1986; Haraldsson 277
et al., 2005) or in-vivo subjects (O’Brien et al., 2010). Our values for PT are however similar to 278
those obtained by Rupp et al. (2000) and Wilson et al. (1999) for bone-ligament-bone complexes.
279
Our results differ from those obtained for bovine by Eleswarapu et al. (2011), likely because we 280
used skeletally mature knees as opposed to one-week-old calves, in which ligaments are still 281
developing and the mechanical properties are clearly inferior to the mature joint. The difference 282
with respect to human PT (Blevins et al., 1994; Butler et al., 1986; Chandrashekar et al., 2012;
283
Flahiff et al., 1995; Haraldsson et al., 2005; Haut and Powlison, 1990; Johnson et al., 1994;
284
O’Brien et al., 2010; Stäubli et al., 1999) may be attributed to the difference in anatomy; in addition 285
to patellar tendon, bovine stifle joint has two other tendons connecting patella to tibia, whereas the 286
human knee has only the patellar tendon connecting patella to tibia. However, animals, especially 287
bovine, remain typical when studying the musculoskeletal biomechanics (Cone et al., 2017).
288
14 289
Due to tissue stiffening as a function of strain rate, which was also evident when comparing the 290
dynamic moduli at different frequencies, it was expected that the sinusoidal loading results in 291
greater modulus compared to the quasi-static test. However, the magnitudes of dynamic modulus 292
were slightly smaller than linear moduli from the ultimate tensile test. The reason for this may be 293
that the strain at which the sinusoidal test was performed was in the toe-region or in the beginning 294
of the linear region for some samples, though pilot measurements showed 8 % to be in the linear 295
region. This could also be the reason for the significantly higher dynamic modulus of PCL (shorter 296
toe region) compared with PT at 0.1 Hz, even though the Young’s modulus obtained from the 297
ultimate test showed no differences. Nonetheless, the strain was well within the physiological 298
range of operation.
299 300
Toe region strains observed in earlier studies for human ligaments and PT with dumbbell-shaped 301
samples (Bonifasi-Lista et al., 2005; Quapp and Weiss, 1998), bone-ligament-bone complexes 302
(Chandrashekar et al., 2012; van Dommelen et al., 2005), fascicles (Butler et al., 1986; Haraldsson 303
et al., 2005) and for rabbit bone-MCL-bone complex (Moon et al., 2006) are smaller than those 304
obtained in this study. Values similar to this study were observed for dumbbell-shaped samples of 305
porcine MCL (Henninger et al., 2013). The reason for the longer toe-region strains in this study 306
could be higher collagen fiber crimp angles combined with higher elastin content. As indicated 307
above, elastin was suggested to provide restorative effect (i.e. return collagen fibers crimped when 308
unloaded) and affect the stress particularly in the toe region (Henninger et al., 2013). Smith et al.
309
(2014) found an elastin content of approximately 10 % of dry weight in canine cruciate ligaments, 310
which could be typical for quadruped animals, as opposed to few percent in humans (Woo et al., 311
15 2005). Elastin and other structural constituents of these samples will be analyzed later by 312
biochemical and microscopical analyses for further clarification of this matter. For instance, 313
quantitative polarized light microscopy (Spiesz et al., 2018) could reveal differences in the 314
collagen crimp patterns.
315 316
The second-order fit coefficient A (Eq. 3) describes the strain dependent modulus at the toe region 317
and thus how fast the modulus increases with increasing strain. This is the first time when this 318
parameter is determined for ligaments. The observations are consistent with the differences in the 319
toe region strains, so that high toe-region strain results in low strain dependent modulus. As 320
expected, these values (ligament mean values between 754 – 1765 MPa) were substantially higher 321
than those reported experimentally for bovine meniscus (224.78 ± 136.08 MPa (Danso et al., 322
2014)) or cartilage (2.29 ± 1.30 MPa (Danso et al., 2014)). The values for constant D (Eq. 5) of 323
the exponential formula obtained here are of similar magnitude than reported for goat MCL (4.0 ± 324
4.2 MPa (Abramowitch et al., 2004)) and higher compared with bovine meniscus (0.34 ± 0.06 325
MPa (Danso et al., 2014)) or cartilage (0.17 ± 0.04 MPa (Danso et al., 2014)). Constant F (Eq. 5) 326
of the exponential formula describes also the mechanical nonlinearity at the toe region and showed 327
similar trend with the strain-dependent modulus (highest value in MCL). This parameter value was 328
comparable with goat MCL (48.4 ± 23.1 (Abramowitch et al., 2004)), and was similar to bovine 329
meniscus (31.79 ± 9.64 (Danso et al., 2014)) and higher than bovine cartilage (5.11 ± 1.82 (Danso 330
et al., 2014)).
331 332
The similarity of linear region lengths between ligaments and PT indicates that once the collagen 333
fibers are straightened, the strain behavior is similar in the ligaments. Ultimate strain in LCL was 334
16 the highest but did not show as clear difference with MCL as in Smeets et al. (2017) where LCL 335
had significantly higher ultimate strain than MCL with a mean value in LCL close to 40 %.
336
Toughness values obtained in this study were consistent with the values reported in the literature 337
(Butler et al., 1986; Chandrashekar et al., 2006; Johnson et al., 1994; Race and Amis, 1994), but 338
exhibited high sample-specific variation. However, the results do not show the behavior observed 339
by Smeets et al. (2017) where LCL had higher toughness at failure than MCL. Possible reason for 340
these differences between the studies could be the different age, as ageing-related collagen 341
crosslinks might be more present in the subjects of Smeets et al. (2017) (aged 74 ± 7 years) 342
compared with bovine samples of this study.
343 344
Limitations 345
Limitations of the study, such as clamping-induced stress concentrations, using dumbbell-shaped 346
samples as opposed to bone-ligament-bone complexes, using bovine instead of human samples, 347
have been discussed in detail in the supplementary material.
348 349
Conclusion 350
In conclusion, bovine LCL exhibits more viscosity than the other ligaments at low-frequency loads 351
and MCL has the highest strain-dependent modulus, Young’s modulus and toughness. The 352
observed differences may indicate adaptation of the ligament material properties to their specific 353
physiological function. This study provides novel information of the linear, nonlinear and failure 354
properties, and viscoelastic properties of bovine knee joint ligaments and may aid, to some extent, 355
in proper construction of computational knee joint models. In the future, biochemical and 356
17 microscopical analysis of the samples will be conducted in order to characterize structure-function 357
relationships.
358 359
Conflict of interest statement 360
Authors declare no conflicts of interest.
361 362
Acknowledgements 363
Financial support from the Academy of Finland (grant 286526) is greatly acknowledged.
364
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21 502
503
22
Table 1. Dynamic modulus 𝐸𝐸𝑑𝑑𝑑𝑑𝑑𝑑 (mean ± SD) at different loading frequencies for ACL, LCL, MCL, PCL and PT.
504
𝐸𝐸𝑑𝑑𝑑𝑑𝑑𝑑 (MPa)
0.1 𝐻𝐻𝑧𝑧 0.5 𝐻𝐻𝑧𝑧 1 𝐻𝐻𝑧𝑧 ACL 163.94 ± 73.98 * 168.73 ± 76.84 * 171.14 ± 78.43 *
LCL 181.66 ± 135.26 * 187.80 ± 140.20 * 190.08 ± 142.14 *
MCL 288.51 ± 102.56 296.60 ± 105.48 298.56 ± 105.96
PCL 214.26 ± 126.21 o 220.15 ± 130.55 222.37 ± 130.26
PT 115.77 ± 93.03 o** 119.38 ± 97.18 ** 120.45 ± 99.14 **
Significant differences compared to MCL are indicated with * (p<0.05) and ** (p<0.01).
505
Significant difference between PCL and PT is indicated with o (p<0.05).
506 507 508
Table 2. Nonlinear mechanical parameters (Eqs. 3, 5) and the length of the linear region for the different ligaments (mean ± SD).
509
A (MPa) B (MPa) C (MPa) D (MPa) F (-) 𝜀𝜀𝑦𝑦𝑦𝑦𝑑𝑑𝑡𝑡𝑙𝑙𝑙𝑙 (%)
ACL 1021.47 ± 405.98 * 2.95 ± 7.83 0.19 ± 0.06 1.23 ± 0.50 24.73 ± 6.33 11.38 ± 1.24
LCL 1085.98 ± 917.43 * 1.20 ± 21.04 0.24 ± 0.17 3.25 ± 5.50 19.91 ± 10.90* 12.29 ± 1.85
MCL 1765.05 ± 588.93 2.93 ± 10.58 0.19 ± 0.09 1.38 ± 0.42 30.27 ± 8.23 11.85 ± 1.32
PCL 1466.99 ± 819.65 o -1.16 ± 18.49 0.22 ± 0.10 2.34 ± 3.57 26.65 ± 12.21 12.33 ± 2.05
PT 753.85 ± 468.65 o** 0.69 ± 14.04 0.28 ± 0.24 1.26 ± 0.61 20.17 ± 4.69* 11.26 ± 1.16
Characterization of the toe region with the fits σ= Aε2+ Bε+ C and σ= D�eFε−1�. 𝐴𝐴 and 𝐹𝐹 describe 510
the strain dependency of the modulus, 𝐵𝐵 the initial modulus and 𝐶𝐶 and 𝐷𝐷 are constants.
511
Significant differences compared to MCL are indicated with * (p<0.05) and ** (p<0.01).
512
Significant difference between PCL and PT is indicated with o (p<0.05).
513 514
Figure captions
Figure 1. A dumbbell-shaped tensile test sample was cut from the central part of the ligament (a) and then subjected to tensile testing (b). Schematic presentation for sinusoidal (c) and ultimate testing (d) with certain analyzed parameters indicated.
Figure 2. Mean (± SD) phase difference at different loading frequencies for ACL, LCL, MCL, PCL and PT. Significant differences are indicated with * (p<0.05) and ** (p<0.01). The used frequencies simulate for example standing, sway or slow walking (0.1 Hz, 0.5 Hz) or walking (1 Hz).
Figure 3. Mean (± SD) stress-strain curves from the ultimate tensile tests of all the samples.
Figure 4. Mean (± SD) toe region end point, yield point and ultimate strength of the samples.
Significant differences are indicated with * (p<0.05) and ** (p<0.01).
Figure 5. Mean (± SD) Young’s modulus, toughness at yield and toughness at failure for different ligaments.
Stress (MP a)
Strain (%)
Toe region end
Yield point
Ultimate strength
K ult (grey area)
E=
Δ ε Stress (MP a) Strain (%) Δσ
Time (s)
A σ A ε
a b
c d
Δσ Δ ε
9 8 7 6 5 4 3 2 1 0
Phase dif ference ( ) γ °
0.1 Hz 0.5 Hz 1 Hz
**
*p<0.05
**p<0.01
*
** ** *
* **
**
10
ACL LCL MCL PCL PT ACL LCL MCL PCL PT ACL LCL MCL PCL PT
ACL
Stress (MP a)
60
10 30 40 50
20
0
Strain (%)
5
0 10 15 20 25 30
LCL
Stress (MP a)
60
10 30 40 50
20
0
Strain (%)
5
0 10 15 20 25 30
PT
Stress (MP a)
60
10 30 40 50
20
0
Strain (%)
5
0 10 15 20 25 30
MCL
Stress (MP a)
60
10 30 40 50
20
0
Strain (%)
5
0 10 15 20 25 30
PCL
Stress (MP a)
60
10 30 40 50
20
0
Strain (%)
5
0 10 15 20 25 30
*
*
**
*p<0.05
**p<0.01
Stress (MP a)
2 4 6 8 10 12 14 16
Strain (h) Toe region end
ACL MCL PCL PT LCL
2 4 6 8 10 12
* *
Yield point
Strain (h)
Stress (MP a)
10 14 50 40 30 60
18 20
22 24 26
20 16
**
*
*
*
Ultimate strength
Strain (h)
Stress (MP a)
70
28 30
10 50 40 30 60
20
18 20 22 24 26
16
*p<0.05
**p<0.01
*p<0.05
**p<0.01
ACL MCL PCL PT LCL
ACL MCL PCL PT LCL
100 200 300 400
0 0
2 4 6
* 8
* * *p<0.05
* *
ACL LCL MCL PCL PT ACL LCL MCL PCL PT
K yield (MP a) K failure (MP a)
Y oung' s m odulus (MP a)
Supplementary Material 1
Sample preparation 2
Anterior cruciate ligament (ACL), posterior cruciate ligament (PCL), medial collateral ligament 3
(MCL), lateral collateral ligament (LCL) and patellar tendon (PT) were carefully dissected from 4
10 bovine stifle joints, obtained from an abattoir, aged 14 to 22 months. The samples were 5
immersed in a phosphate buffered saline (PBS) solution and stored in a freezer (-20 °C) 6
immediately after dissection. Prior to the biomechanical measurement, the sample was allowed to 7
thaw at room temperature, after which a dumbbell-shaped tensile test piece was cut from the central 8
part of the sample (Figure 1a). First, a slice was cut with two parallel razor blades to obtain a 9
desired thickness (approximately 1.8 mm), and then the slice was cut with a custom punch tool to 10
obtain the desired width (approximately 2.0 mm) and dumbbell-shape. Test pieces were cut so that 11
collagen fibers were running along the longitudinal direction. Small dumbbell-shaped specimens 12
were used, because the size and shape were constant in all samples, and reliable material properties 13
could be obtained. Cross-sectional area was determined by measuring the thickness and width with 14
a microscope and assuming an elliptical shape (Duenwald et al., 2009; Eliasson et al., 2007;
15
Provenzano et al., 2001). This assumption was verified accurate by measuring the area of an 16
additional sample directly from its cross-section. Double-sided sandpapers (Mirox P80, Mirka Oy, 17
Uusikaarlepyy, Finland) were glued (Loctite Precision, Henkel AG, Düsseldorf, Germany) on the 18
ends of the sample, resulting in a test length of approximately 10 mm, and the specimen was placed 19
between tensile testing clamps, using a moment of 4 Nm to tighten the clamp screws (Figure 1b).
20
This way, a firm attachment of the sample was achieved, and no slipping was observed, as 21
observed in preliminary repeatability tests. The specimen was in PBS solution at room temperature 22
during the measurement.
23 24
Mechanical testing 25
Mechanical testing was carried out using a material testing system comprised of a controller 26
(Newport, Irvine, CA, USA), a linear actuator (Newport, Irvine, CA, USA; resolution 0.1 µm) and 27
a 25 lb load cell (Model 31/AL311BL, Honeywell, Columbus, OH, USA), controlled by a custom- 28
made LabView software (version 10.0, National Instruments Corporation, Austin, TX, USA). The 29
zero-load length was established by applying a tensile stress of 0.05 MPa (Henninger et al., 2013).
30
The sample was preconditioned with 2 % strain amplitude for 10 cycles using 0.05 mm/s velocity, 31
after which it was allowed to recover for 2 minutes before determining the zero-load length again.
32
Commonly, preconditioning has been performed using similar strains, number of cycles and 33
speeds (Chokhandre et al., 2015; Criscenti et al., 2015; Quapp and Weiss, 1998; Stabile et al., 34
2004) once prior to the test. In this study, the protocol (10 cycles, 2 % strain, zero-load length 35
determination) was repeated five times, which, in preliminary testing, was found to produce a 36
stable zero-load length and more repeatable results. After preconditioning, the sample was allowed 37
to recover for 10 minutes prior to verifying the zero-load length and commencing the experiments.
38 39
Discussion 40
In the toe region parameters (A, B, D, F) and Young’s moduli, the variability was the highest in 41
LCL and PCL. This originates likely from biological variation, but it could also imply that those 42
tissues adapt to the loading by material properties rather than by geometry. It could also indicate 43
that the exact material properties of LCL and PCL are not as crucial to the knee joint function as 44
the material properties of ACL, MCL and PT. This suggestion is partly supported by a 45
computational study of Dhaher et al. (2010), where variation of the ACL material parameters 46
affected most to patellar rotation, tilt and contact stress response sensitivity, with also a 47
pronounced effect of MCL and LCL.
48 49
Limitations 50
Clamping of the samples induces a complex stress state close to the junction. For this reason, 51
rupture could sometimes occur near the clamp. Often the initial rupture location was not clearly 52
seen in the sample, which made it difficult to assess whether or not an unfavorable rupture at the 53
clamps had occurred. We made a statistical assessment of outliers in yield and ultimate data to 54
investigate for an early rupture. The values were normally distributed (Shapiro-Wilk test), and 55
there were no outliers to suggest an early rupture (Grubbs’ test). Hence no samples were excluded 56
from the analyses.
57 58
The tensile test samples were cut from the central part of the ligaments. ACL samples were cut 59
from the anteromedial bundle, though the bundle division was not as clear as with humans. PCLs 60
exhibited no bundle structures. The samples were cut so that fascicles were running along the 61
longitudinal direction, however, the cutting tool was positioned along the longitudinal direction by 62
hand based on visual cues. To minimize the error, the same person cut all the samples with the 63
same tool.
64 65
We used small dumbbell-shaped samples in order to get reliable material properties at a 66
mesoscopic level through constant size and shape. Material properties could be difficult to obtain 67
using bone-ligament-bone complexes, since the cross-sectional area and length are challenging to 68
determine. Studies using bone-ligament-bone complexes hence report typically only structural 69
level properties of the entire ligaments (e.g. stiffness in N/mm) (Kim et al., 2014; Robinson et al., 70
2005; van Dommelen et al., 2005; Wijdicks et al., 2010; Wilson et al., 2012). The size was large 71
enough to encompass several fascicles and a decent amount of interfascicular matrix. However, 72
the used test setup may limit the fascicle sliding, occurring in-vivo for example during joint angle 73
change, and interfascicular matrix deformation, and care should be taken when comparing our 74
loading to in-vivo situation.
75 76
Bovine samples were used in this study. As a quadruped animal, with a stifle joint different to a 77
human knee joint, the results are not directly applicable to human knees. Care should be taken if 78
implementing the material parameter values obtained here to computational models of the human 79
knee. Hopefully later it can be clarified how the tissue properties in bovine correspond to those of 80
humans. This data is however useful in the analysis of structure-function relationships.
81
Nevertheless, biochemical composition of human and bovine ligaments and PT are similar. For 82
example, reported textbook values for collagen content per dry weight in knee ligaments are 83
between 70 and 80 % (Woo et al., 2005) and mean values of bovine ligaments have been shown 84
to range from 71 to 87 % (Eleswarapu et al., 2011). In human ligaments and PT, these values have 85
been reported up to 73 % (Hanada et al., 2014; Samiric et al., 2009; Suzuki et al., 2008; Young et 86
al., 2011). It is also worth noting that several studies that have investigated the tensile properties 87
of cartilage and meniscus (Charlebois et al., 2004; Danso et al., 2014; Li et al., 2005; Sasazaki et 88
al., 2006) have used bovine of the same age as used here. Results of those studies can be compared 89
with ligament properties of the present study (see more in the Discussion). Bovine stifle joint was 90
used due to availability of the material from healthy knee joints and for best comparability to the 91
