Dynamic tensile properties of porcine knee ligament

Abstract

BACKGROUND:

The knee plays an essential role in movement. There are four major ligaments in the knee which all have crucial functionalities for human activities. The anterior cruciate ligament (ACL) is the most commonly injured ligament in the knee, especially in athletes.

OBJECTIVE:

The aim of this study was to investigate the dynamic tensile response of the porcine ACL at strain rates from 800 to 1500 s⁻¹ for simulations of acute injury from sudden impact or collision.

METHODS:

Split Hopkinson Tension Bar (SHTB) was utilized to create a dynamic tensile wave on the ACL. Stress–strain curves of strain rates between 800 s⁻¹ to 1500 s⁻¹ were recorded.

RESULTS:

The results demonstrated that the elastic modulus of the porcine ACL at higher strain rates was six to eight times higher than that of porcine and human specimens at quasi-static strain rate. However, the failure stress was quite similar while the strain was much smaller than that at the lower strain rate.

CONCLUSIONS:

ACL is highly strain rate sensitive and easier to break with lower failure strain when the strain rates increased to more than 1000 s⁻¹. The stress–strain curves indicated that the sketching crimps at the slack region did not happen but switched to the sliding process of collagen fibers and was accompanied by some ruptures, which can develop into tears when strain and stress were large enough. On the other hand, the viscoelastic properties of the ligament, depending on the proteoglycan matrix and the cross-link, showed a limited value in the studied strain rate range.

Keywords

Hopkinson bars ligament tensile

1. Introduction

The growing popularity of sports has led to increased concomitant injuries, especially to the knee [1]. Majewski et al. concluded that 39.8% of sport injuries in 17,397 patients were related to the knee [2]. Loes et al. also concluded that knee injury accounted for 15–50% of all sports-related injuries [3]. There are many types of knee injuries, such as meniscus injury, tendon injury and cruciate ligament rupture [2,4,5]. However, the anterior cruciate ligament (ACL) injury is the most common type of knee injuries, and it is accounted for 25% to 45% of knee joint damages [2,6]. Rupture of cruciate ligament is a frequent clinical problem. If the knee is not treated to restore its initial stability, degenerative changes in the articular cartilage are possible [7]. Reconstruction is often recommended because most injured ACL cannot be stitched back together due to the surrounding environment [8].

Some previous studies pointed out that the porcine ligament is similar to humans in structure and biomechanical properties [9–11]. Moreover, in 2007, Stone et al. used the porcine patellar tendon to transplant for ten patients to replace the ruptured anterior cruciate ligament. The six patients were aggressive in rehabilitation and were satisfactory in a variety of standard orthopedic tests [12]. These studies showed that the porcine ligament has the potential to be human ligament implanting material. An investigation of Zhou et al. in 2009 [13] performed on porcine knee ligaments at 0.33 mm/s concluded that the biomechanics of intact ligament is significantly higher when compared to anteromedial band. However, there is only the ultimate load being higher when compared to posterolateral band.

Burgin and Aspden [14] indicated in their research that in some realistic conditions, such as an accident or acute injuries, the knee could suffer impact at 1000 s⁻¹ or higher strain rates. This study uses a Hopkinson bar to investigate the dynamic tensile response of the porcine ACL at 800 to 1500 s⁻¹ strain rate. The biomechanics of intact porcine ACL at the high strain rate can be used to compare implanted ACL in others research or simulation.

2. Materials and methods

2.1. Specimen preparation and conservation

Fresh pig knees, obtained at the local slaughterhouse, were used in the experiments. None of the knee samples showed patellar instability, knee injuries, or arthritic deformities. One hour after collection, the anterior cruciate ligament is removed from the pig knee and overlying fascia were also removed. After the ligaments are anatomized, they are frozen at −20 °C [15] in sealed bags with little residual air volume to prevent dehydration. Before testing, the specimens were thawed in physiological saline. The specimens were air-dried on both ends to facilitate better clamping, and remaining part of the ligaments were kept moist during this process by physiological saline [15,16]. A total of 22 specimens, with average length 40 mm (gauge length 10 mm) and cross-sectional area 30 mm², were examined. These samples were also kept moist with physiological saline throughout dissection and experimentation within 6 hours. The research of Woo et al. [15] checked the effect of prolonged postmortem freezing storage on the structural properties of the medial collateral ligament (MCL). They concluded that tensile strength and ultimate strain did not change following storage. We forecast, therefore, proper and careful storage by freezing would have little or no effect on the biomechanical properties of the ligaments under dynamic loading.

2.2. Experimental methods

Split Hopkinson tension bar (SHTB) is a commonly used device for characterizing the high-rate tensile behavior of engineering materials. SHTB is composed of a striker, an incident bar and a transmission bar. The specimen is sandwiched between the incident and the transmission bars. Since the first report of hollow tube SHTB by Harding et al. in 1960 [17], designs of SHTB have evolved into 5 categories based on its striker driving method and bar alignments. In this study, a custom-designed SHTB system was utilized, as shown in Fig. 2. This SHTB system is composed of a 400 mm striker bar, a 2000 mm incident bar, a 1000 mm transmission bar and a 400 mm momentum trap bar. The bars are made of 6061 aluminum alloy with 20 mm in diameter. In SHTB system, a collision between the striker and the incident bar generated a tensile wave which transmitted through the surface between the sample and incident Bar. At the interface, a portion of the pulse is reflected while the remaining response waves pass through the samples and finally into the transmission bar [18–21]. Semiconductor strain gauges were utilized to enhance the sensitivity of weak signals. The measured strain data was then utilized to calculate the strain, strain rate, and stress (𝜀_s, ${\varepsilon}_{s}^{\prime }$ , 𝜎_s) of specimens, as shown in Eqs (1)–(3) established based on Kolsky theory with some hypotheses. Firstly, the pulse is longer than the time of the passage along the specimen length. Secondly, the pulses do not disperse. Moreover, the strain profile in all of the cross-sections of the bars and the specimen is uniform [22–25]. $\begin{eqnarray}\displaystyle {\varepsilon}_{s} & = & \displaystyle \frac{-2c_{0}}{l_{s}}\int _{0}^{t}{\varepsilon}_{r}dt\end{eqnarray}$ (1) $\begin{eqnarray}\displaystyle {\sigma}_{s} & = & \displaystyle E\frac{A}{A_{s}}{\varepsilon}_{t}\end{eqnarray}$ (2) $\begin{eqnarray}\displaystyle {\varepsilon}_{s}^{\prime } & = & \displaystyle \frac{-2c_{0}}{l_{s}}{\varepsilon}_{r}\end{eqnarray}$ (3) where c ₀ indicated the wave speed in 6061 aluminum bar, l _s was the initial length of the specimen, E was the elastic modulus of the pressure bar, A and A _s were areas of pressure bars and specimens, respectively [19,20,26,27].

2.3. Fixture design

SHTB experiments of soft biological materials has been a challenge because of the low mechanical impedance and strength of samples and difficulties in clamp design. The method of clamping the ends of a specimen for tensile testing is a major concern with regard to soft biological specimens. Cryogenic methods of fixation have been used by some investigators [28]. However, the temperature gradients generated in soft tissue specimens could affect their mechanical properties. To attach a specimen to the input and output bars of the Hopkinson tension bar, we designed the outer part of clamps of the same diameter and material as Hopkinson bar and the inner part by ABS material. The main purpose of this is to increase the contact area and friction between the specimen and the fixture by changing the geometry of the fixture. We used a 3D printer to make the substrate of ABS into a zigzag shape and install it into the designed fixture. The designed angle is 63° as shown in Fig. 1 [29]. The isolated ligament was fixed on the designed fixture and axially aligned with the Hopkinson bars to ensure the ligament within the designed fixture would not fall out [28,29]. The fixtures were made of aluminum alloy which were the same as incident and transmission bars. That was to not shift the wave propagation in the measurement process.

Fig. 1.

Designed fixtures.

Fig. 2.

Isolated ligament tensile test set up Split Hopkinson tension bar and clamping condition.

Fig. 3.

The stress–strain curves at strain rates from 800 to 1000 s⁻¹.

Fig. 4.

The stress–strain curves at strain rates from 1000 to 1400 s⁻¹.

3. Results

Figures 3 and 4 show the tensile stress vs. strain curves with strain rates below 1000 s⁻¹ and above 1000 s⁻¹, respectively. It is obvious that the stress–strain curves were complex to forecast and greatly diverged. The maximum stress tends to increase with increasing strain rates, from 25 MPa at 946 s⁻¹ to 40 MPa at 1349 s⁻¹. The elastic modulus and maximum stresses were measured and categorized into four groups of strain rates: 800–900, 900–1000, 1000–1200, and 1200–1350 s⁻¹, as shown in Fig. 5. With the increasing strain rate, the maximum stress illustrated a rising trend, and maximum stress of an average of about 35 MPa was observed at the range of strain rate from 1200 to 1300 s⁻¹. The elastic modulus averaged between 900 to 950 MPa for all four strain rate ranges; however, the standard deviation was more than 400 MPa at the lowest strain rate and decreased with increasing strain rate. It is safe to assume the elastic modulus has no analytical difference. Furthermore, the maximum stresses increased from about 18 MPa to 35 MPa with increasing strain rates, and the standard deviation was quite small. The maximum stresses increased with increasing strain rates. On the other hand, the strain of specimens was approximate 11 to 23% length of samples, and the maximum stress happened at 50% of the total strain.

Fig. 5.

Elastic modulus and maximum stress.

4. Discussion

The results of this study were significantly different as they were compared to the characteristics of the porcine and human ligament at a low strain rate. The stress–strain curve of the human and porcine ligament at low strain rate is divided into two regions evidently, slack and linear regions [30–32], while that was not observed in the results of this study. In this study, the slack region [33–37] disappeared, and the anti-stress mechanism changed into the linear region’s next stage. This behavior demonstrated that the flattening of crimps did not occur [37–42] at the high strain rate, and the most probable mechanism of ligaments was decided by the molecular stretching process and the cross-links between the helices [37,39,43]. Figures 3 and 4 also showed that the stress vs. strain curves become even more elusive with increasing strain rates [44]. At the linear region (under yield point at the strain about 0.03), many breakpoints were observed. The phenomenon indicted ruptures of fibers during stretching and molecular gliding [37,39,43]. However, many fibers still connected and maintained the capability to stretch. That generated the second rising wave.

In the tested specimens, some large tears (Fig. 6) were observed at the specimens in the scope of strain rate 1200–1300 s⁻¹ (stress about 35 MPa). These tears were developed from the ruptures appearing in increasing stress and strain process at linear region [37,39,43]. In contrast to stress, the elastic modulus was almost unchanged at all rang of strain rates (Fig. 5). However, the values in each range fluctuated in the low strain rate range and tended to converge in the high strain rate range. This behavior was indicated by the standard deviation which was smaller within increasing strain rate. The remain of elastic modulus also showed that the viscoelastic properties of the ligament, decided by the role of the proteoglycan matrix and the cross-link, reached the maximum value in the studied range of strain rate [39,43].

Fig. 6.

The ligament is slightly torn.

Many researchers studied the performance of ACL at quasi-static (strain rate lower than 1 s⁻¹) condition. Table 1 included four porcine ACL and five human ACL experimental results at quasi-static conditions. Compare to porcine and human ACL tests, results showed that the breakage force was obviously higher for human ACL, approximately 13% and the elastic modulus was lower by about 23%. When the strain rate increased from below 1 s⁻¹ to more than 800 s⁻¹, the elastic modulus increased, and these numbers were about six times the elastic modulus of porcine ACL and eight times of human ACL elastic modulus at the low strain rate. In addition, the maximum stress of the intact anterior cruciate ligament was the highest and reached 32.22 MPa with the standard deviations 15.63 MPa while the elastic modulus was 147.76 MPa, and the standard deviation was 61.75 MPa. Stress values in previous studies are quite similar to the tearing stress in this study, about 35 MPa. This stress is higher (8%) and lower (11%) as compared to porcine and human specimens, respectively, at the low strain rate. Other researchers about implanting the ligament produced on the porcine knee also tested the biomechanical properties of the intact ligament and ligament reconstruction to analyze the effectiveness of reconstruction. The research illustrated that the maximum load capability of the porcine ligament is from 729 to 1194 N when the test is at 20 mm/min [45] or 1120 ± 264 N at 0.833 mm/s [46].

Table 1

Some results of the human and porcine studies

Study	Body	Force (N)	Area (mm² )	Stress (MPa)	Elastic modulus (MPa)	Stiffness (N/mm)
Zhou et al. [13]	Porcine	853.53 ± 252.32	–	32.22 ± 15.63	147.76 ± 61.75	–
Fleming et al. [45]	Porcine	992 ± 137	–	–	–	151 ± 33
Lee et al. [47]	Porcine	1027.4 ± 283	–	–	–	97.4 ± 46.6
Spindler et al. [46]	Porcine	1120 ± 264	–	–	–	112
Noyes et al. [31]	Human	1730 ± 660	44.4 ± 9.7	37.8 ± 9.3	111 ± 26	–
Noyes et al. [32]	Human	1725 ± 269	–	37.8 ± 3.8	–	–
Handl et al. [48]	Human	1,246 ± 243	30 mm²	41.3 ± 8.1	–	182
Marieswaran et al. [6]	Human	1818 ± 699	–	–	128 ± 5	–
Chandrashekar et al. [49]	Human	–	–	24.36 ± 9.38 (39 ages)	113 ± 45	–

The strain was an aspect that illustrated the discrepancy between strain-rate ranges. Failure strains are much higher at the lower strain rate, and maximum stress corresponds to maximum strain [30–32]. That indicated a reduction in fibril strain and molecular sliding at higher strain rates, but this also increased dynamic load to collagen fibrils and cross-link, which caused some failures in ligament micro-structure [37,39,41]. It explained why human ACL tends to fail during sports activities. A sudden change of angle or over-extend of ACL at a higher strain rate could cause serious damage to the ligament’s fibrous structure, hence resulting in a severe knee injury.

5. Conclusion

The purpose of this study is to determine the tensile mechanical properties of the anterior cruciate ligament at the high strain rate and compare them with the characteristics of human and porcine ACL at the low strain rate. The comparison showed that the value of the failure stress of porcine ACL at the high strain rate was similar to that of porcine ACL at the low strain rate but a little lower than the maximum stress of human ACL. The distinction is not significant. Moreover, the strain at the maximum stress is approximately 50% of the total strain. When we analyze the elastic modulus at the high strain rate, it is found out that the elastic modulus remains at the studied scope of the strain rate, and this number significantly differs from the low strain rate. Results in some research also illustrated that the loading capacity of the porcine ACL and human ACL at the low strain rate is similar in all aspects, such as maximum stress, elastic modulus, and the stress–strain curve’s profile. As a conclusion, we think that the mechanical properties of porcine ACL presented in this research should be suitable to predict human ACL behavior at higher strain rate range.

Footnotes

Conflict of interest

None to report.

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