Muscle injury, especially hamstring muscle, frequently happens during sports activities and exercise which could have serious consequences if not diagnosed and treated promptly. This research investigated the quasi-static and dynamic responses of over 30 fresh semitendinosus muscle-tendon-bone structures by utilizing Split Hopkinson Pressure Bars (SHPB) and a material testing system under the strain rates between 0.001 ~ 200 s− 1. Because of the special shape of muscle-tendon-bone structures, PLA-material clampers were produced by 3D printer to properly hold and to prevent slippery during the test process. The mechanical characteristics of the whole muscle bundle, including Young’s modulus and stress-strain curve, are illustrated at various strain rates. The findings showed that the muscle properties were sensitive with strain rate at the passive deformation. Both maximum stress and Young’s modulus increased with the rise of strain rate, and modulus at 200 s− 1 can be as high as 10 times compared with quasi-static conditions.
Research Article
Effect of strain rates on mechanical response of whole muscle bundle
https://doi.org/10.21203/rs.3.rs-2245611/v1
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Journal Publication
published 03 Apr, 2023
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Muscle property
impact damage
Hopkinson Pressure Bar
strain rate
passive tensile
Hamstring muscle strain injury is one of the common sports injuries. It accounted for 11% in all of the injuries in preseason training and 12% in competition soccer seasons in England. The hamstring muscle strain injury can be caused by shortened optimum muscle length, lack of muscle flexibility, hamstring strength imbalance, insufficient warm-up, fatigue, lower back injury, and increased muscle neural tension [1]. The treatment of hamstring muscle injuries, in general, includes three main phases: the resolution of inflammation, angiogenesis and the repair of the muscle tissue itself [2]. Serious muscle injuries, if not diagnosed and treated promptly, can have serious consequences [3, 4].
Understanding the biomechanics of muscles can not only predict and prevent the injury, but it can also help to develop diagnosis and treatment methods. A whole skeletal muscle is a complex structure consisting of skeletal muscle tissue, connective tissue, nerve tissue, blood or vascular tissue. However, the critical component generating the loading capacity of muscle fascicle in muscle-loading model is called the sarcomere [5]. The muscle fiber is comprised of sarcomeres bound by Z-disks, and the collision between myosin filament and the Z-disk is significant in increasing the passive tensile force [5, 6]. The mechanical behavior of muscle tissues has been invested in past decades, including the scale of fiber, bundle, fascicle or whole muscle-tendon architecture. In a study by Sun et al., which performed rabbit muscle-tendon test at stretch rate between 0.5 to 100 cm/min, results showed that responses of muscular tissues depend non-linearly on both strain and strain rate where the effect of strain is more than strain rate [7]. Another research with rabbit muscle-tendon specimens also indicated a similar response of samples as failure load increased at a high stretch rate while maximum strain remained at approximately 0.6 mm/mm [8]. The strain rate is an important aspect of the loading response of muscle tissue; therefore, some other authors invested its effect on muscle of some species at both compressive and tensile biomechanics [9–12]. In a tensile test of Safran et al. at a rate of 10 cm/min, the authors illustrated that increased temperature of muscular bundle improved the failure stress and length of the muscle [13]. On the other hand, some results were found that because of the complex structure, there was a difference in Young’s modulus of muscle at scales from fiber, bundle, fascicle to whole muscle [14, 15]. Thus, it is necessary to construct the property curves at different scales and strain rates in muscle studies.
In this study, we invested the mechanical responses of the whole muscle-tendon-bone structure which was collected from frog legs under quasi-static and dynamic loading conditions, strain rate from 0.001 to 200 s− 1. Experiments with the whole muscle-tendon-bone structure ensured that the architecture of the muscular bundle did not change and mechanical properties also represented the properties between tendon and muscle. This more closely illustrated the response of whole human muscle-tendon bundle as it was extended by a load similar to realistic conditions.
The fresh frog legs were collected from the local market and immediately transferred to the laboratory. The frog legs were put into the physiological saline 0.9% to prevent the loss of water. The frog semitendinosis muscle-tendon fascicles used in this research were 40 ± 3 mm in length and roughly 4 ± 0.5 mm in diameter, which is measured at the center of the muscle bundle. To test the mechanical tensile properties of specimens, we utilized Lloyd Friction Testing machine made by AMETEK for experiments at low strain rates from 0.001 to 0.5 s− 1 and Hopkinson bar for strain rate between 50 to 200 s− 1. In a research by Bing Yu et al., maximum muscle eccentric contraction velocity of about 20 male athletes’ hamstring semitendinosus muscle during sprinting was measured at from 19.3 to 68 m/s. While the peak positive muscle-tendon elonggation velocity was from 1 to 1.5 m/s. [16–18]. The results showed that strain rate 200 s− 1 can properly represent most muscle strain rates in sports activities. A total of over 30 frog semitendinosis muscle-tendon-bone structures were tested in this research and at least 5 specimens were studied in each range of strain rate. Each specimen was only tested one time to reduce the influence of the last experiment process and environmental aspects. Special designed clampers were utilized to ensure that samples are centered on the machine shaft and to eliminate specimen slippage during inspection (Fig. 1). Samples tested at low strain rates were extended to 100% strain. Before starting the test, the samples were pre-stretched by pulling to a force of 0.2 N to aligned the muscle tissues which could be dramatically influenced by titin and the length of sarcomere [5, 6, 19, 20].
The Hopkinson bar system combines 3 bars: 400 mm striker bar, 2000 mm incident bar, and 1000 mm transmitted bar. All bars of the Hopkinson system are made of 6061 alloy aluminum with a 20 mm diameter. However, the transmission signal of soft biological materials is very weak. To solve this problem, the transmitted bar is a hollow rod with an inner diameter of 18 mm [21, 22]. The striker bar is connected to a pneumatic cylinder, and its movement generates a collision between the striker and incident bars. The collision wave of this process propagates in the incident bar until it transits through the face between specimen and incident bar (incident pulse ɛi), this creates the reflect and transmitted pulses (ɛr, ɛt) in the incident and transmitted bars, respectively[21, 23–25]. To measure deformation generated by the pulses in the incident and transmitted bars, four sensors and two Wheatstone bridges are used. The signal is amplified by the amplifier before transferring to an oscilloscope, and the reflect and transmitted pulses (ɛr, ɛt) are calculated from the oscilloscope data by MATLAB software. The muscle-tendon samples are clamped at the ends of the bars, as shown in Fig. 2 (setup of Hopkinson tensile bar). Two clampers made of PLA material by 3D printing method were also used to assist in clamping the bone sections of the samples (Fig .1 b). The clampers could be moved to accommodate different bone sizes to ensure pulse transmission through the sample. In addition, a hollow transmitted bar solved the problem that the waves on the transmitted bar were too weak as mentioned above. The transmitted pulse passing through the hollow bar created an amplified strain signal, which the sensors could measure easily [21, 22]. It was noted that, unliked experiments at quasi-static strain rate, the recorded strain ranges were smaller.
Strain, stress and strain rate (\({\varepsilon _s},{\sigma _s},\varepsilon _{s}^{\prime }\)) of test samples are calculated from the following equations based on one-dimensional stress wave theory [26–29]:
| \({\varepsilon _s}=\frac{{ - {c_0}}}{{{l_s}}}\int\limits_{0}^{t} {({\varepsilon _i} - {\varepsilon _r} - {\varepsilon _t}} )dt\) (1) \({\sigma _s}=\frac{1}{2}E\frac{A}{{{A_s}}}({\varepsilon _i}+{\varepsilon _r}+{\varepsilon _t})\) (2) \(\varepsilon _{s}^{\prime }=\frac{{{c_0}}}{{{l_s}}}({\varepsilon _i} - {\varepsilon _r} - {\varepsilon _t})\) (3) | Where c0: the wave velocity in the incident and transmission bar ls: the initial length of the specimens E: Elastic Modulus of the pressure bar A, As: area of pressure bars and area of specimens. |
The stress-strain curves in Figs. 3 and 4 were collected from 5 similar tests at a quasi-static range and 6 tests at a dynamic range. This study tested the mechanical response of whole muscle-tendon fascicles at a total of six different strain rate values. The average stress vs. strain curves of 4 lower strain rates were calculated and illustrated in Fig. 5. The results showed that the differences in stress-strain curves at the same strain rate were insignificant. Moreover, the profile of curves was parallel to the findings of some research at lower strain rates, in which consisted of two regions (slack and linear regions)[30]. Curves observed at the dynamic strain rate (Fig. 4) only showed a linear region, but it was also similar in shape with other reports at higher strain rates [8, 11, 12, 31]. The tests demonstrated that the mechanical property of the tendon-muscle bundle was sensitive to strain rate. Young’s modulus and the break stress increased at higher strain rate. However, the maximum stress happened at approximately 0.4 strain in all the quasi-static experiments (Fig. 5). The strain corresponding to the maximum stress was not affected by the strain rate. In contrast, strain at maximum stress was about 0.015 (at strain rate 90 s− 1) to 0.035 (at strain rate 200 s− 1) at dynamic conditions. However, this was not the deformation that caused the rupture in the muscle bundles. Because the strains in experiments with the Hopkinson bar system were generated by the deformation pulse, the strain in the sample was not large enough to cause major fractures in the structure of the muscle bundle.
The strain rate's influences on muscle mechanics were confirmed by plotting the magnitude of Young’s modulus and maximum stress (Fig. 6) corresponding to the various strain rates. Young’s modulus fitting curve in Fig. 6 was generated from logarithmic and exponential equations. The equation y = 0.2667ln(x) + 4.8809 was used in strain rate scope from 0.001 to 0.1 while fit curve at 0.1 to 200 s− 1 strain rate was provided by exponential equation y = -0.0003x2 + 0.1966x + 4.5647. Using two equations constructed a curve being most suitable to experimental data. The muscle was found to be sensitive significantly with strain rate. The tearing stress of the muscle-tendon bundle increased from 0.67 to 1.25 MPa (about 1.9 times), corresponding to a change of strain rate from 0.001 to 0.5 s− 1. At the quasi-static strain rate range, the change in maximum stress could be represented by the function y = 0.0961ln(x) + 1.334. The maximum stress value shifted in a large range at the 180 to 200 s− 1 strain rate. However, the average maximum stress was insignificantly different to the 0.5 s− 1 strain rate, and there was no rupture pointed out in samples. A rising was observed in Young’s modulus under the range of strain rate, and it was higher about ten times as compared between dynamic and quasi-static loading conditions.
The response of the whole muscle-tendon structure under load showed at the profile of stress-strain curves were parallel at all scales of muscle architecture of other species. At the quasi-static strain rate, curves exhibited an initial non-linear (slack region) at 0.15 lower strain. A linear region was observed at the next strain range, followed by a non-linear region prior to the gradual failure [5, 30, 32, 33]. The responses of skeletal muscle bundles to passive traction at a low strain rate, as shown in areas of the stress-strain curve, are determined primarily by the property of titin, a large protein that tethered the myoligment and the Z-disc [5, 6, 19, 20]. While the myofilaments were almost not deformed during pulling, and the fibers linking myosins together were thought to be negligible over the physiological range of sarcomere [34–36]. The slack area was assmumed that it was formed by straightening the large folded state in the immunoglobulin domains and the linker regions between the domains adopt a bent configuration in the titin molecule. The small folded regions in the titin molecule would be straightened as the passive stress increases, and this created a linear region in the stress-strain curve [37]. The modification of titin has been demonstrated at the molecular level [38–40]. The responses of skeletal muscle bundles to passive stress were shown to be quite similar to those of titin molecular.
At the high strain rates, the toe region vanished because the helical and folded structures of titin had not enough time to permit [5, 8, 11, 12, 30–33]. This was similar to materials with large molecular structures as polymers. The sensitivity of the biomechanical properties of the whole muscle-tendon bundle to strain rate was clearly shown in Fig. 6. The load-bear capacity of the sample was markedly logarithmical increase even at maximum stress and elastic modulus in the quasi-static strain rate region. These factors continue to increase sharply at the dynamic strain rate (80–200 s− 1) but have not yet reached the tear limit of the samples. The effect of strain rate on muscle properties was also considered in previous studies. Although, response of muscle at all scales was quite similar in contour of the stress-strain curves, the difference was prominent in the value. The previous findings also showed that the passive tension modulus increased 1.24 times from fiber scale to bundle and 1.14 times from bundle to fascicle, and the whole muscle bundle level had the highest value [14, 15]. The increase of modulus across different scales was because of the titin molecular mass, myosin heavy chain isoform distribution, and collagen length. The responses of the whole muscle-tendon bundle to passive tensile in this study showed that the tendon bundle was sensitive to strain rate (the strain-rate sensitivity coefficient: 
in strain rate from 0.001 to 0.5 s− 1 [41, 42]). This coefficient was analogous to the human muscle (m = 0.12) in the strain range from 0.01 to 100 s− 1 [43].
To provide an assessment of strain rate’s effect to passive tension mechanics of whole muscle-tendon bundle, this study was compared to some previous research performed only with muscle bundle [11, 12, 31]. The maximum passive stress of the muscle-tendon structure in this study was higher from 2 to 5 times than active stress created by the stimulus, while Young's modulus was approximately 20 times [44–48]. Passive tensile properties varied widely across species, muscle scale and strain rates. The research in Table 1 showed that the strain rate had a larger influence on the elastic modulus than the maximum stress. The elastic modulus increased about 8 to 15 times at the high strain rate as the maximum stress altered only about two times. Our study also showed a similar rate at the whole muscle scale. These results supported that strain rate generated a similar alteration ratio at all muscle species and scales. However, Young's modulus value in this research was higher from 2 to 30 times than other research performed at the fascicle scale. This result was caused by two reasons: species difference and muscle-bundle scale. In the recent research, Ward et al. experimented with three rabbit muscles (tibialis anterior, extensor digitorum longus and extensor digitorum of the second toe), and found that the Young’s modulus of whole muscle was about 25 times larger than fascicle [49]. Moreover, the modulus of whole muscle was from 2 to 7.5 MPa, and this value was the same as Young’s modulus at the low strain rate in this research. The whole muscle passive response was dominated by extracellular structures creating the large modulus [49–51]. At the whole muscle scale, deformation of the whole muscle bundle occurred in the tendon, muscle structures, and reflected the synthesis property of both parts of the muscle bundle.
|
Specimen |
Location |
Scale |
Strain rate |
Maximum Stress ( MPa) |
Young modulus (MPa) |
Source |
|---|---|---|---|---|---|---|
|
Porcine |
Muscle of ham |
Fascicle |
0.05–2100 s− 1 |
0.4 MPa |
0.5–4 MPa |
[12] |
|
Porcine |
Muscle of ham |
Fascicle |
0.1–3000 s− 1 |
0.2 MPa |
0.04–0.6 MPa |
[31] |
|
Bovine |
Muscle of ham |
Fascicle |
0.01–2300 s− 1 |
0.3 MPa (strain 0.58) |
1–4.5 MPa |
[11] |
|
Rabbit |
Tibialis Anterior Muscle |
Whole muscle |
1, 10, 25 s− 1 |
0.6–1 MPa |
1.3–2.2 MPa |
[52] |
|
Dog |
Sartorius |
Fascicle |
0.1, 1.0, and 10 mm/min |
1.5–2.7 MPa |
-- |
[53] |
|
Frog and mouse |
Semitendinosus and toe |
Fiber and bundle |
20 s− 1 |
0.32 MPa (frog fiber) 0.11 Mpa (mouse fiber) |
0.14 MPa (Frog fiber) 0.05 MPa (Mouse fiber) |
[14] |
|
Human |
Right leg |
Fascicle |
0.01–100 s− 1 |
0.13–0.4 MPa |
0.3–1 MPa |
[43] |
|
Frog |
Frog semitendinosus muscles |
Whole muscle |
0.001–200 s− 1 |
0.68–1.25 MPa |
2.9–29.9 MPa |
This study |
The purpose of this study is to determine the tensile properties of the whole muscle-tendon fascicles at the quasi-static and dynamic strain rate. The results show the alternation of stress and Young’s modulus under various strain rate from 0.001 to 200 s− 1. Both stress and modulus are sensitive to strain rate. Yield stress increases 1.9 times within change of strain rate from 0.001 to 0.5 s− 1 while Young’s modulus changes 1.6 times. A dramatic rise of Young’s modulus is observed at dynamic impact and reaches about 30 MPa at 194 s− 1. At the quasi-static strain rate, the stress-strain curves comprise of three evident regions because the proteins in sarcomere have enough time to straighten. But the property of the sample only indicate a linear region at high strain rate and that is similar to soft tissue. The findings also demonstrated a difference in passive mechanical property of the whole muscle bundle and muscle bundle in an impact. However, it seems to be different about the value while there is no change in the contour of the stress-strain curves. Whole muscle bundles have a larger strength, and that is predicted because the extracellular structures of muscle did not affect by sample isolation. Because of those factors, it is necessary to add the influence factor of strain rate and muscle-bundle scale in constructing muscle mechanisms.
Funding
This work was supported by the Ministry of Science and Technology, Taiwan, MOST 109-2637-E-992-011.
CRediT authorship contribution statement:
Dat Trong Tran: Conceptualization, Methodology, Investigation, Writing - original draft, Review & editing.
Liren Tsai: Methodology, Review & editing, Supervision, Validation, Corresponding author.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Conflict of Interest Disclosure: The authors declare that we have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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No competing interests reported.