Simulation analysis of real-time continuous stiffness in muscle fibers and tendons of the triceps surae during multi-joint movement

doi:10.12307/2025.956

Abstract

Abstract:

BACKGROUND: The stiffness of muscle fibers and tendons within skeletal muscles is regulated by the neuromuscular system and remains variable. However, observing the mechanical properties of muscle fibers and tendons during complex multi-joint movements is challenging, and the real-time variation patterns of their stiffness are not yet clear.
OBJECTIVE: Taking the open-access simulation data of triceps surae at different running speeds and gait phases as an example, to explore the real-time stiffness change rules of muscle fiber stiffness and tendon stiffness.
METHODS: OpenSim simulation results of muscle fiber activation, length, velocity parameters, and tendon length parameters of the triceps surae in five long-distance runners at different running speeds were collected from the Website of Stanford University. The instantaneous slope of the force-length relationship curve of muscle fibers and tendons in the Hill-Zajac muscle model used in the simulation was extracted as the real-time stiffness of the triceps surae muscle fibers and tendons. The temporal changes of stiffness indicators of muscle fibers and tendons during gait were analyzed.

RESULTS AND CONCLUSION: The regulation of muscle fiber activation-length-velocity status and tendon strain resulted in the stiffness of muscle fibers and tendons changing in the same trend as the applied force. Compared with lower running speeds, the stiffness of the gastrocnemius muscle fibers was higher in the early support phase at higher running speeds (P ≤ 0.01), and the tendon stiffness of the medial head of the gastrocnemius was higher in the early support phase (P ≤ 0.02). The stiffness of the gastrocnemius muscle fibers and tendons was lower from the mid-support to the mid-swing phase (P ≤ 0.03), and the stiffness of the soleus muscle fibers was higher during the support phase (P ≤ 0.02). Under all running speeds, the stiffness of the triceps surae muscle fibers and tendons showed a trend of being higher during the support phase than during the pre-swing phase (P ≤ 0.03), and the stiffness of the gastrocnemius muscle fibers and tendons increased again in the late swing phase (P ≤ 0.05). These findings indicate that increasing running speed can increase the stiffness of triceps surae muscle fibers and tendons during the stance phase; when running speed and gait phase change, gastrocnemius and soleus muscles have different patterns of muscle fiber and tendon stiffness changes, whereas gastrocnemius can increase its muscle fiber stiffness and tendon stiffness in the late swing phase through pre-activation phenomenon.

Key words: OpenSim, muscle fiber, tendon, stiffness, simulation, engineered tissue construction

CLC Number:

Li Chen, Liu Ye, Ni Xindi, Zhang Yuang. Simulation analysis of real-time continuous stiffness in muscle fibers and tendons of the triceps surae during multi-joint movement[J]. Chinese Journal of Tissue Engineering Research, 2025, 29(35): 7529-7536.

Figures/Tables 5

2.1 不同跑速下肌纤维收缩行为及实时刚度差异小腿三头肌的肌纤维力与肌肉激活随跑速增加均呈支撑前期升高而支撑后期下降的趋势(F*≥6.727，P≤0.04)，标准化肌纤维缩短速度随跑速增加总体呈支撑期升高的趋势(F*≥7.135，P≤0.02)，标准化肌纤维长度随跑速增加总体呈降低的趋势(F*≥7.489， P=0.01)，见图2。在2 m/s vs. 3 m/s、2 m/s vs. 4 m/s、2 m/s vs. 5 m/s、3 m/s vs. 4 m/s、3 m/s vs. 5 m/s、4 m/s vs. 5 m/s的相互比较中，得到以下结果：①相比较低跑速(2，3，4 m/s)，对应较高跑速(3，4，5 m/s)下：小腿三头肌肌纤维力与肌肉激活在支撑前期更高(P≤0.02)，而在支撑中后期更低(P≤0.03)；腓肠肌标准化肌纤维速度(绝对值)在支撑期内更高(P≤0.02)，比目鱼肌标准化肌纤维速度(绝对值)在支撑前期更高(P≤0.01)，比目鱼肌标准化肌纤维速度(绝对值)在支撑中期更低(P≤0.01)。②相比较低跑速(2，3 m/s)，对应较高跑速(3，4，5 m/s)下的腓肠肌标准化肌纤维长度在几乎整个支撑期及摆动前中期时更低(P≤0.02)，而比目鱼肌标准化肌纤维长度仅在支撑中期更低(P≤0.02)。跑速变化时，小腿三头肌肌纤维激活-长度-速度瞬时状态即时调节，使肌纤维刚度随跑速增加总体呈支撑期升高而摆动期降低的趋势(F*≥8.948，P≤0.05)(图2)，并且在腓肠肌和比目鱼肌中的表现不同。相比较低跑速(2，3，4 m/s)，对应较高跑速(3，4，5 m/s)下的腓肠肌肌纤维刚度在支撑前期更高(P≤0.03)，而在支撑中后期与摆动前中期更低(P≤0.03)，比目鱼肌的肌纤维刚度在支撑前期及中期更高(P≤0.02)。 2.2 不同跑速下肌腱行为及实时刚度差异小腿三头肌的肌腱力、肌腱应变与肌腱刚度均存在不同跑速间差异(F* ≥7.354，P≤0.04)，见图3。在2 m/s vs. 3 m/s、2 m/s vs. 4 m/s、2 m/s vs. 5 m/s、3 m/s vs. 4 m/s、3 m/s vs. 5 m/s、4 m/s vs. 5 m/s的相互比较中，得到以下结果：①在支撑前期，小腿三头肌在较高跑速(3，4，5 m/s)下的肌腱力及肌腱应变高于对应较低跑速(2，3 m/s)(P≤0.02)，腓肠肌内侧头肌腱刚度在5 m/s跑速高于2 m/s跑速(P≤0.02)。②在支撑中后期，比目鱼肌在较高跑速(4，5 m/s)下的肌腱力、肌腱应变与肌腱刚度低于较低跑速时(2，3 m/s)(P≤0.03)。在支撑中后期及摆动前中期，腓肠肌在较高跑速(4，5 m/s)下的肌腱力、肌腱应变与肌腱刚度低于较低跑速(2，3 m/s)(P≤0.03)，腓肠肌在3 m/s跑速下的肌腱力、肌腱应变与肌腱刚度低于2 m/s跑速(P≤0.03)。 2.3 不同时相间的肌纤维刚度与肌腱刚度差异跑步步态中，小腿三头肌肌纤维刚度均呈现支撑期高于摆动期的趋势(H≥3.981，P < 0.01)，见图4A。在3，4，5 m/s跑速下，腓肠肌内侧头肌纤维刚度在摆动后期高于摆动前中期(P≤0.03)。在5 m/s跑速下，腓肠肌外侧头肌纤维刚度在摆动后期高于摆动前中期(P < 0.01)，比目鱼肌肌纤维刚度在支撑期高于摆动期(P < 0.01)。在较低跑速(2 m/s和3 m/s)下，腓肠肌肌纤维刚度在支撑期高于摆动前中期(P≤0.03)，比目鱼肌肌纤维刚度在支撑期高于摆动中后期(P≤0.01)。跑步步态中，小腿三头肌肌腱刚度均呈支撑期高于摆动期的趋势(H ≥680.4，P < 0.01)，见图4B。在较高跑速(4 m/s和5 m/s)下，腓肠肌肌腱刚度在支撑前中期及摆动后期均高于支撑后期至摆动中期(P < 0.02)。在3，4，5 m/s跑速下，比目鱼肌肌腱刚度在支撑前期高于支撑中期至摆动后期(P < 0.02)。在较低跑速(2 m/s和3 m/s)下，腓肠肌肌腱刚度在支撑期及摆动后期均高于摆动前中期(P≤0.03)。在2 m/s跑速下，比目鱼肌肌腱刚度在支撑前中期高于支撑后期至摆动后期(P < 0.01)。"

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