Abstract
Muscles are the actuators that drive human movement. However, despite many decades of work, we still cannot readily assess the forces that muscles transmit during human movement. Direct measurements of muscle–tendon loads are invasive and modeling approaches require many assumptions. Here, we introduce a non-invasive approach to assess tendon loads by tracking vibrational behavior. We first show that the speed of shear wave propagation in tendon increases with the square root of axial stress. We then introduce a remarkably simple shear wave tensiometer that uses micron-scale taps and skin-mounted accelerometers to track tendon wave speeds in vivo. Tendon wave speeds are shown to modulate in phase with active joint torques during isometric exertions, walking, and running. The capacity to non-invasively assess muscle–tendon loading can provide new insights into the motor control and biomechanics underlying movement, and could lead to enhanced clinical treatment of musculoskeletal injuries and diseases.
Highlights
Muscles are the actuators that drive human movement
Assuming that transverse deflection is harmonic in time and space, the shear wave speed, c, is a function of the shear modulus, μ, of the tissue and axial stress, σ, acting on the transverse cross-section of the tendon: c2
The derivation is based on incremental motion about a stressed state, so the shear modulus term, μ, represents the tangential modulus for tendon which exhibits nonlinear material behavior[16,17]
Summary
Model of shear wave propagation in a tensioned tendon. We model tendon as a tensioned Timoshenko beam[14] exhibiting locally linear elastic behavior. The tangential shear modulus term, which can account for nonlinear strain-stiffening, is predicted to have negligible effects on wave speed when compared with the axial stress term This leads to the prediction that squared wave speed should vary in proportion to tendon stress ðc2 / σÞ under physiological loads. We were surprised to see in our initial in vivo experiments that both the tendon and adjacent subcutaneous tissue exhibited similar transient motion as a wave passed by (Fig. 2) This observation, supported by prior surface wave studies in muscle[24] and tendon[25], suggested that tendon shear wave vibrations may be detectable via skin-mounted sensors. Under simple isometric loading conditions, it can be assumed that antagonist muscles are relaxed and tendon moment
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