Gauging force by tapping tendons

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.

Fig. 1

Ex vivo experiment. a. Porcine tendons were clamped and cyclically loaded up to 300 N. A tapper device (Supplementary Fig. 2) delivered an impulsive 20 μm tap in the transverse direction at 40 ms intervals. Ultrasound radiofrequency data were collected at 14,100 frames per second from a single location along the tendon and used to track transverse tendon displacements. Scale bar, 2 mm. b An underdamped standing wave emerged in response to each tap (indicated by arrows) and was used to ascertain the natural frequency and corresponding shear wave speed. c Plotted are the mean (±1 s.d.) wave speeds versus the corresponding tendon stress for 10 porcine digital flexor tendons. The shaded region reflects the wave speed predictions using the wave propagation model (Eq. 2) with the following parameters: ρ = 1730 kg m⁻³; μ = 0.04–1.6 MPa; k’ = 0.9 (see Supplementary Methods, Supplementary Tables 1 and 2)

Fig. 2

In vivo ultrasonic measurement of wave speed. a A linear array ultrasound transducer was strapped over the subject’s Achilles tendon. High frame rate (14,100 frames per second) ultrasonic radiofrequency (RF) data were collected at two points (red, blue lines). A custom tapper device (hammer icon; see Supplementary Fig. 2), which was located distal to the ultrasound transducer, intermittently induced transverse waves in the tendon. Center: transverse tissue velocity was measured at multiple kernels (indicated by boxes; darker shades indicate greater depth) located along each RF collection line (red, blue). Scale bar, 1 cm. b We observed that transverse motion was similar for all kernels along the first (red, lower) and second (blue, upper) measurement locations. Thus, tendon wave motion could conceivably be measured from the motion of subcutaneous tissue

Fig. 3

In vivo wave speed measurements. a Shear wave tensiometers secured over the patellar and Achilles tendons. b The tensiometers consisted of a piezo-actuated tapper and two miniature accelerometers spaced a fixed distance apart. c Representative recording of patellar tendon transverse accelerations demonstrate that the travel time (Δt) between accelerometers is shorter in the high load condition, reflecting faster wave propagation. d Linear relationships between joint torque and squared wave speed (binned means ± 1 s.d. for a representative subject) were observed in both tendons across a range of loading rates

Fig. 4

In vivo gait experiment. a Achilles tendon wave speed, ankle plantarflexion torque, and medical gastrocnemius and tibialis anterior muscle activity over 4 consecutive strides of treadmill walking at 1.5 m s⁻¹. The primary peak in wave speed corresponds to push-off in late stance (stance indicated by shaded regions), when the gastrocnemius is active and ankle torque is high. However, a secondary peak in wave speed is seen in late swing and likely reflects passive tendon stretch due to antagonistic tibialis anterior activity. b Stance phase plots, ensemble averaged over multiple gait cycles for a representative subject show speed-related modulation of both Achilles tendon wave speed and ankle plantarflexion torque

Fig. 5

Running experiments. a Patellar tendon wave speeds speed over the gait cycle when running at a fixed speed with different step rates. b Lateral hamstring (biceps femoris) tendon wave speeds detect utilization of this muscle with increasing speed during both mid-stance (15% of gait cycle), and late swing (85% of gait cycle). Hamstring loading during both phases increased markedly with speed, though stance phase demands greater tissue loads than swing phase in this individual