Estimation of joint torque in dynamic activities using wearable A-mode ultrasound

Abstract

The human body constantly experiences mechanical loading. However, quantifying internal loads within the musculoskeletal system remains challenging, especially during unconstrained dynamic activities. Conventional measures are constrained to laboratory settings, and existing wearable approaches lack muscle specificity or validation during dynamic movement. Here, we present a strategy for estimating corresponding joint torque from muscles with different architectures during various dynamic activities using wearable A-mode ultrasound. We first introduce a method to track changes in muscle thickness using single-element ultrasonic transducers. We then estimate elbow and knee torque with errors less than 7.6% and coefficients of determination (R²) greater than 0.92 during controlled isokinetic contractions. Finally, we demonstrate wearable joint torque estimation during dynamic real-world tasks, including weightlifting, cycling, and both treadmill and outdoor locomotion. The capability to assess joint torque during unconstrained real-world activities can provide new insights into muscle function and movement biomechanics, with potential applications in injury prevention and rehabilitation.

Fig. 1. Overview of the A-mode ultrasound system.

A Exploded view of the wearable transducer mount. Four SETs are mounted on a 3D-printed case and attached to the body using a compressive fabric band. B Photograph of SETs worn on the upper arm over the BB muscle belly. C Photograph of SETs worn on the upper leg over the RF muscle belly. D Representative A-mode ultrasound data during concentric contractions of the parallel BB muscle (top) and the pennate RF muscle (bottom). Red dashed lines indicate superficial and deep muscle boundaries measured with the MBTA. Right insets show representative raw ultrasound data at specific time frames.

Fig. 2. Elbow torque estimation during isokinetic contractions of the biceps brachii.

A Illustration of participants secured on a dynamometer with SETs placed over the BB muscle belly. B Example elbow angle, elbow torque, and BB thickness from a representative participant during passive (pass; gray), concentric (conc; red), and eccentric (ecc; blue) contractions at 60° s⁻¹, 90° s⁻¹, and 120° s⁻¹. Lines and shaded regions represent mean ± SD (n = 7 contractions). C Example relationship between BB thickness, elbow angle, and elbow torque from a representative participant across all conditions, with an overlaid quadratic fit (gray). D RMSEs for different contraction speeds across all participants (n = 10). One-way ANOVA: no significant main effect (p = 0.851, F_2,18 = 0.163). E RMSEs for different contraction types across all participants (n = 10). One-way ANOVA: significant main effects (p < 0.001, F_2,18 = 35.0). Bonferroni post-hoc analysis: pass vs conc (p < 0.001), pass vs ecc (p < 0.001), and conc vs ecc (p = 0.527). For D and E, each box bounds the interquartile range (IQR) divided by the median with whiskers extending up to 1.5*IQR. Each dot represents the RMSE for one participant. *p < 0.05.

Fig. 3. Elbow torque estimation during dumbbell curls.

A Illustration of participants performing dumbbell curls with BB thickness measured with SETs and elbow angle measured with wireless IMUs. B Example elbow angle and BB thickness from a representative participant during curls with no weight (0 kg), a 5 kg, and a 10 kg dumbbell. C Estimated elbow torque during curls with various weights for this participant. D Simulated elbow torque for this participant calculated using a rigid body model based on classical mechanics. For B–D, lines and shaded regions represent mean ± SD (n = 6 repetitions). E Average estimated torque for all participants (n = 5) at different weight conditions. F Average calculated torque for all participants (n = 5) at different weight conditions. For E and F, each color represents data for one participant. Each dot represents the average torque of all contractions (n = 6) within the respective condition.

Fig. 4. Knee torque estimation during isokinetic contractions of the rectus femoris.

A Illustration of participants secured on a dynamometer with SETs placed over the RF muscle belly. B Example knee angle, knee torque, and RF thickness from a representative participant during passive (pass; gray), concentric (conc; red), and eccentric (ecc; blue) contractions at 60° s⁻¹, 90° s⁻¹, and 120° s⁻¹. Lines and shaded regions represent mean ± SD (n = 7 contractions). C Example relationship between RF thickness, knee angle, and knee torque from a representative participant across all conditions, with an overlaid quadratic fit (gray). D RMSEs for different contraction speeds across all participants (n = 10). Friedman’s test: no significant main effects (p = 1.00, χ²₂ = 0.000). E RMSEs for different contraction types across all participants (n = 10). One-way ANOVA: significant main effects (p < 0.001, F_2,18 = 21.8). Bonferroni post-hoc analysis: pass vs conc (p < 0.001), pass vs ecc (p < 0.001), and conc vs ecc (p = 0.894). For D and E, each box bounds the IQR divided by the median with whiskers extending up to 1.5*IQR. Each dot represents the RMSE for one participant. *p < 0.05.

Fig. 5. Knee torque estimation during treadmill and outdoor locomotion.

A Illustration of participants performing various walking and running tasks on an instrumented treadmill with RF thickness measured with SETs and joint kinematics measured with wireless IMUs. B Example estimated knee torque during the stance phase (left column) and corresponding ground truth (right column) for treadmill locomotion at various speeds (0.75, 1.25, 1.75 m s⁻¹ walking and 2.50, 3.00 m s⁻¹ running) and slopes [+10% (top row), 0% (middle row), −10% (bottom row)] from a representative participant. Lines and shaded regions represent mean ± SD across the steps within each condition. C RMSEs for different locomotion types across all participants (n = 5). Student’s two-tailed t tests: walk vs run (p = 0.873). D RMSEs for different slope levels across all participants (n = 5). One-way ANOVA: no significant main effect (p = 0.965, F_2,8 = 0.036). For C and D, each box bounds the IQR divided by the median with whiskers extending up to 1.5*IQR. Each dot represents the RMSE for one participant. E Photograph of a participant performing outdoor locomotion with a backpack containing the A-mode ultrasound electronics. Placements of SETs and IMUs remained unchanged compared to the treadmill test. F Knee torque estimation at different speeds during level ground outdoor locomotion. Lines and shaded regions represent mean ± SD (n = 15 steps). G Knee torque estimation during comfortable-speed downhill and uphill walking and running. Lines and shaded regions represent mean ± SD (n = 15 steps).