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. Author manuscript; available in PMC: 2025 Jun 1.
Published in final edited form as: Med Sci Sports Exerc. 2024 Jan 19;56(6):1077–1084. doi: 10.1249/MSS.0000000000003396

Achilles Tendon Loading during Running Estimated via Shear Wave Tensiometry: A Step Towards Wearable Kinetic Analysis

Alex J Reiter 1, Jack A Martin 1,2,3, Keith A Knurr 2,3,4, Peter G Adamczyk 1, Darryl G Thelen 1,2
PMCID: PMC11096059  NIHMSID: NIHMS1959190  PMID: 38240495

Abstract

Purpose:

Understanding muscle-tendon forces (e.g., triceps surae and Achilles tendon) during locomotion may aid in the assessment of human performance, injury risk, and rehabilitation progress. Shear wave tensiometry is a noninvasive technique for assessing in vivo tendon forces that has been recently adapted to a wearable technology. However, previous lab-based and outdoor tensiometry studies have not evaluated running. This study was undertaken to assess the capacity for shear wave tensiometry to produce valid measures of Achilles tendon loading during running at a range of speeds.

Methods:

Participants walked (1.34 m/s) and ran (2.68, 3.35, and 4.47 m/s) on an instrumented treadmill while shear wave tensiometers recorded Achilles tendon wave speeds simultaneously with whole body kinematic and ground reaction force data. A simple isometric task allowed for the participant-specific conversion of Achilles tendon wave speeds to forces. Achilles tendon forces were compared to ankle torque measures obtained independently via inverse dynamics analyses. Differences in Achilles tendon wave speed, Achilles tendon force, and ankle torque across walking and running speeds were analyzed with linear mixed-effects models.

Results:

Achilles tendon wave speed, Achilles tendon force, and ankle torque exhibited similar temporal patterns across the stance phase of walking and running. Significant monotonic increases in peak Achilles tendon wave speed (56.0-83.8 m/s), Achilles tendon force (44.0-98.7 N/kg), and ankle torque (1.72-3.68 N-m/kg) were observed with increasing locomotion speed (1.34-4.47 m/s). Tensiometry estimates of peak Achilles tendon force during running (8.2-10.1 body weights) were within the range of those estimated previously via indirect methods.

Conclusions:

These results set the stage for using tensiometry to evaluate Achilles tendon loading during unobstructed athletic movements, such as running, performed in the field.

Keywords: ACHILLES TENDON FORCE, TRICEPS SURAE, LOCOMOTION, HUMAN PERFORMANCE, WEARABLE TECHNOLOGY

INTRODUCTION

Understanding muscle-tendon forces in the body may aid in the assessment of human performance, injury risk, and rehabilitation progress. However, it is currently not feasible to directly assess muscle-tendon forces outside of a laboratory setting. The triceps surae and Achilles tendon (AT) are of particular interest in the context of locomotion due to the primary role they play in propulsion. Previous studies have identified how the loading experienced by the AT can affect running economy (1), influence the risk of developing overuse injuries (2), and aid in designing appropriate rehabilitation programs following AT rupture (3). Forces are traditionally estimated using laboratory-based motion analysis and electromyography (EMG) data in conjunction with complex musculoskeletal models (4,5). It is often desirable to understand force generation outside of the laboratory or clinic to capture the natural movements and environments that people experience during daily life, work, or sports. Recent advances in wearable sensors such as inertial measurement units (IMUs), EMG sensors, and instrumented shoe insoles enable movement to be measured during outdoor activity (6–9). However, wearable measures of kinematics and external forces still require musculoskeletal models or machine learning approaches to estimate internal muscle-tendon forces.

Shear wave tensiometry has been introduced as a noninvasive technique for directly assessing in vivo muscle-tendon loading (10). Tensiometry measures the speed of propagating shear waves in tendon as a proxy for axial loading. Previous studies have validated the capability of tensiometry to estimate AT loading during treadmill walking, with tendon force estimates that compared closely with traditional motion analysis estimates (11–13). Tensiometry has also been adapted to a wearable version and combined with other wearable sensors including IMUs to estimate triceps surae loading and work production during outdoor walking (14,15). The wearable tensiometer system could enable a vast array of human performance or sports medicine applications by assessing loading outside of the laboratory. However, previous lab-based and outdoor tensiometry studies have not evaluated highly dynamic locomotor activities such as running.

This study was undertaken to assess the capacity for shear wave tensiometry to produce valid measures of AT loading during running at a range of speeds. Validity was assessed by comparing shear wave estimates of AT loading to synchronous ankle torque derived from traditional lab-based motion analysis techniques. We hypothesized tensiometry would detect increases in AT loading with increasing locomotion speed, and trends would be similar to increases in ankle torque derived via inverse dynamics.

METHODS

Participants

All participants for this cross-sectional study provided written informed consent under a protocol approved by the Health Sciences Institutional Review Board of the University of Wisconsin-Madison. Participants had no history of lower limb fractures, ligament, or tendon injury in the prior 6 months. They were active adults that self-reported being able to sustain a 4.47 m/s (6 min/mile) running pace for approximately 1 minute.

Shear wave tensiometry

AT shear wave speeds were measured at 100 Hz using a shear wave tensiometer (10). The tensiometer consisted of two main components placed in series: an electrodynamic tapping device (ID1674, Adafruit, New York City, NY) and an accelerometer array (352C23, PCB Piezotronics, Depew, NY) (Figure 1A). The two components were attached via custom-designed parts to a fabric-foam material (X-treme, Fabrifoam, Exton, PA) that secured the device around the ankle in contact with the AT (Figure 1B). The tapping device was driven via an amplified (LP-2024A+, Lepy, Jieyang, China) 100 Hz, 3% duty cycle pulse wave. Each impulsive excitation induced a propagating shear wave that was tracked by two accelerometers embedded in silicone (Mold Star 15 SLOW, Smooth-On, Macungie, PA) spaced 8 mm apart. Accelerometer data were amplified (480B21, PCB Piezotronics, Depew, NY) and sampled at 100 kHz (USB-6363, National Instruments, Austin, TX). Wave travel time between accelerometers was computed by finding the shift that maximized the cross correlation between accelerometer signals, with subsample estimates obtained via cosine interpolation (10,16). Shear wave speed was computed by dividing the inter-accelerometer distance by the wave travel time between the accelerometers (11). Tapping device excitation, accelerometer data acquisition, and wave speed calculations were controlled through a custom MATLAB (MathWorks, Natick, MA) script.

Figure 1.

Figure 1.

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The tensiometer consists of an electrodynamic tapping device and accelerometer array attached via custom-designed parts to a fabric-foam material (A). The tensiometer was secured around the ankle with the components in contact with the Achilles tendon (B).

Walking and running

Shear wave tensiometers were secured bilaterally over the ATs of each participant. Participants completed a 20-second walking trial at 1.34 m/s (20 min/mile) and 20-second running trials at 2.68, 3.35, and 4.47 m/s (10, 8, and 6 min/mile, respectively) on an instrumented split-belt treadmill (Bertec, Columbus, OH). AT wave speeds were simultaneously recorded with whole-body kinematic and ground reaction force (GRF) data. An 8-camera motion capture system (Motion Analysis, Rohnert Park, CA) recorded the trajectories of 42 reflective markers placed on the body segments (23 located on anatomical landmarks) at 200 Hz (17). Treadmill GRFs were recorded at 2000 Hz. GRFs were low-pass filtered using a bidirectional, 3rd order Butterworth filter with a cutoff frequency of 50 Hz. Foot contact and toe-off were identified as the times when the vertical GRF rose above and fell below 50 N, respectively (18).

Tensiometer calibration to Achilles tendon force

AT wave speed was calibrated to AT force via a quasi-static, isometric loading task (Figure 2). Participants stood with each foot on a rounded bar spanning the width of the foot. The rounded bars were secured to independent force plates enabling the measurement of the GRF under the first metatarsal head of either foot. Participants were asked to slowly sway side-to-side to increase and decrease the load borne by each foot. A handrail was provided for balance and to enable participants to actively pull themselves downward to increase the loading. Ankles were maintained in a neutral posture (approx. 0° plantarflexion) throughout. AT wave speeds and GRFs were simultaneously recorded during the swaying task. Ankle torque to support the load was assumed to be generated entirely by the triceps surae and transmitted through the AT. Thus, AT force was estimated by multiplying the GRF by the distance from the head of the first metatarsal to the ankle medial malleolus, then dividing by the distance from the AT line-of-action to the ankle medial malleolus. Both distances were measured superficially on the medial side of the foot and ankle. A tensioned beam model predicts that tendon loading varies proportionally to squared wave speed (10). Therefore, linear least squares estimation was used to determine a calibration factor, β (the slope of the linear fit), relating squared AT wave speed to AT force (11). Only data in which GRF was above 100 N was used for the linear fit. Using the calibration factor, participant-specific AT forces, FAT, were calculated from AT wave speeds, c, collected during the walking and running trials. Based on previous studies, 15 m/s was assumed to approximately indicate the zero-load AT state, allowing for AT force to be estimated from AT wave speed as: FAT = β(c2 − 152). Finally, AT force was normalized to participant body mass.

Figure 2.

Figure 2.

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Participants performed a calibration task which enabled simultaneous measures of Achilles tendon (AT) wave speed and net ankle plantarflexion torque. Wave speed was measured via a skin-mounted shear wave tensiometer that consisted of an electrodynamic tapper and accelerometer array in series. AT force was estimated from the ground reaction force with moments arms from the medial malleolus to the first metatarsal head (d1) and the AT (d2) measured externally. Linear least squares estimation was used to determine the participant-specific calibration factor between the AT wave speed squared and AT force. The calibration factor was subsequently applied to wave speeds measured during walking and running to estimate AT force.

Biomechanical modeling

Biomechanical modeling and analyses were completed in OpenSim 4.3 (18,19) using a 37 degree-of-freedom (DOF) full-body linked segment model (20,21). Model anthropometrics were linearly scaled from measurements collected during a static trial for each participant. Ten additional markers were placed for the static pose, which were used to define joint centers. Kinematic and GRF data were filtered using a bidirectional, 4th order low-pass Butterworth filter with a 12Hz cut-off frequency. Joint angles were calculated via inverse kinematics using a weighted least-squares optimization algorithm that minimized the difference between experimental and model marker positions (22). Inverse dynamics analysis was used to determine the net joint torques for each model DOF.

Statistical analyses

A sample size of 10 was estimated for a linear mixed effect model in order to detect differences in peak AT wave speed across the walking and running speeds using GLIMMPSE V3 (23) (Hotelling-Lawley trace, α = 0.05, power = 0.80). Outliers in peak data were identified with a robust nonlinear regression and false discovery rate method (24) using Prism 9.5.1 (GraphPad Software, Boston, MA). Whole trials containing a peak outlier were removed. Of note, only the data type containing the outlier was removed; the other data types were retained in the analysis (e.g., for a participant, if peak AT wave speed at 1.34 m/s was an outlier, peak AT force and peak ankle torque at 1.34 m/s for that participant were retained.). Gait cycle data were ensemble averaged for each remaining walking and running trial using MATLAB. Descriptive statistics of mean with 95% confidence interval (95% CI) were used to describe the AT wave speed, AT force, and ankle torque at each point in the gait cycle. Differences in peak AT wave speed, AT force, and ankle torque across walking and running speeds were analyzed with linear mixed-effects models with repeated measures using JMP Pro 15 (SAS Institute, Cary, North Carolina). Locomotion speed was included as a categorical fixed effect, participant as a random effect, and limb as random effect nested within participant. When a significant speed effect was detected, Tukey-corrected post-hoc tests were used for pairwise comparisons among speeds. Significance was defined as p ≤ 0.05, and model least squares means (LSM) with 95% CIs were reported.

RESULTS

Eleven healthy, young adults were recruited and participated in this study (6/5 males/females, age: 26.5 (4.7) years, height: 1.79 (0.13) m, mass: 73.7 (12.7) kg, note: mean (standard deviation)). Bilateral measurements gave a total sample size of 22 with repeated measures across the four locomotion speeds. Two outlier trials were detected and removed in AT force and ankle torque data (86/88 remaining); none were detected in peak AT wave speed data (88/88 remaining).

Shear wave tensiometry captured cyclic patterns in AT wave speed and force during locomotion that corresponded with ankle torque patterns derived via motion analysis (Figure 3A). Generally, stride-to-stride variability was greater in AT wave speed (Figure 3B) and AT force (Figure 3C) compared to ankle torque (Figure 3D). Qualitatively, AT wave speed over a gait cycle increased from walking to running and modulated with running speed (Figure 4A). Importantly, gait cycle trends in magnitude and temporal features in AT force (Figure 4B) and ankle torque (Figure 4C) were similar to AT wave speed data. A unique aspect of tensiometry is its capacity to capture passive loading during late swing phase (10). AT wave speed and AT force during late swing phase at approximately 95% of the gait cycle also increased with locomotion speed.

Figure 3.

Figure 3.

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Representative data for a participant running at 3.35 m/s. Times series data for five seconds show shear wave tensiometry captured cyclic patterns of Achilles tendon (AT) wave speed and force similar to ankle torque derived via motion analysis (A). All strides and the average curve for the entire 20-second trial reveal greater stride-to-stride variability in AT wave speed (B) and AT force (C) compared to ankle torque (D).

Figure 4.

Figure 4.

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The temporal features of Achilles tendon (AT) wave speed (A), AT force (B), and ankle torque (C) throughout the gait of walking and running. Stance phase magnitudes exhibited increases from walking to running and with increasing running speed. Tensiometry (A and B) detects a loading pulse in late swing that is not evident in the net ankle torque (C). Data are presented as mean with 95% confidence intervals.

Locomotion speed was a significant factor in all three of the peak metrics (all p-values < 0.001). Peak AT wave speed, AT force, and ankle torque were significantly different between all the various locomotion speeds (p ≤ 0.046), except for the 2.68 m/s to 3.35 m/s comparison in peak AT wave speed (p = 0.626) and peak AT force (p = 0.794) and the 3.35 m/s to 4.47 m/s comparison in peak AT force (p = 0.144, Table 1). Monotonic increases in peak AT wave speed, AT force, and ankle torque with increasing locomotion speed confirmed qualitative trends (Table 2). Peak AT wave speed increased from 56.0 m/s [44.9, 67.2] (LSM [95% CI]) during walking to 83.8 m/s [72.6, 94.9] during running at the fastest speed. Peak AT force increased from 44.0 N/kg [27.1, 60.9] during walking to 98.7 N/kg [81.6, 115.8] during running at the fastest speed. Peak ankle torque increased from 1.72 N-m/kg [1.44, 1.99] during walking to 3.68 N-m/kg [3.41, 3.96] during running at the fastest speed. Furthermore, peak AT force and ankle torque showed similar percentage increases from walking to running at every speed.

Table 1.

Comparison of peak Achilles tendon (AT) wave speed, AT force, and ankle torque between locomotion speeds. (Note: Data are presented as least squares mean difference (LSM diff) with 95% confidence intervals (95% CI) and Tukey-corrected p-values. w1.34, walking at 1.34 m/s; r2.68/3.35/4.47, running at 2.68/3.35/4.47 m/s)

Peak AT wave speed (m/s) Peak AT force (N/kg) Peak ankle torque (N-m/kg)
  p-value LSM diff [95% CI]   p-value LSM diff [95% CI]   p-value LSM diff [95% CI]
w1.34 vs r2.68 m/s <0.001 −17.4 [−24.4, −10.4] <0.001 −36.4 [−51.7, −21.0] <0.001 −1.21 [−1.37, −1.06]
w1.34 vs r3.35 m/s <0.001 −20.6 [−27.6, −13.7] <0.001 −41.7 [−57.0, −26.4] <0.001 −1.60 [−1.75, −1.44]
w1.34 vs r4.47 m/s <0.001 −27.7 [−34.7, −20.7] <0.001 −54.7 [−70.5, −38.8] <0.001 −1.97 [−2.12, −1.81]
r2.68 vs r3.35 m/s 0.626 −3.2 [−10.2, 3.8] 0.794 −5.3 [−20.7, 10.0] <0.001 −0.38 [−0.53, −0.23]
r2.68 vs r4.47 m/s 0.001 −10.3 [−17.3, −3.3] 0.017 −18.3 [−34.1, −2.5] <0.001 −0.75 [−0.90, −0.60]
r3.35 vs r4.47 m/s 0.046 −7.1 [−14.1, −0.1] 0.144 −13.0 [−28.8, 2.8] <0.001 −0.37 [−0.52, −0.22]
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Table 2.

Peak Achilles tendon (AT) wave speed, AT force, and ankle torque at different locomotion speeds. (Note: Data are presented as least squares mean (LSM) with 95% confidence intervals (95% CI) and percentage change for running values from walking. w1.34, walking at 1.34 m/s; r2.68/3.35/4.47, running at 2.68/3.35/4.47 m/s)

Peak AT wave speed (m/s) Peak AT force (N/kg) Peak ankle torque (N-m/kg)
  LSM [95% CI] % Change   LSM [95% CI] % Change   LSM [95% CI] % Change
w1.34 m/s 56.0 [44.9, 67.2] - 44.0 [27.1, 60.9] - 1.72 [1.44, 1.99] -
r2.68 m/s 73.5 [62.3, 84.6] 31.1% 80.4 [63.5, 97.3] 82.5% 2.93 [2.66, 3.21] 70.6%
r3.35 m/s 76.7 [65.5, 87.8] 36.8% 85.7 [68.8, 102.6] 94.7% 3.31 [3.04, 3.59] 92.9%
r4.47 m/s 83.8 [72.6, 94.9] 49.5% 98.7 [81.6, 115.8] 124.2% 3.68 [3.41, 3.96] 114.4%
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DISCUSSION

This is the first study to demonstrate the use of shear wave tensiometry to characterize AT loading during running. Trends in AT wave speed and AT force over the gait cycle were similar to trends in ankle torque derived via motion analysis. Furthermore, peak AT wave speed and peak AT force showed similar increases from walking to running and with increasing running speed compared to peak ankle torque. These results set the stage for using tensiometry to evaluate AT loading in the context of human performance, injury risk, or rehabilitation where running or a similarly high-dynamic movement is of interest.

Estimates of peak AT force ranging from 8.2-10.1 body weights (bw) for speeds of 2.68-4.47 m/s in this study were within the range of those reported in literature (5). Estimates of peak AT force via musculoskeletal modeling range from 5.2-5.4 bw while running at 2.9 m/s (3,25) to 4.2-6.6 bw at 3.4-3.7 m/s (26–30) to 7.4 bw at 4.8 m/s (30). A more recent study estimated AT forces to be 6.2-9.6 bw for running speeds from 2-5 m/s (31). The closest previous measurement technique to tensiometry (i.e., direct tissue measurement) involved the use of an implanted, invasive buckle transducer, and estimated 6.5-8.3 bw for speeds of 3-4 m/s (32). Overall, the data suggest that our noninvasive sensor has the capacity to estimate AT loading during running without the need for invasive techniques or costly motion analysis equipment and models.

We observed greater variability across subjects in AT wave speed and AT force data compared to net ankle torque. This observation could reflect sensor noise or greater variability in muscle contributions to joint torque. It has previously been shown in a cat model that individual plantarflexor muscle loading can vary substantially across strides (33). Furthermore, the contributions of other plantarflexors (i.e., tibialis posterior, peroneus longus, peroneus brevis, flexor hallucis longus, and flexor digitorum longus) are not captured by the tensiometer AT wave speed but will contribute to the net ankle torque. Independent of the other plantarflexors, AT subtendon geometry (34) could also affect the tensiometer measurements. There is evidence in humans of differential loading across the triceps surae subtendons during walking (35). Finite element models are providing us insights into the effects of nonuniform subtendon loading on wave speeds. Hence, it is possible that a skin-mounted tensiometer more closely tracks wave speed of the underlying superficial triceps surae subtendon, which may exhibit greater variability in loading than seen in the net ankle torque. Improvements to tensiometer sensor design and wave speed interpretation are ongoing to address potential sensor noise. For example, we have shown that the use of additional accelerometers and a Kalman filter (36) can enhance the accuracy of wave speed measurements in the presence of noise.

We developed a simple calibration method to calibrate the tensiometer to individual subjects. A prior study used an isokinetic dynamometer and ultrasound measurements of AT moment arm to relate AT wave speed to estimates of AT force (11). This study demonstrates that a simpler calibration protocol using ground reaction measures is viable, which could be easily adaptable to a wearable/mobile system. The force plate and foot plate used in this study can be adapted to a portable bathroom-scale type force plate with an attached foot placement device. The GRFs from the portable calibration device could be synchronized with the wave speed measurements from the wearable tensiometer system during a simple calibration task. In a similar manner to this study, the GRFs could be converted to AT force with two quick measurements of the foot allowing for estimates of AT force during dynamic activities.

In some instances, it may be desirable to simplify data collections and eliminate the need for a calibration task all together, such as in a clinical setting or during large-scale human performance assessments. We are developing neural network models to predict AT loading directly from wave speed and accelerometry data, potentially eliminating the need for a calibration task (37). Tensiometry could also prove valuable in characterizing changes in loading over the course of rehabilitation or pre- and post-interventions (e.g., gait re-training, footwear modification, strength and conditioning program). In such cases, percentage changes in wave speed relative to the unaffected limb or baseline values over time (e.g., days or months) can be used to estimate the effects on internal muscle-tendon loading without the need for calibration or absolute metrics.

Several limitations should be considered when interpreting these results. First, our calibration approach assumes that isometric ankle torque is purely generated by the AT. This ignores the possible contributions of dorsiflexors and plantarflexors other than the triceps surae to net ankle torque. Contributions of other plantarflexors would likely result in a slight over-prediction of AT force estimates while cocontraction of antagonist dorsiflexors could lead to under-predictions. Second, we attempted to strike a balance between ease of implementation and functional and anatomical validity when determining the ankle joint center and AT moment arm for the calibration procedure (38–42). Specifically, there is evidence that the functional ankle joint center may be more anterior than the transmalleolar joint center (41), and the AT moment arm from the functional center is larger in a loaded state compared to an unloaded state (42). Given our calibration method involved a loaded, functional state of the ankle, we estimated the AT moment arm from the medial malleolus, as opposed to the (more posterior) lateral malleolus or a subjective point in between. This gave us a reasonable estimate with a procedure that would be repeatable between participants. Since this study did not quantify cocontraction (e.g., antagonist muscle activation) during calibration or directly compare our superficial AT moment arm measurement to imaging-based techniques, we aren’t certain how these potential calibration errors affect AT force estimates. Future work should quantify the precision and bias associated with these. Third, as previously mentioned, wave speed magnitudes exhibit greater variability than might be assumed based on ankle torque measures. Additional investigations are needed to understand to what extent this represents physiological variability in individual muscle contributions to locomotion, and what is attributable to noisy measurements which may be mitigated through improved sensor design and wave speed calculation algorithms. Fourth, participants were healthy young adults, so findings may not generalize to other ages or those with pathological tissue. While tensiometry has proven useful in evaluating other populations (12,13), peak AT force, for example, likely does not represent magnitudes expected in children, older adults, or those with pathologies. Lastly, tensiometry is not yet readily accessible to clinicians or the general public. Device placement, data acquisition, and post-processing currently require some level of expertise and training until the technology further matures and becomes more robust.

CONCLUSIONS

These results set the stage for using wearable versions of tensiometry to evaluate AT loading during unobstructed athletic movements performed in the field. The lab-based system was used in this study for convenience in comparing tensiometry to traditional motion analysis techniques. However, we have recently introduced a wearable tensiometry system that uses onboard signal conditioning and data acquisition to take tensiometer measures outside the lab (14). In addition to evaluating AT force with the use of a mobile calibration platform or machine learning approach, combining tensiometry with other wearables such as IMUs, instrumented insoles, and GPS will enable other kinetic metrics to be estimated in the context of location and terrain. Furthermore, tensiometry could be used to detect longitudinal measures of AT loading to assess injury risk or recovery. In conclusion, tensiometry has been shown to be a viable technique for estimating AT loading during running and presents a promising method for assessing human performance, injury risk, or recovery during high-dynamic movement.

Acknowledgements

Funding was provided by the Department of Defense (129866603), National Institutes of Health (TL1TR002375, T32AG000213, R42AR074897), and the Wisconsin Alumni Research Foundation. The authors thank Elizabeth Schmida and Victoria Heiligenthal for their assistance with motion capture data processing and musculoskeletal modeling. The results of the study are presented clearly, honestly, and without fabrication, falsification, or inappropriate data manipulation. The results of the present study do not constitute endorsement by the American College of Sports Medicine.

Footnotes

Conflict of Interest

J.A.M. and D.G.T. are co-inventors on a patent related to this work (U.S. 10631775). The other authors have no conflicts of interest to disclose.

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