Exploring Variable Achilles Tendon Loading Via Active Acoustics

Abstract

Non-invasive, direct Achilles tendon (AT) load measurements have been a long-standing objective in biomechanics toward elucidating underlying muscle-tendon dynamics during normal and pathological human locomotion. However, traditional methods fail to capture subcutaneous changes due to the disconnect between externally measured forces and internal tendon dynamics. In this study, we introduce Active Acoustics (AA) as a non-invasive approach for measuring AT loads, building on recent developments by leveraging continuous mechanical stimulation in place of intermittent taps or bursts. We assessed AA’s performance against Inverse Dynamics (ID) in 10 healthy subjects. We collected data from 13 tasks designed to capture a wide range of AT force, displacement, and velocity conditions. AA successfully tracked dynamic changes in AT loading while maintaining low computational complexity, achieving the shortest filtering latency in synthetic benchmark tests compared to prior methods. Our benchmark evaluation demonstrated a strong Pearson correlation (r=0.95 ±0.02, n=6) during active, isometric contractions, supporting the feasibility of continuous stimulation for AT load measurements. Across the 13 tasks, AA captured task-specific variations in AT loading, revealing nuanced effectiveness dependent on the specific ankle joint dynamic conditions, and the need for improved under-the-skin reference signals. The continuous stimulation approach enabled a higher output frequency (500 Hz vs 50/5 Hz previous work) and demonstrated consistent performance at an experimentally optimized stimulation frequency of 750 Hz. This study underscores AA’s potential for real-time, low-latency applications in assistive and rehabilitative devices. Future research should explore sensor optimization, expanded task sets, and application-specific features to further enhance AA’s utility.

Graphical Abstract

I. Introduction

Measuring tendon loading has long been a key objective in biomechanics, as it offers critical insights into under-the-skin locomotion dynamics that are essential in helping advance both our understanding of biomechanical data as well as the development of novel therapeutic, assistive, and diagnostic strategies aimed at improving gait and mobility [1], [2], [3], [4], [5], [6]. There have been significant advancements in the estimation of external forces during movement including systems that are portable, achieve near real-time estimations, are able to drive assistive device applications, and more [7], [8], [9], [10], [11], [12]. These leverage a variety of novel inverse dynamics (ID) approaches that utilize motion capture, inertial measurement units (IMUs), electromyograms (EMGs), instrumented foot insoles, and other state of the art sensors that have expanded on the potential mobility applications available across a variety of tasks [7], [13], [14], [15], [16], [17]. Despite these advances, traditional joint-level and EMG-driven biomechanical analyses provide limited information about the internal muscle-tendon forces driving movement due to structural complexities that decouple joint and tissue dynamics [2], [18], [19], [20], [21], [22], [23], [24], [25]. Toward bridging this gap, recent research has aimed to directly capture the intricacies of subcutaneous tissue dynamics across biomechanical processes [26], [27], [28]. Here, we aim to extend the latest research demonstrating feasibility to non-invasively measure internal muscle-tendon forces while seeking to improve accessibility, portability, cost-effectiveness, and real-time performance, paving the way for broader and more immediate clinical applications beyond traditional laboratory environments [25], [29], [30].

The Achilles Tendon (AT) is an ideal target for mobility related applications, as it endures some of the highest forces in the human body and is one of the most frequently injured [31], [32]. AT load may also serve as a reliable proxy for whole-body metabolic energy consumption because of its serial arrangement with the calf muscles [33], [34]. Consequently, the AT has been a focal point in studies aimed at refining tendon loading measurements [27]. Initial direct measurement methodologies, such as laser Doppler vibrometry [35], elastography [36], [37], and shear wave dispersion analysis [22], [38] have all been hampered by the size and complexity of the systems involved and fail to provide the range of temporal resolution required for real-time and dynamic task exploration.

The tendon tapping system developed by Thelen’s group [25], [30], [39], was the first to address many of the limitations in earlier technologies, namely size and near real-time processing speeds, and has shown promising correlations with ground-truth inverse dynamics during repetitive tasks including constrained isometric contractions, walking, and running. This system, comprises a tendon tapper and two accelerometers, allowing for the measurement of shear wave speeds which show high correlation tracking of ankle torques when calibrated. However, this method still carries inherent complexities, notably the strict placement of multiple accelerometers, signal processing requirements, and voltage requirements.

Building on Thelen’s group’s work, Bolus, et al. introduced a simplified approach that reduces mechanical complexity and equipment needs [29]. This system employs burst-mode analysis, a novel method that leverages signal feature extraction to estimate AT loading with only one vibration motor and one accelerometer. In doing so, it introduces data output frequency limitations that result from the latency between the motor’s activation and deactivation, and the ‘quiet’ periods between bursts which restricts output data frequency to just 5 Hz. This frequency is notably low given our goal of capturing rapid dynamic changes common in day-to-day locomotion tasks, where most are non-repetitive and require higher temporal resolution for fully capturing biomechanical intricacies [21], [40], [41], [42].

Most recently, an initiative by Thelen’s group [43] has addressed the complexity and temporal limitations by demonstrating single-sensor shear-wave tensiometry measurement consistency with high frequency shaped wavelets stimulation, which despite the lack of task variety and reference signal comparison, suggests a narrowing gap toward real-time implementation potential.

Here, we aim to address some of the limitations of previous research to develop internal tendon load measurement techniques by transitioning to continuous mechanical stimulation instead of on/off taps, bursts, and wavelets [25], [29], [43]. The premise being that signal power readings for a single accelerometer will inherently reflect changes that correlate with the underlying tendon loading (Fig. 1). To understand and quantify the impact of this simplified approach, we present signal processing latency measurements inherent to each method from a synthetic benchmark test. Secondly, we test our system on both a controlled benchmark task for validation and on a battery of dynamically expanded tasks spanning a wide range of force and displacement contexts aiming to understand the influence of biomechanics on measurement effectiveness to guide future refinements in stimulation-recording profiles. Finally, our work includes the use of a new metric we call fx, which aims to quantify the variance captured by our experimental sensor while minimizing the effects of inherent disconnects between external and under-the-skin sensor measurements. We believe our simplified measurement architecture applied over a comprehensive force-displacement task set has the potential to elucidate and establish new benchmarks while continuing to push development toward novel sensor applications and techniques that could enable real-time ‘in-the-loop’ control of wearable devices capable of steering tendon loads (Fig. 2).

Fig. 1.

System overview. (a) Our active acoustics (AA) system architecture consisting of an accelerometer and vibration motor placed approximately ~5 cm apart on the skin over the Achilles Tendon (AT) directly capturing AT’s response to motor excitation, yielding output signal magnitudes corresponding to changes in the underlying tendon loads. (b) Changes in AT tension levels, shown as Low (L) and High (H), are captured by the raw signal detected by the accelerometer. The signal envelope, derived from the raw data, serves as our primary measure for Active Acoustics (AA).

Fig. 2.

Comparison to previous work and applications. (a) Two main previous work efforts explore direct tendon loading measurements through stimulation and accelerometer readings. This table presents a direct comparison of the most relevant components. (b) Direct tendon loading measurements can be used in various assistive and rehabilitative applications. Our AA system expands potential applications through minimal latency and greater temporal resolution while our study elucidates the need for greater task diversity in future studies.

II. Methods

A. Experimental Protocol

The study was approved by the Georgia Institute of Technology Institutional Review Board (Protocol #H21159). For this study, we recruited 10 healthy voluntary participants (5 male / 5 female, age: 26.5 ± 3.27 years, height: 176 ± 80 cm, weight: 71 ± 4 kg) with no current or previous significant lower-limb injury or gait pathology. We collected data for thirteen tasks (Fig. 3 (a)) selected to test the greatest variability in ankle displacement and loading conditions (Fig. 3 (b)) [44]. Participants performed each task for 30 seconds in fixed order with self-adjusted rest periods (≥1 min) in between as follows: a) constrained ankle flexion: while reclined on the dynamometer (dyno), participants performed isometric contractions by pushing and releasing the torque-measuring footrest with no heel or foot movement, b) free ankle dorsi/plantar flexion: while seated with legs in the air and knees over seat edge, participants plantar and dorsiflexed their foot over its full range of motion, c) calf raises: participants cyclically raised and lowered their heels as far as they could, d) walking: participants walked at 1.25, 1.50, and 1.75 m/s on the instrumented treadmill, e) running: participants ran at 3.25 m/s on the instrumented treadmill, and f) hopping: participants hopped at 1.5, 2.0, and 2.5 Hz on the instrumented treadmill using an audible metronome as a timing aid, and then the same way at the same 3 frequencies on sand (poppy seeds to avoid equipment damage). Note n = 10 and n = 6 reported for dyno to leverage preliminary data collections further validating repeatability and n = 6 for main cohort with all thirteen tasks.

Fig. 3.

Task Set and Task Phases. (a) The most diverse task set of Active Acoustics and Inverse Dynamics data for AT loading. Tasks include a) (red) constrained ankle flexions on a dynamometer (dyno), performing isometric contractions (n=10, validation task), b) (orange) free ankle dorsi/plantar flexion while seated with legs in the air, plantar and dorsiflexing foot over its full range of motion (n=6), c) (green) calf raises, raising and lowering heels (n=6), d) (blue) walking at 1.25, 1.50, and 1.75 m/s on treadmill (n=6), e) (dark blue) running at 3.25 m/s on treadmill (n=6), and f) (purple) hopping at 1.5, 2.0, and 2.5 Hz on treadmill and sand (n=6). Task color coding is consistent throughout the paper. (b) Visual representation of the high displacement, loading, and speed variability targeted in the study, illustrating small vs. large joint displacements and low vs. high muscle-tendon forces. (c) The 4 phases for our time-series tasks to target different loading magnitudes, speeds, and frequencies.

For tasks a-c, we provided participants direction as to how to perform the movements to ensure we covered different frequency and loading magnitudes within a given task. We promoted this variance through the phases presented in Fig. 3 (c)). For the constrained ankle flexions, the phases were as follows: i) increasing: push 3 times, each with increasing force, ii) slow: to gradually ramp up and down once, iii) fast: to do quick pushes for ~5 seconds, and finally, iv) free: to use the remaining time to push in any random pattern they wanted (Fig. 3). For free ankle flexions and calf raises, it was the same 3 increasing, 1 slow, ~5 seconds fast, and then random, with encouragement to attain full range of motion of the respective task. For walking and running tasks, we let participants move with their preferred strides. For hopping, we instructed them to hop at the beat and to use the entire time in between beats to be in the hopping motion in the air and landing to facilitate consistency in form across frequencies. Note that hopping height was not constrained.

B. Active Acoustics

Our experimental AA sensing system consists of pairing a small vibration motor (P2010 B-81, Radio Ears Inc.) with a high-frequency uniaxial contact accelerometer (series 3225, Dytran Instruments, Inc.) by placing them ~5 cm apart on the skin over the AT with the middle point between them aligned with the visible lateral malleolus center (Fig. 1 (a)), both attached to the skin using a double-sided adhesive (Rycote, Gloucestershire) and fabric tape (Kinesio Tex, Kinesio). We drove the motor via a 3V peak-to-peak sine wave and we sampled the accelerometer at 25 kHz which captured the tendon response to the constant sinusoidal stimulation from the motor (stiffer tendons yield stronger signal [29], [38]). Aiming for low latency and increased real-time usage potential, we only processed the AA signal using the MATLAB R2024b (MathWorks) ‘envelope’ function which effectively calculates a moving average (Fig. 1 (b)), with the exception of some minimal noise correction for outlier points. The simplicity of this approach is one of our protocol-differentiating strengths.

To quantify potential on-device performance we simulated real-time latency of various signal processing methods. We generated 1000 distinct synthetic signals at a 25 kHz sampling frequency and repeated the analysis 10 times for each to capture intra-test variability. The methods included (Table I): a) causal root-mean-square (RMS) envelope calculation with a 1400-sample window (our method), b) linear-phase Kaiser-window finite impulse response (FIR) bandpass filter (Bolus et.al. filtering only), c) second-order Butterworth bandpass filter implemented offline with zero-phase for comparability (Martin et.al. filtering only), d) causal Hilbert transform envelope extractor (Schmitz-Thelen et.al. single sensor filtering only), e) Kaiser FIR-based burst processing with feature extraction from 200-ms windows (Bolus et.al considering filter and burst effects), f) Butterworth-based shear wave processing, normalizing, and squaring with 20-ms windows (Martin et.al considering filtering and time windows), and g) causal Hilbert transform envelope extractor and seven-lobe wavelet look-ahead with f_H=2kHz (Schmitz-Thelen et.al. single sensor considering filter and wavelet effects). Note that our real-time simulation isolates algorithmic latency by using causal equivalents of all calculations and omitting hardware related effects. Each method was evaluated under simulated real-time conditions by sequentially feeding 1-ms chunks of data (25 samples per chunk) to mimic real sensor input. Latency was defined as the cumulative delay incurred from processing each chunk sequentially, including any initial buffering required for windowed methods.

Table I.

Signal Processing Time Benchmarks

Method	Pseudo Real-Time Latency Avg. (ms)
AA – RMS Envelope	17 ±1
Bolus et.al. (filter only) – Kaiser-window FIR Bandpass Filter	144 ±5
Martin et.al. (filter only) – Butterworth Bandpass Filter	154 ±5
Schmitz-Thelen et.al. (filter only) – Hilbert Transform	114 ±4
Bolus et.al. (filter and burst) – Bandpass and Burst Effects	159 ±6
Martin et.al. (filter and wave) – Bandpass and Wave Window Effects	171 ±7
Schmitz-Thelen et.al. (filter and wavelet) – Hilbert Transform and Wavelet Window Effects	115 ±4

Average latency across 10 repetitions of 1000 distinct signals shown in milliseconds. Benchmark emulates 25kHz signal fed sequentially as in real-time scenarios instead of having the full signal from the start (as in offline processing). Table shows filter only effects as well as filters combined with the burst/wave/wavelet (f_H=2kHz) time windows.

To narrow down the stimulation frequency to use, we ran a pilot study collecting data for 3 subjects during 3 tasks each (dyno, free ankle, and calf raises) with 6 stimulation frequencies (0, 100, 250, 500, 750, and 1500 Hz) from which we chose 3 (500, 750, and 1500 Hz) through a direct correlation analysis between AA and ID. Further, during our main protocol, we had an initial calibration task that considered the band power of metronome and dynamometer force- controlled isometric contractions. The frequency with the highest signal power was then used for that subject for the main thirteen tasks.

C. Inverse Dynamics

To obtain AT moments to be used for comparison, we first collected ground reaction forces (GRFs) from a dynamometer (System 4 Pro, Biodex Inc.) and an instrumented treadmill (Bertec), and collected joint dynamics through motion capture (MoCap) data (Vicon Motion Systems). For AT moment calculation, we then used the data from the MoCap and GRFs and fed it into our OpenSim [45] model which leverages traditional inverse dynamic methods and Hill-type musculoskeletal models [46] to yield the needed loading estimates through inverse dynamics and static optimization analyses.

D. Data Analysis

We used Pearson’s Correlation Coefficient (r) and our feature X (fx) as our main evaluation metrics. r for its prevalence through the physiology literature and relevance when trying to understand the relationship between AA and ID in the time-series domain [47], [48], [49], and fx to quantify the relationship between the higher-level-signal-variance captured by AA and ID. r was calculated between AA and ID for each task for each subject. Note that since ID’s output frequency is limited at 1000 Hz, we had to down sample our AA signal through interpolation, highlighting the inability to more thoroughly test one of its biggest benefits over previous work. After, we applied a 5-sample smoothing and shifted the signals via cross-correlation (X-Corr) analysis to ensure we eliminated delays caused by equipment triggering without warping (stretching/compressing) the signal. In addition to r, and instead of a strict quantitative analysis matching measured AA voltages (V) to estimated ID torques, we also examined visually qualitative properties of both signals and their tendencies across tasks, as regardless of correlation performance (which already ignores units), there is great value and potential applications that stem from being able to visually capture the changes in the underlying physiology [50].

Toward quantifying the relationship between observed overarching signal features and variance, we developed fx (Fig. 4) which provides a higher abstraction level from that of a time-series analysis and quantifies the relation between the most salient dynamical changes captured by each sensing modality. The development of fx helps fill the analytical gap stemming from the absence of non-invasive ways of directly validate complex under-the-skin dynamics. To calculate fx, we looked at AA and ID signal segments comprised of 25 data points to each side of the largest peaks in the ankle joint angle signal. By focusing on when joint angle changes are bigger, we focus the analysis on the parts of the task with the higher chance of change in AT loading and therefore the experimental signals. To mitigate the influence of noise from high temporal density, our feature selectively analyzes only the largest 25% of signal peaks, disregarding minor directional changes. Because this method lends itself to overfitting if segments are too large and/or the peak percentage is too small, we calibrated them with a random signal so that fx correlations are always under 0.2. That is, we calculate the fx correlation of a random signal against the ID signal and make sure that these parameters keep the fx correlation always under the threshold. This indicates that if there is a strong correlation with the same parameters when comparing against AA, it is because the AA signal relates to ID and not due to overfitting. Note that for our 50 and 25% parameters, we tested random signals against all signals from ID tasks, and on average the random signal yielded a 0.16 ± 0.03 fx correlation. Hence, we trust our fx is helping us capture the underlying variance and relationship between AA and ID, understanding these sensors are proxies to the underlying physiology which at times can differ from both.

Fig. 4.

Sensor signals are all proxies of the under-the-skin physiological truth and how Feature X captures overarching variance. (a) The loads within the Achilles Tendon (AT) are complex and nuanced. Measures from each sensor are proxies of what is happening under-the-skin. Here we represent the relationship between a sensor and the physiological ground truth as a transfer function. In turn, when comparing two sensors, such as Inverse Dynamics (ID) and Active Acoustics (AA), what we get is an evaluation of the similarity between the two transfer functions from the two sensors rather than the relationship between the experimental sensor and the underlying biomechanical ground truth. (b) Feature X (fx) helps quantify captured variance and map the relationship between AA and ID at a higher level than individual points in time as in Pearson’s Correlation (r). fx takes points where changes in ankle joint angle displacement are the largest, and expected loading variance is greatest, and considers them as segments within which to compare local minimum and maximum values. This to capture the relationship between salient physiological changes and features across both sensors and to provide an additional reference metric for comparing AA/ID.

To assess the statistical significance of differences between AA and ID, we looked at cycle averages and peaks for both walking and hopping and employed the Wilcoxon signed-rank test, a non-parametric method suitable for comparing paired samples. This test was chosen due to the non-normal distribution of the data, as it does not assume normality. For each task, two p-values were obtained, one for the signal averages and another for the signal peaks. These p-values indicate whether there is a statistically significant difference in the unit-matched sensor output signals under the given conditions.

III. Results and Discussion

For the first time to the best of our knowledge, we demonstrate the feasibility of accelerometer readings to accurately measure AT load changes during continuous stimulation (Fig. 5). Our dataset is distinctly unique, encompassing a broad range of tasks and employing a more focused time-series analysis approach leveraging movement phases that target variability of AT displacement and loading.

Fig. 5.

Time-series active acoustics (AA) performance across task phases. (a) Time-series comparisons of AA and inverse dynamics (ID) for all 10 subjects during dynamometer-based isometric contractions show high-fidelity tracking through varied loading patterns. Note that the dynamometer produced regular two-peak patterns in the ground truth which are machine noise and not torque changes. These slightly reduce correlation values but are representative of common equipment and analysis limitations. Subjects kept from preliminary sessions for repeatability are shown as S7-S10. (b) Time-series comparisons of AA and ID for subjects during free ankle plantar/dorsiflexion show differing loading magnitudes vs calf raises, ID shows higher loading during calf raises and AA higher loading during free ankle. Salient features from the AA signal include lower power peaks during plantarflexion and the highest magnitudes during dorsiflexion, likely related to isometric stretching of the AT and surrounding posterior tissue. (c) Time-series comparisons of AA and ID for subjects during calf raises show signal shapes that are consistent with the phases and number of calf raises on both devices yet differ between sensors and subjects. (b-c) Ankle angle is represented by the grey shaded region in the background, and while units are not displayed, they range from 25 to −60 degrees with slight variations between subjects. Note low correlation values even when both signals seem to capture the same physiological events. This due to both r’s sensitivity to temporal shifts and to each sensor presumably capturing different physiological nuances within events. ID units represent OpenSim estimated torque and AA units show captured voltages, yet our focus is on signal timing and magnitude of changes given unit calibration needs might differ between applications.

A. Performance Benchmark

Direct comparison of AA to ID during our benchmark dyno task yielded an average correlation (r) of 0.95 ± 0.02 across the main cohort of subjects (n = 6) and 0.94 ± 0.03 when considering preliminary ones (n = 10) (Table II) (the 0.01 shift likely reflecting expected inter-subject and session variability). This further validates repeatability and confirms continuous stimulation performance during constrained tasks yields the same level of performance to previous methods despite the added intra-task variability. The high correlation during isometric contraction patterns of different loading magnitudes and speeds (Fig. 5 (a)) demonstrates the tracking potential in controlled tasks with limited external forces, highlighting AA’s sensitivity to under-the-skin dynamics irrespective of joint kinematics, establishing a comparison baseline of AA’s performance for reference during dynamic tasks. This is the only task without fx since it requires changes in ankle angle, which was kept constant.

Table II.

Task correlation (r) and feature X (fx) results

Task	CORR (r)	fx
Dyno (n=6)	0.95 ±0.02	-
Dyno (n=10)	0.94 ±0.03	-
Free	0.44 ±0.26	0.52 ±0.25
Raises	0.17 ±0.17	0.73 ±0.19
Walk 1.25 m/s	0.75 ±0.09	0.96 ±0.03
Walk 1.50 m/s	0.66 ±0.18	0.88 ±0.20
Walk 1.75 m/s	0.68 ±0.22	0.95 ±0.05
Run 3.25 m/s	0.71 ±0.16	0.95 ±0.06
Hop 1.5 Hz	0.40 ±0.14	0.91 ±0.04
Hop 2 Hz	0.60 ±0.14	0.94 ±0.01
Hop 2.5 Hz	0.66 ±0.11	0.92 ±0.05
Average	0.61 ±0.22	0.83 ±0.15

Pearson correlation is shown as CORR (r) and Feature X correlation as fx, both unitless. The table displays per-task correlation averages for all subjects for each task. Note that the Dyno task does not have an fx value, as fx requires joint angle changes, which were fixed in this task. Dyno also includes preliminary sessions (n=10), while main cohort for all tasks has n=6. These correlation values represent the comparison of AA voltage values with ID moments as calculated through OpenSim.

B. Dynamic Task Analysis

Our dynamic task battery aims to capture biomechanical nuances to help guide future exploration. Hence, a crucial consideration when interpreting direct AA vs ID correlation, is understanding they measure inherently different physiological phenomena (Fig. 4 (a)). This highlighting the fundamental limitation in current evaluation methods and sensing techniques, as the literature is yet to demonstrate a definitive noninvasive under-the-skin ground truth for new device validation that performs in highly dynamic tasks as our own [26], [28]. This is driven by our limited understanding of underlying physiological factors, such as AT moment arm length, strain patterns, and co-contraction, as even when measured directly [51], [52], these factors exhibit complex patterns that remain to be fully characterized [44], [53], [54], [55], [56], [57]. Both in capturing nuances particular to these highly variable tasks and considering the clinical potential of real-time, albeit imperfect, signals, we extended our analysis beyond correlation measures to assess the qualitative properties of both signals and their behavior across tasks, as the ability to visually capture physiological changes offers significant value and potential applications [48].

Our overall results show a cross subject and task average correlation (r) of 0.61 ± 0.22 and an average fx correlation of 0.83 ± 0.15 (Table II), showing great performance variability across tasks and subjects, indicative of areas requiring further research. Results from our calibration task showed 750 Hz as the stimulation frequency with the highest signal power for 9 out of our 10 subjects and 1500 Hz for the remaining one. This supports the notion that optimal stimulation frequency can be system, subject, and task dependent, even if some perform more generally. Further work is needed to fully characterize stimulation frequency interactions and variability. With this context, the following sections examine each task category to better understand the nuanced findings in AA and ID tracking of AT load changes.

1). Non-Cyclical Tasks

a). Free Ankle Plantar and Dorsiflexion

Comparing AA to ID during our free ankle task yielded an average correlation (r) of 0.44 ± 0.26 and an average fx correlation of 0.52 ± 0.25 across subjects (Table II). Salient AA signal features include time matched peaks during both plantar and dorsiflexion (Fig. 5b vs. 5c). Plantarflexion AA peak voltage magnitudes are as expected being lower than calf raises at similar angle peaks, as free ankle is an unloaded condition. However, dorsiflexion AA peak voltages are higher than expected likely due to passive stretching effects on vibration transmission. Notably, without a reference signal able to capture under-the-skin dynamic tradeoffs between passive/active and anterior/posterior elements, further research is needed to disambiguate these sources and quantify the individual element effects. These observations coupled with temporal phase sensitivity, explain the modest r/fx values despite clear event-level alignment. Despite our limitations, it is interesting seeing the potential coupling of sensor signal and AT shortening variability [58] together with similarly intricate under-the-skin dynamics.

b). Calf-Raises

For our AA/ID comparison during calf raises, we obtained an average correlation (r) of 0.17 ± 0.17 and an average fx correlation of 0.73 ± 0.19 across subjects (Table II). The low r may be unexpected given visual similarities between signals and their clear capturing of individual calf-raise peaks (Fig. 5 (c)), yet the large correlation uplift between r and fx suggests this is mainly due to time shift effects on correlation, as physiology driven peak shape and width differences can significantly impact r. Conversely, differences in shape of calf raise peaks between sensors and subjects (Fig. 5 (c)), suggest the potential presence of more intricate physiological variance not previously characterized in the literature.

2). Cyclical Tasks

For cyclical tasks, intra-step tendon dynamics are difficult to interpret beyond cycle averages (Fig. 6), not only due to 30-second trials amplifying inter-subject variability in physiology and locomotion preferences, but due to lack of references given most existing work only considers multi-cycle averages [59]. Hence, our results should encourage the study of time-series physiological events and the underlying relationships between AT loading and physiological factors.

Fig. 6.

Repetitive task performance. (a.1-b.1) Cycle averages for a representative subject during walking (a.1) and hopping (b.1) tasks. AA signals are shown in different shades of blue for walking and purple for hopping, while ID signals are shown in different shades of grey. (a.2-b.2) Box plots of signal averages and (c.4-d.4) of signal peaks across subjects for each task. (a.2-b.4) show walking tasks at speeds of 1.25, 1.50, and 1.75 m/s, while (d.2-d.4) show hopping tasks at cadences of 1.5, 2.0, and 2.5 Hz. AA signals are depicted in blue/purple and ID signals in grey. (c.3-d.3) Box plots of signal averages and (c.5-d.5) of signal peaks across tasks for subjects on each sensor. (c.3-c.5) compare AA and ID for walking tasks, and (d.3-d.5) compare AA and ID for hopping tasks. The box plots illustrate no significant difference between sensors with a p=0.0625 for the walking average (c.3), p=0.5625 for walking peaks (c.5), p=0.3125 for hopping average (d.3), and p= 0.3125 for hopping peaks (d.5).

a). Walking and Running

Our AA/ID comparisons for walking (1.25, 1.5, 1.75 m/s) and running (3.25 m/s) yielded an average correlation (r) of 0.70 ± 0.04 and an average fx correlation of 0.94 ± 0.03 across all subjects and speeds (Table II). Similar to previous work [25], [29], AA captures loads from both the anterior and posterior sides of the leg, adding balance-related activation nuances to otherwise repetitive tasks. Fig. 6 (a.1) captures some of this nuance through the timing and shape of peaks, suggesting the existence of pre-activation before toe-lift and residual tension after, both likely consequences of balance-related co-contraction, similar to the wider walking signals observed in previous work [25]. Additionally, as walking speed increases, we observe a consistent increase in average and peak load magnitudes across subjects, consistent with prior work [25], [29] and with no significant difference between the two sensors (avg. p = 0.0625, peak p=0.5625).

b). Hopping

For our AA/ID comparisons of hopping (1.5, 2.0, 2.5 Hz), we obtained an average correlation (r) of 0.55 ± 0.14 and an average fx correlation of 0.92 ± 0.01 across all subjects and speeds (Table II). The lower r seems related to strong anterior activation likely due to balancing and pre-loading which yields a wider signal peak (Fig. 6 (b.1)). Like previous tasks, AA seems to be capturing activation not seen in ID, offering possible insights into nuanced tendon behavior and/or noise, further encouraging non-traditional time-series analysis, as repetitive tasks can become highly dynamic via balance-related activations and their effects on both active and passive stretching. As in walking, we saw no significant average and peak load magnitudes difference across subjects between the two sensors (avg. p = 0.3125, peak p=0.3125).

Fig. 7 results show our sand hopping AA measurements as they compare to solid ground, yet we did not have ID for comparison due to limitations in measuring ground reaction force vectors on uneven terrain. Main issues with sand (poppy seeds) ID include sand-occluded markers and dispersed ground reaction force vectors. While there are ID methods that can overcome these, as those leveraging shoe insoles for GRFs [7], there is limited research that explores these conditions [60], [61], [62] and that properly controls for variables like hop height, multi-joint activation schemes, and participant technique, all of which influence AT loading, hence leaving ample space for further exploration [63].

Fig. 7.

Time-series AA across hopping tasks. Hopping at cadences of 1.5, 2.0, and 2.5 Hz on overground and sand for a representative subject. AA and ID are compared for overground, but only AA is available for sand due to the lack of reliable ground reaction force measurements in this environment.

C. Performance, Limitations and Areas for Improvement

Our AA system offers a simple, low-latency device for estimating AT loading. It yields meaningful raw signal outputs and through a straightforward envelope calculation, matches ID tendon loading measurements in constrained environments and in dynamic tasks reveals areas with potentially nuanced biomechanical behavior. Our AA system provides advancements by shifting to continuous tendon stimulation in place of discrete bursts, taps, and wavelets [25], [29], [43], aiming to yield an uninterrupted data stream that eliminates signal gaps and the need for signal syncing. This is coupled with the single accelerometer, single motor, envelope processing arrangement which enables the higher output frequency of 500 Hz (vs prior work) and could be higher with a smaller window. Our benchmark also showed ~100 ms lower filtering latency (17 ms), further supporting the real-time application potential of time-series biomechanical data [7], [64], [65]. High-quality components were used in this study to explore varied stimulation frequencies, yet previous work suggests more cost-effective alternatives can still maintain sufficient data fidelity [29]. Our vibration stimulation was typically not perceptible and no discomfort was reported; however, since comfort, temperature, and skin/tissue impact were not instrumented, they remain future evaluation items. Additionally, because fatigue related changes can broaden intra-task variability, it was important to keep a fixed task order; still, we recognize this may introduce time-dependent factors such as sweat or changes in sensor coupling, which could affect signal stability across the session, hence motivating future work to quantify time-on-task effects and coupling robustness.

Although not discussed in the literature [28], the 1–3 kHz wavelets used previously [43] may be sufficiently dispersed by soft tissue to behave quasi-continuously, suggesting the comparable temporal coverage attained by our continuous drive may benefit from the lower theoretical energy requirements. Coupling this notion with the unproven benefits of higher phase velocities [43] and our observations during our pilot and calibration tasks of greater AA signal power at 750 Hz than at 1.5 kHz, we are compelled to promote future exploration of stimulation frequency tuning that may be system-, subject-, and task-dependent, including task-specific frequency selection and potentially dynamic, task-adaptive stimulation, to optimize AT-loading tracking.

Despite the sensing methodology advancements, the high correlation performance observed during constrained tasks, and our leveraging of static optimization standards, the nature of current ID models and having used ID with no EMG to inform internal dynamics as our reference signal, are limiting factors of this study. ID is a well-established technique, extensively validated through thousands of studies [45], [66], [67], and able to approximate under-the-skin dynamics during certain tasks through modern muscle models and tooling [45], [68], [69]. Nonetheless, the simplified implementations of Hill-type muscle models scarcely account for physiological complexities like co-contraction and stability [68], [70], [71], shortcomings which add to the nuanced nature of physiological behaviors [26], [27], and uncertainties inherent of accurately measuring AT dynamics [51], [52], [72], [73], [74], therefore limiting ID’s reference potential during highly dynamic tasks [61]. Note how even after accounting for anterior activations through direct plantarflexion-related AT force estimates via static optimization, we use loading verbiage instead of force, stiffness, or torque, as we believe it more accurately captures what OpenSim estimates represent pertaining the complex dynamic physiological changes seen by the AT. Hence, further research is needed to understand EMG and additional sensor informed ID performance during the dynamic tasks and phases in this work, toward obtaining more comprehensive reference validation data for AA and other AT loading measuring techniques. Such data promises to help characterize recurring features as either physiological phenomena or additional artifacts. However, it is important to note that the need for further experimentation and lack of reference work is greatly due to the traditional reliance of studies on cycle-average analyses, seldom looking at highly variable time-series data as targeted by our distinct task phases [11], [40], [75].

Even with the discussed methodological differences, AA, burst approaches, and tendon tapping, all aim to assess tendon responses to stimulation using accelerometers. As our reference ground truth is limited, we used our new fx metric to quantify the relationship in variance captured by AA and ID and enable a higher-level comparison of the captured features with higher resistance to the temporal nuances affecting traditional correlation measures (r) [76] and toward minimizing the impact caused by disconnects between external and internal measurements [2], [18], [19], [20], [21]. fx provides a broader perspective by evaluating salient signal features where we expect the largest loading variance and most significant physiological changes. However, fx’s inherent limitations as a metric, lie in that the comparison pertains two sensors which might differ in their own ways to the underlying ground truth they attempt to capture (Fig. 4). None withstanding, if we assume accurate sensing, low fx values could indicate physiological conditions warranting further investigation, hence helping identify areas of interest for future research. Ultimately, both fx and our qualitative analysis aim to highlight how common data manipulation practices often mask true sensor performance and how in doing so, they obscure insights into the sensitivities required for real-time applications [10], [77], [78].

IV. Conclusion and Future Directions

In this study, we assessed the feasibility of continuous stimulation as a new excitation modality for active acoustic measurements as well as the performance of such sensing across a diverse set of tasks targeting high variability of movement force, displacement, and speed toward capturing underlying physiological dynamics of AT loading. By shifting from tap, burst, and wavelet-based methods to continuous stimulation sensing, our system provides an uninterrupted, high-frequency signal with low computational overhead, making it well-suited for real-time applications. Despite limitations with our reference ID ground truth, the varied dynamic conditions in this study, serve as guidance for future research and encourage more comprehensive AA and ID data spaces toward deeper understanding of AT physiology. Similarly, due to the wide array of potential applications spanning from real-time control of exoskeletons requiring near-perfect assistance triggers [7], [9], [79], [80], [81], to long-term monitoring of joint loading for rehabilitation and injury avoidance [28], [82], we believe target sensor accuracy should lie in a continuum of speed-accuracy trade-offs. Furthermore, the suggested expanded data space will enable application specific optimizations of the speed-accuracy continuum and will open the door for leveraging the latest in artificial intelligence (AI) toward more general cross-subject optimizations. These in turn would be capable of motivating AA specific HW developments and the integration of direct AT loading measurements with other sensing technologies to enable more holistic real-time physiology tracking. This is due to applications being able to leverage the benefits of low-latency, non-invasive, in-situ sensing even when the extent of the sensor accuracy and what physiological phenomena it is capturing is not fully characterized. As we continue to explore AA as a sensing modality, we will learn how to better fine-tune equipment, process signals, and establish targets that leverage the sensor’s strengths. As a result, novel systems that can leverage ‘tendon-in-the-loop’ paradigms for assistive and rehabilitative device control as well as biofeedback will be possible and will become part of the key tools that help us unlock improved mobility for all.