IMU-Based Kinematics Estimation Accuracy Affects Gait Retraining Using Vibrotactile Cues

Wearable sensing using inertial measurement units (IMUs) is enabling portable and customized gait retraining for knee osteoarthritis. However, the vibrotactile feedback that users receive directly depends on the accuracy of IMU-based kinematics. This study investigated how kinematic errors impact an individual’s ability to learn a therapeutic gait using vibrotactile cues. Sensor accuracy was computed by comparing the IMU-based foot progression angle to marker-based motion capture, which was used as ground truth. Thirty subjects were randomized into three groups to learn a toe-in gait: one group received vibrotactile feedback during gait retraining in the laboratory, another received feedback outdoors, and the control group received only verbal instruction and proceeded directly to the evaluation condition. All subjects were evaluated on their ability to maintain the learned gait in a new outdoor environment. We found that subjects with high tracking errors exhibited more incorrect responses to vibrotactile cues and slower learning rates than subjects with low tracking errors. Subjects with low tracking errors outperformed the control group in the evaluation condition, whereas those with higher error did not. Errors were correlated with foot size and angle magnitude, which may indicate a non-random bias. The accuracy of IMU-based kinematics has a cascading effect on feedback; ignoring this effect could lead researchers or clinicians to erroneously classify a patient as a non-responder if they did not improve after retraining. To use patient and clinician time effectively, future implementation of portable gait retraining will require assessment across a diverse range of patients.


I. INTRODUCTION
T HE degradation of cartilage in knee osteoarthritis is a progressive and irreversible process.For the one in five individuals over the age of 40 who live with this disease [1], walking becomes increasingly challenging and painful as cartilage degrades; interventions focus on pain reduction [2] until knee replacement surgery is unavoidable [3].Compressive loading in the knee joint is implicated in the onset [4] and progression of knee osteoarthritis [5], [6], with the medial compartment being particularly susceptible [7].Consequently, many non-surgical treatments target the reduction of medial contact force or surrogate measures of knee loading for managing osteoarthritis [8], [9].
Gait retraining, or teaching the patient a way of walking that could reduce knee loading, has emerged as a promising intervention for individuals with knee osteoarthritis [8].One technique aims to change the foot progression angle during gait, or the amount that the toe points in or out during stance, with respect to the direction of gait progression [10], [11], [12], [13], [14], [15].This modification can reduce the knee adduction moment, a non-invasive surrogate measure of knee contact force [16] that is correlated with loss of medial tibiofemoral cartilage in patients with knee osteoarthritis [6], [17].Studies on retraining the foot progression angle to reduce the knee adduction moment have been largely successful in reducing pain and improving functional outcomes [10], [11], [12], [13], [14], [15].Subjects typically receive real-time feedback on their retraining performance at each step, either via vibrotactile [11], [15] or visual [12], [13] cues.However, this process necessitates frequent visits to the gait laboratory for subjects to fully internalize the new gait, making this promising therapy accessible only to research laboratories and the few clinicians with optical motion capture systems.
Inertial measurement units, or IMUs, offer a portable and low-cost alternative to optical motion capture.By building on existing methods to track the foot progression angle using IMUs embedded in the shoe [18], [19], [20] or worn on top of the foot [21], [22], inertial systems could enable patients to one day carry out their gait retraining therapy at home.However, when compared to motion capture, inertial estimates Fig. 1.Experimental setup and data collection.All subjects performed one-minute baseline and toe-in walking trials in the lab while optical motion capture and inertial sensor data were recorded.The inertial sensor was worn on top of the foot, and vibration feedback was provided to the medial and lateral sides of the shank based on the inertially estimated foot progression angle.The accuracy of the inertial estimate was evaluated through comparison with the foot progression angle computed from the highlighted calcaneus and second metatarsal markers, with respect to the direction of gait.Subjects were then divided into three balanced groups: those who performed four five-minute blocks of training in the laboratory, those who performed four five-minute blocks of training outdoors, and those who did not receive any toe-in gait training.All three groups were evaluated in a separate outdoor location on their ability to maintain the new gait in the absence of feedback.
of the foot progression angle can vary in accuracy across subjects [20], [21], [22], [23], even in cases where outlier data are removed in post-processing steps.Because feedback is provided once per gait cycle, foot progression angle estimates must be accurate at the level of a single step, not averaged across several strides.
Motor learning relies on dependable feedback [24].Furthermore, the effectiveness of a retraining intervention is determined by whether the newly learned gait persists beyond the training environment [25].In this study, we examined how errors that occur in IMU tracking impact an individual's ability to learn and retain a therapeutic gait in the lab or the natural environment.We hypothesized that in both environments, higher tracking error would negatively affect response to feedback cues, as well as cumulative learning rate during retraining.We also hypothesized that higher tracking error would negatively impact performance in the evaluation condition for subjects who retrained with vibrotactile feedback, but not for those in the control group, who received no feedback or retraining.To explain the variability in tracking accuracy, we hypothesized that foot size and foot progression angle magnitude influence tracking error, conducting post-hoc analyses to confirm.

II. METHODS
The study consisted of three phases: initial data collection on a laboratory treadmill, retraining the gait in the laboratory or outdoors, and an evaluation in a new outdoor environment (Figure 1).Thirty healthy adults (Table I) provided written informed consent to participate in the study following a protocol approved by the Carnegie Mellon University Institutional Review Board.None of the participants had previously retrained gait with or without a wearable feedback device.Prospective subjects were excluded if they had a history of lower-limb injury or surgery, were experiencing pain in a lower limb at the time of pre-screening, could not walk comfortably for up to 20 minutes, or were pregnant.

A. Instrumentation
We captured laboratory gait with a 20-camera optical motion capture system (Optitrack, Corvallis, USA), sampling Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
at 100 Hz.Subjects were outfitted with a 27-marker modified Rizzoli marker set [26].Marker data were filtered with a fourth-order low-pass zero-lag Butterworth filter at 15 Hz.The ground-truth foot progression angle was computed as the angle between the vector from the calcaneus marker to the second metatarsal marker and the anterior-posterior axis of the split-belt treadmill (Bertec, Columbus, USA).We estimated heel-to-toe length as the mean distance between the calcaneus and second metatarsal markers during stance.
All subjects wore a SageMotion vibrotactile feedback device (Kalispell, USA) on the dominant leg.The device consists of an IMU worn on top of the foot and two vibrotactile units on the medial and lateral shank, secured above the malleoli with an elastic hook-and-loop strap.The IMU was placed centered over the metatarsals such that it did not impede flexion of the ankle or phalanges, and it was not repositioned during the study.Subjects wore a waist pack containing a battery-powered processing unit that streamed foot progression angle data in real time to a local computer via a Bluetooth connection.Regardless of group membership, all subjects wore the IMU device throughout the study in order to maintain measurement consistency of the foot progression angle, as optical motion capture was not available for the outdoor trials.
The IMU gyroscope and accelerometer were used to estimate the foot progression angle in real time via a step-detection and angle-estimation algorithm [20].For any step outside of the pre-determined target angle range (five degrees medial of their baseline foot progression angle, with a two-degree tolerance to either side), vibrotactile feedback was provided via a transient vibration from one of the two vibrotactile units; "pull" feedback [27] prompted the subject to adjust their foot in the direction of vibration.The vibrotactile cue had a duration of 0.5 s and was delivered by an eccentric rotating mass motor with a peak frequency of 165 Hz.Feedback cues occurred at the push-off phase of gait, allowing subjects the entirety of the swing phase to interpret the cue and plan their next step.If a step was inside the target angle range, no feedback was given.

B. Data Collection
Subjects were assigned to one of three groups via counterbalanced randomization to ensure equal sex ratios.Ten subjects retrained in the laboratory (laboratory group), ten subjects retrained in a natural environment (outdoor group), and ten subjects received only verbal instruction to maintain a toe-in gait, but no vibrotactile feedback or any other form of retraining (no-training group).
1) Baseline Trial: First, we calculated over-ground walking speed as the average of three walking trials over a fixed 7.32-meter distance in the gait laboratory.All three groups then performed a one-minute baseline walking assessment in the motion capture gait lab on the treadmill.Subjects were instructed to walk normally, with both bands of the treadmill set to their preferred walking speed.The SageMotion device was turned on to passively collect foot progression angle data, but no feedback was provided at this time.
2) Toe-in Trial: All three groups were instructed to maintain a five-degree toe-in foot progression angle, relative to the angle calculated during the baseline trial, for a one-minute toe-in walking assessment on the treadmill.The experimenters first provided verbal and visual examples of a five-degree adjustment, using two lines marked on the floor that corresponded to a five-degree change in angle.The two groups that received vibrotactile feedback (laboratory and outdoor groups) were informed that the vibrotactile feedback would be turned on and to adjust their foot in the direction of the feedback; a correct step would receive no feedback.
3) Retraining Period: The two groups receiving vibrotactile feedback then performed four sessions of five minutes of toe-in gait retraining, with two-minute breaks between retraining bouts.The laboratory group walked at their self-selected speed on the lab treadmill.The outdoor group proceeded directly to an outdoor location approximately one minute away from the laboratory, to retrain along a level sidewalk approximately 350 m in length.Some participants in the outdoor group turned around midway through the five-minute trial; these turning steps were removed during post-processing, as described below.The no-training group proceeded directly to the evaluation portion of the experiment.
4) Evaluation: All 30 subjects were then immediately evaluated in a new outdoor location on a level sidewalk approximately 350 m in length.The evaluation site was approximately a two-minute walk from both the laboratory and the outdoor retraining site.We asked all participants, including those who retrained in the laboratory or outdoors, as well as those who received no training or feedback, to walk for five minutes while maintaining the newly learned toe-in gait without feedback.The IMU device remained on, passively collecting foot progression angle data.

C. Data Processing
Foot progression angles from optical motion capture and from the IMU were expressed relative to the subject's baseline foot progression angle, where a negative angle indicated toe-in.To account for a difference in alignment between the sensor-derived anterior-posterior axis and the laboratory anterior-posterior axis, IMU-derived foot progression angles were corrected by a constant offset based on the mean foot progression angle computed from optical motion capture.We also removed any turning steps from the outdoor retraining group: during a turn, the IMU device transiently estimates the foot progression angle to be very large, and it takes approximately two steps after a turn for the angle estimation to re-orient to the new heading direction.We identified turning steps as local peaks greater than three standard deviations from the trial average that occurred no closer than two minutes apart; the three steps before and after each of these peak values were removed.
Retraining performance, responsiveness to feedback cues, cumulative learning rate, and evaluation performance were computed from IMU data to enable fair comparison between the laboratory and the outdoor environment groups.Retraining and evaluation performance were the percentage of steps that fell within the target toe-in angle range, out of all steps taken during the specified walking bout.Responsiveness to feedback cues was expressed as the percentage of steps that were substantially corrected in the direction cued by the feedback on the previous step, out of all steps where feedback was given: a responsiveness of 100% means that the subject adjusted their next step in the direction cued by the feedback every time they received a vibrotactile cue.Only changes that were greater than the standard deviation of the subject's foot progression angle at baseline were considered intentional and factored into the calculation of responsiveness.Cumulative learning rate during retraining was calculated as the average slope of the running tally of steps that fell in the target toe-in range plotted against the number of steps taken so far; this slope always falls within [0, 1], which enables comparison across subjects with differing numbers of steps during the retraining period.Both responsiveness and cumulative learning rate capture motor learning behavior during the retraining period.
To compare the accuracy of the IMU-based kinematics to marker-based motion capture, we computed the absolute error and the root-mean-square error (RMSE) between the foot progression angles calculated with the IMU and with optical motion capture during the toe-in trial for all 30 subjects.We also performed a Bland-Altman analysis on the subjects with the highest and lowest tracking error to assess the limits of agreement in the angle estimates.We summarized the performance of the IMU in calculating the foot progression angle using confusion matrices that report feedback cues given versus the cue that would have been provided if the foot progression angle were estimated from optical motion capture instead.For each subject, we also segmented and averaged the gyroscope and accelerometer data by stride to compare angular velocity and acceleration profiles across subjects.

D. Statistical Analysis
We tested our first hypothesis, on how tracking error affects the learning process, using a Spearman's rank correlation analysis, as the RMSE was found to be non-normally distributed per the Kolmogorov-Smirnov test and we did not wish to presume a linear relationship between the variables.For the 20 subjects who retrained their gait with feedback, we computed the correlations between IMU RMSE during the toe-in condition and A) their responsiveness to feedback during the last retraining block and B) their cumulative learning rate over the entire duration of retraining.To assess the validity of these relationships, we also computed the Spearman's correlation coefficient between sensor RMSE and performance in the one-minute toe-in trial for the no-training group as well as those who received feedback.A significant correlation for the no-training group would imply that IMU-derived learning measures may have been corrupted by sensor error.
To test the second hypothesis that higher tracking error has a negative effect on evaluation performance for the subjects who retrained with feedback, but not those who received no training, we used the analysis of covariance (ANCOVA) test.IMU RMSE was the independent variable, performance in the evaluation condition was the dependent variable, and whether the subject performed retraining with feedback (N = 20) or performed no retraining (N = 10) was the covariate.We examined the main effects as well as their interaction.To identify the critical region of the IMU RMSE where the relationship between group membership and evaluation performance becomes statistically significant, we performed the Johnson-Neyman analysis [28] using the interactions package for R [29].
Post-hoc analyses were conducted to understand factors influencing IMU error on an individual level as well as for the test population as a whole.First, we assessed the relationship between a subject's heel-to-toe length and their toe-in IMU RMSE using Spearman's correlation coefficient.The Spearman correlation was chosen because it is less sensitive to the influence of values far from the mean than the Pearson correlation.Second, for all steps taken by all subjects in the toe-in trial, we also evaluated the Spearman correlation between the magnitude of the foot progression angle, calculated with motion capture, and the magnitude of the absolute error between the motion capture and inertial kinematic estimates.Steps outside of the [−20, 20] degree range were excluded to limit the analysis to the foot progression angles that would occur most frequently in a therapeutic context.
Significance for statistical tests was set at α = 0.05, with a Bonferroni correction of n = 2 for evaluating the first hypothesis to account for the two parameters tested.P-values less than 0.05/n are flagged with one star ( * ), p-values less than 0.01/n with 2 stars ( * * ), and p-values less than 0.001/n with three stars ( * * * ).Mean and standard deviation values are reported in mean ± SD format.

III. RESULTS
Tracking error had an immediate negative effect on performance and continued to negatively impact responses to feedback throughout retraining.Sensor RMSE was negatively correlated with performance during the one-minute toe-in trial for the subjects who trained with feedback (ρ = −0.70,p = 0.00091).RMSE was not related to one-minute toe-in performance for the no-training group (ρ = 0.061, p = 0.868), as these subjects solely relied on joint proprioception instead of vibrotactile feedback to achieve the toe-in angle.When tracking error was high, subjects were more likely to ignore or respond incorrectly to vibrotactile cues.Average responsiveness was comparable between the laboratory (67.0%± 9.5%) and outdoor (66.5% ± 5.9%) groups.Sensor RMSE had a negative effect on responsiveness for the subjects who trained with feedback (ρ = −0.66,p = 0.0041) (Figure 2A).
Subjects with a high tracking error also learned at a slower rate than those who retrained with accurate tracking (Figure 2B).IMU RMSE had a negative effect on cumulative learning rate (ρ = −0.69,p = 0.0020).On average, the cumulative learning rate for the laboratory group (0.470 ± 0.197) was similar to that of the outdoor group (0.471 ± 0.145).Furthermore, angle estimates were not only inaccurate, but also imprecise (Figure 3).The limits of agreement were considerably wider for the subject with high tracking error, indicating low precision in the angle estimates.
The influence of IMU RMSE on evaluation performance depended on whether the subject received feedback (Table II).Evaluation accuracy was 41.6% ± 18.3% for subjects who trained with feedback (indoor 41.8% ± 15.6%; outdoor 41.4% ± 21.6%).The no-training group had an evaluation accuracy of 28.2% ± 14.7%.Evaluation performance was significantly different between subjects who trained with and without feedback (p = 0.0061), such that on average, training with feedback resulted in improved performance.Similarly, the significant main effect of IMU RMSE on performance (p = 0.0117) suggests that poor tracking can be a detriment to retention of the learned gait.The presence of a significant Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.Agreement between IMU and motion-capture estimates of the foot progression angle.Scattered data points represent the level of agreement in foot progression angle estimates at each step during the toe-in trial for the subject with the highest tracking error (light green) and the lowest tracking error (black).Horizontal solid lines representing the mean difference are near zero for both subjects because pre-processing steps removed any bias between IMU and motion-capture estimates.The dashed lines representing the limits of agreement show significantly worse measurement consistency for the subject with high tracking error.interaction indicates that the relationship between group and evaluation performance varied across different levels of IMU RMSE.With the Johnson-Neyman analysis, we found that the critical value of sensor RMSE above which the relationship between group and evaluation performance becomes no longer significant (p > 0.05) was 7.46 degrees.Above this RMSE value, training with feedback resulted in an evaluation performance that was no better than that of the no-training group.
Both heel-to-toe length and magnitude of the foot progression angle were related to inertial kinematics accuracy.Heel-to-toe length had a negative correlation with IMU RMSE (Figure 4A) (ρ = −0.481,p = 0.0332), where tracking error was higher for subjects with smaller feet.For all 1,551 steps analyzed, the magnitude of the foot progression angle and the absolute error at that step were positively correlated (ρ = 0.193, p < 0.0001) (Figure 4B).From visual inspection, average dorsiflexion gyroscope (Figure 5A) and anterior-posterior accelerometer (Figure 5B) trajectories for the subject with the largest feet and low tracking error showed larger peaks at heel strike than for the subject with the smallest feet and high tracking error.
Kinematic tracking error negatively impacted the quality of feedback that subjects received.During the baseline trial, the mean ± SD mean absolute error (MAE) of the foot progression angle estimated by motion capture and the IMU was 2.60 ± 1.01 degrees, which was acceptably accurate for determining a subject's five-degree toe-in angle.However, the accuracy of the IMU on a step-by-step basis determined whether the feedback given was correct (Figure 6).When the IMU estimated that the foot progression angle during a step was within range, no feedback was provided; however, the subject also received no feedback if the IMU failed to calculate the angle at that step, which happened if the step was not detected.For each step taken when feedback was Fig. 6.Tracking accuracy impacts feedback provided.The kinematic tracking error has a cascading effect on feedback quality.As shown in the confusion matrices summarizing performance of the inertial tracking system with respect to the optical motion capture system during the oneminute toe-in trial, (A) the high error group (RMSE > 7.46 degrees) received correct feedback (boxes outlined in gray) only 23.5% of the time, (B) whereas the low error group (RMSE < 7.46 degrees) received correct feedback 46.1% of the time.TI indicates toe-in, OK indicates that the foot progression angle was within-range and therefore no feedback was given, TO indicates toe-out, and MISS indicates that the step was not detected and no feedback was given.being provided, the three possible outcomes occurred at the following rates on average: correct feedback (39.4%); no feedback provided when it should have been (30.1%); or incorrect feedback provided (30.5%).After separating subjects into those above or below the 7.46-degree cutoff identified by the Johnson-Neyman analysis, we found that the high error group (N = 6) received correct feedback for 23.5% of their steps on average and the low error group (N = 14) received correct feedback for 46.1% of steps.

IV. DISCUSSION
In this single-session gait-retraining study, some subjects appeared to learn the toe-in gait well, whereas others performed poorly.This variation in outcomes can be linked to inconsistent kinematics tracking, resulting in vibrotactile cues that conflict with a subject's proprioceptive awareness of their foot progression angle.Such tracking errors and Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
inconsistent feedback hindered learning rate and ability to maintain the new gait, regardless of their training environment.For subjects with a high tracking error, training with feedback for 20 minutes resulted in an evaluation performance that was equivalent to the no-training control group, who did not receive feedback.Notably, tracking errors were greater for subjects with smaller feet or for steps with large foot progression angle magnitudes, possibly due to factors including mounting location and kinematic cross-talk.These findings underscore the importance of accurate kinematics tracking for effective gait-retraining interventions.
Several limitations of this work should be acknowledged prior to interpreting its experimental outcomes.First, because our experimental setup did not support optical motion capture in an outdoor setting, we assessed responsiveness and learning rate by relying on angle estimates from a kinematic estimation previously identified as inaccurate.Nonetheless, we hold cautious confidence in the integrity of the relationship between IMU RMSE and retraining outcomes; although there was a strong relationship between RMSE and toe-in accuracy for the groups who received feedback, there was no correlation between RMSE and toe-in accuracy for the notraining group.If retraining outcomes were indeed corrupted and systematically biased against those with a high RMSE, we would expect to observe a similarly strong correlation between RMSE and toe-in accuracy for the no-training group, which was not present.A related limitation is the absence of a ground-truth estimate of IMU RMSE for the outdoor retraining group; RMSE was estimated from the toe-in trial in the laboratory, but error may have changed after subjects moved outdoors.We did not reposition the IMU after starting data collection, which helped ensure that any error caused by IMU placement was consistent throughout the study.Finally, we did not perform sensor-to-segment calibration, relying instead on careful manual placement of the IMU in line with the long axis of the foot at the start of the experiment.Our data indicating that tracking error was higher at larger foot progression angles may have been partly affected by kinematic crosstalk resulting from lack of sensor-to-body calibration.We were limited by engineering constraints: the vibrotactile feedback device we used is the only commercially available haptic feedback system for gait retraining that facilitates real-time foot progression angle estimation, but it requires additional development to incorporate calibration data into the onboard algorithm [20].We hope that the open-source code provided by SageMotion, as well as our publicly available data (https://simtk.org/projects/imufpaaccuracy),can enable the development of these capabilities in the future and provide insight into how calibration may affect our study's conclusions.
The subject-specific nature of the kinematic tracking error can be attributed to physical factors.Assuming the foot to be a rigid body, a subject with shorter feet would wear the sensor placed closer to the ankle, shortening the lever arm about the point of rotation and resulting in a reduced accelerometer signal magnitude, as seen in Figure 5.The subject with smaller feet also walked more slowly (1.05 m/s) than the subject with larger feet (1.28 m/s), which may have resulted in the shallower peaks seen in their gyroscopic signal.Combined, these non-standard IMU signal profiles affect the peak estimation and gait event segmentation at the core of the kinematic algorithm.The SageMotion device pre-processes accelerometer data with a constant 0.29 s Hanning window before estimating foot progression angle [20].The optimal window size is a tunable parameter that can dynamically depend on context-specific factors such as sensor noise and IMU placement: a larger window span smooths the signal but might attenuate peaks, while a smaller window retains peak saliency but filters out less noise.Ensuring that kinematic tracking is consistent for subjects with different foot dimensions and walking speeds could potentially reduce the need for patient supervision for widespread take-home gait retraining.
Although the MAE of the kinematic tracking algorithm was within the range reported in previous studies [20], [21], [22], [23], the average RMSE-more sensitive to outlier values than MAE-was considerably larger.Furthermore, the wide limits of agreement seen in the Bland-Altman analysis indicate that the error was highly inconsistent for some subjects, making it challenging for those individuals to gauge the reliability of the feedback.As a result of this high tracking error, the percent of steps where correct feedback was provided was only slightly above chance on average.If tracking error was high, subjects had to rely on their natural proprioception of foot progression angle and decide whether to ignore potentially incorrect feedback cues to retrain successfully.In fact, we found that the higher the tracking error, the less likely the subject was to respond to the feedback cue appropriately by the last retraining block, indicating that they were ignoring the feedback provided.Future work might seek to quantify a patient's baseline proprioceptive capability to determine its effect on learning.Similar instances of unmonitored error might account for the heterogeneous responses to feedback in other contexts, such as when gait retraining relies on temporal cues extracted from wearable IMUs for gait rehabilitation of individuals with Parkinson's disease [30] or reducing tibial acceleration in recreational runners [31].
Patients with knee osteoarthritis may be particularly affected by kinematic estimation error and erroneous feedback cues.Whereas some healthy participants in this study were able to overcome inconsistent feedback and learn the new gait by relying on proprioception, patients with knee osteoarthritis may find this retraining more challenging, as proprioception has been shown to degrade with age and disease progression [32] [33].Moreover, women are at greater risk for developing knee osteoarthritis than men [34]; they also tend to have smaller feet, even when controlling for height [35].Validating emerging smart-rehabilitation technologies across a diverse set of patients will ensure that key segments of the clinical population equitably benefit from this intervention.
V. CONCLUSION Kinematic estimation errors fundamentally impact the potential of wearable feedback for gait retraining, limiting the efficacy of this technique for on-demand rehabilitation.Gait retraining studies require considerable time investment from patients and researchers, with typical sessions lasting 15 to 20 minutes repeated over several weeks [8].Knowledge of the quality of the feedback provided will enable adequate evaluation of the treatment progress.If a patient does not show improvement in retraining performance or self-reported outcome measures, the clinician may unknowingly categorize them as a non-responder to the intervention and advance their treatment to invasive options, which do not always restore function or minimize pain [36].We recommend that future kinematic estimation algorithms be comprehensively assessed, with accuracy reported over diverse user populations and types of gait.

Fig. 2 .
Fig. 2. Effect of device accuracy on retraining response and learning rate.Regardless of whether subjects trained in the laboratory or outdoors, there was a significant effect of device error on response to retraining.Both the (A) average responsiveness to a vibrotactile cue and (B) normalized cumulative learning rate were negatively impacted by high tracking error.Dashed lines represent the lines of best fit.

Fig. 3 .
Fig. 3.Agreement between IMU and motion-capture estimates of the foot progression angle.Scattered data points represent the level of agreement in foot progression angle estimates at each step during the toe-in trial for the subject with the highest tracking error (light green) and the lowest tracking error (black).Horizontal solid lines representing the mean difference are near zero for both subjects because pre-processing steps removed any bias between IMU and motion-capture estimates.The dashed lines representing the limits of agreement show significantly worse measurement consistency for the subject with high tracking error.

Fig. 4 .
Fig. 4. Effect of foot size on kinematic tracking accuracy.(A) Tracking accuracy varied across subjects and tended to be worse for those with small feet.The two subjects with the largest and smallest feet are highlighted: one with an RMSE of 4.4 • and heel-to-toe length of 0.247 m (solid shading), and one with an RMSE of 17.1 • and heel-to-toe length of 0.184 m (dashed outline).The line of best fit is represented by a dashed line.(B) Absolute error in estimating the foot progression angle was larger at bigger absolute foot progression angles.Each step taken by the 30 subjects in the toe-in trial is represented with a semi-opaque dot, with the line of best fit shown as a dashed line.

Fig. 5 .
Fig.5.Sample accelerometer and gyroscope profiles.(A) Mean and standard deviation of dorsiflexion angular velocity over all strides for the two representative subjects with the longest and shortest heelto-toe lengths show that the subject with poor tracking and a short foot length (dashed line) had a less prominent trough in the gyroscopic signal at heel strike than the subject with good tracking and a longer foot length (solid line).(B) The mean and standard deviation of anterior-posterior acceleration for the same two representative subjects also show reduced signal amplitudes at heel strike for the subject with a shorter foot.

TABLE I SUBJECT
DEMOGRAPHICS: MEAN (SD)

TABLE II ANALYSIS
OF COVARIANCE RESULTS