A machine learning approach for gait speed estimation using skin-mounted wearable sensors: From healthy controls to individuals with multiple sclerosis

Gait speed is a powerful clinical marker for mobility impairment in patients suffering from neurological disorders. However, assessment of gait speed in coordination with delivery of comprehensive care is usually constrained to clinical environments and is often limited due to mounting demands on the availability of trained clinical staff. These limitations in assessment design could give rise to poor ecological validity and limited ability to tailor interventions to individual patients. Recent advances in wearable sensor technologies have fostered the development of new methods for monitoring parameters that characterize mobility impairment, such as gait speed, outside the clinic, and therefore address many of the limitations associated with clinical assessments. However, these methods are often validated using normal gait patterns; and extending their utility to subjects with gait impairments continues to be a challenge. In this paper, we present a machine learning method for estimating gait speed using a configurable array of skin-mounted, conformal accelerometers. We establish the accuracy of this technique on treadmill walking data from subjects with normal gait patterns and subjects with multiple sclerosis-induced gait impairments. For subjects with normal gait, the best performing model systematically overestimates speed by only 0.01 m/s, detects changes in speed to within less than 1%, and achieves a root-mean-square-error of 0.12 m/s. Extending these models trained on normal gait to subjects with gait impairments yields only minor changes in model performance. For example, for subjects with gait impairments, the best performing model systematically overestimates speed by 0.01 m/s, quantifies changes in speed to within 1%, and achieves a root-mean-square-error of 0.14 m/s. Additional analyses demonstrate that there is no correlation between gait speed estimation error and impairment severity, and that the estimated speeds maintain the clinical significance of ground truth speed in this population. These results support the use of wearable accelerometer arrays for estimating walking speed in normal subjects and their extension to MS patient cohorts with gait impairment.


Introduction
The ML model technique for estimating walking speed utilizes supervised learning to train a statistical model relating measurements of walking kinematics with speed. In practice, walking kinematics are often measured by one (or several) body-worn accelerometer(s) and decomposed into a series of parameters (features) that summarize the kinematics. These parameters are also sometimes combined with anthropometric information including subject height, weight, and leg segment lengths. A model that relates these kinematic and anthropometric parameters to walking speed is then 'learned' from a series of training examples collected at a variety of walking speeds and from a variety of subjects. The hypothesis is that larger 'training sets' yield models that more accurately capture the true relationship between the measured kinematics (and anthropometric characteristics) and speed. Several studies have employed this technique to translate data from accelerometer-only and accelerometer and gyro based wearable devices into estimates of walking speed [23][24][25][26]. One study, that employs a belt-worn accelerometer, found that a support vector regression model produced superior results to output from human gait model based approaches that exploit relationships between stride frequency and step length [23]. They reported a coverage probability (95% confidence interval), relative to a gold standard perambulator, of 0.46 (0.12-0.70) at the 0.1 m/s error level from a study of 17 normative subjects walking over ground at 4 self selected speeds [23]. However, 8 subjects from their training set were included in their testing set, which could artificially improve this level of agreement. Another study utilized treadmill walking data collected from 20 subjects walking at speeds ranging from 0.7 to 1.7 m/s to assess a mobile phone (located in the subject's pocket) based algorithm for estimating walking speed [25]. The authors report an RMS error of 0.12 m/ s for an accelerometer-only feature set and a leave-one-subject-out error estimation approach. While existing studies demonstrate that the accuracy of the direct integration and human gait model techniques is superior to that of the ML model technique, the accelerometer-only measurement requirements drastically reduce the barrier to deployment outside of the clinic. Accordingly, it is important to understand if there are device locations, or combinations of locations, that can further improve walking speed estimation accuracy using this approach.
Walking speed is a primary indicator of outcome in clinical research and practice involving MS patients [27]. New wearable technology, and the ML model based approaches described above, could provide a means for characterizing walking speed in more naturalistic environments. Traditionally, an ML model for estimating walking speed in patients with MS would require a training dataset sampled from a population of patients with varying levels of MSinduced gait impairments walking at a variety of speeds. However, collection of these data puts patients at heightened risk for falls which could yield significant physical and emotional injury, negatively impacting ambulation (and therefore quality of life [8]) for weeks, months, and years following the accident. One potential solution, which would obviate the need for collection of training data on patients with MS-induced gait impairment, is to train ML models for walking speed on data from healthy subjects. However, it is then important to explore how these models developed on normal subjects generalize to populations with gait impairments, and in the case of MS, how the model performs as a function of impairment severity. For example, one study explored the performance of walking speed estimations provided by a beltworn commercial activity tracking device, and their model trained on subjects without neurological disorders, in a sample of 51 MS patients spanning the disability spectrum (EDSS 2.0-6.5) [28]. They found that estimations were accurate for subjects with mild impairment (EDSS 2.0-3.5), but the accuracy degraded considerably for moderately (EDSS 4.0-5.5) and severely (EDSS 6.0-6.5) impaired subjects.
Here we develop a ML-based technique for estimating walking speed using a new, conformal wearable device. We utilize accelerometers from multiple body locations to characterize gait speeds during treadmill walking in normative subjects (control), and during treadmill walking for a population of subjects diagnosed with multiple sclerosis (MS). We further investigate how different combinations of device locations influence estimation accuracy, and if estimated speeds maintain the clinical relevance of the ground truth speed values.

Methods
Research conducted at the University of Illinois at Urbana-Champaign (UIUC) was approved by the UIUC Institutional Review Board (IRB Protocol Number: 15853). Research at MC10, Inc. and UIUC were conducted according to the principles expressed in the Declaration of Helsinki. Written, informed consent was obtained from each subject prior to participation.

A. Study design
The BioStamp Research Connect™ system (BioStampRC-MC10, Inc., Lexington, MA) was used to design two experimental protocols, one for a sample of normative subjects (Protocol A) and one for a sample of MS patients and healthy controls (Protocol B). Protocol A included a series of 6-minute treadmill walking tests executed at 5 predefined speeds (0. 5

C. Protocol
Following collection of informed consents, subjects in Protocol A were instrumented with BioStampRC Sensors and instructed to walk on a treadmill. The treadmill speed was ramped until the desired walking speed was achieved for a given test (see S1 Appendix for validation of treadmill reported speeds). Once the treadmill had reached steady state, the study administrator used the BioStampRC Investigator Application to indicate the beginning and end of the walking test, and to record the walking speed. This sequence was repeated until tests for the five walking speeds had been completed.
For Protocol B, subjects completed a verbal health history and physical activity readiness questionnaire (PAR-Q) during a phone screen and, if found to meet the inclusion criteria, were scheduled for an onsite visit at the Motor Control Research Laboratory at the University of Illinois at Urbana-Champaign. During the onsite visit, subjects provided written informed consent, and completed questionnaires including a Patient Demographics Survey, the Twelve Item MS Walking Scale (MSWS), the Self-Reported Expanded Disability Status Scale (EDSS SR ), and the Fall, Trips, and Slips 6 Month Survey. Subjects were then instrumented with BioStampRC Sensors and completed a series of functional tests designed to assess balance and mobility impairments in MS patients including the PCT, the Timed 25 Foot Walk Test, the Timed Up and Go, and the 6MWT. Herein, we consider data from the PCT and the 6MWT in particular. For the PCT, subjects were tested twice in each of three conditions (eyes open, eyes closed, and eyes open standing on a foam pad) for 30 seconds. The study administrator used the BioStampRC Investigator Application to indicate the beginning and end of each PCT, during which the subject's speed was assumed to be 0 m/s. For the 6MWT, subjects were tested at three different speeds (comfortable, 20% above comfortable and 20% below comfortable). The study administrator used the BioStampRC Investigator Application to indicate the beginning and end of each 6MWT. Immediately after indicating the beginning of the test, subjects began to walk on the treadmill while the administrator increased the speed until the desired walking speed was achieved. The steady-state treadmill speed for each test was recorded on a test datasheet, copies of which were provided for each subject for analysis.

D. Instrumentation
Subjects in Protocols A and B were instrumented with five BioStampRC Sensors (See Fig 1A), affixed to the skin at the locations illustrated in Fig 1B (sacrum, bilateral thigh, bilateral shank). Each sensor was configured to log accelerometer (measurement range-Protocol A: +/-8G, Protocol B: +/-4G) data to onboard flash memory at a rate of 50 Hz. Each accelerometer sample, from each device, was recorded with a corresponding absolute time stamp thus allowing direct comparison of data across devices. Following the completion of all data collection activities for each subject, data were downloaded from the sensors using the Investigator Application, and uploaded to the BioStampRC Investigator Portal in the MC10 cloud for further analysis.

E. Pre-processing and feature extraction
BioStampRC Sensors were secured to the body such that the axis orthogonal to the plane of the device (Z) was directed roughly in the anterior (thigh, shank) or posterior (sacrum) directions. The accelerometer data from each axis is low-pass (12 Hz cutoff [29]) and band-pass (0.25-12 Hz cutoff) filtered, yielding a total of six time series, from each device, for analysis. The prescribed device placement constrains the direction of the Z-axis, but the remaining axes (X,Y) are largely arbitrary. To remove further dependence on device orientation, we take the vector magnitude of accelerometer signals in the X and Y directions (XY = sqrt(X 2 + Y 2 )), yielding two time series, Z and XY, for each filtering approach (band-pass, low-pass), for further analysis. These time series are segmented into 5-second non-overlapping windows. Each window represents one sample or observation. Thus, a single 6MWT yields 72 samples or observations for model training. Data from each window are parameterized by a set of time and frequency domain features [30] to inform estimates of walking speed. Time domain features include mean value, range, kurtosis, signal entropy, range of auto-covariance and correlation coefficient (XY with Z). Frequency domain features include spectral entropy, value and magnitude of dominant frequency, and ratio of energy in the dominant frequency to the band-limited frequency spectrum. A total of 32 features are extracted from each window of data, for each device location.

F. Model training and performance evaluation
To estimate walking speed from these accelerometer-based features, we define support vector regression models [23] (f) of the form where s is the average walking speed during a 5-second period of time andã is an M-element vector composed of 32 time and frequency domain features extracted from the corresponding 5-second window of accelerometer data, from each of the desired sensor locations. We train models for seven combinations of the sacrum, right thigh, and right shank locations in Python using Scikit-Learn [31] and a supervised-learning approach. The training dataset consists of data from the subjects of Protocol A (N = 10) and the control subjects of Protocol B (N = 7), which together yield a total of 17 normal subjects for model development and analysis (data for each device location combination available in S1 File). The treadmill speeds from these tests provide ground-truth speed values (s) that enable training of walking speed models (f).
To establish the accuracy of these models on normal subjects, we employ a leave-one-subjectout approach, where a walking speed model is trained on 16 subjects, and used to estimate speed during tests completed by the remaining subject. This process is repeated until all subjects have been left out of the training set. To establish model performance on impaired subjects, we train walking speed models using all 17 normal training subjects and estimate speed during the 6MWTs completed by each of the 30 subjects diagnosed with MS (data for each device location combination from each MS subject available in S2 File). For both the normal and impaired tests, we compute the median of the estimated speeds for comparison to the ground-truth values reported by the treadmill. This approach yields a total of 114 observations (5 tests from each subject in Protocol A, 9 tests from each control subject in Protocol B, and one extra 6MWT completed by a subject in Protocol B) for the analysis of performance on normal gait, and 91 observations (one subject completed an extra 6MWT) for the analysis of performance on impaired gait (data for each device location combination available in S3 File).
To analyze the performance of the walking speed estimations for normal and impaired subjects, we report the root-mean-squared-error (RMSE), the Bland-Altman limits of agreement (LOA), and the slope (m) and intercept (b) of the following linear model where y corresponds to the truth values, andŷ corresponds to the associated estimates (median speed from each walking test). The Bland-Altman limits of agreement describe the 95% confidence interval for the difference between measurement techniques which provides an indication of the minimal detectable difference in the estimated speed [32]. The intercept (b) indicates the systematic difference between measurement techniques, and the slope (m) indicates how closely one measurement technique is able to detect changes in the other. We examine error in the walking speed estimates as a function of impairment level in two ways. First we examine the relationship between error and MSWS and EDSS SR scores for each subject by considering the Pearson product moment correlation coefficient (r). We then divide the MS patients into Mild (N = 14), Moderate (N = 10), and Severe (N = 6) impairment groups and compare the error in estimated speed within each group. Subjects were assigned to groups based on their comfortable walking speed during the Timed 25 Foot Walk Test: Mild-speed > = 1.1 m/s, Moderate-0.7 m/s < speed < 1.1 m/s, and Severe-speed < = 0.7 m/s [33].
Finally, we establish concurrent validity in the context of MS, by examining the relationship between estimated and ground truth walking speeds sampled from the comfortable 6MWT of Protocol B and indicators of mobility impairment and fall risk. Specifically, the Pearson product moment correlation coefficient is used to characterize the relationship between walking speed and MSWS and EDSS SR scores, and the Mann-Whitney U test is used to test for a significant difference in walking speed between subjects who reported a fall in the six months prior to the test and those who did not. For all statistical analyses, significance is assessed at the α = 0.05 level.

Results
We trained support vector regression [23] models to estimate walking speeds based on feature sets extracted from a combination of devices secured to the sacrum, thigh and shank. The 17 subjects with normal gait exhibited speeds ranging from 0.0 to 1.7 m/s (0.0 m/s speeds from the PCT tests of Protocol B). Results from the leave-one-subject-out error estimation for each of the seven possible device location combinations are shown in Table 1. For each device location combination, we report the RMSE, LOA, and the regression analysis of Eq (2).  We also considered the Bland-Altman and regression plots for the Sacrum, Thigh, Shank model of Table 1 in Fig 2A and 2B, respectively. Each point of the Bland-Altman plot represents a single walking speed test, where the y-coordinate is the error in the speed estimate and the x-coordinate is the average between the estimated and true speed. The solid black line indicates mean error in the speed estimate, and the dashed red lines indicate the limits of agreement (95% confidence interval). Similarly, each point of the regression plot represents a single walking speed test, where the y-coordinate is the estimated speed and the x-coordinate is the true speed. The line of best fit is plotted as a solid black line, the 95% confidence region for the regression is shaded in grey (estimated via bootstrap), and a dashed red line with unit slope and zero intercept, is shown for reference.
We now assess the accuracy of walking speed estimations for patients with gait impairments from models trained on 17 subjects without gait impairments. Table 2 reports error metrics for models trained on data from each of the seven device location combinations for 30 MS patients, with varying levels of gait impairment. Actual walking speeds during these tests ranged from 0.13 to 1.88 m/s. We further examine the error in walking speed estimates for the Sacrum, Thigh, Shank model of Table 2 by considering the Bland-Altman and regression plots shown in Fig 3A and 3B, respectively.
To better understand the relationship between accuracy and impairment level, we report the RMSE and LOA for the Mild, Moderate, and Severe subject groups, and the Pearson product moment correlation coefficient between estimation error and EDSS SR and MSWS scores, for each of the seven device location combinations, in Table 3.
We further examine the accuracy of walking speed estimations across impairment levels with the Sacrum, Thigh, Shank model in Fig 4A and 4B, where we plot speed estimation error versus MSWS and EDSS SR scores, respectively. Each point in Fig 4A/4B, where the y coordinate is the speed estimation error and the x coordinate is the MSWS/EDSS SR score, represents a single 6MWT. In each plot, the red dashed line is the best-fit line for the data.
Finally, we quantify the ability of each model to preserve the clinical relevance of the ground truth data by correlating estimated and ground truth walking speeds with MSWS and EDSS SR scores. We also test for differences in speed between groups of subjects who reported a fall in the 6 months prior to the study (Fall) and those who did not (No Fall, none of the differences were statistically significant). Subjects in the Fall group are expected to have slower comfortable walking speeds than those in the No Fall group [7]. Results are presented in Table 4.

Discussion
We present a technique for estimating walking speed based on data from an array of wearable accelerometers, and conduct a detailed analysis of the influence of device placement combinations on estimation accuracy in a sample of subjects without gait impairments. We further   Table 1 show high accuracy of the proposed technique for estimating walking speed in subjects without gait impairments across a variety of device location combinations. Generally, performance improves with both distal device locations and additional  devices. For example, walking speeds estimated by a model trained on data from just the sacrum device has a RMSE of 0.15 m/s, with a 95% confidence interval for error of (-0.31, 0.29) m/s, the ability to quantify changes in speed to within 3%, and a systematic bias of 0.03 m/s. In contrast, the model trained on data from the shank device improves upon these error characteristics by estimating walking speed with a reduced RMSE (0.13 m/s), smaller 95% confidence interval for error (-0.26, 0.25) m/s, better ability to quantify changes in speed (within 2%), and a reduced systematic bias (0.02 m/s). This increase in performance is achieved by simply placing the BioS-tampRC Sensor to a different body location. The performance of these single-device models compare well with the best single-device approach reported in the literature that is able to quantify walking speed with an RMSE of 0.12 m/s (or 0.11 m/s after gps-based subject-specific calibration) [25]. Adding additional devices can further improve these results, provided that care is taken to avoid over-fitting. This is evidenced by the error characteristics for the model trained on data from the sacrum, thigh, and shank locations, which yields a RMSE of 0.12 m/s, a 95% confidence for the error of (-0.25, 0.22) m/s, is able to quantify changes in speed to within less than 1%, and systematically overestimates speed by only 0.01 m/s. The Bland-Altman and regression plots of Fig 2A and 2B, highlight the unbiased speed estimate provide by the threedevice model, and demonstrate the homoscedasticity of the variance. The results of Table 2 establish how the proposed modeling approach for estimating walking speed generalizes to subjects with MS-induced gait impairments, and illustrates how changes in the number and location of devices affects accuracy. Specifically, the results suggest the opposite trend observed in the non-impaired sample, namely that error increases with distal device placements. For example, a model trained on data from the sacrum device yields a RMSE of 0.12 m/s, 95% confidence interval for the error of (-0.25, 0.22) m/s, the ability quantify changes in speed to within 4%, and systematically overestimates speed by 0.05 m/s. In contrast, a model trained on data from the shank yields larger RMSE (0.16 m/s), wider limits of agreement (-0.32, 0.31), more limited ability to detected changes in speed (within 11%), and a larger systematic bias (0.10 m/s). This could be due to gait impairments manifesting as larger deviations in the kinematics of the distal body segments, where mass center (or sacral) kinematics need to be more tightly constrained to enable even severely impaired ambulation. Nevertheless, the inclusion of distal device locations with the sacrum, acts to alter the bias-variance characteristics of the estimation error. Namely, a model trained on data from the sacrum, thigh, and shank devices yields slightly higher variance as evidenced by increased RMSE (0.14 m/s) and wider limits of agreement (-0.27, 0.27), but reduces bias with improvements in the ability to quantify changes in speed (now within 1%) and the systematic bias (overestimate speed by only 0.01 m/s). The Bland-Altman and regression plots of Fig 3A and 3B, respectively, help to visualize the performance of this model across a wide range of walking speeds and the associated gait impairment levels. This model seems to introduce a slight heteroscedasticity, where the slowest speeds seem to elicit slightly larger error variance, however this could also be due to our dataset, which contains fewer observations at faster speeds.
To this end, we examine error characteristics within each impairment level (mild, moderate, severe) as a function of the device location combinations in Table 3. This analysis demonstrates that the sacrum is the single best location for estimating walking speed across impairment levels with very little difference between levels. Ultimately, this suggests that the proposed approach for estimating walking speed is able to generalize across gait impairments. This compares favorably to existing methods for estimating walking speed from accelerometer data. Specifically, a validation study of the actibelt 1 , a belt-worn accelerometer-based device, in a sample of 51 MS patients with gait impairments demonstrated that error in walking speed estimates differed significantly across impairment levels. For subjects with mild, moderate, and severe impairments, the reported mean (standard deviation) error in walking speed estimation was -0.02 (0.11), -0.10 (0.16), and -0.26 (0.12) m/s, respectively [28]. For comparison, the sacrum model presented herein yields mean (standard deviation) error in walking speed estimations of 0.01 (0.12), -0.04 (0.12), and -0.04 (0.11) m/s for subjects with mild, moderate, and severe gait impairments, respectively. This improvement in results across impairment groups could be due to the conformal, skin-mounted nature of the BioStampRC sensor (vs. the belt-worn actibelt 1 ), or differences in the modeling approach and/or feature set employed for estimating speed. To further confirm the lack of relationship between error in the walking speed estimations and gait impairments, we correlate walking speed error with EDSS SR and MSWS scores for models trained with each device location combination in Table 3. Estimation errors for none of the walking speed models show significant (α = 0.05) correlations with MSWS scores, and only 2 of the 7 models (Shank; Sacrum, Shank) show correlation with EDSS SR score. These results further confirm the lack of relationship between error in the walking speed estimations and impairment level for many of the device location combinations. This is an important result, as it suggests that the proposed approach allows extension of models for estimating walking speed developed on data from normal subjects to MS subjects with gait impairments without introducing additional error that could potentially confound interpretation of the results.
Finally, we examine the relationship between the ground truth and estimated walking speeds during tests conducted at the comfortable walking speed, and clinical measures of impairment and fall history to assess if the proposed technique is able to capture the clinical significance of this important variable. Table 4 demonstrates that both ground truth and estimated speeds are significantly, and similarly, correlated with MSWS scores (estimated: r −0.84,p < 0.01, ground truth: r = −0.87,p < 0.01) such that walking speed decreases as MSWS score, and therefore walking impairment, increases. These results agree well with existing literature that reports a correlation between walking distance during the 6MWT and MSWS score of r = −0.81. Similarly, both ground truth and estimated speeds are significantly, and similarly, correlated with EDSS SR score (estimated: r −0.72,p < 0.01, ground truth: r = −0.79,p < 0.01) as well. These results also agree well with existing literature that reports a correlation between walking distance during the 6MWT and EDSS score of r = −0.73 [5]. Lastly, there is a relationship between speed and if the subject reports falling in the last 6 months. Specifically, the comfortable walking speeds for subjects who have fallen in the last six months are 0.22 m/s slower than those who have not where models estimate differences between 0.19 and 0.25 m/s. The directionality of these results agree well with existing literature examining the relationship between walking speed and fall history [7]. These results clearly demonstrate that the proposed technique for estimating walking speed is able to preserve the relationship between the true speed and clinical assessments of MS symptom severity (EDSS SR and MSWS) and fall history.
The primary limitation of this study is that results are based on data collected during treadmill walking. As a result, the performance may not generalize to ambulation in naturalistic environments. Future studies should explore changes in performance that result from employing the proposed technique for estimating walking speed during over-ground ambulation in subjects with and without MS-induced gait impairments. The study presented herein explores how models trained on subjects with unimpaired gait generalized to those with MS-induced gait impairments. A future direction could also focus on developing methodologies for the training of individualized models for each MS patient. This type of personalized approach, enabled by the BioStampRC technology, could improve the reported results further.

Conclusion
In this study, we characterize the accuracy of walking speed estimations enabled by the combination of machine learning and the BioStampRC system, which includes a new skin-mounted, conformal wearable sensor, in subjects with and without MS-induced gait impairments.
Within each group, we analyze the relationship between estimation accuracy and device location combinations. Finally, we assess the ability of the resulting walking speed estimations to maintain the clinical relevance of the ground-truth values. Specifically, we establish the accuracy of this technique on treadmill walking data sampled from subjects with normal gait patterns and find that accuracy improves with more distal device locations and the inclusion of additional devices, with the best model systematically overestimating speed by only 0.01 m/s, detecting changes in speed to within less than 1%, and achieving a root-mean-square-error of 0.12 m/s. We then assess the performance of models trained on normal subjects in a population of subjects with MS-induced gait impairments, and find that accuracy improves with proximal locations, and the inclusion of additional devices. The best performing model systematically overestimates speed by 0.01 m/s, quantifies changes in speed to within 1%, and achieves a root-mean-square-error of 0.14 m/s. We further demonstrate that the estimated walking speed maintains the clinical significance of the ground truth speed in this population, where the ground truth and estimated speeds during comfortable walking tests are highly correlated with impairment severity as quantified by EDSS SR (r −0.72) and MSWS (r −0.84) scores. These results support the extension of accelerometer-based models for estimating walking speed developed on data from normal subjects to MS patients with gait impairments. Based on the results presented herein, and the wearable nature of the BioStampRC devices, this approach points toward the future ability to monitor parameters that characterize mobility impairment, such as gait speed, outside the clinic.