Assessing a low-cost accelerometer-based technique to estimate spatial gait parameters of lower-limb prosthesis users

Background and aim

A common clinical outcome for evaluating lower-limb prosthesis (LLP) intervention and rehabilitation is gait quality, often characterized through temporal-spatial parameters.^1–5 The parameters of step length (SL) provide information on a prosthesis user’s ability to effectively ambulate with their prosthetic limb and used to characterize gait symmetry.^1–5 Additionally, timed walking tests are often used clinically to measure distance walked and steady-state walking speed (SSWS) as a measure of mobility and endurance during rehabilitation. ⁶ Inexpensive and clinically accessible systems for characterizing prosthetic gait would allow clinicians to readily evaluate and monitor patient gait quality. A method has been established for the estimation of SL in able-bodied gait using body center-of-mass (BCOM) accelerations collected by an accelerometer fixed to the lower back.^7,8 This method has been implemented in commercial devices (e.g. G-Walk (BTS, Milan, Italy) and DynaPort (McRoberts, The Hague, Netherlands)), but validation results for use in LLP users have been reported for only one system. ⁹ This study aimed to develop and assess a low-cost accelerometer-based system for estimating SL and distance walked in LLP users that may serve as an alternative to more expensive systems to characterize gait in a clinical environment. As correction factors (CFs) are often applied to account for the underestimation of SL using accelerometer techniques, ⁸ the use of subject-specific CFs was explored.

Technique

For this system, a commercially available three-axis accelerometer (X6-2; Gulf Coast Data Concepts, Waveland, MS, USA) was fixed to the fourth lumbar vertebrae region using Velcro straps (Figure 1) to approximate BCOM position. This accelerometer was selected for clinically preferable features: low cost, on-board data storage, and universal serial bus (USB) compatibility. As recommended by the manufacturer, a “tumble test” was performed prior to data collection to estimate offsets and scaling factors of each axis for device calibration to fine tune the linear relationship between the sensor output and acceleration in units of g-force. ¹⁰ The tumble test involved attaching the accelerometer to a rigid square tube and resting the tube on a level surface in six orientations such that 10 s of data were collected while each axis direction (±x, ±y, ±z) was aligned with gravity acceleration vector. For each axis, offsets were estimated by averaging the accelerometer readings when the axis was perpendicular to gravity, and scaling factors were estimated by calculating the difference between average readings when in positive and negative gravity and dividing by 2. BCOM acceleration data were collected at 160 Hz and low-pass filtered at 10 Hz using a fourth-order, zero-lag Butterworth filter. The Northwestern University Institutional Review Board provided ethical approval for this study and informed consent was obtained from participants prior to data collection.

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Figure 1.

(a) Three-axis accelerometer that is fixed to a plastic base (US quarter shown for scale) and (b) firmly secured around the participant using Velcro straps.

Following collection and processing, acceleration data were transformed to align the accelerometer reference frame with the global reference frame using gravity as an indicator. ⁷ Globally aligned, and hence anatomically aligned, accelerations are necessary for SL estimation, and this process accounts for accelerometer misalignment when attached to participants. Acceleration data were then used to estimate foot initial contact, defined as local maxima of the BCOM anterior–posterior acceleration. ⁸ The BCOM inferior–superior position was estimated by double-integration of the inferior–superior acceleration and high-pass filtering at 0.1 Hz using a fourth-order, zero-lag Butterworth filter to address integration drift. SL was estimated as follows

SL = 2 × 2 × L × h − h 2

(1)

where L is leg length (distance between femoral trochanter and floor) and h is the difference between maximum and minimum inferior–superior BCOM position during one-step cycle. ⁸ Post-processing was completed using MATLAB software (MathWorks, Natick, MA, USA).

Able-bodied assessment

To evaluate the system prior to application with prosthesis users, a validity and reliability assessment was performed with five able-bodied individuals (72 ± 14 kg, 174 ± 5 cm). The purpose of this assessment was to establish the baseline functionality of the accelerometer system (hardware and software) before assessing its validity with prosthesis users. The protocol involved tracking the motion of retro-reflective markers attached to the participants’ heels using an eight-camera optical motion capture (OMC) system (Motion Analysis Corporation, Santa Rosa, CA, USA) at 120 Hz as they performed two sets of five walking trials. During the experiment, subjects initiated gait from a standing position within the OMC system capture volume and ambulated along the laboratory walkway. BCOM accelerations were simultaneously collected with the accelerometer, and the accelerometer was removed and reattached between each set of trials. Validation was performed by comparing individual SLs as estimated by the accelerometer system, SL_a, and OMC system, SL_m. For the OMC system, initial contact of each step was defined as the heel marker local minimum in the vertical direction (confirmed through visual inspection of marker trajectories), and SL was defined as the anterior distance between heel marker positions at initial contact along the walking trajectory. The optimal group CF (unitless) for this system was estimated by minimizing the absolute difference from zero of the mean error, E_able, across all steps of all participants (n)

E a b l e = ∑ i = 1 n ( S L a , i − S L m , i ) n

(2)

Test–retest reliability was quantified with the intraclass correlation coefficient (ICC(2, 1); absolute agreement model, subjects as random effects, 95% confidence interval) of the mean accelerometer-estimated SLs while at SSWS (excluding the first two steps) between each set of walking trials. To complement the test–retest reliability, a Bland–Altman analysis was conducted to illustrate the presence of errors (i.e. if the accelerometer system errors demonstrated fixed or proportional bias) and absolute agreement in SL measurement between the two systems. A one-sample t-test was used to assess whether the mean error was significantly different than zero (i.e. fixed bias), and Pearson’s correlation coefficient was estimated to assess whether measure error and average of the two systems were strongly and significantly correlated (i.e. proportional bias).

Amputee assessment

Acceleration data were collected on 20 LLP users (83 ± 19 kg, 176 ± 7 cm; 8 unilateral transfemoral, 9 unilateral transtibial, and 3 bilateral amputation (2 transtibial/transtibial, 1 transtibial/transfemoral)) while walking a straight 20-m path (measured with a meter stick) from a standing position to a complete stop. Individual SLs were estimated using the accelerometer system, and validity was assessed by comparing the estimated distance walked (= summation of SLs), SL_estimate, to the measured distance walked, SL_measured. An optimal (group average) CF (unitless) was estimated by minimizing the absolute difference from zero of mean error, E_amputee, across all participants (n)

E a m p u t e e = ∑ i = 1 n ( S L e s t i m a t e , i − S L m e a s u r e d , i ) n

(3)

To explore the use of subject-specific CFs, a backward stepwise linear regression (removal criterion = probability-of-F ⩾ 0.1) was performed using SPSS software (v22, IBM, Armonk, NY, USA) to identify an equation that predicted a participant CF that minimized their error. The clinically relevant regression variables that may affect SL estimation included the following: body mass with prosthesis, most-proximal amputation level, and L. A one-sample t-test was used to assess whether the mean error was significantly different than zero.

The critical α was set to 0.05 for all statistical analyses. For each group, mean accelerometer-estimated SL while at SSWS (removing first and last two steps) was calculated. For comparison purposes, the Cohen’s d effect size (ES) was calculated between the LLP user group mean SL and a selection of literature values to illustrate magnitude of differences between these values. ¹¹

Results and discussion

The accelerometer system demonstrated excellent test–retest reliability (ICC = 0.909; 95% confidence interval = 0.388–0.990) and adequate validity during the able-bodied assessment (Table 1), with SLs agreeing with literature values (0.71 m). ¹² Average gait speed for able-bodied individuals (estimated from motion capture data as mean SL divided by mean step time) was 1.3 ± 0.2 m/s. Regarding within-subject variability for the reliability assessment, the average difference in gait speed between trials and the grand mean was 2.7% ± 2.2% (range: 0.0%–7.7%), and average difference in speed between the two sets was 1.0% ± 0.9% (range: 0.2%–2.6%). These small differences in speed suggest that velocity effects would be minimal on this analysis. One source of error was occasional overestimation of SL for the first step (Figure 2), but this step was included as one of the functions of this device is to estimate the total distance walked, and inclusion of the first step would reflect assessment as performed in a clinic. Able-bodied estimates did not demonstrate noticeable fixed bias (Figure 3), and this was confirmed by mean error not significantly different than zero (p = 0.625) and correlations between error and average estimates that were weak and not significant (p = 0.794, r = 0.015). Although mean error in SL was small, the 95% limits of agreement were relatively large and noticeably affected by outliers, the majority of which (69%) were the first step (Figure 3).

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Table 1.

Validation results and step length (mean ± 1 SD) as estimated from the accelerometer system with literature values for comparison.

	Able-bodied	Prosthesis user
Optimal correction factor	1.16	1.06
Mean error (%)	−0.1 ± 17.1	−1.0 ± 15.3	Group	Literature value (ES)	Reference
Step length (m)	0.74 ± 0.08	S: 0.59 ± 0.08 P: 0.68 ± 0.03	Unilateral transtibial	S: 0.69 ± 0.06 (1.4)P: 0.74 ± 0.06 (1.3)	Isakov et al. 1
				S: 0.61 ± 0.07 (0.3)P: 0.64 ± 0.07 (0.7)	Isakov et al. 2
		S: 0.60 ± 0.13 P: 0.70 ± 0.12	Unilateral transfemoral	S: 0.65 ± 0.03 (0.5)P: 0.74 ± 0.01 (0.5)	Uchytil et al. 3
				S:0.65 ± 0.09 (0.4)P: 0.68 ± 0.11 (0.2)	Lythgo et al. 4
		0.65 ± 0.06	Bilateral	Bilateral transtibial: 0.57 ± 0.12 (0.8)	Su et al. 5

SD: standard deviation; ES: effect size.

Reported mean error (relative to the mean of both methods) and step lengths include the group correction factor. Able-bodied and bilateral amputee data are averaged over both limbs, with data for unilateral amputees separated for the sound (S) and prosthetic limb (P). The Cohen’s d ES between the prosthesis user values and those from the literature are included in brackets next to the literature values.

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Figure 2.

Exemplary data of step lengths while walking from a standing position as estimated by the accelerometer and motion capture system for one able-bodied subject. The displayed overestimate of the first step (i.e. gait initiation) occurred in 38% of all able-bodied trials.

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Figure 3.

Bland–Altman plot for individual step lengths as estimated in able-bodied participants using the accelerometer and optical motion capture (OMC) system.

Average gait speed for prosthesis users (estimated as 20 m divided by the time required to walk 20 m) was 1.3 ± 0.2 m/s. The accelerometer system either overestimated or underestimated distance walked across amputee participants, resulting in a group CF near 1.0, but estimated SLs generally agree with literature values (Table 1), with ESs ranging from small to large ¹¹ depending on the literature source. The stepwise regression resulted in a predictive model (p = 0.029, r = 0.488) for estimating subject-specific CFs with the following equation

CF = 2 . 588 − 1 . 582 × L

(4)

Using equation (4) only reduced the relative E_amputee from −1.0% to 0.8%, suggesting that subject-specific CFs did not add any considerable benefit. The mean error using either CF method was not significantly different than zero (p ⩾ 0.589), suggesting no presence of fixed bias. However, the variability of estimated distance walked was high and suggested that estimations could be inaccurate up to 30% (= 2 standard deviation (SD) from mean error), and this may be clinically unacceptable. Anecdotally, those participants with visually apparent gait deviations (e.g. lateral circumduction or hip-hiking) displayed some of the greatest errors and are likely due in part to a violation of the model that underpins accelerometer-based SL estimation that implicitly assumes movements associated with gait are restricted to the sagittal plane. Refinement of this system to improve accuracy may be warranted for use with prosthesis users that produce considerable motion outside of the sagittal plane. A commercially available accelerometer system that is capable of estimating temporal-spatial gait parameters demonstrated similar relative mean errors for SL in LLP users (−0.05%), but considerably less variability (5.32%). ⁹ The smaller variability may be related to differences in hardware, software, and validation parameters, but the objective of this study was to assess the utility of inexpensive systems for prosthetic gait characterization.

A limitation of this study is that individual SLs were not validated for LLP users as was performed with able-bodied individuals, and this precluded further analysis into effects of compensatory mechanisms on step-to-step variability. Additionally, estimated CFs were based on SSWS and may not account for speed-dependent changes in gait characteristics, ¹² and this should be considered when applying these results to speeds other than SSWS. Future studies should also focus on assessing the influence of distance and turning on estimates of SL as only one fixed distance and (straight-line) path was used for validation. Finally, although accelerometers are capable of capturing temporal parameters (e.g. step time and cadence) and estimates of gait asymmetry, ¹³ this study was limited to the assessment of SL. Additional studies are warranted to assess the validity and reliability of additional metrics in conjunction with the selected hardware.

Overall, results suggest the refinements to this accelerometer system and additional experimentation with LLP users to account for additional subject-specific factors are required before establishing clinical suitability. Although variability was high, errors may be considered sufficiently low to encourage use of this system as a practical method for characterizing gait of prosthesis users within a clinical environment. The low cost of this system and use of easily implemented algorithms may serve as an alternative to more expensive equipment for monitoring gait quality of LLP users in clinical environments. Importantly, these instruments can supplement information collected during standard clinical assessments (e.g. 2-min walk test) to monitor patient outcomes as related to SL.

Key points