This study demonstrated that the use of within-socket residual EMG of transtibial amputees can be used, in conjunction with shank kinematics of the sound limb, to continuously predict normative ankle kinematics and kinetics of the sound limb across ambulation conditions and terrain transitions. Additionally, the single-network, closed-loop NARX model had the ability to characterize normal gait patterns of ankle angle and moment of able-bodied participants. The need for explicit identification of gait events or selection of locomotion modes was eliminated due to the ability of the autoregressive model to continuously predict ankle dynamics within and across ambulation conditions (i.e., level overground walking, stair ascent, and stair descent), including transitions between terrains.
The proposed NARX model could be used in real-time to generate continuous ankle angle and ankle moment commands for the control of an active ankle-foot prosthesis using impedance, stiffness, or similar control schemes [3, 17, 21, 54]. It is believed that this work is the first in which a fully closed-loop model with predictive capabilities (i.e., future estimates) has been developed to continuously predict ankle state. In the closed-loop NARX model, prior model error was directly encoded during training because output predictions were fed back as recurrent inputs instead of using error-free target data (as in open-loop models). A closed-loop structure would make the system robust to model uncertainties (e.g., error accumulation and undesired fluctuations), thus ensuring accuracy and stability when implemented in a feedback control system. Moreover, the prediction of future limb state enables a control system to counteract control and actuation delays, and allows gait changes to be modified proactively in response to terrain changes perceived by the user. Results show that similar performance can be achieved for prediction intervals ranging from 8 to 142 ms (Fig. 4 and Additional file 1: Supplementary Fig. 5) which would accommodate prosthetic delays (e.g., 40–50 ms response time of ankle-foot prostheses [1, 60, 61]) and enable future predictions given the physiological electromechanical delay from onset of surface EMG to the neuromotor drive (4-170 ms for lower leg muscles [62]), while keeping ankle angle error less than 5 degrees [37]. These features make the recurrent (closed-loop) NARX model appealing for real-time feedback control in a wide variety of lower limb robotic devices, including actuated orthoses and exoskeletons.
In lower limb amputees, gait asymmetries between the sound and prosthetic limb are primary attributed to limitations in the prostheses, even active prostheses, and are a major concern in achieving normal gait [58, 63–65]. The practical need to adapt to such asymmetries often leads to differences in kinematics and kinetics of the sound limb when compared to able-bodied controls [66, 67]. The approach presented here, mapping ankle dynamics of the sound limb with residual EMG of the prosthetic side (i.e., aligned), takes an important step toward establishing a more normal gait by overlaying the dynamics of the sound limb onto the prosthesis to create symmetric gait patterns. However, the long-term impact on gait is dependent on the interaction between the model prediction and the human user as they adapt and react to changes (e.g., muscle recruitment, environment, and control errors). In previous work, a human-in-the-loop model was developed to simulate the user's EMG in response to changes in ankle dynamics [68]. Real-time performance of the autoregressive model during human-in-the-loop control is needed to ensure safety and stability of the physical prosthetic system prior human testing.
Despite amputees in this study having a wide array of residual ankle dorsiflexor and plantarflexor profiles with different levels of EMG activation and co-activation, walking patterns, and foot placement strategies during stair ambulation, the closed-loop NARX model performance was accurate and robust across amputees and ambulation conditions, including terrain transitions (R2 = [0.886, 0.982]), suggesting that the model can be used consistently across amputees. The strength of the model lies in its ability to account for individual’s specific variations of limb dynamics and muscle activity by training and optimizing the model to maximize performance for each amputee. Similarities in ankle angle and moment RMSE (across gait cycles and ambulation conditions) between individual amputees and the ABcEMG group suggest that the combination of antagonistic residual EMG along with sound-limb shank motion can effectively predict normative ankle dynamics. Importantly, the contribution of natural residual EMG signals of amputees, to the prediction of ankle dynamics across ambulation conditions, was consistent with normal muscle activity of able-bodied participants (Fig. 7 and Additional file 1: Supplementary Fig. 9). In contrast to proportional myoelectric control systems, the ability to use natural, yet altered, amputee muscle activation profiles, eliminates the need for conscious, intentional muscle contraction, extensive user training, and high quality, independent muscle signals. When implemented in a prosthesis, the cognitive and physical demand on the user is expected to be less than current myoelectric control systems [12, 15, 21, 22].
The use of shank kinematics and antagonistic surface EMG signals allowed for accurate and robust model performance that included information about limb state and direct user intention. While the model developed here used shank linear velocity, other measures of shank kinematics (e.g., angle, angular velocity) could be used as well [25, 29, 42, 69]. A benefit of using shank kinematics in transtibial amputees is that the motion of the residual shank is still governed by the central nervous system and contains information about the limb state in relation to the gait cycle. Furthermore, in real-time application, shank kinematics could be obtained intrinsically from sensors embedded in the prosthesis (e.g., inertial measurement units, gyroscopes, accelerometers), similar to within-socket EMG, minimizing design complexity and facilitating donning and doffing of the prosthesis.
Ankle angle and moment predictions closely matched the experimentally measured targets in all ambulation conditions for all participants. However, deviations in the predicted values were still present, particularly at local minima and maxima. Analyses revealed a number of critical points where predictions of amputee and ABcEMG models repeatedly fell outside the variability of the targets. While sample size may have been a contributing factor, differences in model predictions may not necessarily correlate with practical disruptions of gait. For example, ankle angle predictions deviated from the targets at one critical point during the stance phase of level walking and stair descent. Studies suggest that foot placement during stair use is not a factor that contributes to a stumble or fall [70], especially if the obstacle is seen beforehand [71]. Since the foot was already in contact with the surface, trip-related fall risk or injury from such prediction errors would be minimal. However, more generally, the impact of critical point errors on prosthetic control during gait remains an underdeveloped area of study in the field, particularly during human-in-the-loop control of an active prosthesis.
While the influence of push-off has not been linked to fall risk [72], limb asymmetry and offsets in the timing of push-off have been associated with increased metabolic rates, excessive limb loading, osteoarthritis, and back pain among lower limb amputees [73–77] and controls [78]. Although significant differences were also found at peak moments for the amputees, the peak percentage differences across ambulation conditions were lower than those present in commercially available ankle-foot prostheses (i.e., active to SACH) compared to able-bodied individuals (LW: 28% [58, 64, 67, 79], AS: 41% [58, 63, 80, 81], DS: 50% [58, 63]). Moreover, timing differences relative to the desired profile were present in the peak moments of those commercial prostheses, unlike the prediction peaks in this study (> 84% of moment predictions in amputees were within one time step of the targets). It is known that push-off timing is a key factor to maintain gait stability and stride variability [78]. The ability of lower limb amputees to adapt to these limitations in their own prostheses [82] suggests that the moment prediction errors of the NARX model may not negatively impact the robust control of a prosthesis.
The recurrent (closed-loop) NARX model predicted ankle angles and moments over a wider range of conditions at levels comparable to, and in some instances better than, other continuous gait models [28–35]. Most models have used a feedforward structure to estimate (i.e., one-step-ahead estimate) ankle dynamics of healthy individuals limited to level walking (\({RMSE}_{\theta }\) < 4.7°, \({R}_{\theta }^{2}\) > 0.74; \({RMSE}_{M}\) < 0.16 Nm/kg, \({R}_{M}^{2}\) > 0.86; [28–32]). In impaired populations, ankle angle errors (RMSE) ranging from 1.2 to 5.4 degrees and from 0.82 to 9.3 degrees have been reported for transtibial amputees [36] and spinal cord injury patients [34], respectively, during level treadmill walking. For the errors of transtibial amputees, ankle angle of their passive prostheses was predicted 100 ms ahead of time using two antagonistic within-socket residual EMG (i.e., same limb) as inputs to an open-loop NARX model [36]. In the current study, even with a greater model complexity, similar errors were achieved in transtibial amputees during level ground walking (RMSE < 2.8° for τ = 58 ms) with the inclusion of shank kinematics as inputs. In comparison to the 2-input open-loop NARX model developed previously [37], while ankle angle and moment errors increased by at least a factor of two across ambulation conditions for the closed-loop model, they remained less than 2.7 degrees and 0.11 Nm/kg for able-bodied participants with correlations greater than 0.95 for both models. Zarshenas et al. obtained favorable results (R2 > 0.8) using a time delay neural network with ankle kinematics and EMG inputs to predict ankle moment of healthy participants up to 1 second ahead of time [38]. Their model exploited the cyclic nature of treadmill walking at a constant speed which resulted in high accuracy over large prediction intervals, although performance was not examined during noncyclic features of gait such as terrain transitions. Gupta et al. estimated (i.e., excluding future predictions) ankle angle of able-bodied individuals during level ground walking (RMSE = 2.44 ± 0.45°, r = 0.97), stair ascent (RMSE = 3.61 ± 1.00°, r = 0.93), and stair descent (RMSE = 5.04 ± 1.56°, r = 0.85) using NARX models trained for each terrain individually [35]. It is believed that the NARX model was implemented as an open-loop model using error-free targets. The closed-loop model presented here had better performance, possibly due to the use of more relevant inputs (shank versus knee kinematics) and the absence of discontinuities in the training data, with the added benefit of being implemented in a single-network model capable of continuous prediction across ambulation conditions and terrain transitions.
The use of contralateral EMG to align residual EMG from the prosthetic side with sound-limb dynamics was a viable approach that yielded accurate predictions of ankle dynamics. While this approach provides a path toward the implementation of sound-limb ankle dynamics in the prosthetic limb, there remains room for improvement. When comparing able-bodied groups, where the only training difference was the use of aligned contralateral EMG instead of data from the same limb (EMG, ankle angle and moment, and shank velocities), the ABcEMG group had worse performance in all metrics (e.g., higher errors, lower correlations, model predictions that fell outside the variability of targets) than the able-bodied group (AB). Assuming limb symmetry in able-bodied participants [83], large discrepancies in EMG profiles and ankle dynamics were observed during transition steps onto and off the staircase due to differences in step limb dynamics between the lead limb (i.e., limb of ankle kinematic and kinetic predictions) and the aligned trail limb (i.e., limb of contralateral EMG) (Additional file 1: Supplementary Fig. 4). The limiting factor was the lack of EMG trials from both legs as the lead limb. The use of contralateral EMG collected as the lead limb would be expected to improve model performance by more accurately matching step dynamics with EMG signals.
In this study, the impact of post-processing motion artifacts on model performance was not analyzed in depth for the electrode-housing test socket design. Given the consistency of trial-wise variability and the absence of high-frequency, large amplitudes in the EMG linear envelopes across amputees, the potential impact on the current results was considered minimal. Additionally, it has been shown that a similar design using the same EMG electrodes and filtering techniques (i.e., band-pass filter at 20–450 Hz) in a transfemoral amputee produced negligible motion artifacts during level walking and stair ambulation, and produced a high level of user comfort when compared to other designs and electrodes [49]. Furthermore, the effects of variations in EMG signal due to changes in electrode placement and electrode-skin interface were not evaluated. Although studies suggest that these factors can adversely affect myoelectric pattern recognition [84–86], preliminary testing of trained NARX models with EMG from subsequent days suggests the impact may be more limited. However, further research is needed to validate robustness over time. Finally, while the current results demonstrate the feasibility to continuously predict ankle angle and moment across a subset of common ambulation conditions and transitions, additional work is needed to validate the model training and performance with a larger cohort of participants under additional ambulation conditions (e.g., ramps, cadence modulation, noncyclic activities) and in response to untrained situations such as recovering from an unexpected perturbation.