The adaptive drop foot stimulator – Multivariable learning control of foot pitch and roll motion in paretic gait
Introduction
In many cases, stroke leads to impaired motor function. Even after weeks of rehabilitation, many patients suffer from a limited ability to lift the inner (medial) or the outer (lateral) edge, or both, of the foot by voluntary muscle activation. This syndrome is known as drop foot (or foot drop), and it also appears in patients with other neurological disorders. As Fig. 1 indicates, foot drop leads to a pathological gait with an increased risk of fall. A common treatment is to fix the foot in the lifted (dorsiflexed) position by an orthosis. While this approach may improve safety and stability in the patient’s gait, it promotes muscle atrophy and joint stiffness.
Drop foot neuroprostheses, also known as peroneal stimulators, represent an alternative treatment that aims at generating a natural foot lift via activation of the patient’s shank muscles, cf. [1]. The technology known as Functional Electrical Stimulation (FES) facilitates the artificial generation of action potentials in subcutaneous efferent nerves by applying tiny1 electrical pulses via skin electrodes or implanted electrodes. By modulating the frequency or dimensions of these pulses, one can control the contraction of paretic muscles and induce movements in the affected limbs. Unfortunately, FES may also trigger action potentials in afferent nerves, causing discomfort at medium and pain at high stimulation intensities. In most subjects, however, the sensation is weak enough to allow the generation of functional movements without discomfort. Abundant research demonstrates the potential of FES in neuroprosthesis design, beyond the application of drop foot treatment, see for example [2] and references therein.
For drop foot treatment, a few commercially available solutions make use of FES, some via skin electrodes, others via implanted electrodes. The review articles by Lyons et al. [3] and Melo et al. [4] provide an excellent overview of drop foot stimulators in research and industry and classify them in several ways. Until now, all commercially available devices have been solely based on open-loop architectures, they only use sensors to time the stimulation [4]. Most of them employ heel switches to detect two gait phases: one when the heel of the paretic foot is on the ground and the other when it is not. In each stride, as soon as the heel is lifted, FES is applied with a fixed stimulation intensity profile over time, typically a trapezoidal shape tuned by an experienced clinician. The ankle joint, however, exhibits two degrees of freedom that are actuated by the shank muscles in a nontrivial, coupled way. Thus, finding stimulation parameters that yield a physiological foot motion can be cumbersome, as illustrated in Fig. 1.
Moreover, FES dynamics are typically very time-variant. When activated by FES, muscles may fatigue rapidly [5]. Moreover, residual voluntary muscle activity as well as, for example, the muscle tone (spasticity) in antagonistic muscles often change within a few strides. In all of these cases, repeated manual adaptations of the intensity profile are required to maintain a physiological foot motion for more than a few strides. An obvious escape strategy that is often pursued is to choose larger stimulation intensities and accept exaggerated foot lift. While this strategy provides a certain amount of safety and functionality, increasing the stimulation intensity may accelerate muscular fatigue and lead to a salient peculiarity in the patient’s gait, cf. Fig. 1.
The described challenges can be faced in a much more effective and elegant way by the use of feedback control. The stimulation parameters can be adjusted automatically to delay the onset of fatigue and to induce the optimal level of foot lift. This requires measurement of the foot motion via, for example, an inertial sensor or a goniometer. It was recently demonstrated that a foot-mounted inertial sensor can be used to detect four gait phases [6] and to measure the foot orientation with respect to the horizontal plane [7]. See Figs. 2–4 for illustration.
Despite increasing efforts in the last decades to make closed-loop gait neuroprostheses a reality, it is still a challenging task to control paralyzed limbs with FES [4]. Several control techniques have been proposed, and some respectable results have been obtained at least for the much simpler case of a sitting or lying subject, i.e. without the tight time constraints and the strong disturbances imposed by gait. For example, Kobravi and Erfanian [8] and Valtin [9] proposed a fuzzy controller and an iterative learning controller, respectively, and performed experimental trials with sitting subjects. Hayashibe et al. [10] and Benedict and Ruiz [11] suggested the use of predictive control and PID control, respectively, but tested their controllers in simulation studies only. Artificial neural networks were employed by Chang et al. [12] and Chen et al. [13], who validated the controller in trials with subjects lying on a bed.
Besides those experimentally simplified studies, intense efforts have also been made to close the loop on FES during walking. Veltink et al. [14] used an inertial sensor on the foot to tune an implantable drop foot stimulator such that a desired foot orientation just prior to initial contact was achieved. Negård [15] proposed run-to-run control of the maximum foot pitch angle occurring during swing phase and tested the controller in trials with a walking drop foot patient. Previously, Mourselas and Granat [16] had briefly reported similar results obtained with a bend sensor and a fuzzy logic algorithm.
While these latter results represent important technical improvements with respect to all commercially available stimulators, one major shortcoming remains: The entire foot motion is reduced to a single scalar measure, for example a minimum foot clearance [17] with respect to ground or a desired foot pitch angle at initial contact. Obviously, this is a strong simplification of the control problem. As we will demonstrate, conventional stimulation intensity profiles may yield (for example) a desired maximum foot pitch angle, while causing too weak or too strong foot lift during the first half of the swing phase, or while using larger intensities than necessary.
With respect to overcoming these limitations, it was demonstrated in [18] that iterative learning control (ILC) can be used to control the entire foot pitch angle trajectory of drop foot patients during the swing phase, cf. Fig. 4. This approach yields a stimulation intensity profile over time that induces a foot motion close to those of healthy walkers, while using only as much FES as needed. However, the roll motion of the foot is neglected completely, which represents a strong simplification.
In a recent conference article, we demonstrated that ILC can be employed for the two-dimensional problem of controlling both the foot pitch and the foot roll motion simultaneously [19]. To the best of our knowledge, this is the first time that automatic feedback control of the entire foot pitch and roll angle trajectory is achieved in walking drop foot patients. In the present contribution, we explain the methods that enabled this result, and we extend the approach by taking the cross-couplings between the FES parameters and both foot orientation angles into account. To this end, we first describe the motions that are caused by applying two-channel FES via a three-electrodes setup. Since both the pitch and roll angle of the foot are influenced by both FES channels, we adopt a nonlinear decoupling strategy that facilitates the implementation of a decentralized ILC scheme. In contrast to the vast majority of previous contributions, we demonstrate the effectiveness of this approach in drop foot patients walking on a treadmill and on level ground.
The remainder of this contribution is organized as follows. In Section 2, we discuss the basic principles of FES-induced foot motion and propose a three-electrode setup that enables the manipulation of two independent stimulation intensities (pulse charges) via only three surface electrodes and, nevertheless, ensures a zero net current. Subsequently, in Section 3 we use a pair of nonlinear FES intensity parameters to solve the problem of interdependent saturation limits in multi-channel FES and compensate most of the multivariable cross-couplings between the stimulation intensities of both channels and the foot motion they trigger during gait. With this static decoupling scheme in place, two decentralized iterative learning controllers (one for the pitch and one for the roll angle) are designed in Section 4. The resulting adaptive drop foot stimulator is then evaluated in drop foot patients walking on a treadmill and on level ground in Section 5.
Section snippets
Inducing foot pitch and roll motion by FES
The human ankle includes the talocrural joint and the subtalar2 joint. The former admits dorsiflexion and plantarflexion, i.e. lift and drop of the foot with respect to the tibia, which corresponds to foot pitch in Euler angle notation. In contrast, the subtalar joint allows for supination and pronation, which corresponds to rotation of the foot about a combined pitch, roll and yaw axis that is oriented 16° from the sagittal
Choosing suitable stimulation intensity parameters
The force generated by FES increases monotonously with the frequency and the charge (i.e. the product of pulse width and amplitude) of the applied current pulses. Therefore, adjusting the stimulation intensity typically relates to adjusting either (or both) of these quantities. For the sake of brevity, we assume a fixed pulse frequency6 of 50 Hz and manipulate only the pulse
Improving FES parameters by realtime learning control
We will now design a controller network that manipulates the FES intensity parameters in order to influence the orientation angles of the paretic foot during walking. Recall that the gait events heel-off thr, j, toe-off tto, j, initial contact tic, j and full contact tfc, j of the paretic foot are detected in realtime for every stride j. Recall furthermore that the control objective is to manipulate the stimulation intensity parameters and such that the pitch and roll
Experimental evaluation in stroke patients
In experimental trials with drop foot patients, we now evaluate the previously designed ILC scheme in combination with decoupling parameterization proposed in Section 3. The four patients that were recruited for these trials are ambulatory, aged 50–70, BMI 20–27, at least three months post-stroke and suffer from a drop foot syndrome in combination with at most moderately increased muscle tone (hypertonia) of the leg musculature. Some of them use a walking stick or an ankle-foot orthosis in
Discussion of the results
In the previous section, we found that the proposed three-electrode setup leads to different foot movements when stimulating on each of the channels separately. This is in accordance with earlier studies concerning two-channel stimulation of superficial and deep peroneal nerves [14], [24] or tibial nerves just above the knee [26]. In these studies, however, implanted FES electrodes were used. Surface electrodes, as used in the present contribution, are known to cause a less selective
Conclusions
FES-based drop foot treatment via surface electrodes has been considered. Benefits of a closed-loop approach were discussed, as well as the challenges arising from the multidimensionality of this task and from large delays and disturbances. We proposed a three-electrodes setup that allows us to recruit m. tibialis anterior and m. fibularis longus via two independent FES channels without violating the zero-net-current requirement. We then characterized the domain of admissible stimulation
Ethical approval
Informed consent of the patients was obtained and the trials have been approved by the ethics committee of Charité Universitätsmedizin Berlin (Number EA2/015/13).
Funding
This work was conducted within the research project BeMobil, which is supported by the German Federal Ministry of Research and Education (FKZ 16SV7069K).
Competing interests
None declared.
Acknowledgments
We would like to express our deep gratitude to the patients who participated in the trials. Furthermore, the valuable contribution and skillful support of Mirjana Ruppel and Boris Henckell are highly acknowledged.
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