Application of FES for Therapy of Hemiparetic Gait

Markus Weber*, Friedrich Pfeiffer

Institute for Applied Mechanics, Technical University of Munich, Garching, Germany

Introduction

Apoplexy is one of the common causes for disability, characterized by disturbance of memory and paralysis mainly on one side (hemiplegia). The associated social isolation and the lack of mobility imply research for suitable methods in therapy of hemiparetic walking.

In recent surveys, Functional Electrical Stimulation, in addition to physiotherapy, is increasingly used to improve the hemiparetic gait. The theory of FES and its application is already known in the field of paraplegia, where a desired movement of the patient (e.g. standing up) is achieved by stimulating the atrophied muscles using a prosthesis [5]. In this respect, the necessity of appropriate models for the human body including the muscles could be shown. The emerging parameters are mostly determined by regression equations [2] or calculated by preceding measurements [1].

In terms of movement control, several approaches are proposed. [3] gives an overview of different designs of feedback control. Furthermore, the application of neuronal networks and finite state control can be found in literature.

In this paper a therapy method for hemiparetic walking employing FES is described. The general approach is presented, and modelling as well as controller design are described. Simulation and experimental results referring to the human-muscle model and control design are shown, completing with a discussion about future work.

Methods

The main idea of FES-based gait therapy on hemiparetic walking is to enable the patient to activate his muscles at the right time of the gait cycle by giving him a haptic feedback. Over time, the patient relearns the natural gait. In order to achieve fast improvements, a combination of physiotherapy and muscle stimulation is used in order to restore the patients’ unassisted mobility within 4-5 weeks.

A patient who has suffered an apoplexy gets a physiotherapeutic treatment to restore the flexibility of the joints and the muscles (ca. 1-2 weeks). In the following, a stimulation of the muscles is exerted to the person. For therapy with FES, computed stimulation parameters (pulse width, electric current, frequency) are transmitted to the patient using electrodes, so that the generated joint torque assists the patient’s gait. The resulting joint angles are measured by an optical system based on markers and sent back to the control. The control algorithm then alters the stimulation parameters to improve the patient’s gait (Figure 1).

In contrast to paraplegia patients, who get no nerval feedback because of the lesion in the spinal column, the hemiparetic patient has a remaining autonomous motor activity (AMA) after the 2 weeks physiotherapy. This AMA has to be considered by computing the parameters for stimulation. In order to get the AMA, the patient’s movement without stimulation is measured every day during therapy.

Figure 1: schematic structure for FES

These measurements also serve as a basis to monitor the patient’s progress. The therapist can estimate the patient’s AMA by regarding the interference with FES and the patient’s state (e.g. patient’s fear impairs the actual AMA).

On the other hand, a desired value of the state variables (joint angles) must be found. This part of the therapy plays an important role, because the joint angles must be computed to ensure a stable gait cycle for each day of therapy. Furthermore these defined joint angles must include the patient’s improvements. In this context, the therapist defines the patient’s “daily learning target”, e.g. the knee joint angle should be increased from 30° to 50° in the initial-swing phases of gait cycle. On the basis of gained experiences, an automated procedure must be developed in the future. This algorithm has also has to ensure an optimal devolution of the therapy by using the therapist’s experience.

By knowing the reference and the patient’s remaining joint trajectories, the stimulation parameters can be computed, using the inverse models of human body and muscle:

The used kinematical human model is based on the theory described in [2]. The human body is described by 12 segments (upper arm, forearm, head, Thorax-Abdomen, Pelvis, Femoral, Shank, Foot) with 42 DOF. [2] shows that the dynamics of head and arms are of smaller importance than the rest of the body. Additionally, these extremities are not planned to be stimulated, so these segments were removed from the model [2]. The implemented human model thus comprises of 8 bodies with 27 DOF.

Due to the application of object-orientated programming language, adjustments such as restructuring or simplification/detailing the body system can be made easily. Future investigations will improve the model of the human body by detailing the spinal column.

The used muscle model is based on the model among others presented in [4]. It is divided into 3 functional parts: the activation dynamics (AD), the contraction dynamics (CD) and the global balance (GB). In order to achieve good results, the model should match real muscle properties.

The AD describes the relationship between the stimulation parameters (pulse width, electric current, frequency) and the activation of the muscle. This muscle-activation is a standardised value, which equals 1 when all muscle fibres are activated and the maximum muscle force is produced. This maximum force is dependent on the angular joint position. Likewise, it equals 0 when no fibres are activated.

The CD takes the influence of joint angles and joint angular velocities on the muscle force into account. The coefficients are designed such that the maximum isometric force is calculated, when the contraction velocity equals 0 and the muscle length is optimal.

In the GB, the muscle forces are mapped on the joint torques. Furthermore, elastic and viscose properties of the muscle are projected onto the joint and added to the joint torque. The elastic and viscose torques regarding each joint (e.g. knee) are given by equations [1], because not all muscles can be parameterised and a more exact torque can be computed in that way for the complete joint. After the summation of all torques concerning a joint. The resulting torque is used for computing the direct dynamics.

As both physiological and artificial generated muscle force are based on the same theory, it is possible to compare the stimulation parameters computed from the AMA and from the reference joint angles. This comparison is made using the differencing method. It is necessary, because only the deviation of gait must be stimulated to assist the patient’s gait. Principally there are two ways of differencing. Either to make the comparison on the level of the joint torques or on the level of the stimulation pulses. Considerations have shown that the differencing method on basis of the joint torques gives better results. Furthermore, the computed stimulation patterns must also consider the overlap regarding the muscle fibres, activated by natural and artificial stimulation.

Concerning control design, a cascaded feedback control is applied in order to compensate disturbances or inaccuracies. These errors appear, as the patient’s behaviour can only be estimated roughly (the patient’s remaining motor activity has a direct influence on the movement that can perturb the whole system behaviour). Noise from the measuring system and other hardware components also affect the system behaviour.

Generally, the outer controller (kinematical controller) gets the information about the current and the desired joint angles. In the following, the control algorithm computes the joint torques to compensate for the deviations from the reference trajectory and measured motion. The algorithms used are PID, PID model-based and feedback-linearisation (FL) (enables to apply methods of linear control design). The inverse muscle-model generates the desired muscle-activation, which is sent to the inner controller (muscle control). This controller also gets information about the actual muscle activation, which cannot be measured and is evaluated by simulation, and calculates the stimulation parameters to minimize the difference between actual and desired activation.

Due to the fact that not all joints can be stimulated (e.g. arms, thorax-abdomen), the realisation of a full-body-control is not possible. In principle, the control of the non-stimulated joint angles could be regarded as a kind of natural control, but the lack of proving experiments and the limited patient’s ability to control the affected side require the use of constraints.

Results

Although the muscle model described above is proposed widely in literature, confirming experiments must be done. The parameters used for describing the muscle model are acquired by statistic measurements. Thus, there is a deviation in these parameters as different patients (age, paralysis) are stimulated. Therefore, a single joint stimulation at the knee flexion was performed as a rectangle function (Figure 2a). The desired motion was provided by 2 antagonistic groups of muscles: Vasti (Knee-Extension) and Hamstring (Knee-Flexion). Moreover, the stimulated subjects were normal persons without paralysis. The generated movement was measured by goniometers and the stimulation was open-looped, as only human and muscle models had to be verified.

Comparing measured and simulated movement, the amplitude and frequency of the movement were identical. Exceptions are the overshoots in the measured motion, which are not seen in simulation. This discrepancy cannot be justified in the muscle or human model, as the used stimulation pattern had a similar continuous devolution like the joint angle devolution. The overshoots are caused by the proband’s reaction to the changing stimulation parameters. An attenuation of the overshoots can be seen after some seconds. The proband got used to the stimulation pattern, so the influence of the proband‘s motor activity on the knee movement decreased. In order to avoid these overshoots, an adequate control, regarding the patient’s AMA, must be used.

Different approaches in control design were illustrated in the previous sector to enable a comparison between linear and non-linear control. Therefore, the human standing on the right leg has been simulated (Figure 2b). Thus, the system stability, the offset and the control response time can be derived from the devolution of the joint angles. Thereby, flexion- and extension group of muscles concerning knee-motion were used to generate the computed joint moments. Constraints were only given by the maximal muscle force that can be produced by each muscle.

Regarding the simulation diagrams concerning the kinematical control (Figure 2b), PID control is characterized by a significant overshoot, which leads to a hyperextension of the knee-joint. Furthermore, the choice of the PID-control parameters has a great influence on the system behaviour (stability) and optimal values differ from the desired control-problem. On the other hand, the FL control is more affected by inaccuracies or modelling errors and the PID control is more suitable for a real-time application as it is less computationally expensive. Comparing the different muscle-control algorithms, best results can be achieved by using the simplified model. Like the kinematical control, a sensitivity of the PX-control parameters towards the stability can be determined.

Discussion

A method for therapy of hemiparetic gait is presented, giving more detailed information about human modelling (body, muscle) and control strategies. Moreover results from simulations and experiments are given.

Further investigations will concentrate on improving the model, the control and the gait planning. In particular, the spinal column will be detailed in the human body model. Concerning control, an observer will be used to minimize noise disturbance and the influence of the muscle behaviour on the kinematical control. Furthermore the computing-time must be reduced to guarantee stimulation in real-time.

References

[1] T. Edrich; R. Riener; J. Quintern, “ Analysis of passive elastic joint moment in paraplegics”, IEEE Transactions on Biomedical Engineering, Vol. 47 (2000), No. 8, pp. 1058-1065

[2] C. Lutzenberger, “Dynamik des menschlichen Ganges”, Fortschritts-Berichte VDI, Vol. 17: Biotechnik/Medizintechnik, No. 218, 2001

[3] M. Ferrarin, R. Riener, J. Quintern, “Model-based Control of FES-Induced Single Joint Movements”, IEEE Transactions on neuronal systems and rehabilitation engineering, Vol. 9, No. 3, pp. 245 – 257, 2001

[4] R. Riener, T. Fuhr, “ Patient-Driven Control of FES-Supported Standing Up: A Simulation Study”, IEEE Transactions on Rehabilitation Engineering, Vol. 6, No. 2, pp. 113-124, 1998

[5] Yo-Luen Chen, Yen-chen Li, “The development of a closed-loop controlled functional electrical stimulation (FES) in gait training”, Journal of medical Engineering & Technology, Vol. 25, No. 2, pp. 41 – 48, 2001