Arm modelling

The dynamic characteristics of arm movement may be divided into those properties describing its behaviour in the absence of voluntary effort (passive) to which are added the properties determining the response to voluntary control (active). For stroke participants these are compounded by the motor control impairments already discussed (see section 2.1.2).

A dynamic model of the stimulated arm system is required for use in the analysis of treatment, and the design of the stimulation controller. This is used specifically to provide details of participants’ passive and active arm properties that are used as outcome measures analyse each participants’ performance and to design the advanced control schemes governing the level of stimulation applied to participants over the course of the intervention.

Dynamic models have been produced, firstly for stroke patients with residual voluntary movement to enable analysis of the kinetic and kinematic characteristics of their movements (Beer et al., 2000). These models have incorporated the total torque due to the combined effect of the remaining passive arm properties and voluntary effort. Additionally models have been developed for unimpaired and paralysed limbs (with no voluntary action) that fully incorporate passive arm properties and also include the application of ES (Dou et al., 1999).

Control schemes exist in which EMG from the stimulated muscle is used in order to obtain a direct measure of overall muscle activity, however, the EMG amplitude does not necessarily correlate with either muscle force or limb movement. In addition the EMG signal may often be weak and unreliable and the artefact produced by the stimulation signal may corrupt the natural EMG signal (in which case blanking techniques may be applied).

Little work has been done to produce dynamic models suitable for stroke patients’

arms (with residual function) which either explicitly account for all passive arm

66 properties or include the application of ES. This is partly due to the difficulty

associated with measuring or estimating the degree of voluntary effort supplied by the participant.

Model Development

Spasticity and the biarticular nature of triceps were taken into account in developing the model. Evidence has shown that the stretch activation of triceps can produce joint torques at the shoulder (Sangani et al., 2007). Passive properties of stroke patients have been shown to be repeatable intra-session but may vary between sessions (Lum et al., 1999) and can only be assumed to be uncoupled if the level of spasticity is mild. It has been shown that it is possible to model the triceps as uni-articular with respect to applied FES, with careful electrode placement to minimise the degree of biarticulate flexion (Lan, 2002).

A mathematical dynamic model was derived incorporating the passive arm

properties, and was used to calculate the torque generated by the voluntary effort of stroke participants during reaching movements. The torque generated by triceps in response to ES (represented by the torque generated by an electrically stimulated muscle acting about a single joint) was subsequently added and the model tested in the absence of voluntary effort supplied by the participant.

To estimate the parameters present in the model identification tests were

undertaken. The tests were designed to collect the essential data in the minimum time to reduce possible fatigue. They included:

i) Stimulation parameters – the ES electrode position on the triceps brachii was tested in situ to ensure maximum movement in the given plane of motion, whilst minimising any shoulder torque. The stimulation used was asymmetric biphasic with a fixed amplitude and a period of 40Hz. The pulsewidth was variable from 0 to 300 µs with a resolution of 1µs. The amplitude, which was fixed throughout all

subsequent tests, was determined by setting the pulsewidth equal to 300µs and slowly increasing the applied voltage until a maximum comfortable limit was reached. This was verified over the full range of elbow extension.

ii) Biometric data – for each participant the distances from the acromium to the coracoid process of the elbow, and from the coracoid process to the 1^st proximal interphalangeal joint were measured. The participant was then seated in the robot

67 with strapping to restrict trunk flexion. With the dominant (or in the case of a stroke participant, their hemiplegic) arm strapped into the robot arm holder, maximum reach across the workspace was measured. Using the measured lengths, the angle between robot and human arm and an appropriate sampling time, the discrete trajectories were produced.

iii) Passive Dynamics with Applied ES

First an isometric model of the torque produced by the triceps in response to stimulation was produced by the following procedure.

The participant was seated in the robot and was instructed to apply no voluntary effort. The participant’s arm was held stationary by the robotic arm and a triangular input was applied to the triceps. The force at the end effector was recorded and the moment about the elbow was calculated. A model of muscle contraction dynamics was then fitted which involved a static non-linearity (the “isometric recruitment curve”), multiplied by a linear model of muscle contraction dynamics (the “linear activation dynamics”). For further details see (Freeman et al., 2008c).

Passive dynamics with no ES were also investigated with neurologically intact and stroke participants. This was done by using the robot to move the human arm through a set of trajectories which excite all the system dynamics of interest and recording the force applied at the end effector. Details of this can be found in (Freeman et al., 2008b). The first test consisted of six trajectories each of 40s duration in which the shoulder angle was held constant and the forearm angle moved between predetermined comfortable limits. The time taken for each movement was slowly reduced from 10s to 1s by increasing the velocity. The second test was similar but involved movement of the shoulder angle between predetermined limits whilst the elbow angle was held constant. For the stroke participants the results from these tests were found to vary significantly over time.

To avoid the necessity of repeatedly performing identification tests, standard parameter values were used.

Experimental results have been published (Freeman et al., 2008b) confirming the efficacy of the model and accompanying identification procedures. To further examine the accuracy of the identified models of the electrically stimulated passive arm further tests were conducted. The arm model was then applied to the situations where firstly ES was used in the absence of voluntary action, and then subsequently where voluntary control is present and ES is not applied. Finally a method was

68 proposed which modelled the effect of applied stimulation while the participant simultaneously exerts voluntary effort.