Investigation of the Hammerstein hypothesis in the modeling of electrically stimulated muscle.

To restore functional use of paralyzed muscles by automatically controlled stimulation, an accurate quantitative model of the stimulated muscles is desirable. The most commonly used model for isometric muscle has had a Hammerstein structure, in which a linear dynamic block is preceded by a static nonlinear function. To investigate the accuracy of the Hammerstein model, the responses to a pseudo-random binary sequence (PRBS) excitation of normal human plantarflexors, stimulated with surface electrodes, were used to identify a Hammerstein model but also four local models which describe the responses to small signals at different mean levels of activation. Comparison of the local models with the linearized Hammerstein model showed that the Hammerstein model concealed a fivefold variation in the speed of response. Also, the small-signal gain of the Hammerstein model was in error by factors up to three. We conclude that, despite the past widespread use of the Hammerstein model, it is not an accurate representation of isometric muscle. On the other hand, local models, which are more accurate predictors, can be identified from the responses to short PRBS sequences. The utility of local models for controller design is discussed.

Apparatus to measure simultaneously 14 isometric leg joint moments. Part 1: Design and calibration of six-axis transducers for the forces and moments at the ankle.

An apparatus has been developed for making isometric measurements of the joint moments corresponding to the 14 degrees of freedom of the legs, in postures ranging between sitting and near full extension. The apparatus is called the multi-moment chair system (MMCS) and is described in the companion paper. This paper describes the most critical components of the MMCS, which are the six-axis transducers for measuring the force and moment components on the plantar-flexion axis of each ankle while the feet are laced into fixed shoes. The transducers are made of steel bars, on which strain gauges are mounted, joined by clamps. The design of the transducer and methods of calibration and error estimation are described. The RMS errors are less than 2 N for the forces and 1 Nm for the moments, but these may be correlated. A method for error reduction that compensates for the finite compliance of the transducer does not reduce the measured errors.

Apparatus to measure simultaneously 14 isometric leg joint moments. Part 2: Multi-moment chair system.

An apparatus has been developed that measures isometrically the 14 lower limb joint moments corresponding to the degrees of freedom of the hips, knees and ankles. This is the second of two papers describing the development of the multi-moment chair system (MMCS). It presents the overall design and changes that were implemented to compensate for problems. These were primarily to improve the accuracy of hip joint moments; a compromise between accuracy and practicalities, because of force-moment responses being measured at the ankles. All joint moment errors have been calculated to be of the order of a few newton metres. Since these represent errors of less than 10% when considering peak joint moment responses, this is considered sufficiently accurate for the proposed application. The MMCS is being used in a programme to investigate the restoration of lower limb functions, principally standing, in paraplegics by electrical stimulation of the lumbosacral anterior roots.

Speeding-up the cure of one-part silicone rubber, when encapsulating neurological prostheses: the permeable mould.

The Note describes a procedure for encapsulating the implantable microelectronics in an air-curing silicone rubber, by which the shape of the casting is fully defined, and cure is achieved within an acceptable time.

Measurement of posture by triangulation using potentiometers.

To measure the posture of a paraplegic while standing up, an economical method has been developed. Markers, glued over the joints, hook onto strings which run to rotary potentiometers mounted on a fixed frame. Springs maintain a near-constant small tension in the strings, and the potentiometers rotate as the strings wind onto pulleys. The positions are calculated by triangulation, using two potentiometers per joint, assuming that body segment lengths are constant, or three potentiometers without this assumption. Using a second-order polynomial fit, the random error in length measurement for each potentiometer is less than +/-2 mm for the string length from 0 mm to 1100 mm, or less than +/-1 mm in actual range from 600 mm to 1000 mm. With two potentiometers per joint, using a second-order polynomial fit and assuming the ankle position is known exactly, an estimate of the resulting errors in the knee and hip marker positions are 4 and 8.5 mm, respectively.

A radial basis function model of muscle stimulated with irregular inter-pulse intervals.

Paralysed muscle, or skeletal muscle which is to be used for cardiac assistance, may be given an artificial function if it is electrically stimulated to contract and the response can be adequately controlled. To design a controller, a model of the muscle or system is usually required. The most commonly used models are analogues, originating from A.V. Hill's model. However muscles exhibit many nonlinear and time-varying phenomena which, if they are to be modelled, make the analogue complex and cumbrous to work with. The system may further be complicated by pathological changes and secondary effects of stimulation. We propose that such a system can be modelled by nonlinear networks ('neural networks'). The radial basis function network (RBF) has two advantages over the better-known multi-layer perceptron (MLP). We describe the use of an RBF network to model rabbit muscle that is supramaximally stimulated at irregular inter-pulse intervals.

An implant for chronic selective stimulation of nerves.

An implantable stimulator system has been developed for nerve stimulation. The system is capable of stimulating selectively, either by fibre position, fibre size or by sending action potentials in one direction only, based on the use of nerve cuffs. The stimulator produces either quasi-trapezoidal current pulses, to allow anodal blocking, or conventional rectangular-shaped current pulses, of amplitude 20 microA to 5 mA (in 20 microA steps) with duration of 16 micros to 1 ms (in 8 micros steps). For safety, both active and passive charge balancing is used. The amplitude of the active charge-balancing phase can be varied between 1/7 and 1/47 of the pulse amplitude. During manufacture, each implant is customised so as to drive either 6 quasi-tripolar (dipolar), 4 tripolar or 2 pentapolar cuffs. Possible applications of the device are: improved defaecation and bladder voiding after spinal cord injury, by stimulation of the sacral motor roots; neuromodulation to reduce hyperreflexia without concomitant muscle contractions; in stroke patients, to enable balanced inversion-eversion while dorsiflexing the ankle by stimulating the peroneal nerve. It may also be used in chronic animal experiments.This paper describes the implant system, its hardware and communication protocol, and shows results from in vitro tests of the device and the first acute anodal-blocking experiments in pigs.