MODELING OF MUSCLES WITH CONSIDERATIONS OF NEUROMUSCULAR COMPARTMENTS

Abstract

The aim of this thesis is to examine and model muscles with neuromuscular compartments with applications to functional electrical stimulation, FES. Functional electrical stimulation is a technique of electrically stimulating paralysed muscles to obtain useful function. In this thesis, experimental animal models using the long head of triceps in rabbits (for a cheaper alternative) and the forearm muscles of the macaca (monkey) (for closer correlation to the human) were studied. The long head of triceps in rabbits was found to consist of three neuromuscular compartments, each compartment with different volumes and muscle type contribution. Similarly the forearm muscles of the monkey (macaca) were implicated to consist of neuromuscular compartments on the basis of the number of motor points to each muscle. An intelligent functional electrical stimulator was designed and developed into its second generation. The first generation stimulator had four stimulation channels supported by a few external chips including four DAC's, three Timers and an SK RAM. The second-generation stimulator was designed so that eight stimulation channels were available. The hardware implementation was simplified with a) pulse-amplitude modulation removed (hence no DAC's), b) timing being driven by software (hence no external timers) and c) the software written in assembly rather than C language (hence no external RAM). The stimulators were designed for both modelling and control of single muscle. It has the flexibility to meet various experimental needs using multichannel analogue input, electrical biphasic output options and possible modifications for clinical applications. The static muscle models were investigated and were represented as a sigmoid function, an off-linear-saturated model and a three-linear-segment model. The three-linear-segment model gave the least sum-square-error, i.e. error between the model prediction and actual force output, of the three. The sum-square error of the off-linear-saturated model is slightly greater than that of the three-linear-segment model, but the former is less complex and thus more suitable. A phenomenon known a "segmental contraction" was observed, i.e. when the proximal motor point is stimulated a contraction was observed at the proximal segment of the muscle, however, an elongation or passive stretching of the muscle occurs at the distal segment. Based on these observations, a modified static Hill model for muscles with two or more neuromuscular compartments was proposed. Furthermore, it was shown that the knowledge of neuromuscular compartments can potentially be used to reduce fatigue. Various dynamic models of single motor point stimulation were developed. These includes a) a 2nd order model derived from inspection of step responses, b) 2nd and 3rd order models using recursive identification techniques and c) fuzzy models using recursive identification techniques. Second order models from inspection of a step response are crude and should only be used when accuracy is not critical. The errors of the 2nd and 3rd order models derived from recursive identification techniques were not significantly different. This is consistent with the reported literature. Fuzzy models of muscles have also been developed and they had a better least sum-square-error compared with the earlier models studied. Furthermore, both static and dynamic characteristics of the muscle can be obtained from this scheme.