Modeling the Step-like Response in the Upper Limbs of Hemiplegic Subjects for Evaluation of Spasticity

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The purpose of this study is to develop a new modeling technique for quantitative evaluation of spasticity in the upper limbs of hemiplegic patients. Each subject lay on a bed, and his forearm was supported with a jig to measure the elbow joint angle. The subject was instructed to relax and not to resist the step-like load which was applied to extend the elbow joint. The elbow joint angle and electromyogram (EMG) of the biceps muscle, triceps muscle and brachioradialis muscle were measured. First, the step-like response was approximated with a proposed mathematical model based on musculoskeletal and physiological characteristics by the least square method. The proposed model involved an elastic component depending on both muscle activities and elbow joint angle. The responses were approximated well with the proposed model. Next, the torque generated by the elastic component was estimated. The normalized elastic torque was approximated with a dumped sinusoid by the least square method. The reciprocal of the time constant and the natural frequency of the normalized elastic torque were calculated and they varied depending on the grades of the modified Ashworth scale of the subjects. It was suggested that the proposed modeling technique would provide a good quantitative index of spasticity as shown in the relationship between the reciprocal of the time constant and the natural frequency.

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