Quantitative Evaluation of Spasticity in Upper Limbs in Hemiplegic Subject Using a Mathmatical Model

This is a proposal for a new technique for evaluating spasticity in the upper limbs of hemiplegic patients. Each subject sat on a chair or stood up, and his or her forearm was extended or flexed by a physician. The subject was instructed to relax. The elbow joint angle, torque, and electromyograms (EMGs) of the biceps brachii, triceps brachii, and brachioradialis muscles were measured. The relationship between the elbow joint angle and torque was approximated with a mathematical model, which consisted of elastic components depending on both muscle activities and elbow joint angle, by the least squares method. The inertia and visco-elastic coefficients were obtained. The elbow angle response was then estimated with the obtained inertia and visco-elastic coefficients by the Runge-Kutta method, and the estimated elbow angle was compared to the observed one. The relationships between the elbow angle and torque were approximated well with the model. Next, the average elasticity was calculated and compared to the modified Ashworth scale. The average elasticity had a tendency to increase as the Ashworth scale increased. In addition, the average elasticity varied depending on the posture of the subjects