Characterization of Spastic Ankle Flexors Based on Viscoelastic Modeling for Accurate Diagnosis

Quantitative Modeling of Spasticity for Clinical Assessment, Treatment and Rehabilitation

“…The obtained measures may allow understanding of some aspects of the neurophysiology of spasticity, and could potentially be applied to the development of treatments. For example, Shin et al [ 69 ] arrived at optimized parameters μ which represents the muscle spindle firing rate at 50% motor neuron recruitment, and σ as the standard deviation of the Gaussian cumulative distribution that represents the function of the alpha motor neuron pool. A lower μ means a lower minimum spindle firing rate which indicates hyper-reflexia in the muscle [ 90 ].…”

“…To model the neural and physical components of spasticity, several studies have designed theoretical controllers that include the musculoskeletal geometry, musculotendon dynamics, muscle spindle, motor neuron pool and subsequent muscle activations. The theoretical controllers receive the measured kinematics as inputs to estimate the force [ 68 ] or torque [ 34 , 69 , 70 , 71 ] generated by the muscles (due to reflex) for a given passive movement. The controller parameters consist of neural and non-neural parameters (e.g., muscle spindle firing rate, passive viscoelasticity, etc.)…”

“…and are optimized to fit to the measured data. The estimated force or torque is generally represented as a sum of the effects of inertial, gravitational, and active muscle forces [ 69 ]: where is the measured torque, represents the torque from the moment of inertias, is the torque generated by gravity, and is the muscle torque consisting of a passive and active element, as in the following equation [ 69 ]: …”

“…The passive torque is characterizable beforehand by a slow, passive movement (e.g., joint angle speed of 15 deg/s), which minimizes muscle activation, leaving only the passive parameters to be identified by fitting the measured torque-angle curve [ 69 ]: where is the moment arm about the joint, is the muscle length, the coefficient of the elastic exponential curve, the rate of change of the curve slope, the viscosity coefficient, and the elastic curve shape parameter. The active torque generated by the muscle was calculated based on the Hill-type muscle model, such as in [ 69 ]: where the relation between moment and rate of change of muscle length, the relation between moment and muscle length, and is the muscle activation function, which includes the muscle spindle and motor neuron pool models.…”

“… Example of system identification algorithm used by Shin et al [ 69 ] for parameters characterizing the spastic reflexes, using muscle spindle, motor neuron pool, muscle activation dynamics, and musculoskeletal models to estimate the activate muscle torque generated by the spastic muscle during reflex. …”