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Development of a mathematical model for predicting electrically elicited quadriceps femoris muscle forces during isovelocity knee joint motion.

  • Author(s): Perumal, Ramu;
  • Wexler, Anthony S;
  • Binder-Macleod, Stuart A
  • et al.


Direct electrical activation of skeletal muscles of patients with upper motor neuron lesions can restore functional movements, such as standing or walking. Because responses to electrical stimulation are highly nonlinear and time varying, accurate control of muscles to produce functional movements is very difficult. Accurate and predictive mathematical models can facilitate the design of stimulation patterns and control strategies that will produce the desired force and motion. In the present study, we build upon our previous isometric model to capture the effects of constant angular velocity on the forces produced during electrically elicited concentric contractions of healthy human quadriceps femoris muscle. Modelling the isovelocity condition is important because it will enable us to understand how our model behaves under the relatively simple condition of constant velocity and will enable us to better understand the interactions of muscle length, limb velocity, and stimulation pattern on the force produced by the muscle.


An additional term was introduced into our previous isometric model to predict the force responses during constant velocity limb motion. Ten healthy subjects were recruited for the study. Using a KinCom dynamometer, isometric and isovelocity force data were collected from the human quadriceps femoris muscle in response to a wide range of stimulation frequencies and patterns. % error, linear regression trend lines, and paired t-tests were used to test how well the model predicted the experimental forces. In addition, sensitivity analysis was performed using Fourier Amplitude Sensitivity Test to obtain a measure of the sensitivity of our model's output to changes in model parameters.


Percentage RMS errors between modelled and experimental forces determined for each subject at each stimulation pattern and velocity showed that the errors were in general less than 20%. The coefficients of determination between the measured and predicted forces show that the model accounted for approximately 86% and approximately 85% of the variances in the measured force-time integrals and peak forces, respectively.


The range of predictive abilities of the isovelocity model in response to changes in muscle length, velocity, and stimulation frequency for each individual make it ideal for dynamic applications like FES cycling.

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