A planar computer model was developed to investigate paraplegic standing induced by functional neuromuscular stimulation. The model consists of musculotendon dynamics (pulse train activation dynamics and musculotendon actuator dynamics), body-segmental dynamics, and an output feedback control law.

The model of activation dynamics is an analytic expression that characterizes the relation between the stimulus parameters (pulse width and interpulse interval) and the muscle activation. Hill's classic two-element muscle model was modified into a musculotendon actuator model in order to account for the effects of activation change and the in-series tendon on force development of the musculotendon actuator. The body-segmental model accounts for the anterior-posterior movements of the body, and consists of head and trunk, thigh, and shank. Arm movement was modelled as an external disturbance and imposed to the body-segmental dynamics by means of a quasistatic analysis. Output feedback was employed to investigate how measurements affect the performance.

Linearization or linear approximation of the computer model enabled us to compute a constant feedback-gain matrix. The feedback control strategy computes joint-torque-actuator activations and distributes them to individual muscles based on energy minimization. Energy minimization was motivated by an assumption that minimization of energy expenditure lessens muscle fatigue.

Two types of body motion were simulated. First, the segmental orientations are initially perturbed from the vertical, and all muscles are assumed inactive at the initial position. Once the upright position is recovered, arm movement is then applied to the body to investigate how muscles act to overcome the external disturbance.

Simulated body motion indicated that the current output control law functions well so that the body can recover upright posture from up to 40° of initial perturbations in the segmental orientations, and maintain the body position within a small range from the vertical under external disturbances.

The simulation results showed three consistent activation patterns based on energy minimization;​ (i) no coactivation occurs between any antagonistic muscle pair, (ii) strong muscles should be recruited before weak ones, and (iii) fast muscles should be recruited before slow ones. The reason for the second and third observations is that energy liberation rate depends heavily on the relative amount of muscle activation. Thus, strong muscles do not have to be activated as much as weak ones. Since a specific torque is needed at a prescribed time in the current control law, recruiting a fast muscle at low activation level consumes less energy than recruiting a slow one at high activation level.

Though the output feedback control law functions well according to our simulation results, the static optimization process would, in practice, take too much computational time to make it practical. Based on the consistent activation patterns found in the simulations, I therefore developed a simpler (suboptimal) activation-distribution scheme that takes much less time and still gives nearly identical performance.