Closed-loop control of muscle length through motor unit recruitment in load-moving conditions

Abstract

Neuroprostheses aimed at restoring lost movement in the limbs of spinal cord injured individuals are being developed in this laboratory. As part of this program, we have designed a digital proportional-integral-derivative controller integrated with a stimulation system which effects recruitment of motor units according to the size principle. This system is intended to control muscle length while shortening against fixed loads. Feline sciatic nerves were exposed and stimulated with ramp, triangular, sinusoidal, staircase and random signals as test inputs. Changes in muscle length and effective time delay under different conditions were measured and analyzed. Differences of tracking quality between open- and closed-loop conditions were examined through analysis of variance as well as the differences between small (250 g) and large (1 kg) loads. The results showed that parameters used to compare muscle length output to the input signals were dramatically improved in the closed-loop trials as compared to the open-loop condition. Mean squared correlation coefficients between input and output signals for ramp signals increased by 0.019, and for triangular signals by 0.12. Mean peak cross correlation between input and output signals for sinusoidal waveforms increased by 0.06, with decreases in time to peak cross correlation (effective time delay) from 195 to 38 ms. In slow random signals (power up to 0.5 Hz), peak cross correlation went from 0.74 to 0.89, and time-to-peak cross correlation decreased from 205 to 55 ms. In fast random signals (power up to 1 Hz), peak cross correlation went from 0.82 to 0.89, and time-to-peak cross correlation from 200 to 65 ms. For staircase signals, both rise times and mean steady-state errors decreased. It was found that, once the length range was set, the load weight had no effect on tracking performance. Analysis of mean square error demonstrated that for all signals tested, the feedback decreased the tracking error significantly, whereas, again, load had no effect. The results suggest that tracking is vastly improved by using a closed-loop system to control muscle length, and that load does not affect the quality of signal tracking as measured by standard control system analysis methods.