An Assessment of Six Muscle Spindle Models for Predicting Sensory Information during Human Wrist Movements

The muscle spindle is an important sensory organ for proprioceptive information, yet there have been few attempts to use Shannon information theory to quantify the capacity of human muscle spindles to encode sensory input.

Computer simulations linked kinematics, to biomechanics, to six muscle spindle models that generated predictions of firing rate. The predicted firing rates were compared to firing rates of human muscle spindles recorded during a step-tracking (center-out) task to validate their use. The models were then used to predict firing rates during random movements with statistical properties matched to the ergonomics of human wrist movements. The data were analyzed for entropy and mutual information.

Three of the six models produced predictions that approximated the firing rate of human spindles during the step-tracking task. For simulated random movements these models predicted mean rates of 16.0 ± 4.1 imp/s (mean ± SD), peak firing rates <50 imp/s and zero firing rate during an average of 25% of the movement. The average entropy of the neural response was 4.1 ± 0.3 bits and is an estimate of the maximum information that could be carried by muscles spindles during ecologically valid movements. The information about tendon displacement preserved in the neural response was 0.10 ± 0.05 bits per symbol; whereas 1.25 ± 0.30 bits per symbol of velocity input were preserved in the neural response of the spindle models.

Muscle spindle models, originally based on cat experiments, have predictive value for modeling responses of human muscle spindles with minimal parameter optimization. These models predict more than 10-fold more velocity over length information encoding during ecologically valid movements. These results establish theoretical parameters for developing neuroprostheses for proprioceptive function.