Effects of motoneuron properties on reflex stability in spastic subjects: a simulation study

The influence of motoneuron pool properties on the stability of the stretch reflex at the ankle in subjects with spinal cord injury was tested using a comprehensive model of the reflex pathway. This model included the passive and active components of the triceps surae muscles, muscle spindles, neural transport delays, limb mechanical properties, and a lumped parameter model of the motoneuron pool input-output relationship. Simulations show that as the motoneuron firing threshold was reduced (reflecting increased excitability of spinal motoneurons), normal reflex responses became unstable and oscillations developed similar to those observed in spastic patients. In parallel, when reflex delay times typical for triceps surae in man were chosen, and motoneuron excitability increased progressively, oscillatory ankle movements were readily elicited. Conversely, as pathway delays were reduced, reflex stability increased, as :the oscillatory behavior usually damped out. Decreases in motoneuron pool synaptic gain had a stabilizing effect on the reflex response, as low motoneuron gains tended to eliminate oscillatory behavior. Using an Absolute Stability Analysis, we found that reflex pathways containing long neural transport delays and muscles with slow dynamics tended to place the largest stability constraints on the motoneuron pool. These findings support the hypothesis that unstable oscillatory behavior, such as the oscillations observed in clonus, will occur when the motoneuron excitability increases in a reflex pathway containing long delays.