Limit cycle behavior in spasticity: analysis and evaluation.

We examined ankle clonus in four spastic subjects to determine whether this oscillatory behavior has the properties of a limit cycle, and whether it is driven by peripheral sensory input or by a spinal generator. Using Floquet Theory and Poincare sections to assess reflex stability, we found that cycle-to-cycle variability was small, such that the Floquet multipliers were always less than unity. Furthermore, the steady-state periodic orbit was not dependent on the initial position of the ankle. Both of these findings, coupled with strong correlations between the size of the applied load and the frequency of ankle movements and electromyogram burst frequency suggests that clonus behaves as a locally stable limit cycle driven from peripheral receptors. To better understand how nonlinear elements might produce stable oscillatory motion, we simulated the ankle stretch reflex response. We found that delays in the pathway caused the reflex to come on during the shortening phase of movement, so the additional reflex torque required to sustain oscillatory ankle movements was quite small. Furthermore, because the resistance to stretch is largely due to passive mechanics whose properties are quite stationary, the system is robust to small perturbations within the reflex pathway.

A simulation study of reflex instability in spasticity: origins of clonus.

Clonus is defined as an involuntary rhythmic muscle contraction that generally occurs in people who have sustained lesions involving descending motor pathways in the neuraxis, and is usually accompanied by other signs of reflex hyperexcitability such as spasticity. This paper hypothesizes that clonus arises when two conditions occur simultaneously: 1) the reflex pathway contains long delay times (implying innervation of distal limb muscles, exacerbated when these muscles display slow twitch properties) and 2) the excitability of the motoneurons is enhanced. This paper tested this dual hypothesis by developing a computer model representing the ankle reflex pathway. This model included the ankle muscles, afferent and efferent pathways, and a monosynaptic spinal link between spindle afferents and motoneurons. Simulations show that as the motoneuron current 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 we choose reflex delay times typical for distal leg muscles in man, system stability is poor, and oscillations occur readily with increasing motoneuron excitability. As simulated pathway delays are reduced, oscillatory behavior is also reduced, and usually damps out. Conversely, as simulated reflex delays are increased, oscillations increase in amplitude and do not decay. Finally, these two phenomena interact, so that increasing motoneuron excitability will induce reflex oscillations for intermediate loop delays. 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. This change in excitability is mediated by a reduction in motoneuron firing threshold, rather than by an increase in feedback gain. Furthermore, we demonstrate that sustained oscillations occur readily through self reexcitation, which reduces the need to propose that a "central oscillator" must be involved in generating clonus.