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Limit cycle behavior in spasticity: analysis and evaluation.

J M Hidler¹, W Z Rymer

¹Department of Biomedical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208, USA.

IEEE Transactions on Bio-Medical Engineering

|December 28, 2000

Summary

Ankle clonus in spastic subjects exhibits properties of a stable limit cycle. This oscillatory behavior is driven by peripheral sensory input, not a spinal generator, suggesting a robust reflex pathway.

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Area of Science:

Neuroscience
Biophysics
Systems Biology

Background:

Ankle clonus is an involuntary oscillatory movement observed in spasticity.
Its underlying mechanisms, whether peripheral or central, remain debated.

Purpose of the Study:

To determine if ankle clonus exhibits limit cycle properties.
To investigate whether clonus is driven by peripheral sensory input or a spinal generator.

Main Methods:

Analysis of ankle clonus in four spastic subjects.
Application of Floquet Theory and Poincare sections to assess reflex stability.
Simulation of the ankle stretch reflex response.

Main Results:

Clonus demonstrated low cycle-to-cycle variability with Floquet multipliers less than unity.

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The periodic orbit was independent of initial ankle position.

Load size correlated with movement and electromyogram burst frequency.

Simulations indicated delays in the reflex pathway sustain oscillations with minimal reflex torque.

Conclusions:

Ankle clonus behaves as a locally stable limit cycle.
The behavior is driven by peripheral receptors, not a central spinal generator.
Passive mechanics and pathway delays contribute to the robustness of the spastic ankle oscillation.