An investigation of stretch reflex in physiological tremor

This paper describes a theoretical consideration on muscle stretch reflex in physiological tremor (abbreviated as tremor). In making a model, the function of rostro-caudal homonymous motoneurone pool as well as the interaction between spinal cord mechanism and supraspinal system is investigated. The known physiology of the neuromuscular oscillations is used to evaluate the responses of a set of differential equation that represents lumped system dynamics underlying the stretch reflex process of tremor. According to the model, the stretch reflex along with the mechanics of limb is behaving as a filter. With sharp resonant peaks and without the need of any external inputs, the filter selects oscillators and sustains tremulous movement. These reflex features, especially the findings of an existence of two sharp resonant centers, are particular valuable in an explanation of the two spectral peaks observed in tremor. It is demonstrated that (1) the two peaks of tremor, which vibrate at 10 Hz and 20 Hz, largely depend on the coupling lambda between spinal and supraspinal system, i.e., lambda leads to "spontaneous symmetry breaking" producing a peak doubling; (2) the two peaks are attributable to two decoupled states found in our model. The pea with 10 Hz is attributed to the state Z+ (t) describing an average state of spinal+supraspinal system, while the one with 20 Hz denotes the state Z-(t) which presents a relative movement of spinal and supraspinal system. With regarding to the nature of tremor under various conditions such as loading, fatigue, and pseudo-gravity, this paper discusses the possible connections of lambda to these experimental environments. Also, this paper argues that representation of stretch reflex by the decoupled states is more essential than other traditional representations used in approaching to tremor phenomena.