THE USE OF NONPARAMETRIC METHODS OF STATIONARY POINT PROCESSES IN THE STUDY OF COMPLEX INTERACTIONS IN THE NEUROMUSCULAR SYSTEM

Abstract

In this paper we study the complex interactions involved in the incoming stimulus, from a gamma (γ) and/or an alpha (α) motoneuron, and the outgoing response from the muscle spindle transmitted by the Ia sensory afferent neuron to the spinal cord. The most interesting case is the γ and α coactivation to the function of the muscle spindle, while the effect from a single (γ or α) motoneuron is also presented as a comparison. The mathematical background of this analysis is based on the theory of stationary point processes. A kernel type method of estimating second- and third-order conditional densities is used. Under certain conditions the asymptotic distributions of these estimates are Normal and the construction of 95% approximate confidence intervals is feasible. The application of these asymptotic results to the system of the muscle spindle enables us to detect and interpret its excitatory and/or inhibitory behavior.