Mathematical modeling of the mechanisms of locomotory pattern formation under epidural spinal cord stimulation with consideration of peripheral feedback

The mechanisms of nervous regulation of locomotory activity of the spinal cord and participation of afferent peripheral feedback from lower limb muscles in the formation of locomotory patterns were investigated. The set of electromyograms of lower-limb muscle groups recorded in experiments on mesencephalic cats with application of electric epidural stimulations of lumbar segments of the spinal cord is described by a nonlinear dynamic model constructed on the basis of the Van-der-Pol equation with the compelling member. The conditions of occurrence of the regime of self-oscillations were investigated depending on the parameters of external influence. A modified equation was proposed, which takes into account the role of the afferent feedback and delay between the beginning of stimulation and muscle reaction. The conformity of the mathematical model with experimental data was shown, which makes possible its use both for the description of the mechanism of locomotory pattern formation under epidural spinal cord stimulation and the choice of optimum stimulation conditions.