Isometric muscle contraction induced by repetitive peripheral magnetic stimulation (RPMS)—Modeling and identification

Repetitive peripheral magnetic stimulation (RPMS) is an innovative approach in treatment of central paresis, e.g. after stroke. In this article we present a neuromuscular model for the RPMS-induced isometric muscle contraction. This model is the basis for our two recent goals in research: improvement and assessment of the RPMS therapy by means of position controlled induction of functional movements and with automated system identification based therapy evaluation. In order to adapt the model parameters to the individual a nonlinear on-line system identification method is proposed. Physiological systems may be complex and detailed so that in many cases macroscopic models of the dominant characteristics are built. Therefore, mathematical descriptions of these models and respective parameter identification methods have to cope with uncertainties. This paper presents a separable nonlinear regression model of Hammerstein structures that maximizes the possibility of incorporation of a priori knowledge and is still flexible to structural uncertainties. A robust on-line identification method based on the Levenberg–Marquardt algorithm is presented that works in a reduced parameter space, due to the separability of the model equation.