Modeling and estimating the model adequacy in muscle tissue electrical stimulator designing

The research object is the mathematical modeling of human skeletal muscle electrical stimulation characteristics during therapy. The subject of research is mathematical models of electrical stimulation characteristics that relate muscle contraction amplitude to the amplitude, the rate of stimulating effects, and other parameters. The research purpose is to study such models, develop an algorithm for their correction and a method for estimating their adequacy. The methods used: mathematical modeling methods, methods of structural and parametric identification of models, optimization methods, methods for estimating the adequacy of models, and interval methods. The results: an algorithm for muscle electrical stimulation characteristics mathematical models correcting during several sessions in case of their change is proposed; a method for estimating the model adequacy area in the external variables space in order to control its adequacy is proposed; using the interval mathematics methods to construct the adequacy actual area is justified; an interval estimating of the error in modeling a certain output characteristic is introduced, that, in the case of characteristic monotonicity, allows checking the adequacy maintaining by checking some inequalities. The results can be used in the design of electrical stimulators and for determining the electrical stimulation effects of individual parameters during one session or a series of sessions. The scientific originality: the interval mathematics methods for approximating the mathematical model adequacy area in a hyperparallepiped and checking for nesting in the target area in the external parameters space in order to control the adequacy during the model correction in electrical stimulation is proposed and justified.