SIMULATION AND PARAMETERS-IDENTIFICATION METHODS OF HETEROGENEOUS ABNORMAL NEUROLOGICAL MOVEMENTS IN MULTICOMPONENT NEURO-BIOSYSTEMS WITH COGNITIVE FEEDBACK

Abstract

The foundations of mathematical modeling and identification of parameters of heterogeneous abnormal neurological movements (ANM) in multicomponent neuro-biosystems with cognitive feedback have been developed. Based on the methods of integral transformations and spectral analysis developed by the authors for heterogeneous media, a new approach to the construction of hybrid models of wave signal propagation is proposed that describes unwanted tremors of the patient's arm (T-object) as a result of an unconstrained contraction of skeletal muscles due to the cognitive effects of a certain group of neural nodes in the cortex cerebral (CC). A hybrid model of a neuro-biosystem is developed, which describes the state and behavior, namely, the segment-by-segment description of 3D elements of the ANM trajectories of the T-object, taking into account the matrix of cognitive influences of the groups of neuro nodes of the CC. On the basis of hybrid integral Fourier transforms a high-speed analytical vector solution of the model is obtained, which describes the elements of the trajectories on each AND-segment. A new method for calculating of hybrid spectral function, spectral values and matrix of cognitive influences of CC neuronodes is proposed, which determine hybrid integral transformation of solution construction. New non-classical problems of multi-parameter identification of neuro-feedback systems in heterogeneous media based on minimization of the residual functional between observation trajectories and their model analogs are formulated and solved. High-performance algorithms of the amplitude-frequency characteristics identifying of a feedback-system in analytical expressions for the gradients of the residual functional have been constructed, which allow parallel-computations on multicore computers. Computer modeling and identification of ANM trajectories of the studied neuro-feedback-system have been performed.