Knowledge about the specificity of changes in the activity of neural networks associated with realization of thought processes can be used to construct the personalized medical rehabilitation systems. This approach is of particular interest for people with the speech function disturbance due to stroke, since the development of aphasia with the loss of speech leads to severe social maladaptation that worsens the disease outcome. The study was aimed to assess the functional activity of individual neural networks based on the theory of combining the EEG microstate identification technique with the method of determining spatial localization by solving the EEG inverse problem in 27 individuals (15 males and 12 females) with an average age of 52 years, who had speech impairment due to acute atherothrombotic stroke. Mathematical analysis of the scalp bioelectrical activity multichannel recording from the system for EEG microstate model isolation was carried out under changing environmental conditions caused by the auditory-speech load together with the EEG inverse problem solution for each subject. It was found that the speech disorder development depends not only on the fact of damage to brain structures, but also on the deep functional restructuring of both neural streams involved in implementation of brain function and the entire speech connectome. The disease with a predominant motor disorder, that has shown the possibility of transferring functions to the intact hemisphere prefrontal structures, in contrast to sensory disorders representing global changes in the entire speech connectome, can probably be considered the most favorable variant of aphasia.