Neurofeedback training is increasingly used for ADHD treatment. However some ADHD patients are not treated through the long-time neurofeedback trainings with common protocols. In this paper a new graph theoretical approach is presented for EEG-based prediction of ADHD patients' responses to a common neurofeedback training: rewarding SMR activity (12-15 Hz) with inhibiting theta activity (4-8 Hz) and beta2 activity (18-25 Hz). Eyes closed EEGs of two groups before and after neurofeedback training were studied: ADHD patients with (15 children) and without (15 children) positive response to neurofeedback training. Employing a recent method to measure synchronization, fuzzy synchronization likelihood, functional connectivity graphs of the patients' brains were constructed in the full-band EEGs and 6 common EEG sub-bands produced by wavelet decomposition. Then, efficiencies of the brain networks in synchronizability and high speed information transmission were computed based on mean path length of the graphs, before and after neurofeedback training. The results were analyzed by ANOVA and showed synchronizability of the neocortex activity network at beta band in ADHDs with positive response is obviously less than that of ADHDs resistant to neurofeedback therapy, before treatment. The accuracy of linear discriminant analysis (LDA) in distinguishing these patients based on this feature is so high (84.2%) that this feature can be considered as reliable characteristics for prediction of responses of ADHDs to the neurofeedback trainings. Also difference between flexibility of the neocortex in beta band before and after treatment is obviously larger in the ADHDs with positive response in comparison to those with negative response which may be a neurophysiologic reason for dissatisfaction of the last group to the neurofeedback therapy.
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