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Traumatic brain injury (TBI) is the leading cause of death and disability in children and adolescents in the U.S. This is a pilot study, which explores the discrimination of chronic TBI from normal controls using scalp EEG during a memory task. Tsallis entropies are computed for responses during an old-new memory recognition task. A support vector machine model is constructed to discriminate between normal and moderate/severe TBI individuals using Tsallis entropies as features. Numerical analyses of 30 records (15 normal and 15 TBI) show a maximum discrimination accuracy of 93% (p-value = 7.8557E-5) using four features. These results suggest the potential of scalp EEG as an efficacious method for noninvasive diagnosis of TBI.