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Gait is a complex process involving both cognitive and sensory ability and is strongly impacted by the environment. In this thesis, we propose the study of the impact on cognitive task during gait on the cerebral blood flow velocity through a dual task methodology. Both cerebral blood flow velocity and gait characteristics of eleven participants with no history of brain or gait conditions were recorded using transcranial Doppler on mid-cerebral artery and a treadmill. The cognitive task was induced by a backward counting starting from 10,000 with decrement of 7. Central blood flow velocity raw and envelope features were extracted in both time, frequency and time-scale domain along with information-theoretic metrics were extracted, and statistical significances. A similar feature extraction was performed on the stride interval signal. Statistical differences between the cognitive and baseline trials, between the left and right mid-cerebral arteries signals and the impact of the anthropometric variables where studied using linear mixed models. No statistical differences were found between the left and right mid-cerebral arteries flows or the baseline and cognitive state gait features, while statistical differences for specific features were measured between cognitive and baseline states. These statistical differences found between the baseline and cognitive states show that cognitive process has an impact on the cerebral activity during walking. The state was found to have an impact on the correlation between the gait and blood flow features.