This thesis considers how to reliably estimate the causal conditional directed information, which describes the flow of information between different sources, and it is computed with estimators based on the k-nearest neighbors due to their enhanced performance in high dimensions compared to other types of estimators. Both well-known estimators and a new and better estimator are derived, which are tested on both synthetic data and actual EEG data. The hypothesis is that the occipital and frontal areas of the brain are known to have a stronger connectivity when the eyes are closed compared to when they are opened. Therefore, the causal conditional directed information is computed between these areas of the brain when the eyes are both opened and closed, and the differences between these computations are then assessed. The results show that there are only minor differences when the eyes are closed compared to when they are opened, and further studies are required.