Data-driven approach to the estimation of connectivity and time delays in the coupling of interacting neuronal subsystems

One of the challenges in neuroscience is the detection of directionality between signals reflecting neural activity. To reveal the directionality of coupling and time delays between interacting multi-scale signals, we use a combination of a data-driven technique called empirical mode decomposition (EMD) and partial directed coherence (PDC) together with the instantaneous causality test (ICT). EMD is used to separate multiple processes associated with different frequency bands, while PDC and ICT allow to explore directionality and characteristic time delays, respectively. We computationally validate our approach for the cases of both stochastic and chaotic oscillatory systems with different types of coupling. Moreover, we apply our approach to the analysis of the connectivity in different frequency bands between local field potentials (LFPs) bilaterally recorded from the left and right of subthalamic nucleus (STN) in patients with Parkinson’s disease (PD). We reveal a bidirectional coupling between the left and right STN in the beta-band (10–30 Hz) for an akinetic PD patient and in the tremor band (3–5 Hz) for a tremor-dominant PD patient. We detect a short time delay, most probably reflecting the inter-hemispheric transmission time. Additionally, in both patients we observe a long time delay of approximately a mean period of the beta-band activity in the akinetic PD patient or the tremor band activity in the tremor-dominant PD patient. These long delays may emerge in subcortico-thalamic loops or longer pathways, comprising reflex loops, respectively. We show that the replacement of EMD by conventional bandpass filtering complicates the detection of directionality and leads to a spurious detection of time delays.