Weighted average of shared trajectory: A new estimator for dynamic functional connectivity efficiently estimates both rapid and slow changes over time

Background: Dynamic functional network connectivity (dFNC) of the brain has attracted considerable attention recently. Many approaches have been suggested to study dFNC with sliding window Pearson correlation (SWPC) being the most well-known. SWPC needs a relatively large sample size to reach a robust estimation but using large window sizes prevents us to detect rapid changes in dFNC. New method: Here we first calculate the gradients of each time series pair and use the magnitude of these gradients to calculate weighted average of shared trajectory (WAST) as a new estimator for dFNC. Results: Using WAST to compare healthy control and schizophrenia patients using a large dataset, we show disconnectivity between different regions associated with schizophrenia. In addition, WAST results reveals patients with schizophrenia stay longer in a connectivity state with negative connectivity between motor and sensory regions than do healthy controls. Comparison with existing methods: We compare WAST with SWPC and multiplication of temporal derivatives (MTD) using different simulation scenarios. We show that WAST enables us to detect very rapid changes in dFNC (undetected by SWPC) while MTD performance is generally lower. Conclusions: As large window sizes are unable to detect short states, using shorter window size is desirable if the estimator is robust enough. We provide evidence that WAST requires fewer samples (compared to SWPC) to reach a robust estimation. As a result, we were able to identify rapidly varying dFNC patterns undetected by SWPC while still being able to robustly estimate slower dFNC patterns.