Assessing statistical significance of phase synchronization index - An application to study baroreflex function in critically-ill infants

Phase differences of two signals in perfect synchrony exhibit a narrow band distribution, whereas the phase differences of two asynchronous signals exhibit uniform distribution. We assess the statistical significance of the phase synchronization between two signals by using a signed rank test to compare the distribution of their phase differences to the theoretically expected uniform distribution for two asynchronous signals. Using numerical simulation of a second order autoregressive (AR2) process, we show that the proposed approach correctly identifies the coupling between the AR2 process and the driving white noise. We also identify the optimal p-value that distinguishes coupled scenarios from uncoupled ones. To identify the limiting cases, we study the phase synchronization between two independent white noises as a function of bandwidth of the filter in a different second simulation. We identify the frequency bandwidth below which the proposed approach fails and suggest using a data-driven approach for those scenarios. Finally, we demonstrate the application of this approach to study the coupling between beat-to-beat cardiac intervals and continuous blood pressure obtained from critically-ill infants to characterize the baroreflex function.