Direct modulation index: A measure of phase amplitude coupling for neurophysiology data.

Neural communication across different spatial and temporal scales is a topic of great interest in clinical and basic science. Phase-amplitude coupling (PAC) has attracted particular interest due to its functional role in a wide range of cognitive and motor functions. Here, we introduce a novel measure termed the direct modulation index (dMI). Based on the classical modulation index, dMI provides an estimate of PAC that is (1) bound to an absolute interval between 0 and +1, (2) resistant against noise, and (3) reliable even for small amounts of data. To highlight the properties of this newly-proposed measure, we evaluated dMI by comparing it to the classical modulation index, mean vector length, and phase-locking value using simulated data. We ascertained that dMI provides a more accurate estimate of PAC than the existing methods and that is resilient to varying noise levels and signal lengths. As such, dMI permits a reliable investigation of PAC, which may reveal insights crucial to our understanding of functional brain architecture in key contexts such as behaviour and cognition. A Python toolbox that implements dMI and other measures of PAC is freely available at https://github.com/neurophysiological-analysis/FiNN.