Modulation index-based phase-amplitude coupling does not encode temporal polarity

Abstract

Phase-amplitude coupling (PAC) is widely used to quantify interactions between neural oscillations across timescales and is often interpreted as reflecting temporally meaningful coordination between slow and fast neural activity. Combining empirical EEG data with mathematical analysis, we show that the modulation index (MI), a widely used PAC metric, remains unchanged when the phase of the low-frequency oscillation is inverted by 180{degrees}. By contrast, preferred phase rotates by exactly 180{degrees}, as expected. Thus, opposite temporal organisations of cross-frequency coupling can yield identical MI values. This finding defines a fundamental interpretational limit of MI-based PAC: MI quantifies the strength of phase-dependent amplitude modulation, but not its temporal polarity. Accordingly, MI alone cannot distinguish between temporally aligned and temporally inverted coupling configurations or support inferences about temporal alignment, phase polarity, or directionality. Because PAC is widely used across neuroscience, these results establish an important boundary on what one of the fields most common cross-frequency coupling measures can validly reveal about neural coordination.