A mixed effects model framework for the assessment of nonlinear interactions in event-related potentials (ERPs) elicited by identical successive stimuli

The recording of brain event-related potentials (ERPs) is a widely used technique to investigate the neural basis of sensory perception and cognitive processing in humans. A commonly used assumption, when dealing with potentially overlapping ERPs elicited by successive stimuli with interstimulus interval (ISI) smaller than the latency of the ERPs, is that their interaction is linear. These overlaps are usually dealt by using averaged waveforms, mostly to enhance the signal-to-noise ratio (SNR) and performing algebraic waveform subtractions. In this paper, we examine the hypothesis of linear interactions by providing a statistical framework that examines the presence of nonlinear additive effects between overlapping ERPs elicited by successive stimuli with short ISIs. The statistical analysis is designed for single trial rather than averaged waveforms. The results suggest that there are no nonlinear additive effects due to the time overlap per se but that, for the range of ISIs examined, the second ERP is modulated by the presence of the first stimulus irrespective of whether there is time overlap or not. In other words, two ERPs that overlap in time can still be written as an addition of two ERPs, with the second ERP being different to the first. The modulation effect on the second ERP by the first stimulus varies for different ISIs.