CARLA: Adjusted common average referencing for cortico-cortical evoked potential data

Human brain connectivity can be mapped by single pulse electrical stimulation during intracranial EEG measurements. The raw cortico-cortical evoked potentials (CCEP) are often contaminated by noise. Common average referencing (CAR) removes common noise and preserves response shapes but can introduce bias from responsive channels. We address this issue with an adjusted, adaptive CAR algorithm termed "CAR by Least Anticorrelation (CARLA)". CARLA was tested on simulated CCEP data and real CCEP data collected from four human participants. In CARLA, the channels are ordered by increasing mean cross-trial covariance, and iteratively added to the common average until anticorrelation between any single channel and all re-referenced channels reaches a minimum, as a measure of shared noise. We simulated CCEP data with true responses in 0-45 of 50 total channels. We quantified CARLA's error and found that it erroneously included 0 (median) truly responsive channels in the common average with ≤42 responsive channels, and erroneously excluded ≤2.5 (median) unresponsive channels at all responsiveness levels. On real CCEP data, signal quality was quantified with the mean R² between all pairs of channels, which represents inter-channel dependency and is low for well-referenced data. CARLA re-referencing produced significantly lower mean R² than standard CAR, CAR using a fixed bottom quartile of channels by covariance, and no re-referencing. CARLA minimizes bias in re-referenced CCEP data by adaptively selecting the optimal subset of non-responsive channels. It showed high specificity and sensitivity on simulated CCEP data and lowered inter-channel dependency compared to CAR on real CCEP data.