In this tutorial review, we detail both the rationale for as well as the implementation of a set of analyses of surface-recorded event-related potentials (ERPs) that uses the reference-free spatial (i.e. topographic) information available from high-density electrode montages to render statistical information concerning modulations in response strength, latency, and topography both between and within experimental conditions. In these and other ways these topographic analysis methods allow the experimenter to glean additional information and neurophysiologic interpretability beyond what is available from canonical waveform analyses. In this tutorial we present the example of somatosensory evoked potentials (SEPs) in response to stimulation of each hand to illustrate these points. For each step of these analyses, we provide the reader with both a conceptual and mathematical description of how the analysis is carried out, what it yields, and how to interpret its statistical outcome. We show that these topographic analysis methods are intuitive and easy-to-use approaches that can remove much of the guesswork often confronting ERP researchers and also assist in identifying the information contained within highdensity ERP datasets.

This paper describes methods to analyze the brain's electric fields recorded with multichannel Electroencephalogram (EEG) and demonstrates their implementation in the software CARTOOL. It focuses on the analysis of the spatial properties of these fields and on quantitative assessment of changes of field topographies across time, experimental conditions, or populations. Topographic analyses are advantageous because they are reference independents and thus render statistically unambiguous results. Neurophysiologically, differences in topography directly indicate changes in the configuration of the active neuronal sources in the brain. We describe global measures of field strength and field similarities, temporal segmentation based on topographic variations, topographic analysis in the frequency domain, topographic statistical analysis, and source imaging based on distributed inverse solutions. All analysis methods are implemented in a freely available academic software package called CARTOOL. Besides providing these analysis tools, CARTOOL is particularly designed to visualize the data and the analysis results using 3-dimensional display routines that allow rapid manipulation and animation of 3D images. CARTOOL therefore is a helpful tool for researchers as well as for clinicians to interpret multichannel EEG and evoked potentials in a global, comprehensive, and unambiguous way.

Using electroencephalography (EEG) to elucidate the spontaneous activation of brain resting-state networks (RSNs) is nontrivial as the signal of interest is of low amplitude and it is difficult to distinguish the underlying neural sources. Using the principles of electric field topographical analysis, it is possible to estimate the meta-stable states of the brain (i.e., the resting-state topographies, so-called microstates). We estimated seven resting-state topographies explaining the EEG data set with k-means clustering (N = 164, 256 electrodes). Using a method specifically designed to localize the sources of broadband EEG scalp topographies by matching sensor and source space temporal patterns, we demonstrated that we can estimate the EEG RSNs reliably by measuring the reproducibility of our findings. After subtracting their mean from the seven EEG RSNs, we identified seven state-specific networks. The mean map includes regions known to be densely anatomically and functionally connected (superior frontal, superior parietal, insula, and anterior cingulate cortices). While the mean map can be interpreted as a "router," crosslinking multiple functional networks, the seven state-specific RSNs partly resemble and extend previous functional magnetic resonance imaging-based networks estimated as the hemodynamic correlates of four canonical EEG microstates.