Analysing event-related potentials Waveform analysis

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passive paradigms, which is an advantage in populations that may be difficult to engage in cognitive tasks. Second, because of their high temporal resolution, neurophysiological measures can be used to study the information flow from sensory to association brain regions, and to determine the stage at which information processing is impaired.

4.1.1 Assessing event-related potentials

Event-related potentials are positive or negative voltage fluctuations that are time locked to an external stimulus. These potentials can be recorded non-invasively from the human scalp and calculated from the ongoing EEG by means of stimulus-locked signal averaging. The main assumption behind averaging is that the brain signal is time and phase locked to the stimulus, while noise and unrelated signals are randomly distributed and vary between epochs, and thus increasing the number of trials used for averaging increases the signal to noise ratio [119].

Furthermore, simultaneous recording from multi-channel locations is crucial to measure different components in the ERP and to disentangle overlapping components or artifacts based on topographies. Although the optimal number of channels is not clear, the use of high-density electrode arrays may provide the proper geometry on the surface to cover the different orientations of intracerebral generators [235].

Historically, the most used ERP paradigm is the oddball paradigm applied to study sensory discrimination and prediction error, as well as memory and language in healthy and clinical population, with more than 2000 publications following search words “oddball paradigm” on PubMed.

Although ERPs can be evaluated in both frequency, time and spatial domains, this thesis focuses on the last two domains, meaning on the ERPs as waveforms and topographies that plot the voltage fluctuations as a function of time. Two analysis methods are described, one based on multiple channel waveforms, focusing on amplitude and latencies of the peaks, and a second one based on the spatial reconstruction of the electric field, focusing on topographic maps.

4.1.2 Analysing event-related potentials Waveform analysis

The high temporal resolution of electrophysiological recordings offers the opportunity to study the brain electrical activity preceding and following a stimulus, millisecond by millisecond, meaning the waveform analyses focus on how the components vary over time across experimental conditions or across groups.

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A prevailing approach includes the analysis of amplitude and latency of ERP components based on specific hypotheses which usually needs a prior selection of time periods and components of interest based on prior research.

The amplitude quantification results from the averaging process and considers two main assumption: the signal invariance across the averaged epochs (meaning the amplitude happened at the same time in the constituent epochs) and the effect amplitude invariance (meaning that the amplitude strength generated by the underlying sources is equal across the averaged epochs) [119, 128]. However, as it is impossible to fully meet these assumptions, when amplitude differences are observed across conditions or groups, possible peak variation and jitter of amplitude across epochs must be considered to correctly interpret amplitude changes [119].

The ERP latency measurement is also quantified through the averaging process. Typically, the latency changes or differences across conditions/groups are interpreted as the time when divergent brain responses can be measured. However, the onset of latency changes seen in the waveform may not be identical with the onset of changes in the neural activity [128].

The potential field at the scalp level is measured as a difference between an “active” electrode and a “reference” electrode. So, changing the reference will change the morphology of the waveforms, the variance around the ERP and further the statistical results [235]. More, a voltage fluctuation at the reference electrode will influence the active electrodes, even if the potential at their site is stable and thus one main pitfall of analyzing ERP waveforms is the reference-dependence [235, 237].

However, although the reference position is a choice and thus a potential source of bias introduced by the experimenter, most of the experiments either rely on the reference selections proposed by prior studies in order to compare the analyzed waveforms and the results interpretation, or compute the average reference offline, which means a ‘‘re-centering’’ of electrode values to a common average reference.

Additionally, to overcome the reference limitation, the topographic analysis of the potential field is required.

Topographic analysis and field strength

The electrical activity is recorded at the electrode level as a two-dimensional voltage array made of two variables, time and space. The spatial distribution of the electric fields at the scalp level can be seen as a potential field map with two characteristics: its topography, the shape and its global field power, the strength [234].

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The topographic representation is a reference independent method mapping different orientations of the active cluster of neurons at a given moment in time, and thus topographical differences allow to detect different neuronal configuration across time between experimental or clinical conditions [234, 235, 237].

The measures used to quantify the topographic analyses are: Global Field Power (GFP) and Global Map Dissimilarity (GMD) [238].

The GFP is a single measure that quantifies the field strength and is mathematically defined as the standard deviation of the average-referenced electrode values at a given time point.

Moreover, high GFP peaks can be interpreted as high signal to noise ratio and high response strength [235, 238].

This measure is calculated using the following formula: where n is the number of electrodes, v the voltage measured at electrode i and is the mean potential across electrodes [238].

The GMD indexes a single measure of shape configuration dissimilarities between two electric fields at a given point in time [235, 238] and is equivalent to the spatial Pearson`s product-moment correlation coefficient between the potentials of the 2 maps to be compared [235]. The GMD measure is calculated using the following formula:

where 𝑢𝑖 is the voltage of map 𝑢 at the electrode 𝑖, 𝑣𝑖 is the voltage of map 𝑣 at the electrode 𝑖, 𝑢 is the average voltage of all electrodes of map 𝑢, 𝑣 is the average voltage of all electrodes of map 𝑣, and 𝑁 is the total number of electrodes [238].

Map dissimilarities are statistically assessed using a topographical bootstrapping approach: the topographic analysis of variance (TANOVA) that requires a non-parametric randomization approach and not an analysis of variance as might be misconceived from the name of the analysis [234, 235, 238].

Topographic mapping of the ERP is often preceding the source localization and is crucial to conduct a proper analysis and interpretation of topography before attempting to define the underlying brain sources [236].

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Figure 9. Analysis pipeline for auditory evoked responses: starting from the continuous EEG recording by averaging process the ERPs time locked to the auditory external stimulus. The voltage is measured across the scalp, and the value of every electrode is represented in a color-coded manner from positive (red) to negative (blue) values.

In conclusion ERPs may provide insights into sensory and cognitive processing in healthy and clinical population by analysing neuronal activities of cortical and subcortical brain areas at the scalp level with millisecond resolution, and thus providing real-time imaging of the brain temporal dynamics.

4.2 Assessing cortical and subcortical gray matter volumes with Structural