5.9: Exercise- Global Field Power

Last updated
Save as PDF

Page ID: 108170

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

Another useful reference-free transformation is mean global field power. If you have a reasonable number and spread of electrodes, any given ERP component will produce a systematic gradient in the amplitude across electrode sites that is proportional to the amplitude of the internal generator. For example, Screenshot 5.4 (which I generated with the Viewer in the Measurement Tool) overlays all 28 scalp electrodes for the unrelated-minus-related difference wave in the N400 experiment (referenced to the average of P9 and P10). The spread of voltage values across electrode sites is proportional to the amplitude of the N400. We can quantify this spread by taking the standard deviation across sites at any given time point. This standard deviation is called the global field power or GFP. Because the reference electrode contributes equally to each channel, it is effectively a constant and has no impact on the GFP.

coOjQI6zMf4DUK2IKr3VeiM25oKeTSLurfCOC46UkFHJGs3qjnRyYLqjYoNzW0S3vh-DHTn_gwmXbK9IgO0lBz-mLMOBocfEcKd08TAUOChb9AYMYS1nm_OFSyYs6A — Screenshot 5.4

Let’s compute the GFP for the data in the N400 data. Load Grand_N400_diff.erp into ERPLAB if it’s not already loaded, and make sure that it’s the active ERPset. Select EEGLAB > ERPLAB > ERP Operations > ERP Channel Operations, clear out any equations that remain in the text box from the last time you used this routine, and change the Mode to Modify existing ERPset. We’re going to create a new channel (channel 31) with the GFP for the EEG channels (channels 1–28). To do this, put the following equation in the ERP Channel Operations text box:

ch31 = mgfperp(1:28) label GFP

Now click RUN, and then plot the data from Bin 5. At the bottom of the plot, you should see a channel labeled GFP (see Screenshot 5.5). This waveform is the standard deviation across channels 1–28 at each time point, and you can see that the time course matches the time course of the difference wave at the other electrode sites. However, when we look at the GFP, we no longer have to worry about that pesky reference electrode issue.

GFP has some other virtues as well. For example, it is typically cleaner than the individual-channel waveforms (because noise is typically minimized by transformations that combine the data from multiple sites). In addition, rather than having to choose which electrode site or sites to use in your statistical analyses (which can be a source of bias), you can just measure the amplitude or latency from the GFP waveform (Hamburger & Van der Burgt, 1991). However, you should keep in mind that the standard deviation across channels will increase as the noise level increases, so special methods are necessary to compare GFP amplitudes across conditions that differ in the number of trials or any other factor that might impact the noise level (Files et al., 2016).