eeg_positions

When recording electroencephalography (EEG) data, electrodes are usually placed according to an international standard. The 10-20, and by extension the 10-10 and 10-05 systems are established sets of rules for this case [1]. Even when the actual electrode locations have not been empirically measured during the recording, an approximation of these positions is important for for plotting topographies or visualizing locations of sensors with the help of analysis software.

While standard locations are available in many places such as from Robert Oostenveld's blog or directly from electrode cap manufacturers such as Easycap, it is seldom specified how these electrode locations are calculated.

This repository contains code to compute the standard EEG electrode locations in 3D for the 10-20, 10-10, or even 10-05 system. There are also utility functions to project the 3D locations to 2D space and plot them.

Cite

If you find this repository useful and want to cite it in your work, please go to the Zenodo record and obtain the appropriate citation from the "Cite as" section there.

At a glance

• The electrode locations are computed on a geometrical sphere centered on the origin and with radius 1 (arbitrary units).
• The function uses an algorithm to compute positions at fractions along contour lines defined by three points: See the find_point_at_fraction function in the eeg_positions/utils.py file.

How to work with it

• git clone the repository (or download as .zip and unpack)
• cd eeg_positions
• Using your python environment of choice, install the package and its dependencies locally using pip install -e .
• Run the tests using pytest --doctest-modules (you might have to pip install pytest first)
• Calculate and plot electrodes by calling python eeg_positions/calc_positions.py
• Check out contour_labels.py for the order how electrodes are computed
• ... and see utils.py for the find_point_at_fraction function that is the core of the computations.

References

• [1] Oostenveld, R., & Praamstra, P. (2001). The five percent electrode system for high-resolution EEG and ERP measurements. Clinical neurophysiology, 112(4), 713-719. doi: 10.1016/S1388-2457(00)00527-7

Acknowledgements

My thanks to:

• Robert Oostenveld for writing his blog post on electrodes
• Ed Williams for the helpful correspondence and discussions about "intermediate points on a great circle" (see his aviation formulary)
• "N. Bach" and "Nominal Animal" who helped me to figure out the math for the find_point_at_fraction function (see this math.stackexchange.com post)

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Examples

Read the data into MNE-Python

• NOTE: Please download the 3D 10-05 data from here and save as standard_1005.tsv.

import mne
import numpy as np
import pandas as pd


# we saved this file before ...
fname = 'standard_1005.tsv'

# Now read it
df = pd.read_csv(fname, sep="\t")

# Turn data into montage
ch_pos = df.set_index("label").to_dict("index")
for key, val in ch_pos.items():
    ch_pos[key] = np.asarray(list(val.values()))

data = mne.utils.Bunch(
    nasion=ch_pos["Nz"],
    lpa=ch_pos["T9"],
    rpa=ch_pos["T10"],
    ch_pos=ch_pos,
    coord_frame="unknown",
    hsp=None,
    hpi=None,
)

montage = mne.channels.make_dig_montage(**data)

# plot it
montage.plot()

Interactively viewing 3D coordinates

reproduce by running python eeg_positions/calc_positions.py

Projections to 2D

reproduce by running python eeg_positions/calc_positions.py

10-20 system

10-10 system

10-05 system

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Details

Coordinate System Conventions

3D Axes and Cartesian Coordinate System

• Imagine the x-axis pointing roughly towards the viewer with increasing values
• The y-axis is orthogonal to the x-axis, pointing to the right of the viewer with increasing values
• The z-axis is orthogonal to the xy-plane and pointing vertically up with increasing values

Relationship of Coordinate System to a Human Head

For simplicity, we assume a spherical head shape of a human. Roughly speaking, the x-axis goes from the left ear through the right ear, the y-axis goes orthogonally to that from the inion through the nasion, and the z-axis goes orthogonally to that plane through the vertex of the scalp.

We use the following anatomical landmarks to define the boundaries of the sphere:

Cartesian Coordinates

• The left preauricular point = (-1, 0, 0) ... coincides with T9
• The right preauricular point = (1, 0, 0) ... coincides with T10
• The nasion = (0, 1, 0) ... coincides with Nz
• The inion = (0, -1, 0) ... coincides with Iz
• The vertex = (0, 0, 1) ... coincides with Cz

Hence, the equator of the sphere goes through T9, T10, Nz and Iz.

Note that these are ASSUMPTIONS. It would be equally valid to assume the equator going through T7, T8, Fpz, and Oz.

EEG Electrode Position Data

You can also just download the pre-computed electrode positions in tab-separated data format.

3D

• standard_1020
• standard_1010
• standard_1005

2D via a stereographic projection from 3D

• standard_1020
• standard_1010
• standard_1005