Hello, my name is Arnaud Delorme, and this is a video about trying to find the best EEG
reference.
This subject has been debated for several decades now, and it still is.
However, in some circumstances, we know what the best reference is.
So first, what is an EEG reference?
When we measure any electrical potential, and that includes EEG, we measure the potential
of one electrode compared to another one.
So, for example, we measure the potential of E2 with respect to E1.
In EEG, you can also measure the potential of several electrodes, here from E2 to E5,
with respect to a common reference E1.
The reference location can be anywhere.
Usually, you want to pick a location where there is almost no brain signal.
This is why people use the nose or earlobes.
However, sometimes, we also use references on the scalp, such as Cz at the vertex or
mastoid electrodes.
In this case, you can only compare your data to experiments using the same reference unless
you re-reference the data offline.
And we will see how to do that.
So let's assume we're recording channels CZ and T7 we respect to reference on TP10, which
is the right mastoid behind the ear.
Channel 1 is the potential of Cz minus TP10, and channel 2 is the potential of T7 minus
TP10.
Imagine we want to compare with another study that used Cz as a reference.
Even though we did not use Cz, we can use simple math to compute the potential of T7
and TP10 as if we used Cz as a reference.
For the first channel, it is easy.
We can just compute the opposite: so instead of Cz minus TP10, we have TP10 minus Cz.
We take the opposite, as shown here.
To get Cz minus TP10, we can simply subtract the signal from the first channel to the second
channel.
As you see here, TP10 cancels out, and we now have the potential of T7 with reference
to Cz.
That's relatively simple, but often you will see the reference as linked ears or linked
mastoid.
How do we do that?
You can't record the data with two reference channels, so you record the signal with one
reference and calculate the linked reference offline.
Now let's say we have Channel 1 is FZ minus ear1, and Channel 2 is ear2 minus ear1.
Instead of ear1 as the reference, we want the reference to be the average of ear1 and
ear2.
This is what linked earlobe reference is.
To do that, we can just compute channel 1 minus channel 2 divided by two.
We will call these channels: channels 1prime and 2prime.
Channel 1 prime is equal to this, which simplifies to Fz minus the average of the two ear channels.
Channel 2 prime is equal to the ear2 minus the linked ears.
And we can compute channel 3 prime equals to minus channel 2 minus channel 2 divided
by 2 to obtain ear1 minus the linked ears.
This was for linked ears, but if we had mastoid references, we could do the same for linked
mastoids.
Then we have other types of reference, which are usually used for epilepsy.
These are bipolar references, meaning that electrodes are referenced in a daisy chain.
Electrode A is referenced B, B is referenced to C, C is referenced to D, etc.
The first bipolar montage is called double banana because, as you see here, it looks
like two bananas.
The arrows indicate the reference.
This is used by clinicians in epilepsy: when they look at the data referenced in this way,
they can get the approximate location of the epileptogenic source.
They sometimes also use another bipolar montage, the circumferential montage, to get a better
idea of the approximate source location.
These montages are not used in EEG research, though.
In EEG research, we used the average reference: it is also called CAR, C, A, R, for common
average reference.
The average reference comes from the fact that if you have electrical current sources
inside the head, the net current potential on a 3-D spherical surface that represents
the head is 0.
As an approximation, we consider that the net potential across the scalp is 0.
However, there are two potential issues with average reference.
First, recent work has proven that, even if it is true for spheres, this is not the case
for other geometries, like the ones we used to model the brain, skull, and scalp.
Second, even if it was true, we usually do not have a uniform distribution of electrodes
on the head surface.
We rarely have electrodes on the face, for example, and we do not have electrodes inside
the neck.
Yet, average reference is still the most widely used reference, so let's see how we compute
it.
We cannot collect EEG data with an average reference.
Instead, we collect EEG data with a common reference -- and it can be any type of reference
-- and then we transform the reference.
The average reference assumption is that the sum of the potential of all the channels is
zero.
Let's say we sum the activity of all the 64 channels recorded with reference TP10.
Then this sum is equal to the sum of the potential of all channels minus 64 times the reference.
Now, here comes the trick.
With the average reference assumption, the sum of all channel potential is 0.
It turns out that, under the average reference assumption, the potential of the common reference
TP10 is equal to minus the sum of all channels divided by 64.
If we want the potential of one channel, for example, F10, we can just add back the calculated
TP10 potential.
Now we have the potential of F10 under the average reference assumption.
And we can do that for all channels, of course.
Two minor points here.
First, the potential of TP10 with a common TP10 reference is 0 at all times.
However, we can include it in the average reference.
In this case, TP10 is minus the sum of all channels divided by 65 instead of 64.
Typically, we would include a scalp channel in the reference, but not a non-scalp channel
like linked ears or nose.
Second minor point, what if you remove bad channels?
Then the average reference is biased.
In this case, in EEGLAB, we allow people to temporarily interpolate bad channels for computing
the reference.
Another type of reference is called the Infinity reference and is allegedly the least biased
method.
It was designed by Yao in 2001 and has become popular over the past two decades.
The method is based on the reasonable assumption that you do not want brain potential to affect
the reference signal.
So you can place the reference very, very far away.
Even with the nose or earlobes, you are capturing brain activity.
And, of course, it makes little sense to use a reference that would not be on the body
of the subject because it would be sensitive to all kinds of noise.
But in theory, a noise-free reference far from the subject, if possible at an infinite
distance, would be ideal.
How do we compute it?
Imagine two sources X1 and X2 that project onto the scalp, where we record the potential
V1, V2, and V3.
Then, based on Maxwell's equations, you have a linear transformation matrix.
Here is an example of transformation.
V1 equals 0.34 X1 plus 0.23 X2 and V2 and V3 are a different linear combination of X1
and X2.
If we write this in matrix format, this is how it would look like, and this is the summary
notation when we represent capital V as the vector V1, V2 V3, and capital X as the vector
X1 and X2.
This is only for two sources, but usually, matrix G is calculated for a couple of thousand
sources, for example, 2000 sources for standard Loreta.
Matrix G is also called the Leadfield matrix.
To calculate this matrix, we do not need to know the reference.
Instead, we can use a bunch of math that considers the head's geometry and the conductance of
each tissue.
The calculation assumes an ideal reference not affected brain sources, in other words,
an infinity reference.
Now here comes the trick.
Using simple math not shown here, I can calculate Gaverage from G, which is the Leadfield matrix
assuming an average reference.
Then by combining the two equations, I can compute V, the potential with an infinite
reference, using Vaverage, the potential of the electrode with average reference, G and
Gaverage.
And this is not specific to average reference.
I could do the same for a mastoid reference.
I could compute Gmastoid, and derive the potential at infinity in a similar way.
Now, this solution is not perfect.
One issue is that it depends on the accuracy of your head model, as outlined in this paper.
You also have other reference-free techniques, and I want to briefly mention here ICA, independent
component analysis, which EEGLAB pioneered.
ICA component activities are reference-free.
In fact, if you run ICA in EEGLAB, then re-reference the data, the ICA scalp topography will change,
but the component activity will not.
Now, let's look at what the EEG data looks like when using different references.
In this plot, we have ERPs associated with face photographs.
We can see that the ERP waveform is different based on the reference, for example, on the
Nose channel how different the ERP looks based on the reference.
For electrode P04 you can see that the N170, which is an ERP at about 170 ms post-stimulus
specific to faces, is present for the nose and average references but is greatly reduced
in amplitude for the mastoid reference.
This other article shows the scalp topography of alpha power for different references.
We can see that both the amplitude and the topography look different based on the reference.
Finally, here we have another typical ERP, called event-related negativity or ERN for
short, comparing the ERP of correct responses versus errors in a discrimination task.
The ERN is measured between 200 and 400 ms post-response.
Here we see the mean and standard deviation for the correct in red and errors in blue.
Note that this is part of a large linear model with many variables.
It makes sense that changing the reference would influence the statistics at one channel.
This is because the difference between conditions might be more prominent on some channels than
on others.
However, is there a reference that is better than all others?
This is what we tried to test.
We use EEG data from an auditory oddball task, so imagine beep, beep, boop, beep, and the
task of the subject is to press a button on the boops only.
Here is how it sounds.
The beep sounds are frequent and called standards, the boops are rare and called oddballs.
In this kind of oddball task, we usually observe a difference between the ERPs of oddball and
standard.
Here we looked at all the channels and saw that in between 400 and 500 ms, about 50%
of the channels were significant, although that varied across subjects, as shown by the
red-shaded area.
The rationale for using the percentage of significant channels is that, even if an effect
is localized in one brain area, because of volume conduction, it will be visible on most
channels.
Here we have a brain source, and its potential is visible on most channels.
Our main question was: if we change the reference?
Does that change the percentage of significant channels?
Here you see the general pipeline.
For each subject, we preprocess the data differently -- in this case, changing the reference -- then
we extract standard and oddball trials and count the number of significant channels.
To be able to create confidence intervals, we actually select randomly 50 oddball and
50 standard trials repetitively.
This is indicated here by "bootstrap."
We do that for each subject, and this is plotted here.
Each dot is a subject, and the ordinate represents the difference in significance compared to
the raw signal after high-pass filtering at 0.5 Hz.
In this case, the hardware reference is the Internal CMS/DRL Biosemi reference.
So the two points here at -50 indicate two subjects for which the percentage of significant
channels decreases by 50 when you use a mastoid reference.
This could be due, for example, to extreme noise in one of the mastoid channels.
On top of these dots, we also show the mean and the standard error.
Now let's look at other references.
This is a special experiment because the data was recorded with many different types of
reference, including nose and earlobes, to check for the effect of re-referencing.
We have, in order from left to right, linked mastoids, linked earlobes, nose, electrode
Cz, the robust referencing method in the PREP pipeline, two average references computed
using EEGLAB or Fieldtrip, the median, the REST infinity reference, and the longitudinal
and circumferential bipolar montage.
The surprising fact, as you can see, is that these are significantly below 0.
The standard error does not overlap with 0, so a paired t-test would be significant.
The nose reference is the worst and shows extreme changes compared to the hardware reference.
This was known before.
Now, you may think that this result is specific to this experimental setup.
We have also tried two other experiments.
In this one, participants saw photographs, one at a time, and pressed a button whenever
they saw an animal.
This is shown here.
When we looked at the ERP, we picked the range 250 to 350 ms as the one where the difference
between animal and distractor trials had the highest number of significant channels.
Again we tried different references and found that none of them increased the number of
significant channels, and most of them decreased it significantly.
Here the amplifier reference was Cz.
Finally, this is a popular face categorization dataset available online.
In this one, we compared familiar faces vs. scrambled faces, as shown here.
The maximum number of significant channels was in the 250 to 350 ms time range.
We found that none of the references increased the number of significant channels.
This experiment used a Nose reference.
The take-home message is that, in terms of reducing the noise in the data, not referencing
the signal is probably best.
So in this table, I show, to the best of my knowledge, the current consensus on what type
of reference to use in different circumstances.
For computing significance, you might want to use the hardware reference.
If you do, you can compute a significance mask and use it on a version of the data with
the reference of your choice.
If you use a reference when computing significance, know that whichever reference you use probably
does not make much difference.
For showing scalp topographies, you should use the reference that other people have used
in the past in similar experiments, so results can be compared.
In general, this will be an average reference.
For source localization, you should use the average reference or the infinity reference.
There is consensus that the infinity reference is superior to the average reference, although
it will certainly take time before it is more widely used.
Finally, I want to mention the reference to use when running ICA.
The best reference is unclear.
What is important is that the data is full rank meaning that no channel is linearly dependent
on other channels.
Once you have run ICA, you can then re-reference the data, and ICA components will be re-referenced
as well, at least in EEGLAB.
That's it for this video.
Thank you for your attention, and I hope to see you in one of my future videos.