Fwd: [FIELDTRIP] Reference electrode in lead field

[Robert Oostenveld]

Dear Georges,

Thanks for raising this very good point.

As discussed before, the choise of the reference is quite irrelevant
for most analysis that involve a **linear transformation** of the
data, such as the computation and visualisation of the topography of
an ERP. But for non-linear transformations, the reference becomes
relevant.

Consider a simple statistics example. If you want to show a
significant effect in an auditory evoked potential (AEP) given a
standard and deviant tone, the optimal reference is the mastoid, which
maximizes the potential at Cz. So Cz minus M1, or Cz minus (M1+M2)/2,
i.e. linked ears, results in the largest signal on Cz. Subsequently
you compute the average ERP in both conditions and you compute the
variance from which you can compute the standard-error of the mean.
Then you compute the t-value, i.e. the difference in means  divided by
the pooled standard-error of the mean. That is all for the values
recorded in the Cz channel. Had you referenced Cz to the tip of the
nose, then the spatial topography of the AEPs and the spatial
topography of the AEP difference would not be qualitatively different
(only a difference in the color scale, but that color scale is
arbitarry chosen anyway). But the noise over trials in the Cz AEP
would probably be larger for the nose reference than for the linked
ears  reference. That noise is expressed in the variance, which is in
the denominator of the t-value. So the t-value would be less. The t-
value would become even smaller for a Fz reference.

Another example: if you compute spectral power using a FFT or warevelt
transform, the power is expressed as a squared number. At the
reference electrode the power is zero (per definition), whereas around
the reference electrode it would increase. Had I measured oscillatory
activity from auditory cotrex using a linked-ears reference, I would
see the maximum over the vertex, i.e. Cz. For a nose reference, the
maximum in power probably still would be over the vertex. But had I
choosen Cz itself as the reference, then at the vertex there would be
no power any more. Or less extreme, had I choosen Fz as reference,
then probably the power would _not_ be maximal over the vertex any
more, but rather along the lower electrode rim (T3/T4 a.k.a. C7/C8 and
the lower occipital electrodes). The spatial topography of the power
would also be qualitatively different for the different references.
You can think of it like "pushing the maximum in the power topography
around over the scalp" by changing the reference. In general, the
power will be largest further away from the reference and small close
to the reference. Of course the true power distrubution depends on the
underlying source activity, so this is a bit of a simplification.

In both examples above a non-linear transformation on the data is
involved. Offline rereferencing is a linear transformation of the
data, i.e. it only involves the addition and/or subtraction of some
value. The computations above (t-value, spectral power) are non-
linear, and they are non commutative (see http://en.wikipedia.org/wiki/Commutativity)
. In short (1+1)^2 is not equal to (1)^2+(1)^2.

The estimation of the phase from a signal is also a non-linear
transformation of the signal. After decomposing it into a sine and
cosine contribution at a specific frequency (with the FFT), the sine
and cosine contribution are combined to get the phasae (i.e. using the
arctangent, or using the complex-number representation). Everything
that is subsequently derived from the phase is therefore also non-
linear. So coherence and phase-locking values will be qualitatively
different depending on the choise of reference. One cannot simply
first compute coherence, and then afterwards apply a re-referencing.

Note that the estimation of the source strength of a dipole using any
source reconstruction technique (dipole fitting, beamforming, minimum
norm linear estimation) is a linear operation. It assumes a linear
mixing model (data = leadfield*source + noise) and a linear unmixing
model. In the estimate of the "unmixing matrix" for most techniques
there is a particular choise for dealing with the noise (i.e.
beamformer: try to suppress it, dipole fit: try to minimize the
squared error). Dealing with the noise and with the fact that the
linear system is either underdetermined or overdetermined causes a non-
linear effect. So there is some influence of the choise of reference
on the result of the source estimate, but in general not too much. If
you take a really extreme referencing scheme, i.e. all bipolar
electrodes over the scalp from the front to the back (a so-called
banana montage) which is more sensitive for superficial sources, then
the source reconstruction will be biassed for these superficial
contributions. For a linked mastoid reference, the source
reconstruction will be slightly biased for deep sources. For an
average reference, there is no specific bias to be expected. Overall,
the effect of the reference electrode will be quite small, and be the
least biassed for an avereage reference. Therefore, the average
reference is de facto the default in all source reconstruction
packages for EEG (commercial and non-commercial).

best regards,
Robert

PS for people who want to see these effects: you can use
DIPOLESIMULATION to generate simulated raw data with added noise, and
pass that through PREPROCESSING to re-reference to a reference of
choise. Subsequently you try the various  analysies discussed above,
i.e. TIMELOCKANALYSIS, TIMELOCKSTATISTICS, FREQANALYSIS and
SOURCEANALYSIS or DIPOLEFITTING.


On 2 Oct 2009, at 12:19, Robert Oostenveld wrote:

>> From: "Dr. Georges Otte" <georges.otte at telenet.be>
>>
>> ...
>> I have followed the discussion on reference and already contacted
>> Dien. I agree but what about non ERP data ? Phase information and
>> coherence. Can we safely use the averaged common reference for
>> that. Robert Thatcher (neuroguide) quoting rappelsberger is opoosed
>> to it and shows in his neuroguide package that in small channel
>> systems (19-22) a ACR scrambles phase information between channels.

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