# Reference electrode in lead field

Dr. Burkhard Maess maess at CBS.MPG.DE
Tue Sep 29 09:09:16 CEST 2009

Dear Mark,

concerning the average reference. ...
You are right the voltage is defined as difference of potentials. Therefore one always needs a reference point, but there is no need for a physical existence of a reference point  as long as a mathematical definition exists.
Classical unipolar electrodes provide voltage signals like e.g. :

(1) U_i_ref = V_i - V_ref

The average reference is computed as the mean signal over all N electrodes:

(2) U_avref = \frac{1}{N} \sum{i=1}^{N}U_i_ref

You can rewrite this using expression (1)

(3) U_avref = \frac{1}{N}\sum{i=1}^{N}V_i - V_ref = mean(V_i) - V_ref

One can see that the reference point for the average reference is the same as for all single electrodes.
Now, we rerefence all electrodes to the average reference:

(4) U_i_avref = U_i_ref - U_avref = V_i - V_ref - mean(V_i) - V_ref

The simplified expression does not contain the original V_ref!

(5) U_i_avref = V_i - mean(V_i)

Introducing the average reference is loss free as long as you store the mean average signal. Otherwise some data is lost because the V_ref signals vanishes from the expressions.
Why to transform to average reference? As you said the lead field is dependent on the location of the reference electrode. Introducing the average reference means to become less dependent on the location of a single (reference) electrode.

All the best,
Burkhard

Dr. Burkhard Maess
Max Planck Institute for Human Cognitive and Brain Sciences
Stephanstr. 1a, P.O. Box 500355, D-04303 Leipzig
Aussenstelle Bennewitz, phone/fax: +49(3425)8875-2526/-2511   mail: maess 'at' cbs.mpg.de,           http://www.cbs.mpg.de

----- Original Message -----
From: "Mark Drakesmith" <mark.drakesmith at POSTGRAD.MANCHESTER.AC.UK>
To: FIELDTRIP at NIC.SURFNET.NL
Sent: Monday, September 28, 2009 9:29:08 PM GMT +01:00 Amsterdam / Berlin / Bern / Rome / Stockholm / Vienna
Subject: [FIELDTRIP] Reference electrode in lead field

Hi all

I am experimenting with source reconstruction and was wondering how a
reference electrode is defined in the lead field. Looking through the
scripts it looks like the average reference is used, but this is a
physical impossibility, as there must be a physical reference to which
differences in electrical potential can be measured. The lead field will
be differ depending on the location of the reference electrode.

Firstly, is there a way to specify a reference electrode when
constructing an EEG lead field in fieldtri p and not jsut use the
average reference.

Secondly, looking through  the code for 'inf_medium_leadfield' (called
equations used for calculating the lead field look a little strange:

radius = position (vox) - position(elec)
R (resistivity?) = 4 x pi x conductivity x sum(radius^2)^(1.5)

Where the the exponential to 1.5 come from? Is there a reference to
somewhere where this method is used. I'm confused as to sure how this
calculation works.

Many thanks

Mark

--

Mark Drakesmith
PhD Student

Neuroscience and Aphasia Research Unit (NARU)
University of Manchester

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The aim of this list is to facilitate the discussion between users of the FieldTrip  toolbox, to share experiences and to discuss new ideas for MEG and EEG analysis. See also http://listserv.surfnet.nl/archives/fieldtrip.html and http://www.ru.nl/neuroimaging/fieldtrip.

----------------------------------
The aim of this list is to facilitate the discussion between users of the FieldTrip  toolbox, to share experiences and to discuss new ideas for MEG and EEG analysis. See also http://listserv.surfnet.nl/archives/fieldtrip.html and http://www.ru.nl/neuroimaging/fieldtrip.