[Eeglablist] Signal/noise loss, re-referencing Biosemi data

[Lloyd Smith]

In response to Tom Ferree's post -- in brief, ActiveTwo stores a monopolar
signal (channel) for each active electrode.  One must subtract one channel
or the average of some number of channels (e.g. A1 & A2, or common average,
which is the average of all scalp channels) to compute a referenced EEG
signal.  Although you can display a referenced EEG signal in the ActiView
data acquisition software, the signal is never saved in a referenced format.
A reference subtration must be performed off-line.  The common mode
interference is reduced (signal/noise is increased) by the act of
subtracting an EEG reference.

Below is a more thorough discussion of how the ActiveTwo system measures
voltage and how the measurements are stored by Coen Metting Van Rijn of
BioSemi.

================

In greater detail, voltage is defined as the difference in electrical
potential between points (for example on the scalp).  In principle, you can
measure a voltage with two inputs and two electrodes.  This is what you do
when you use a meter to measure a battery voltage.  The problem with
semiconductor amplifiers (transistor inputs) is that you need a third
connection to archive a really high input impedance on the two inputs used
for the voltage measurement.  This third connection is the "ground"
electrode (for the technically interested: it provides the bias current for
the two high-impedance inputs).  The amplifier now takes two voltage
measurements: E1 with respect to GND, and E2 with respect to GND.  By
subtracting the two voltage readings, the amplifier "calculates" the voltage
between E1 and E2.  Both measurements with respect to GND are polluted with
inference, because of interference currents flowing through the GND
electrode. However, because this error signal is the same for both
measurements - it is Common Mode - it cancels in the reference subtraction
(common mode rejection).  

In the ActiveTwo system, instead of a simple GND electrode, an active
feedback circuit with two electrode is used: CMS and DRL.  This offers
better CMRR and subject safety than a simple passive GND electrode.
However, for easy understanding of the topic decribed now, you can regard
the CMS as equivalent of the conventional GND electrode, and forget about
the DRL. 

In general, the voltages E1-CMS and E2-CMS are large (polluted with common
mode interference), while the voltage E1-E2 is small (clean EEG).  In the
old days, analog EEG systems wrote EEG data directly to paper during
acquisition, so it was important to be able to reject line noise on-line.
Even in the beginning of the digital era, dynamic range remained very
limited because only 12 bits were available in the ADC.  In addition, mains
instead of battery power supply caused high levels of Common Mode
interference.  The combination of high CM and small dynamic range, forced
older EEG equipment to do the calculation to E1-E2 directly in the first
amplifier stage.  The method used was analog subtraction by an
instrumenation amplifier (differential amplifier with fixed gain, a clever
transistor circuit that amplifies only the voltage difference between two
inputs).  However, with increase of dynamic range of the electonic circuitry
(mainly by the introduction of 24 bit ADCs), and the introduction of battery
power supply, it became possible to process (amplify and digitize) the raw
voltages (E1-CMS and E2-CMS), and postpone the subtraction to the end of the
signal chain (with the advantages of a completely symmetric system setup,
increased stability, and the ability to reject also interference and errors
picked up after the input stage).  Thus, in the ActiveTwo we do the
subtraction in a digital way in the PC.  It is important to realize that
valid EEG signals only appear after the last subtraction step is made.  EEG
is hidden in the raw signals (the voltages with respect to CMS), but it is
still distorted and polluted with interference.  Only after the referencing
step do all errors cancel and a valid voltage measurement appears. 

Up to this point, we have talked about measuring one voltage between two
potentials.  In a typical EEG recording, many electrodes are used to
determine many potentials.  Consequently, there are many reference options: 

- Monopolar: select one of the electrodes as a reference, calculate the
voltage between every other electrode and the reference electrode (V1 =
E1-REF, V2 = E2-REF, etc.) 
- Bipolar: select pairs of electrodes (V1 = E1-E2, V2 = E2-E3, etc.) 
- Linked reference: Use the average of several potentials (electrodes) as a
reference. Calculate the the voltage of every electrode with respect to this
reference. For example, use the average between ears as a REF, thus REF =
(EA1+EA2/2), then V1 = E1 - (EA1+EA2/2), etc. 

In the old analog days, you only could use differential amplifiers to make
these subtractions.  A differential amplifier can only calculate the
difference between two inputs (the non-inverting and the inverting input).
This is OK for bipolar reference schemes, but with Monopolar and Linked
Reference schemes, accuracy and interference problems are inevitable.  In
the Monopolar case, the reference electrode has to drive many inputs of
differential amps, which causes a low input impedance for the reference
input.  In the Linked Reference case, resistors have to be used to calculate
the average potential, which means that the accuracy of the average
calculation (the weight factors) depends entirely on the equality of the
electrode impedances.  A last problem is that the reference scheme had to be
determined in hardware, by switches changing signal paths.  This introduced
unreliability, and meant that a file was always saved with a fixed reference
scheme -- it couldn't be changed afterwards. 

The digital reference calculation used in the ActiveTwo fully eliminates all
these problems: every electrode always sees a single amp input with
optimally high input impedance (the active electrode circuit), every
possible reference scheme can be chosen in software (no unreliable
switches), and every possible choice of reference scheme remains possible
off-line (raw signals are saved). 

================
Lloyd Smith
Owner
Cortech Solutions, LLC
 
Office: 910-362-1143
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E-mail: LSmith at cortechsolutions.com
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