Neural L19 - 22

What is EEG?

EEG measurement

EEG measurement
Typical signal

EEG measurement
EEG can be measured from

EEG measurement
The electrodes must be

EEG waveforms: Normal Awake

EEG waveforms: Standardising
EEG is so varied that it defies standardisation. However, some common frequency ranges have been defined for reference:

Artefact
Other sources contribute to the EEG measurement. This is known as artefact.

Uses of EEG

Currents exist in the brain because of

Electric fields of the brain

The flow of ions into and out of neurons generate charge differences in the CSF that cause currents that can be measured by the EEG.
Cell membranes are highly resistive and currents within the cell DO NOT contribute to the EEG.

Electric fields of the brain

Electric fields in the brain are caused by

Single Charges

Single Charges
Electric potential (voltage) is related to electric field as

Many charges
The total electric potential generated by many charges is dictated by the principle of superposition, that is, the sum
of all charges.

When there are only two charges, known as a dipole, this equation simplifies to

Because the measurement of EEG is far from the sources, a volume containing many charges can be

Equivalent Current Dipoles
For equivalent electric dipoles we still need to know a rough
distribution of all charges in the brain. This is difficult!

MACROSCOPIC PITENTIALS
(HOMOGENOUS MEDIUM)

G ( rS , rR ) is known as the

Macroscopic Potentials
(Inhomogeneous medium)
The human head is NOT
homogeneous.

Simplifications
Parallel dipoles generate potentials much larger than dipoles that are randomly oriented.
If you have N parallel dipoles, you need N^2
randomly oriented ones to generate the same field.

Simplifications
In the brain, the neurons in the cortex are aligned and often large areas are activated together.

Simplifications
Resulting model of EEG measurement

Synchronicity
Synchronous dipoles, that is, dipoles activated in unison, generate potentials much larger than dipoles that asynchronous.
If you have N synchronously active dipoles, you need N2 asynchronous ones to generate the same field.

Macroscopic EEG
Using this model, simulations show that the measured voltages are affected by large areas of cortex.
Nearby dipoles affect the EEG more than far away ones.

Macroscopic EEG
In reality all recordings are bipolar. Larger areas are involved.

Even before re-referencing, voltages are measured between two points. The reference electrode normally used is on top of the head.

MACROSCOPIC EEG
Because large areas affect the EEG, a large measurement of EEG can be equally generated by

SUMMARY
• The EEG is a measurement of the average activity of a relatively large area of cortex that contains up to billions of neurons.
• The EEG usually contains artefact, which can be caused by many different sources.
• The EEG is very useful in the diagnosis, treatment, and research of disorders such as epilepsy.

Meso-scopic Models
modelling the brain
Simplifications are required:

The Cortical Column

Phenomenological Models
Phenomenology:

Pyramidal neurons

A cortical column is modelled as

A Model of a Column
Even this rather simple system is very difficult to analyse. The complications are:

Analysis of the column Model

Linearise the Model
Linearisation is
Linear systems are much easier to analyse.

OPERATING POINT

The linearised model is a good

The linearised model
Transfer function, Input and Output.

The linearised Model
The overall system transfer function is:

Analysing Stability
We can use the linear system transfer function to analyse stability.
This is done by finding the poles of the system.

Examples of systems shows stability

Examples of systems shows stability

Analysing Stability
The system can be reduced to a three co-ordinate system:

Analysing Stability
Using the three co-ordinate system, the boundaries of stability can be found.

Analysing Stability

The behaviour of the model can be analysed by studying how parameters affect the simulated EEG and comparing to experimentally recorded EEGs.

Hebbian learning is a rule where a synapse is strengthened if pre- and postsynaptic neurons are

Spike-Timing Dependent Plasticity
(STDP)

STDP Learning Rule