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Neural L19 - 22
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- 1What is EEG?“an electrical recording of what is inside the head”
• Measures the time evolution of the electric potential (voltage) generated by the brain.
• Chemical currents generated in everyday brain function get translated to electrical measurements at different locations on the head. - 2EEG measurement- Measures time varying voltages (mV)
- Spatial distribution from multiple electrodes - 3EEG measurement• Typical filters:
– 0.15 Hz high pass
– 105 Hz low pass
• Typical digitisation
– 256/512 Hz sampling rate
– 14 bit A/D conversion
– 32-64 channels - 4EEG measurement EEG can be measured from• the scalp,
• intracranially on the cortex (subdural EEG), • deeper parts of the brain (depth EEG).
SCALP, CORTICAL, & DEPTH. - 5EEG measurement The electrodes must be- The electrodes used at each location must be of the appropriate size and materials.
- Intracranial electrodes must be bio-compatible.
- 6EEG waveforms: Normal AwakeAlpha rhythm:
- 8-12Hz rhythm observed in most people when they close their eyes.
- Occurs generally in posterior electrodes.
- Considered a sign of good mental health, although some perfectly healthy people have no alpha rhythm. - 7Alpha rhythm - Normal Awake
- 8Normal Asleep In sleep, there are generally slower EEG waveforms because the brain is in a less active/attentive state.
- 9EEG waveforms: Standardising EEG is so varied that it defies standardisation. However, some common frequency ranges have been defined for reference:– Delta: less than 3 Hz. Dominant rhythm in infants (< 1 year old) and in stages 3 and 4 of sleep
– Theta: 3.5 – 7.5 Hz. “Slow” activity
– Alpha: 7.5 – 13 Hz. Appears when closing the eyes and relaxing
– Beta: 14 – 20 Hz. “Fast” activity. Dominant rhythm when eyes are open
– Gamma: 20-100 Hz. “Faster” activity
- 10Artefact EEG is used to measure electrical potentials generated by the brain. However, other sources contribute to the measurement. This is known as artefact.Analysis must account for this unwanted interference.
- 11Uses of EEGThe EEG is a useful medical tool:
- Diagnosis: Helps with identifying a disorder.
- Treatment: Helps with ensuring that treatment is correctly administered.
- Research: Helps us investigate a wide variety of problems. - 12Generators of the EEG electrical potential results in the flow of electrons in a metal.In biology, charge is transmitted by ions.
Bioelectromagnetism describes the electric
potentials generated by chemical currents.
The same principles are used to describe both electromagnetism and bioelectromagetism - 13Currents exist in the brain because offlow that occurs:
- At the synapses
- At the cell body (start of action potential)
- At the axon (action potential transmission)
- In the extra-cellular body (CSF)
The extra-cellular currents are the most important for the EEG - 14Electric 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.
- 15Electric fields of the brain Electric fields in the brain are caused byChemical currents of charged ions.
Because of the movement of ions is slow, we can ignore magnetic effects and concentrate on electric phenomena.
Currents are caused by the attraction between charged particles, described by forces between them.
We start by looking at the electric fields generated by single charges. - 16Single ChargesThe electric field generated by a particle is described by
- 17—rR = an arbitrary position vector
ε0 = permittivity of free space
q = charge of the particle
r = unit vector pointing in the direction from source location rS to recording location rR
|| ||=magnitude of the vector rR – rS = R
Electric fields are measured in units of V/m
- 18Single Charges Electric potential (voltage) is related to electric field as
- 19Many charges The total electric potential generated by many charges is dictated by the principle of superposition, that is, the sum of all charges.
- 20When there are only two charges, known as a dipole, this equation simplifies to
- 21Because the measurement of EEG is far from the sources, a volume containing many charges can beapproximated by a single dipole, provided there is roughly an equal number of positive and negative ions within it.
This is known as an equivalent dipole and is useful in approximating the activity in small volumes of the brain. - 22Equivalent Current Dipoles For equivalent electric dipoles we still need to know a rough distribution of all charges in the brain. This is difficult!Instead, we use a current dipole, with current sources and
sinks instead of positive and negative charges.
A current dipole produces an electric potential similar to a charge dipole
- 23MACROSCOPIC PITENTIALS (HOMOGENOUS MEDIUM)The electric potential generated by many small volumes of the brain matter can be approximated by the sum of the equivalent dipole representing each small volume.
- 24G ( rS , rR ) is known as theGreen’s function; it represents the effects of the material between source location, rS, and recording location, rR.
In a homogeneous medium, the properties of the material are the same throughout. G(rS,rR) is a function of the distance between distance and how conductive the material is. - 25Macroscopic Potentials (Inhomogeneous medium) The human head is NOT homogeneous.Green’s function of a realistic head model must include the boundaries between the layers of different types of materials found in the head.
Macroscopic potentials can be estimated numerically or analytically when the head is simplified to a spherical model. - 26Simplifications 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.
- 27Simplifications In the brain, the neurons in the cortex are aligned and often large areas are activated together.Because of this alignment the potentials in the cortex are much more influential to the EEG than those in deeper structures.
An appropriate simplification is to consider a sheet of dipoles rather than a volume. This sheet is a representation of the dipoles in the cortex only.
- 28Simplifications Resulting model of EEG measurement
- 29Synchronicity 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.
- 30Macroscopic 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.
- 31Macroscopic EEG In reality all recordings are bipolar. Larger areas are involved.
- 32Even before re-referencing, voltages are measured between two points. The reference electrode normally used is on top of the head.
- 33MACROSCOPIC EEG Because large areas affect the EEG, a large measurement of EEG can be equally generated by1. A few dipoles near the electrode.
2. Many dipoles far away from the electrode
3. A few dipoles of large magnitude.
4. Many dipoles of small magnitude.
5. A few synchronously active dipoles
6. Many asynchronous dipoles
or a combination of any of these.
THE EEG IS AN AMBIGUOUS MEASUREMENT
This is supported by large variability observed in the EEG. The EEG is limited in what it can tell us. - 34SUMMARY • 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.Summary
• The EEG generators can be approximated by the sum of dipoles, each describing the average activity of neurons in a small volume
• Because aligning dipoles generates much larger potentials than if they are randomly oriented, the scalp EEG is predominantly a measurement of cortical activity.
• The activity in the cortex can be modelled/approximated as a sheet of dipoles.
• Because of the large cortical are as involved,the EEG is an ambiguous measurement. - 35Meso-scopic Models modelling the brain Simplifications are required:• Model the average activity in a small region of cortex.
• Reduce the parameter space – model just the average firing rates.
• Tackle a smaller problem – just model a relevant area of the brain. - 36The Cortical ColumnWe assume that the average activity within sub- systems of the brain sufficiently describes the activity of interest.
The sub-system that is usually considered is called the
“cortical column”. - 37—
- 38Phenomenological Models Phenomenology:used in science to describe a body of knowledge that relates empirical observations of phenomena to each other
- 39Pyramidal neuronsa type of neuron found areas of the brain including the cerebral cortex, the hippocampus and the amygdala.
- 40A cortical column is modelled asinterconnected populations of neurons.
- 41A Model of a Column Even this rather simple system is very difficult to analyse. The complications are:• The non-linearity, as in the equation below.
• The delay in the model, which makes it infinite dimensional. - 42Analysis of the column ModelTypical analysis proceeds as follows:
1. Compute steady state solutions. All variables are constant.
2. For each steady state solution, linearise the model.
3. Using the linearised model, analyse its stability.
4. Interpret stability boundaries in the context of the EEG signal. - 43Linearise the Model Linearisation is Linear systems are much easier to analyse.a way to estimate a non-linear model as a linear model.
Linearisation is performed by approximating a non-linear curve f (x) by a linear one. This is done at an OPERATING POINT Xo as
- 44OPERATING POINT
- 45The linearised model is a goodapproximation of the non-linear model if any changes made to the system are small. if large changes occur, the linearisation is not valid.
- 46The linearised model Transfer function, Input and Output.
- 47The linearised Model The overall system transfer function is:
- 48Analysing Stability We can use the linear system transfer function to analyse stability. This is done by finding the poles of the system.If all real parts of the poles are negative then the system is stable.
Thus, the imaginary axis forms the instability boundary. - 49Examples of systems shows stability
- 50Examples of systems shows stability
- 51Analysing Stability The system can be reduced to a three co-ordinate system:
- 52Analysing Stability Using the three co-ordinate system, the boundaries of stability can be found.This was performed by Breakspear et al. (2006) who found this stability region:
- 53Analysing Stability
- 54The behaviour of the model can be analysed by studying how parameters affect the simulated EEG and comparing to experimentally recorded EEGs.We will look at:
1. Simulating the normal EEG
2. Simulating the seizure EEG - 55Hebbian learning is a rule where a synapse is strengthened if pre- and postsynaptic neurons are“simultaneously active”.
- 56Spike-Timing Dependent Plasticity (STDP)Synapses are potentiated if the synaptic event (EPSP) precedes the postsynaptic spike.
Synapses are depressed if the synaptic event follows the postsynaptic spike.
- 57STDP Learning RuleDo it later slide 11 L21
- 58—
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- Fichas sobre Neural L19 - 22, creado por Bhagya Babuji el 03/11/2015.
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- Bhagya Babuji · nov 2015
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- 19 feb 2016
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- Creado por Jaber Rising · 3 nov 2015
- Copiado por Bhagya Babuji · 3 nov 2015
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