EEG / MEG

Question 1

Physiology - ac potential recording, ps potential recordings

Answer 1

AP Surface electrodes cannot usually detect action potentials due to the timing of the action potentials and the physical arrangement of the axons.
If two neurons send their action potentials down axons that run parallel to each other and the action potentials occur at exactly the same time, then the voltages from the neurons will summate and the voltage recorded from an electrode nearby will be approximately twice as large. However, if one neuron fires slightly after the other, the current at a location will be flowing into one axon at the same time that it is flowing out of the other axon: they cancel each other out and produce a much smaller signal. For the voltages to sum, the neurons have to fire within microseconds of each other, which rarely happens. So action potentials in different axons will typically cancel each other out.

PP
Postsynaptic potentials occur essentially instantaneously rather than traveling down the axon at a fixed rate. When an excitatory neurotransmitter is released at the apical dendrites of a pyramidal cell, current will flow from the extracellular space into the cell. There’s now a negativity on the outside of the cell in the region of the apical dendrites. To complete the circuit, current will also flow out of the cell body and basal dendrites. There’s a positivity in this area outside of the cell body and basal dendrites. Together, the negativity at the apical dendrites and the positivity at the cell body create a tiny dipole. To be able to measure neurons, a few conditions must hold:
- Many neurons have to fire at the same time. One dipole is too small to be recorded from a distant scalp electrode. However, when many neurons summate, it is possible to measure the resulting voltage at the scalp.
- The dipoles from the individual neurons have to be spatially aligned. If the neurons are at random orientations with respect to each other, the positivity from one neuron may be adjacent to the negativity from the next neuron. This way, they cancel each other out.
- The neurons should receive the same type of input. If one neuron receives an excitatory neurotransmitter and another receives an inhibitory neurotransmitter, the dipoles will be in opposite directions and will cancel out.
All these conditions are most likely to occur in cortical pyramidal cells, thus ERPs usually reflect the activity of these pyramidal neurons.
Electricity travels at nearly the speed of light, so the voltages recorded at the scalp reflect what is happening at the same moment in time.

Question 2

Which other measurements measure what?

Answer 2

It is almost impossible to completely isolate a single neuron’s postsynaptic potentials in an in vivo extracellular recording.
Single-unit recordings: in vivo recordings of individual neurons that measure action potentials (and thus not postsynaptic potentials)
When recording many neurons simultaneously, both their summed action potentials or postsynaptic potentials can be measured. The only way to record the action potentials from a large number of neurons is to place a high impedance electrode (that is only sensitive to nearby neurons) near the cell bodies.
Multi-unit recordings: recordings of action potentials from large populations of neurons.
Local field potential recordings: recordings of postsynaptic potentials from large groups of neurons.

Question 3

Folded cortex

Answer 3

The cortex is not flat but has many folds. This complicates the summation of the individual dipoles.
The summation of many dipoles is essentially equivalent to a single dipole formed by averaging the orientations of the individual dipoles (this is called an equivalent current dipole (ECD)). However, whenever the individual dipoles are more than 90 degrees from each other, they will start to cancel each other out to some extent. At 180 degrees, they cancel each other out completely.

Question 4

Volume conduction

Answer 4

When a dipole is present in a conductive medium such as the brain, current is conducted throughout that medium until it reaches the surface (volume conduction).
The voltage that will be present at any given point on the surface of the scalp depends on:
- The position and orientation of the generator dipole
- The resistance and shape of the various components of the head (especially the brain, skull, and scalp)
There are two factors that cause the surface distribution of voltage to blur:
- Electricity doesn’t just run directly between the two poles of a dipole in a conductive medium. The electricity spreads out through the conductor. ERPs thus spread out as they travel through the brain.
- Because electricity tends to follow the path of least resistance, ERPs spread laterally when they encounter the high resistance of the skull.

Question 5

Magnetic fields

Answer 5

An electrical dipole is always surrounded by a magnetic field and these fields summate in the same manner as voltages. Whenever an ERP is generated, a magnetic field is also generated, running around the ERP dipole. A dipole that is perpendicular to the surface of the scalp will be accompanied by a magnetic field that leaves the head on one side of the dipole and enters back again on the other side.
The skull is transparent to magnetism, thus the magnetic fields are not blurred by the skull. This leads to much greater spatial resolution.

Question 6

ERP Localization

Answer 6

From an observed voltage distribution, you are not able to tell the locations and orientations of the dipoles (the inverse problem). It is ill-posed: there is not just one set of dipoles that can explain a given voltage distribution. It is thus impossible to know with certainty which one of the configurations is the one that is actually responsible for producing the observed voltage distribution.

Question 7

Primary and secondary current (intracellular and extracellular)

Answer 7

Intracellular current (primary current) is converted from the chemical energy stored in the cell. The magnetic field produced by these currents are measured by MEG.
Extracellular current (secondary current) leaks out through the skull to the scalp. This is what is measured by the EEG.
Types of sources
Radial sources: point towards the surface. The magnetic field of these sources is parallels to the MEG sensors, so they are not picked up by the sensors.
Tangential sources: point along the surface. These currents leave the head on one side and re-enter the head on the other side, so they are picked up by the MEG sensors.

Question 8

What is eeg?

Answer 8

EEG (electroencephalography) consists of the voltage differences on the scalp caused by electrical activity of active neurons. EEG reflects brain electrical activity with millisecond temporal resolution.
Spontaneous EEG is brain activity when the participant is in a spontaneous state. It can be helpful in clinical environments (e.g. for diagnosing epilepsy or tumors, detecting abnormal brain states or classifying sleep stages).
In science, EEG is usually not spontaneous. Instead, it’s related to a task.

Question 9

WHAT DOES EEG MEASURE?

Answer 9

EEG measures scalp potentials that are produced by post-synaptic potentials. It measures the sum of all dendritic synaptic activity. You can look at neuronal activity at different scales:
- If you record very close to some neuron (or intracellular) you can see spiking activity.
- When you record further away, you can see the local field potential (LFP).
- If you put an electrode on the surface of the cortex, you start to see something that looks a bit like EEG.
- If you record from outside the skull, the small details wash out. You cannot see the activity of the individual generators, only the total one.
EEG can only measure activity of many neurons that fire synchronously and that are nicely aligned. Otherwise the sum of activity is not big enough to record or the activities cancel each other out. EEG mostly measures activity from pyramidal neurons (bottom right in picture).
There’s tissue in between the neurons and the EEG electrodes (CSF, dura, skull, scalp). These have different conductive properties, which cause blurring of the signal. Because of blurring, you’re always recording post-synaptic brain activity of quite a large area.

Question 10

20/10 SYSTEM

Answer 10

To make EEG more comparable between people, there’s a standard placement of the electrodes, using electrode caps. The distance between external anatomical landmarks is measured and used to divide it into 10/20/20 percent areas:
- Distance between the nose (nasion) and the small bumb at the back of your head (inion).
- Distance between the points where the jawbone meets the skull.
The system specifies the names of the electrodes at each position:
- Electrodes on the central line: Z
- Electrodes to the left: odd numbers
- To the right: even numbers
- Closer to the middle: lower number
- Central (C), occipital (O), parietal (P), temporal (T), frontal (F)
The electrodes send their signal over the wire to a box. Active electrodes have their own amplifier, meaning that the signal is amplified before it goes to the box. An amplified signal is less sensitive to picking up environmental noise.
Gel is used to increase the conductivity with the scalp to improve the signal quality.
An EGI system uses salt water instead of gel. Is quicker than EEG, but there are electro bridges so signal quality is not great.

Question 11

Reference

Answer 11

EEG always requires a reference. EEG records a potential difference. One electrode (the reference electrode) is attached to a place where it can be attached very firmly (ear, nose, ear lobe, front of head). The potential at all other locations is measured relative to the reference electrode. The signal depends on the reference: if you put the reference at a different place (or use something else as a reference), you are going to get different signals.
Common average reference: take the average of all electrodes as reference (instead of just one).

Question 12

Ground electrode

Answer 12

There’s a very large difference between environmental noise and brain signal. The ground electrode helps making the amplifier more sensitive to the brain signal. It improves the detection of very small differences in the presence of a very large mode of background noise by removing this common mode. The ground removes only the part of the signal that is the same for all electrodes. The ground electrode doesn’t affect the interpretation of the signal. It only affects how much environmental noise you pick up.
So for an n-channel EEG system, there are n+2 electrodes (ground + reference).

Question 13

ARTEFACTS IN EEG

Answer 13

Physiological artefacts:
- Muscular activity (jaw, neck, face muscles, squinting, eyebrows, swallowing, etc.)
- Eye blinks: when you blink, there’s a small movement of the eye because of the eye lid, which causes potential differences
- Eye movements
- Reading aloud/talking
- Heart
Non-physiological artefacts:
- 50 Hz line
- Electrode loses contact with the scalp
Identifying and removing artefacts is done prior to averaging process. E.g. use reference electrodes to measure background physiological activity and use pre-processing techniques to identify eye blinks.

Question 14

PROS AND CONS eeg

Answer 14

Pros of EEG:
- High temporal resolution.
- Cheap and easy to use.
- Not cumbersome for the subjects (they can sit and move a bit). More natural for recording in a semi-natural environment.
- Diverse subject populations (you can do experiments on 65+ and babies).
- Can do multiple experimental sessions.
- Easier to record for a longer time.
- Can be combined with other recording techniques.
Cons of EEG:
- Selective measure of neuronal activity (only pyramidal cells).
- Spatial resolution is low. The signal is very smeared.
- Experimental duration can be long.
- Preparation takes a lot of time.
- You need many trials for a reasonable signal.

Question 15

what is meg

Answer 15

MEG (magnetoencephalography)
When there’s an electrical current, there’s a magnetic field. Magnetoencephalography (MEG) records the magnetic field distribution around the scalp.

Question 16

SQUIDs

Answer 16

MEG has magnetic detectors called SQUIDs (Superconducting Quantum Interference Devices). They are super conductive magnetic field sensors.
They have two Josephson Junctions (JJs). When magnetic current flows through it, electrons form pairs and flow past both sides of the loop. The resistance over the junctions will slightly increase, depending on the amount of magnetic field that passes through it. The loop is very small, so an antenna is attached to it (a flux transformer). This takes the magnetic flux from a larger area and transforms it into a magnetic flux in a smaller area. It’s also super conductive. The resistance can be measured with an amplifier.
Both the antenna and SQUIDs have to be immersed in liquid helium.

Question 17

IMPROVING SIGNAL QUALITY

Answer 17

The magnetic fields from the brain are way smaller than the fields around us (~10e15 times smaller than the noise and ~10e10 times smaller than the earth’s magnetic field).
There are a few ways to make the signal better:
- Passive shielding with a magnetically shielded room.
- Active shielding with noise cancellation coils
- Magnetometers and gradiometers (flux transformers)

Question 18

Magnetically shielded room (MSR)

Answer 18

An MSR is a passive shield against environmental magnetic noise. It has concentric shells of mu-metal and aluminium. The layer of aluminium works as a faraday cage. The magnetic fields bend around it. A con is that the room is expensive and big (which e.g. in a hospital can be inconvenient).

Question 19

Noise cancellation coils

Answer 19

Noise cancellation coils compensate for the disturbing fields with locally generated opposing fields.
- External active shielding: the external magnetic field is monitored and are then compensated by producing magnetic fields in the opposite direction in the large noise cancellation coils that surround the MSR the room.
- Internal active shielding: the magnetometers of the MEG system monitor the disturbing magnetic fields, and compensating fields are generated in the noise cancellation coils inside the room.

Question 20

Magnetometers and gradiometers

Answer 20

Magnetometers are simple loops that are highly sensitive to signals and send them to the SQUIDs. However, they also measure environmental noise sources. The magnetometer is more sensitive to far away sources (deep in the brain but also outside noise that is further away).

Question 21

Gradiometers

Answer 21

Gradiometers consist of two coils that are in opposite direction.
- Axial gradiometers have two coils, where one is closer to the brain and the other is further away. Any magnetic field that goes through the bottom coil doesn’t create activity in the second coil. Any activity that is the same at the top and bottom coil will not be passed to the SQUID, since they create activity in opposite directions and cancel out. The top coil removes environmental noise. It doesn’t record signals from the brain as it’s far away. A small imperfection in one of the coils (e.g. top coil is 1% smaller than the bottom coil) means that 1% of the common field will still be passed to the SQUID. 1% of a big signal is still significant.
- Planar gradiometers have two coils that are in one plane. If the field through both coils is the same, it will not be send to the SQUID. Both coils are close to the head, so both are suppressing environmental noise and picking up brain activity. The two coils form a figure 8. You can rotate them 90 degrees to change the direction of the fields (this is not possible with an axial radiometer).

Magnetometers and axial gradiometers show a positive vs. negative distribution of the magnetic field. Planar gradiometers don’t have a large positive vs. negative distribution over the source. The sensor is sensitive to steepness and has a direction (which you can change by rotating the coils).
- Magnetometers/axial gradiometers:
o Far away from the source, the coil picks up the magnetic field going in one direction (either positive or negative depending on the side).
o Directly over the source, the recorded signal is not strong. This is because it runs almost parallel to the coils, making it hard to pick it up.
o If the coil is on the other side of the source, it picks up the magnetic field going in the different direction, so it has the other sign than in the first note.
o If you move even further away from the source, the signal gets weaker and weaker so the measured field is lower.
- Planar gradiometers:
o Further away from the source, the coil picks up the magnetic field going into one direction.
o If the coil is moved over the source, the signal is strongest. The signal enters one of the coils via one direction and the other coil via the other direction. Because of this, the two signals add up.
o If the coil is them moved further away again in the other direction, the signal enters the other coil in the other direction (than in the first part), so it has the same sign as the signal on the other side of the source.

Question 22

MEG SYSTEM

Answer 22

The subject has to lay down and can’t move.
MEG doesn’t have a reference like EEG, but due to the design of the flux transformer, the signal is going to look different depending on the transformers.
The scanners have many sensors (~300). The way the sensors are arranged in the helmet is fixed, but the number depends on the system/manufacturer. With MRI is doesn’t matter what kind of scanner you have, with MEG It does. Usually, a system has chips that contain multiple sensors (e.g. two gradiometers in different directions and one magnetometer). A typical MEG system:
- Planar or axial gradiometers
- About 300 sensors
- Is placed in a magnetically shielded room (+ active noise cancellation sometimes)
- A 2000+ Hz sampling rate
The system in Nijmegen (CTF system) has 275 sensors, tubes instead of chips, and the coils are at the top and bottom of the tube. The coils are.
Developments in MEG: now they’re designing MEG scanners that heat something (idk what) up instead of cooling it down. The sensors are more flexible and can be moved around like electrodes. They still need a magnetically shielded room. These scanners are not used in cognitive research yet.

Question 23

ARTEFACTS IN MEG

Answer 23

ARTEFACTS IN MEG
Magnetized metal influences the MEG signal. These are usually very slow. E.g. tattoos, underwired bras, braces, buttons. They can be dealt with, but it’s a nuisance (more artefacts -> more cleaning).
Signal space separation: technique to remove noise. All channels record signals from inside the brain and outside. Using mathematical techniques, you try to distinguish sources from inside and outside the helmet by modelling these sources.
- The spatial topography of sources inside the head and helmet have to be vocal, as they are close to the sensors.
- If all sensors have a similar pattern, the source must be further away.

Question 24

PROS AND CONS of meg

Answer 24

Pros of MEG
- Preparation time is very fast
Cons of MEG
- It’s very expensive (both setting up the room/equipment (~$1.500.00) and the helium (~$80.000/year).
- MEG scanners have fixed size helmets.
- The subject has to sit very still

Question 25

EEG vs. MEG

Answer 25

EEG vs. MEG
Source estimation:
- MEG fields are less spatially smeared than EEG fields (because magnetic fields can go through the skull uninterrupted).
- Simpler ‘head model’ for MEG.
- You don’t need to know about tissue conductivities for MEG (which you do need to know for MEG because they influence the electrical current).
- MEG measures intracellular currents and EEG measures extracellular currents. With MEG you are slightly closer to the primary currents, which make it easier to interpret
Sensitivity:
- EEG always requires a reference.
- MEG is insensitive to radial sources. EEG can measure both radial and tangential sources. Luckily the head is not exactly a sphere, so there are some radial sources that can be measured a bit. Sources deep in the brain however are always radial, so MEG cannot measure these.
- MEG is more sensitive to external noise sources.
Cost efficiency:
- MEG is very expensive (acquisition and maintenance).
- MEG requires way less preparation time than EEG.

Question 26

AC/DC

Answer 26

Alternating current (AC): changes fairly rapidly over time. 50 Hz. For example the outlets in the wall.
Direct current (DC): generated by a chemical reaction (metal and non-metallic saline solution). They have a constant “offset”. In theory it’s 0 Hz, but this is not always the case, so it’s the “very slowly changing things”. For example the current from a battery.
In the discussion of amplifiers, DC can so mean direct coupled (as opposed to capacitively coupled). This means that the amplifier can amplify direct current signals.

Question 27

ERPs and ERFs
EVENT-RELATED POTENTIALS (ERPS)

Answer 27

ERPs (event-related potentials) are the average EEG following a stimulus. You record activity for many stimuli, align the signals to the stimulus onset, and average. This averages out noise.
Habituation: the subject gets used to the stimulus and the brain signal is weakened. Exogenous early sensory activity (in the brainstem) doesn’t habituate.
Trial based segmentation (left): prior to averaging the data, you have to segment it. Send a marker code to the computer that is digitizing the EEG when a stimulus is given. Then segment the data around the stimulus of interest.
Trial based averaging (right): averaging the segmented data. You can selectively average if you have different stimuli (e.g. average all “O” stimuli and all “X” stimuli separately).

Signal-to-noise ratio (s/n ratio): averaging cancels out the noise in the signal and improves the s/n ratio. If you have x trials, the background activity will be √x times smaller compared to a single trial.
You can average over trials in one subject or over subjects.
Baselining: the difference between the reference and electrode of interest (offset potential) can fluctuate. The ERP lies on top of this fluctuating wave. You can deal with this by estimating the potential difference just prior to the stimulus onset. Compute the mean value and subtract it from the whole epoch.
ERP components
Most components are related to the experimental manipulation, and not to the presentation of a stimulus. E.g. the N170 differs for houses and faces. However, e.g. N1 is always there when a stimulus is shown, so this one is not related to the experimental manipulation.
You can either label components based on their latency or on their ordering (P300 vs. P3). Latencies can vary a lot, depending on the task (e.g. P300 latency depends on how easy it is to distinguish the oddball).
P300: related to the processing of an oddball stimulus. An oddball stimulus is a stimulus that occurs less often than the standard stimuli. The brain signal is different for the deviant/oddball stimulus than for a stimulus that is present many times. With an oddball paradigm you can elicit the P300.
N2PC (N2-posterior-contralateral): attention-related component that is primary observed at the posterior scalp sites contralateral to the position of the target item, 200-300 ms after stimulus-onset. It is typically observed for visual search arrays containing targets.

Question 28

EVENT-RELATED FIELDS (ERFS)

Answer 28

Event-related fields (ERFs) are the magnetic counterpart of ERPs. They are indicated with an “m”. E.g. N400 vs. N400m.
N400(m) is related to language: when there is an unexpected word in a sentence. Seems to relate to the semantic integration of the word into the sentence. It is most prominent over the le ft hemisphere.

Auditory N100m: appears when you present a beep (of 1000 Hz). It’s spatial distribution is dipolar: this can be explained by two down pointing curving arrows on the sides of the head. The topography (magnetic field distribution) is very similar to that of the N400 which suggests that the auditory cortex seems involved in auditory processes and creating the N400m.

Question 29

Oscillations

Answer 29

Spontaneous EEG has patterns that are not simply noise. These have a periodic nature. There are a number of rhythms that occur at different locations in different situations. They were named in succession of when they were discovered.
- Alpha: 8-13 Hz. Occipital (and sensori-motor areas). Bigger when the eyes are closed, smaller when the eyes are opened.
- Beta: 13-30 Hz. Parietal/frontal. Decreases during movement.
- Theta: 4-8 Hz. Frontally most strong, but can be quite distributed. Increases during sleep.
- Delta: 0.5-4 Hz. Large amplitude and slow waves. Increases during sleep.
- Spiking activity/spike-wave complexes: seizures in epilepsy. Abnormal, but of physiological source.
ALPHA OSCILLATIONS (8-13 HZ)
The Hz of the alpha band is very narrow within a subject and between subjects (~2-3 Hz).
Strongest occipitally in rest. More central (sensory motor regions), there’s also some activity. You can use it to check whether subjects are still attentive and/or doing the task properly.
When the eyes are closed the alpha is very large. When they are opened, alpha decreases. Moving also decreases alpha.
You can look at the data by:
- Wavelet analysis
- Rectifying the data (making everything positive) and then averaging in time
Alpha activity in memory tasks
Experiment: subjects were presented a list of letters to memorize. After a 3 second retention window (nothing on the screen), they had to say whether a probe letter was part of the learned list or not. The brain activity in the retention window was measured. The more letters the list to learn contained, the larger the central parietal alpha activity at 10 Hz was. So alpha increased with working memory load.
Function of alpha
Hypothesis: alpha is not an idling mechanism. It represents active functional inhibition. So alpha is not necessarily related to the processing of sensory input. It might be related to a more top-down mechanism. The visual stream might be suppressed because it can be distracting.
BETA (13-30 HZ)
It is usually present in the sensory motor regions. It is topographically modulated by movements and somatosensory activation. Prior to the onset of (perceived) movement, beta decreases. Shortly after the movement, beta rebounds (it returns to the basic level/previous state).
You can localize it using the homunculus….????
Beta seems to always be present but disappears when you start doing something or when you observe movements (so it might have a role in the mirror neuron system (?)).
Function of beta
Hypothesis: beta reflects an inhibition of primary motor areas. When you plan for movements, the inhibition gets smaller. It prevents you from making movements all the time. Parkinson patients have abnormal beta band activity.
GAMMA (30-100 HZ)
The Hz changes a lot more (than alpha) within subjects/trials. It has a smaller amplitude so it is harder to see.
Function of Gamma
The binding problem: if we have a complex visual scene, how can we make sense of the features of the objects in the scene and them being separate objects? If you have a neuron that picks up activity from part of the world from one object vs. a neuron that picks up activity from another object, how do they know they are looking at different objects?
Hypothesis was that gamma synchronization has something to do with this. Some experiments suggest that gamma band activity is involved in binding in human perception:
- Neurons were recorded that have non-overlapping receptive fields. Something was presented that could be bound together (e.g. a big bar moving in a direction) and in another condition something was presented that could not be bound together (e.g. two smaller bars moving in different directions). Gamma activity of the neurons was synchronized when the objects were perceived as one object, not when they were perceived as separate objects.
- Gamma band activity was similar after showing a real triangle compared to an illusionary triangle. When the illusionary triangle disappeared or when it was less clear, the gamma activity was smaller.
- Gamma was higher when subjects saw an object in a random dot pattern compared to when they didn’t.
- Salient stimuli have higher gamma than less salient stimuli (I think).
Gamma oscillations reflect visual stimulus representations and might be involved in processing in general. Attention modulates gamma too (gamma is larger for attended stimuli).
THETA (4-8 HZ)
Mostly frontal, but the exact sources are not clear.
It seems to be related to working memory: frontal theta increases with memory load.
FOURIER TRANSFORM
Describes a complex signal as sines and cosines. You can use it to represent a signal in the frequency domain. This way you can see which oscillations are present in the signal.
Fast-Fourier Transform (FFT): take a piece of data, describe the waveform in that window as the sum of sines and cosines, slide the window a bit, and compute it again for the new piece. Average the output of all the pieces. Usually, the segments are chosen to be partially overlapping. Because of this, the data in the overlapping parts contributes twice to the output. To fix this, a window function is applied (tapering/windowing). The data is tapered towards the edges, so the sides contribute a little less than the middle.

Evoked responses: time-locked (latency is fixed). If you average them in time, you get an averaged response (ERP). You can calculate the powers in the signal from this average.
Induced responses: the activity is a bit shifted in time. If you average them in the time domain, there’s no response. You can’t see the oscillatory effect in the ERP.
Wavelet analysis (very similar to FFT): used to make induced responses visible. Instead of first averaging over time, you calculate the powers for each specific timepoint first, and average those (so average over frequency instead of time). Evoked responses are also still visible.

Question 30

dipole fit

Answer 30

You have a bunch of potential differences distributed over the scalp. When you record MEG, you get a bunch of lines that show the time course of the electrical potential or magnetic field (left). After pre-processing, you get the image in the middle. This shows the distribution of the activity of a magnetic dipole.
Then you want to pinpoint the source of that topography to a location in the brain. You want to estimate where this activity is coming from by finding the most plausible location of the source (inverse problem).
Dipole fit: find best location for the dipole and project it on an MR image.

Question 31

FORWARD PROBLEM

Answer 31

Forward problem (not as interesting but you need to know about it for the inverse problem): other way around. A part of cortical tissue is active and you can model the potential distribution that you would observe given that source.
Forward model: a part of the cortex is active and we can model what kind of fields we will measure with the MEG machine given that topography. We know the cause -> effect chain:
- Cause: active patch of cortex which generates a magnetic field or electrical current.
- Effect: the fields that you measure with the MEG machine.
The forward model is a model of this effect. If you have an assumed source, that you can think of as a dipole, it has a particular location and orientation. Now you have to build a volume conduction model of the head (of the volume through which the currents float) to find out where we will measure the activation of that source with the sensors (which we know the locations of).
It can be a simple sphere model. Essentially you don’t know if it’s a good model or not: it’s only as good as the assumptions you put on it. Back in the day, the sphere model was the only model that could solve the problem in a reasonable amount of time
For EEG, you need to take into account the different conductivities (all tissues have different conductivities), as the volume currents (which we measure) flow through the tissue. For MEG, it’s not so important as the magnetic field of volume currents are very small.
The maths of it all
So we can build a model of the magnetic field on a certain location (see the fancy mathematical formula that we don’t need to know on the right). That formula is for one electrode. You have multiple electrodes.
If you assume some activity (current) q at location r, you can build a forward model that models the measurements at the level of the channels: a projection of the source to the channels. If you have a current that generates volume currents/magnetic fields, these currents are in principle visible on every sensor/electrode. The extent to which they are visible depends on the location: far away electrodes pick up less current. This gives the spatial fingerprint of a particular source (H in the slide).
So the basic observation model of EEG/MEG is:
- B(t) at multiple locations at once is a mixture of underlying sources.
- H is spatial fingerprint of underlying source
- q is time course of activating sources
- n is some noise
Forward models are linear. Linear superposition means that when source 1 goes through the volume conduction model and whatever and gives a model of what we’re going to measure and source 2 goes through a similar black box operation and gives a model of that source, then if both sources are active at the same time, their resulting model is the sum of both models separately.

Question 32

INVERSE PROBLEM

Answer 32

Source reconstruction/modeling is an inverse problem. First we build a forward model. Then, given observations B and this forward model H, we want to find the potential distributions of locations and activations of underlying sources (q) that can explain the underlying data. Each of the sources can be described as a mixture of the channels.
How do channels unmix to the sources? This is also a linear problem (matrix multiplication: u = W * x), so you need the W matrix.
As a neuroscientist, we start on the right and go to the left. We want to go from observed activity to a source. The biophysical formula is from left to right.
Motivation for source modeling
EEG has some weak points:
- You have a measurement from outside the brain and you don’t know where the sources come from.
- You have an overlap of components.
- Low spatial resolution.
Source modeling helps target some of these weaknesses.
If you have an ERP/ERF component, you want to characterize it in physiological terms
- Time and frequency are the “natural” characteristics.
- The location needs more work. You need an interpretation of the scalp topography (e.g. dipole is already an interpretation of the scalp topography). The inverse model helps to interpret this topography.
Forward and inverse modeling help to disentangle the overlapping time series and the different cognitive components (peaks and troughs might be result of activation of different parts of the brain) and it helps with connectivity (how the sources interact).
The inverse problem is ill-posed, but you can add some constraints to make it less ill-posed (to make it so that there’s only one unique solution):
- Give a number of sources to the model.
- Give a location of the source (or depth or something like that).