LFP's Lecture 1

Question 1

Give the four electrophysiological methods applicable during task performance of animals according to the lecturer

Answer 1

Single-Unit Activity (SUA)
-Spike activity of single neurons isolated
from other cells

•Ensemble recordings

•Multi-Unit Activity (MUA)
-Lumped spike activity from many
neurons around the electrode
-Useful when recordings cells are similarly
tuned

•Local Field Potentials - EEG
-Synaptic mass activity
-Indicative of network states
-Transmissive and Coding properties
(Oscillations)

Question 2

What is the Local Field Potential (LFP)? (generalities)

Answer 2

• The LFP signal captures key integrative synaptic processing that cannot be measured by observing the spiking activity of some neurons

• Multiple processing are contributing to the generation of the LFP. Signal is more ambiguous and difficult to interpret than spikes

• We need a good understanding of the ‘measurement physics’ of the LFP (the link between neural activity and what it is measured)

Question 3

Describe Richard Caton’s contributions to EEG

Answer 3

First to record electric currents in the brain (1875)

Question 4

Describe Bergers contributions to EEG

Answer 4

First to record cranial activity from the surface (1929); made some extensive findings through three papers . Described oscillations and standard patterns when eyes are closed, open etc. People called his wave the Berger wave, he called it alpha. Could make recordings from a living subject for first time & quite easily. Difficult to make assumptions, draw inferences or fundamental rules etc.

Question 5

What was used in 1957 to record from single electrodes which we still use today?

Answer 5

Tungsten microelectrodes

Question 6

Why was a diagram of a cortical column shown in these slides? How can this be misleading?

Answer 6

It acts as a computational unit and demonstrates how assemblies can be placed and how they interact. Assemblies as a concept are not spatially dependent though (long range connections are not super relevant or abundant however).

Question 7

Give three invasive modalities in which you can measure field potentials

Answer 7

(Micro-)ECoG (ECoG sits below dura on cortical surface, Micro is much more invasive but records from less columns)

Laminar probe- multi-site, multi-channel, linear probes with the benefit of a conical-shaped tip to reduce trauma upon dura puncture; better idea of a column and can compare to LFP; ca go quite deep

Micro - Can record ideally from one cell and membrane potential; relate IPSPs and EPSPs to the LFP

Question 8

How are EEG and MEG similar?

Answer 8

The biophysics are the same; while they record different fields they have the same origin

Question 9

When might an EEG signal become more or less synchronised?

Answer 9

Resting state : synchronised EEG, more alpha waves
Rodent’s movements: more hippocampal
theta waves
Active animal: cortically desynchronised EEG

Question 10

Describe the case study involving a 29-year old man suffered from hypoxic-ischemic brain injury after choking on a piece of meat while dining at a restaurant.

Answer 10

After the initial ICU treatment and period of slow neurological recovery, spontaneous movement and speech disappeared and severe impairment of arousal evolved, requiring intensive stimulation to have him maintain the wakeful state. No structural lesions were found using CT and MRI. Moreover, there was no evidence of
epilepsy on EEG-recordings.

Actual clinical assessment: No signs of spontaneous speech or vocalisation on request. The patient was able to respond to questions or commands with movements, though with a severe prolonged latency of responses, muscle rigidity, and with a considerable inconsistency.

Question 11

What diagnosis did the non-chewing case study patient receive?

Answer 11

Neurological evolution consistent with an Akinetic Mutism, a severe disorder of diminished motivation. Person is conscious but absent and rigid

Question 12

What could this patient possibly be treated with?

Answer 12

Some patients have the ability to respond to Zolpidem, Zolpidem is a type-A GABA receptor agonist. It works similar as benzodiazepines. It has strong hypnotic properties and weak anxiolytic, myorelaxant, and anticonvulsant properties. Induced recovery of spoken language, cognitive and motor functions following administration of zolpidem in severely brain-injured subjects with disorders of consciousness are well documented however the mechanisms of Zolpidem are not well known and why it works in some patients and not other is also unknown.

Question 13

How was this Zolpidem problem tackled?

Answer 13

EEG was taken and the profile pre and post Zolpidem was characterised. A characteristic shift was found and connectivity was assessed to see how different channels behaved.

Question 14

What were the results of the study?

Answer 14

Pre-zolpidem patients had a much higher covariance and shared connectivity. Activity between areas had been locked in a kind of connectivity with each other (synchrony?) and became disconnected from the outside world. GABAergic activity increased inhibition to prevent such activity. This was observed as zolpidem reducing amplitude envelope correlations at beta frequency band (see docs)

Question 15

How viable is Zolpidem therefore as a cure?

Answer 15

You can’t use zolpidem everyday due to spikes in tolerance but you could use these recordings as a marker and try to recreate this activity through stimulation of subcortical structures. This current experiment treatment is currently in data collection phase.

Question 16

What can this study teach us

Answer 16

Chew your food

While it is a rough measurement, EEG can be clinically relevant and insightful.

Question 17

Name and describe the two models in uncovering the mechanisms of LFP generation

Answer 17

Forward modelling scheme: extracellular potentials are modelled from neural transmembrane currents (LFP => mechanims)

Inverse modelling: Neural currents are modelled from recorded potentials (Mechanisms => LFP)

Question 18

Why is inverse modelling (intracellular recordings to LFP) so difficult?

Answer 18

You have a lot of assumptions and possible solutions.

Question 19

What is the posited mechanism from which LFPs arise? (in short)

Answer 19

LFPs arise from transmembrane currents passing through cellular membranes in the vicinity of an electrode

Question 20

What is forward-modelling based on?

Answer 20

The multi-compartmental neuron model

Question 21

What is an electric potential in regards to EEG?

Answer 21

EEG/ LFP measures electric potential difference between two measurement sites. Charges exert forces on charges (Coulomb’s law). Charges set up an electric field. An electric difference is defined as a change in potential energy by moving a test charge from A to B.

Google: The electric potential is defined as the amount of work energy needed to move a unit of electric charge from a reference point to the specific point in an electric field.

Question 22

What is electric current?

Answer 22

As charges exert force on other charges, charges (ions) move in the direction of E. This is called current.

Question 23

How do you calculate current (2)

Answer 23

I = V / R
current = voltage / resistance

or

I = Q / t

If a charge Q flows through the cross-section of a conductor in time t, the current I then I=Q/t.

Question 24

How are voltage differences in the brain useful to us?

Answer 24

Voltage differences between two locations originates an electric field. In the brain, electric fields can be recorded by extracellular electrodes. Electric fields can also be used to interpret several aspects of cortical computations

Question 25

Name three assumptions of the proposed biophysics of LFP generation

Answer 25

• Volume Conductor Theory: It assumes the extracellular medium is treated as a three-dimensional continuum
• Extracellular electrical potentials are generated by cellular transmembrane currents.
• It needs multiple compartments with differences in voltage(dendrites, soma, etc) to generate currents

Question 26

What fundamental equation that describes the contribution of the activity in a multicompartmental neuron model to the extracellular potential? What does it imply?

Answer 26

An extension of Ohm’s law:
Ø(r_e, t) = (1 / 4πσ ) ( Σ I_n (t) / |r_e - r_n|)

Here, I_n (t) denotes the transmembrane current (including the capacitive membrane current) in compartment n positioned at r_n (reference electrode), r_e is the position of the electrode tip, the sum includes all N compartments, and σ is the extracellular conductivity. This formula, which is mathematically identical to Coulomb’s law but has a different physical interpretation, implies that the LFP contribution from a transmembrane current will be inversely proportional to the distance between the compartment and the electrode. The extracellular conductivity σ reflects the ease with which ions can move in the convoluted extracellular medium.

Question 27

What neural model can help explain the biophysics of LFPs as shown in the lecture?

Answer 27

The model of the membrane potential as an electric circuit can help explain the biophysics of LFPs. The weighted average of the EPSPs and IPSPs as described by the current flowing between the the intracellular and extracellular space is recorded by the electrode. (?)

Question 28

Describe the relationship between LFPs, the depth of the device and action potentials

Answer 28

LFPs show a certain correspondence to action potentials at a lower depth, you cannot observe it but you can maybe see the consequences. You can see transmembrane current changes, change in polarisation, bursts of activity Signal is more ambiguous at the surface but still some bursting activity can be seen.

Question 29

Describe the biophysics of when LFPs are desychronised at a basic level

Answer 29

When LFPs are desynchronised, there is more cancellation and therefore less amplitude. Synchronised EEG suggests the neurons are doing similar things or acting in a more cohesive manner; therefore less cancellation and higher amplitudes

Question 30

Aside from transmembrane currents, name 6 other contributors to the LFP

Answer 30

•Fast action potentials
•Calcium spikes
•Intrinsic currents
•Spike afterhyperpolarizations
•Gap junctions neuron-glia interactions
•Ephaptic effects

Question 31

What is meant by an intrinsic current?

Answer 31

Current given by channels which are always open.

Question 32

What are meant by ephatic effects ?

Answer 32

Current flow into or out of a neuron generates local changes in extracellular potential that can influence the excitability of nearby neurons. This type of signalling is known as ephaptic signalling

Question 33

What are meant by spike afterhyperpolarisations?

Answer 33

Elevation of the intracellular concentration of a certain ion may trigger influx of other ions through activation of ligand-gated channels, and this will in turn contribute to Ve. For example, bursts of fast spikes and associated dendritic Ca2+ spikes are often followed by hyperpolarisation of the membrane, owing to activation of a Ca2+-mediated increase of K+ conductance in the somatic region

Question 34

Why is resolution outside skull much worse than in tissue?

Answer 34

LFP spatial spread: Currents spread along the direction of least resistance (volume conduction). This is largely due to:
1. Composition of the extracellular medium
2. Geometry of the tissue

The skull plays a large role due to the resistivity of bone

Question 35

The extracellular medium could be considered as both a capacitor and a resistor. What problem is posed with this and how is it typically solved?

Answer 35

If the EC medium is also a capacitor then the relationship is not direct, makes the calculation much more complex. It is easier to just make it a resistor.

Question 36

How viable is this practice of treating the EC medium solely as a resistor ?

Answer 36

In a study with monkeys, impedance (an expression of the opposition that an electronic component, circuit, or system offers to alternating and/or direct electric current) was measured in Ohm was measured as a function of frequency in Hz. It was found that impedance is is independent of frequency, homogeneous and tangentially isotropic within gray matter. This relationship between voltage and resistance was shown to be mostly linear and therefore the relationships can be theoretically predicted assuming a pure-resistive conductor (no capacitor).

Question 37

Is this finding generalisable across the brain? What is this relationship called?

Answer 37

There could be certain pockets and systems with a capacitor at play but in general it can be assumed that the relationship is ohmic.

Question 38

How does the neuronal signal source affect spatial drop off?

Answer 38

Geometry of the tissue is an important factor determining spatial drop-off. A single neuronal source can be modeled as a dipole
- Single dipolar source: Potential falls off with 1 / r^2; quite fast
- Monopolar source: Potential falls off with 1 / r

Question 39

What are the two main determinants of signal strength

Answer 39

The two main determinants of the extracellular strength of the LFP
are the spatial alignment of neurons and the temporal synchrony of the active dipole

Question 40

Cortical architecture of neurons can be categorised into two main branches relevant to EEG and spatial allignment. What are these and where are they most commonly found respectively

Answer 40

Closed and open fields; nuclei are typically closed field while the cortex and hippocampus are typically open field

Question 41

What neurons do LFPs typically pick up on and why?

Answer 41

Open field neurons which are spatially alligned in the cortex typically sum and the total vector is much larger. Individual vectors in closed field architecture point different directions and thus cancel, making it difficult to record from a distant electrode. EEG tends to record from the summed post synaptic potentials of radial apical pyramidal neurons in the cerebral cortex.

Question 42

Is more amplitude created by L2/3 or L5 pyramidal cells? Why ?

Answer 42

L5 pyramidal neurons project higher to more superficial layers, creating more distance between the ‘cylinders’ (~500um); on the distance between
cylinders containing the basal and apical dendrites. L2/3 pyramidal neurons are much shorter in comparison (~250um). The contributions of these cells to the recorded LFP correspond to this inter-cylinder distance with larger distances corresponding to a higher contribution measured by uV.

Question 43

How does field potential amplitude depend on the distribution of synaptic inputs?

Answer 43

If the distribution of inhibitatory synapses and excitatory synapses are homogeneous, the IPSPs and EPSPs will cancel each other out and not influence the signal as much. If they are heterogeneous with only inhibitatory synapses in one cylinder and excitatory in the other then this will create a much larger change in the amplitude and affect the LFP.

For example the following three ensembles increase proportionally in their average LFP absolute amplitude:
1. Both AMPA and GABA synapse distributed over the entire surface of the cell.
2. GABA synapses are
distributed only in the lower cylinder, with AMPA synapses distributed over the entire cell. (Most common)
3. GABA synapses distributed only in the lower cylinder and AMPA
synapses only in the upper cylinder.

Question 44

Why are hippocampal cells not picked up well by EEG? What method is better for this?

Answer 44

Activation of neurons are not well aligned in the temporal plane and thus are difficult to pick up. MEG is better at this

Question 45

Sum up what type of neurons affect the LFP, how they do this and how it effects it in a couple sentences.

Answer 45

Cells which are well aligned in space and in the temporal plane, have a large distance between their soma ad dendrites and have a heterogeneous distribution of their inhibitory and excitatory synapses create a larger dipole which can modify the shape, amplitude and main frequency of the LFP.

Question 46

How local the LFP is is a question which is up for active debate. Describe two studies which attempted to answer this

Answer 46

To measure the size of the recorded region directly, researchers used a combination of multielectrode recordings and optical imaging. They determined the orientation selectivity of stimulus-evoked LFP signals in primary visual cortex and were able to predict it on the basis of the surrounding map of orientation preference. They recorded and identified single cells first then recorded more and more of the surrounding tissue to find an optimum. Conclusion: The origin of field potentials in the cerebral cortex is
local, with more than 95% of the signal originating within 250 μm of the recording electrode

Others examined this conclusion by comparing LFP, current source density (CSD), and multiunit activity (MUA) signals in macaque auditory cortex. Estimated by frequency tuning bandwidths, these signals’ “listening areas” differ systematically with an order of MUA < CSD < LFP. Computational analyses confirm that observed LFPs receive local contributions. Direct measurements indicate passive spread of LFPs to sites more than a centimetre from their origins. Auditory cortical LFPs can be traced up to the dorsal surface of the brain. Conclusion: LFP represents a mixture of local/global activity of active neurons (passively transmitted by “volume conduction”)

Question 47

What is current source density analysis?

Answer 47

It represents a local estimation of the currents that are perpendicular to an electrode recording. Thus, it can provide a better estimation of sources and sinks of the local generators

Question 48

What are sources and sinks?

Answer 48

Source is a flow of positive charges from the intracellular
to the extracellular

Sink is a flow of positive charges from the extracellular to
the intracellular

Question 49

How can we calculate (or represent) the voltage potential provided by a source?

Answer 49

We already known that passive transmission of electrical fields follows Ohm’s law (V=IR), so the voltage potential Φ produced by a source I can be represented:
Φ(d) = I / (4πσ𝛿)

where the potential at a radial distance (d) from the generator is directly proportional to the injected current (I), and inversely related to a resistive impedance term related to the conductivity of the medium (σ; analogous to permittivity in free space)

Question 50

The previous equation derived from Ohms law provides a useful description of what is already known, but cannot be used empirically to detect and measure unknown current generators. Why not (3)?

Answer 50

First, it is rigidly structured, based on the location and intensity of individual generators.

Second, the resulting potential is expressed with reference at infinity.

Finally, the direction of local current flow in the medium (i.e.,orthogonal to the isopotential lines in Fig. 1) is ignored.

The end result of these shortcomings is that, even though potential differences can be measured empirically, an
unknown generator remains unknown.

Question 51

What solution is there to these three problems?

Answer 51

These three problems may be resolved by a vector interpretation of Ohm’s Law:
J = σE

where J is the current density, E is the electric field, and σ is the conductivity tensor for the medium. This
equation concisely describes the directional properties of the current flow through the medium, independent of any recording reference.

Question 52

What can we achieve by replacing the equations?

Answer 52

Replacing the Equations, we can obtain a (vector) measurement of J but based in voltage:
Im = -σ(→_V^2)Φ

The Laplacian operator (→_V^2) is a second spatial derivative similar to acceleration in the F = m x a equation

Question 53

Is current source density applied in EEG or invasive LFP measurements?

Answer 53

CSD can be applied to identify current generators underlying LFP (depth profile), but also in scalp EEG

Question 54

Why can referencing be an issue in LFP recordings?

Answer 54

Current sources contributing to EEG are both noiseand signal. Noise consists of electric artifacts (e.g. 50 Hz) noise but especially artifacts from the body movements (muscle movements) or EKG. The voltage readings should represent a pure measure of activity a the recording site, but voltage is a relative measure that necessarily compares the recording source with another (reference) site. If there is activity at the reference, this will contribute equally to the resulting
voltage recording. Thus, referencing is another very important source of LFP distortion

Question 55

How does referencing stray from the ideal scenario?

Answer 55

Ideally the recording site would show some activation pattern, the reference site would have no activation and the final result would reflect solely the recording site. Typically, however, the reference site shows some activity and this is integrated into the final result.

Question 56

Name four ways in which to solve the reference problem

Answer 56

• Common referencing
• Average referencing
• Bipolar referencing
• Current source density (CSD)

Question 57

How is common referencing carried out?

Answer 57

Most “common” technique
• Use a common reference site situated at a distance from the recordings sites
• Reference site is contributing to the recordings, but it will doing so equally to all the recordings
• Their relatives differences remain informative
• Typical examples (EEG): mastoids (behind ears) and nose

Question 58

Why not use references elsewhere in the body?

Answer 58

References that are far from the head are not optimal (because of the neck and contamination with ECG)

Question 59

When is common referencing problematic?

Answer 59

Problematic in high-density electrode recordings

Question 60

What is involved in average referencing?

Answer 60

Average of all electrodes recordings:
• Subtraction of the average to each electrode
• Underlying principle: electrical events produce both, positive
and negative poles. The integral of this potentials in an sphere
(head) sums zero
• Average represents an estimate of the reference recording
(which is present in all the recordings)
• Quite common in EEG

Question 61

What is the main problem of average referencing?

Answer 61

The head is not uniformly represented (bottom half respect of the top half)

Question 62

When is averaging not useful? Why?

Answer 62

Not useful in connectivity analysis (e.g. coherence), since subtraction artificially injects the same signal in all channels

Question 63

What is bipolar referencing?

Answer 63

Local subtraction of neighbouring electrodes

Question 64

When is bipolar referencing typically employed?

Answer 64

Widely used in connectivity measures (e.g. coherence, Granger)

Question 65

What is the principle behind bipolar referencing

Answer 65

Voltage readings of neighboring electrodes are similar, therefore, subtraction eliminates commonalities induced by reference

Question 66

Describe bipolar referencing mathematically

Answer 66

• P1 is potential at electrode 1 (E1) and P2 is potential at electrode 2 (E2). PR is the reference potential.

Signal from E1 is:
S1 = P1 - PR
and signal from E2 is:
S2 = P2-PR
Let SD the differentiated signal:
SD = S2-S1
SD = (P2-PR)-(P1-PR)
= P2-PR-P1+PR
= P2-P1 (local potential)

Question 67

What is a drawback of the bipolar referencing approach?

Answer 67

In this approach, information about voltage differences between non-adjacent pairs is not present

Question 68

What is the relationship between LFPs and Oscillations?

Answer 68

Low-frequency perturbations cause a cascade of high-frequency energy dissipation. Widespread low-frequency events modulate local high-frequency events. Oscillations represent behavioural states of the animal (e.g., awake, sleep)

LFPs are though to be a system of coupled oscillators. 1/f behaviour depends on the neuronal architecture. LFPs can play a causal role in the generation of cortical UP states. This is consistent with the current theories about the origins of LFPs