Introduction to EEG

using NeuroAnalyzer

The Brain: A Multidimensional Information Processing System

Scale and Complexity

• Neurons: Approximately 10¹¹ (100 billion) neurons in the human brain.
• Neuron Density: 10⁴ neurons per mm³.
• Synapses: Around 5×10¹⁴ (500 trillion) synapses, forming a vast network for information processing.
• Neocortex Thickness: 2-4 mm, containing most of the brain’s neuronal circuits.
• Pyramidal Neurons: About 8,500 pyramidal neurons per mm² of the cortical surface.

Signal Characteristics

• Typical Signal Amplitude: 10-100 μV10 at the brain level (e.g., EEG signals).
• Synaptic Delay: 0.5-1 ms, enabling rapid communication between neurons.

Information Processing

• Multidimensional Space: The brain processes information across multiple dimensions, including:
  • Spatial: Different brain regions specialize in distinct functions (e.g., visual cortex, motor cortex).
  • Temporal: Neuronal activity is coordinated in millisecond-scale timing (e.g., oscillations, action potentials).
  • Functional: Integration of sensory, motor, and cognitive processes.

Neocortex

• Structure: The neocortex is the outermost layer of the brain, responsible for higher-order functions such as perception, cognition, and voluntary movement.
• Organization: Composed of six layers, each with distinct types of neurons and connections.

Pyramidal Neurons

• Role: Pyramidal neurons are principal neurons in the cortex, involved in excitatory signaling and long-range communication.
• Density: High density of pyramidal neurons allows for complex information processing and integration.

Functional Neuroimaging Methods

1. Electrophysiological Methods

• EEG (Electroencephalography):
  • Inventor: Hans Berger (1910).
  • Purpose: Records electrical activity from populations of neurons.
  • Strengths:
    • Excellent temporal resolution (milliseconds).
    • Measures neural synchrony and real-time brain activity.
  • Limitations:
    • Poor spatial resolution (inverse problem: difficult to localize sources).
    • Sensitive to artifacts (e.g., muscle activity, eye movements).
  • Applications:
    • Mapping brain activity in activated states (e.g., eyes open while reading, eyes closed while calculating).
    • Studying sleep stages and cognitive processes.
• MEG (Magnetoencephalography):
  • Purpose: Records magnetic fields generated by neural activity.
  • Strengths:
    • Millisecond temporal resolution.
    • Better spatial resolution than EEG (less affected by skull/soft tissue).
  • Limitations:
    • Expensive and less portable than EEG.
    • Still limited in spatial precision compared to fMRI.

2. Hemodynamic Methods

• fMRI (Functional Magnetic Resonance Imaging):
  • Purpose: Measures blood oxygenation changes (BOLD signal) linked to neural activity.
  • Strengths:
    • Excellent spatial resolution (millimeters).
    • Can localize brain regions involved in tasks.
  • Limitations:
    • Poor temporal resolution (seconds).
    • Indirect measure of neural activity (via blood flow).
• fNIRS (Functional Near-Infrared Spectroscopy):
  • Purpose: Measures hemoglobin concentration changes using near-infrared light.
  • Strengths:
    • Portable and non-invasive.
    • Moderate spatial resolution (centimeters).
  • Limitations:
    • Limited depth penetration (mostly cortical activity).
    • Slower temporal resolution (seconds).

Comparison of Methods

Method	Temporal Resolution	Spatial Resolution	Strengths	Limitations
EEG	Milliseconds	Poor	Real-time, portable, inexpensive	Inverse problem, artifacts
MEG	Milliseconds	Moderate	High temporal, less distortion	Expensive, less portable
fMRI	Seconds	Excellent	High spatial resolution	Slow, indirect neural measure
fNIRS	Seconds	Moderate	Portable, non-invasive	Limited depth, slower resolution

Comparison: Single-Neuron Recording, Local Field Potentials (LFPs), and EEG

1. Single-Neuron Recording

• Definition: Records the electrical activity of individual neurons using microelectrodes.
• Method:
  • Invasive: Requires insertion of microelectrodes into the brain tissue.
  • High Precision: Captures action potentials (spikes) from single neurons.
• Temporal Resolution: Sub-millisecond (precise timing of spikes).
• Spatial Resolution: Micrometer scale (single neuron or small groups).
• Advantages:
  • High specificity: Directly measures activity of individual neurons.
  • Detailed neural coding: Reveals how single neurons encode information.
• Limitations:
  • Invasive: Not suitable for human studies outside surgical settings.
  • Limited coverage: Records from a small number of neurons at a time.
• Applications:
  • Studying neural coding, plasticity, and circuit-level mechanisms in animal models.
  • Used in neuroprosthetics and brain-machine interfaces.

2. Local Field Potentials (LFPs)

• Definition: Records extracellular electrical activity from a local population of neurons (within ~1 mm radius).
• Method:
  • Semi-invasive: Requires insertion of electrodes into the brain but records from a local population.
  • Low-Pass Filtered: Captures synaptic activity and local neural oscillations (e.g., gamma, theta).
• Temporal Resolution: Milliseconds (reflects population activity).
• Spatial Resolution: ~1 mm (local neural networks).
• Advantages:
  • Population-level activity: Reflects local network dynamics and synaptic inputs.
  • Less invasive than single-neuron recording: Can record from multiple sites simultaneously.
• Limitations:
  • Still invasive: Requires surgical implantation.
  • Mixed signals: Combines activity from many neurons, making it harder to isolate individual contributions.
• Applications:
  • Studying local neural circuits, oscillations, and synaptic activity.
  • Used in deep brain stimulation (DBS) research and epilepsy studies.

3. EEG (Electroencephalography)

• Definition: Records scalp-level electrical activity from large populations of neurons.
• Method:
  • Non-invasive: Electrodes placed on the scalp.
  • Macro-scale: Captures synchronized activity of thousands/millions of neurons.
• Temporal Resolution: Milliseconds (excellent for tracking real-time brain dynamics).
• Spatial Resolution: Poor (~centimeters; inverse problem limits localization).
• Advantages:
  • Non-invasive and safe: Suitable for humans, including clinical and research settings.
  • Whole-brain coverage: Provides a global view of brain activity.
  • Portable and cost-effective: Easy to set up and use.
• Limitations:
  • Low spatial resolution: Difficult to pinpoint exact neural sources (inverse problem).
  • Sensitive to artifacts: Muscle activity, eye movements, and environmental noise can contaminate signals.

Resting Potential

Definition

• The resting potential (\(V_m\)) is the electrical potential difference across the membrane of a neuron at rest.
• Typical range: -60 to -80 mV (commonly -70 mV).
• This potential is maintained by ion gradients and selective permeability of the membrane.

Ion Distribution and Equilibrium Potentials

The resting potential is influenced by the concentration gradients of key ions and their equilibrium potentials (calculated using the Nernst equation).

Ion	Outside Concentration	Inside Concentration	Equilibrium Potential
Na⁺	150 mM	15 mM	+62 mV
K⁺	5 mM	100 mM	-80 mV
Ca²⁺	2 mM	0.0002 mM	+122 mV
Cl⁻	120 mM	10 mM	-65 mV

Mechanism of Resting Potential

• K⁺ Permeability:
  • At rest, the membrane is highly permeable to K⁺ due to leak channels.
  • K⁺ ions flow out of the cell (down their concentration gradient), making the inside of the cell negatively charged.
  • The outflow of K⁺ slows as the membrane potential becomes more negative, reaching equilibrium at the Nernst potential for K⁺ (-80 mV).
• Balanced Forces:
  • At \(V_m\) = -62 mV(close to the Nernst potential for K⁺), the electrical gradient (pulling K⁺ in) balances the concentration gradient (pushing K⁺ out).
  • The actual resting potential (~ -70 mV) is a compromise between the equilibrium potentials of all permeable ions, primarily K⁺ and Na⁺.

Scale of Neuronal Potential

• The potential difference of -70 mV across a neuron’s membrane is proportionally enormous when scaled up.
• If a neuron were the size of a typical battery, its voltage would be equivalent to 300,000 volts.

Ion Flow and Extracellular Field Potential

• Ion Channels and Pumps:
  • Ions flow through ion channels (passively, along their electrochemical gradients).
  • ATP-dependent pumps (e.g., Na⁺/K⁺ pump) actively move ions against their gradients, maintaining the resting potential.
• Extracellular Field Potential:
  • Movement of ions in and out of neurons at focal sites causes changes in the extracellular electric field.
  • DC Shifts: Slow changes in the extracellular field potential caused by ATP-dependent pumps (cannot generate oscillations faster than 1 Hz).
  • Faster Oscillations: Must be attributed to ion channels (passive flow).

Action Potential

An action potential is a rapid, temporary change in the membrane potential of a neuron, caused by the flow of ions through voltage-gated channels. It allows neurons to communicate over long distances.

Properties

• Amplitude: ~110 mV (from -70 mV to +40 mV).
• Duration: ~1 ms.

Stages of the Action Potential

1. Depolarization (1 ms)

• Voltage-gated Na⁺ and Ca²⁺ channels open in response to a threshold stimulus.
• Na⁺ and Ca²⁺ influx increases the membrane potential.
• Overshoot: Membrane potential reaches +30 mV before Na⁺ and Ca²⁺ channels close.

2. Repolarization (1 ms)

• Voltage-gated K⁺ channels open, allowing K⁺ to flow out of the cell (efflux).
• Membrane potential returns toward the resting potential.

3. Hyperpolarization (1 ms)

• Delayed closure of K⁺ channels causes an overshoot of the resting potential, leading to hyperpolarization.
• The Na⁺/K⁺ pump restores ion gradients, returning the membrane to the resting potential.

4. Refraction (2 ms)

• Absolute Refractory Period: Neuron cannot fire another action potential (occurs during depolarization).
• Relative Refractory Period: Neuron requires a stronger stimulus to fire (occurs during hyperpolarization).

Ion Channels and Pumps

• Inward-Rectifier K⁺ Channel: Activated by hyperpolarization, allowing K⁺ to enter the cell and stabilize the membrane potential.
• Na⁺/K⁺ Pump: Actively transports Na⁺ out and K⁺ in to maintain resting potential.

Propagation and Space Constant

• Propagation: Action potentials travel along the axon due to local current flow between adjacent membrane regions.

Space Constant (\(\lambda\)): - Describes how far the potential change spreads along the axon. - Formula:

\[ \lambda = \left( \frac{d R_m}{4 R_i} \right)^{0.5} \]

where:
\(R_m\) is the membrane resistance,
\(R_i\) is the internal (axoplasmic) resistance
\(d\) is the diameter of the axon.

Oscillating Currents: Drop faster due to capacitance effects absorbing current proportional to the rate of potential change.

Extracellular Field and Synchronization

• Extracellular Space: Dissipation of current is complex, with no simple analytic solution.
• Synchronization:
  • Closely located neurons firing together with a 1-2 ms delay create small, reverberating local currents.
  • Larger groups of neurons: For external electrodes to detect signals, neurons must fire synchronously. Individual neuron activity is canceled out by jitter if not synchronized.

Neuronal Variability

• Ion Channel Density and Kinetics: Vary across neuronal classes.
  • Some neurons fire at faster rates due to differences in K⁺ channel properties.
• Action Potential Duration: Typically lasts 1-3 ms, with rapid drop-off over distance.
• Synaptic Currents: Slower currents influence the electric field over larger distances.

Source of EEG/MEG Signals

• Post-Synaptic Potentials (PSPs) are the primary source of EEG/MEG signals.
  • Excitatory Post-Synaptic Potential (EPSP): Causes depolarization of the neuron.
  • Inhibitory Post-Synaptic Potential (IPSP): Causes hyperpolarization of the neuron.
• Duration: 50-200 ms.
• Amplitude: ≤10 mV.

Action potentials are short and biphasic - not ideal for summation (cancellation of amplitudes). PSPs last longer and are monophasic - ideal for summation.

EPSP (Excitatory Post-Synaptic Potential)

• Ion Flow: Inflow of positive ions (e.g., Na⁺), causing depolarization.
• Extracellular Potential: Negative due to the local outflow of positive charge from the extracellular space into the neuron.

IPSP (Inhibitory Post-Synaptic Potential)

• Ion Flow: Inflow of negative ions (e.g., Cl⁻) or outflow of positive ions (e.g., K⁺), causing hyperpolarization.
• Extracellular Potential: Positive due to the local inflow of positive charge or outflow of negative charge.

Integration and Action Potential Generation

• Dendritic Travel: EPSPs and IPSPs travel down the dendrites to the cell body.
• Spatial and Temporal Summation: PSPs are summed at the axon hillock.
• Threshold Potential: If the summed potential reaches -50 to -55 mV, an action potential is triggered.
• Synaptic Transmission: At the synapse, Ca²⁺ enters through voltage-gated channels, triggering vesicular exocytosis of neurotransmitters.
• Inward-Rectifier Potassium Channels: Activated by hyperpolarization, helping to stabilize the membrane potential.

Shunting Inhibition

Mechanism: When excitatory and inhibitory potentials occur simultaneously, the inhibitory potential does not eliminate the excitatory potential but shunts it, reducing its effectiveness in depolarizing the neuron.

EEG Signal Polarity

Superficial Depolarizations:

• EPSPs generated in superficial synapses of pyramidal neurons result in a negative EEG signal.

Deep Depolarizations:

• EPSPs generated in deeper synapses of pyramidal neurons result in a positive EEG signal at the scalp.
• The local field potential (LFP) outside deeper synapses is negative, while the LFP outside superficial synapses is positive.

Factors Modifying the EEG/MEG Signal

1. Electrical Conductivity of Tissues

• The conductivity of tissues (e.g., cerebrospinal fluid, gray matter, white matter, skull) between the electrical source and electrodes affects signal strength and clarity.

2. Orientation of the Electrical Source

• The alignment of the neural source (e.g., pyramidal neurons) relative to the electrodes influences signal detection.
  • Radial sources: Easier to detect with scalp EEG.
  • Tangential sources: Better detected with MEG.

3. Conductive Properties of Electrodes

• Size, Material, and Resistance of electrodes can affect signal quality.
  • Larger electrodes may average signals over a broader area.
  • Material properties can influence impedance and noise levels.

Brain Electric Field

Generation of Electric Fields

Postsynaptic Potentials:

• Presynaptic neurotransmitter release triggers postsynaptic dendritic transmembrane currents, generating postsynaptic potentials (PSPs).
• PSPs cause changes in the local field potential (LFP) at the dendrite and soma of neurons.
• This creates a primary intracellular current along the somadendritic axis and an extracellular return current in the opposite direction.

Synchronous Activation:

• When tens of thousands of neurons with similar dendritic orientation are activated simultaneously, their individual magnetic fields add up, producing a detectable signal.
• Pyramidal neurons in layers III and V of the neocortex are the primary contributors to EEG/MEG signals due to their aligned somadendritic axes and perpendicular orientation to the cortical surface.

Signal Strength:

• EEG/MEG records the synchronized activity of 10,000-50,000 neurons (covering 6-10 cm² of cortical area).
• Timing is crucial: Synchronized neurons produce a stronger signal.

Contributors to EEG/MEG Signals

• Postsynaptic Potentials (PSPs):
  • Excitatory PSPs (EPSPs) and inhibitory PSPs (IPSPs) are the main contributors to LFPs and EEG/MEG signals.
• Action Potentials:
  • Typically not recorded by EEG due to their short duration (<10 ms).
  • However, synchronized action potentials in a local population may contribute to high-frequency components of the LFP.

Current Sources and Dipoles

• Monopole:
  • A single source or sink of current.
  • Current density decreases with distance from the source.
• Dipole:
  • Formed by adjacent current monopoles of opposite polarity.
  • Current flows from the positive to the negative pole.
  • Potential falls off inversely with the square of the distance from the source.
• Quadrupole:
  • Formed by two adjacent dipoles of opposite orientation placed end-to-end.
  • Potential falls off inversely with the cube of the distance from the source.
  • Equipotential surfaces have a cloverleaf configuration.
  • Approximates the potential generated by an action potential propagating along an axon.

Orientation and Detection

• Radial Dipoles:
  • Perpendicular to the cortical surface.
  • Well-detected by EEG due to their orientation.
• Tangential Dipoles:
  • Parallel or tangential to the scalp.
  • Better detected by MEG than EEG.
  • Dipoles at the bottom of a sulcus or with complex orientations may be poorly detected or missed by scalp EEG.

Properties of Brain Electric Fields

• Transmembrane Currents:
  • Any transmembrane current leads to intracellular and extracellular voltage deflections.
• Amplitude Scaling:
  • Amplitude decreases with the inverse of the distance between the source and recording site.
• Spatial Averaging:
  • EEG/MEG signals include contributions from multiple sources, leading to spatial averaging.
• Temporal Coordination:
  • Synchrony of current sources shapes the extracellular field.
• Layer 5 Pyramidal Neurons:
  • Largest amplitude up-down shifts of membrane voltage occur in these neurons.
• Neuron-Glia Interactions:
  • Glia may contribute to slow and infra-slow field patterns (<0.1 Hz).
• Cancellation Effects:
  • Widely scattered or asynchronously active neurons may cancel each other’s electromagnetic fields.

EEG Signal Strength:

• Strongest signal: Radial dipoles aligned perpendicularly to the cortical surface (a).
• Strongest MEG signal: Tangential dipoles (b).
• Cancellation: Oppositely oriented dipoles cancel each other out (c).
• Weaker signal: Dipoles not optimally oriented (d).

Amplification

Differential Amplification

• Principle: EEG amplifiers use differential amplification to measure the voltage difference between two inputs: \(\text{Signal} = \text{input}_1 - \text{input}_2\)
• Waveform Conventions:
  • Negative potentials are displayed as upgoing waves.
  • Positive potentials are displayed as downgoing waves.

Gain and Amplification

Gain: Amplifiers increase the signal amplitude. For example, a ×10 gain amplifies the input difference by a factor of 10.

Amplification Formula:

\[ V_{out} = (V_1 - V_2) \times \text{gain} \]

where:
\(V_{out}\) is the output voltage,
\(V_1\) and \(V_2\) are the input voltages from two electrodes.

Common Mode Rejection Ratio (CMRR)

Definition: CMRR measures an amplifier’s ability to reject common-mode signals (noise or interference present at both inputs).

\[ \text{CMRR} = \frac{\text{Applied Common Input Potential}}{\text{Output Potential}} \]

Higher CMRR values indicate better noise rejection.

Ground and Reference

Ground Potential: Both input potentials are measured relative to a common reference or ground.

Ground Electrode: Attached to the patient to provide a stable reference point. - Location: Does not significantly affect measurements as long as the electrode-patient connection has low impedance.

Polarity Convention

Direction of Deflection: In neurophysiology, an upward deflection indicates a more negative input, while a downward deflection indicates a more positive input.

Example: - Channel 1: F8-T8 = -20 μV - (-100 μV) = 80 μV (downward deflection). - Channel 2: T8-P8 = (-100 μV) - (-20 μV) = -80 μV (upward deflection).

Relative Nature of EEG Signals

Relative Measurement: EEG output is always the difference between two electrodes. To determine the absolute sense of the signal, comparisons between adjacent channels are necessary.

Noise and Interference

• Amplifier Noise: Typically around 10⁻⁵ V.
• Line Hum: Interference from electrical lines, typically 10⁻³ V.

Gain in Decibels (dB)

Formula:

\[ \text{dB} = 20 \times \log \left ( \frac{V_{out}}{V_{in}} \right ) \]

EEG Amplification Range: Gain settings typically range from 2,000 to 1,000,000 to amplify the small EEG signals (microvolts) to measurable levels.

Instrumental Phase Reversal

Phase Reversal: Apparent reversal of signal phase at different electrodes due to electrode arrangement. This is a normal artifact of differential recording and does not indicate a problem with the signal.

Electrodes

Biopotential Measurement Basics

When measuring a biopotential (\(V\)), a small current (\(i\)) is drawn from the source:

\[ i = \frac{V}{R_i + R_o} \]

where: \(i\) is the current drawn from the source,
\(V\) is the biopotential (voltage),
\(R_i\) is the imput impedance of the measuring device (e.g., electrode + amplifier),
\(R_o\) is the output impedance of the biological source.

To minimize current draw and accurately measure \(V\), the sum of \(R_i + R_o\) must be high. The measured voltage (\(V\^\prime`\)) is close to \(V\) when \(R_i \gg R_o\): \(V^\prime = V \times \frac{R_i}{R_i + R_o}\).

Impedance Considerations

• Electrode Impedance: Electrodes typically have higher impedance than the biological source.
• Amplifier Impedance: The amplifier (or preamplifier/head stage) must have even higher impedance to minimize signal distortion.
  • Input Impedance: Extremely high (e.g., >100 MΩ).
  • Output Impedance: Low (e.g., a few ohms) to ensure signal integrity during transmission.
• Optimal Electrode Impedance: <5 kΩ for EEG.
  • Low impedance ensures the signal reflects internal brain activity rather than external noise.

Calibration

• Machine Calibration: Uses a known signal (e.g., “shark fin” waves) to verify all channels are functioning correctly.
• Electrode Calibration: Ensures all channels from the same electrode provide consistent readings.

Types of Electrodes

1. Disposable Electrodes

• Gel-less: No gel required; often used for quick setups.
• Pre-gelled: Come with pre-applied gel for immediate use.

2. Reusable Electrodes

• Materials: Gold, silver, steel, or tin.
• Advantages: Cost-effective for repeated use; durable.

3. Headbands or Electrode Caps

• Design: Electrodes embedded in a cap or headband for easy placement.
• Use Case: Standard in clinical and research EEG setups.

4. Wet Electrodes

• Saline-based: Use saline solution for conductivity.
• Gel-based: Use conductive gel for better signal quality.

5. Dry Electrodes

• No Gel Required: Suitable for quick and easy application.
• Pins (e.g., SAHARA): Penetrate the skin slightly for better contact.
• Spring-loaded Pins: Apply gentle pressure for stable contact.
• Foam-based Sensors: Use conductive foam for comfort and signal quality.
• Bristle Sensors: Use tiny bristles to penetrate hair and reach the scalp.
• Epidermal Electronics: Flexible, skin-like electrodes for long-term wear.

Passive Electrodes

Design: Traditional electrodes that passively conduct signals to the amplifier.

Active Electrodes

Design: Contain a built-in amplifier (e.g., Brain Products).

Advantages:

• Amplify the signal at the electrode site, reducing electromagnetic artifacts.
• Lower susceptibility to noise during transmission.

Subdural Grid Electrodes

Use Case: Implanted directly on the brain’s surface for intracranial EEG (iEEG).

Advantages: High spatial resolution for precise localization of brain activity.

Volume Conduction

Volume Conductor: The body s tissues act as a conducting medium for electric potentials generated by neural activity.

Nonhomogeneous Medium: The body is not uniform - different tissues (e.g., brain, cerebrospinal fluid, skull, scalp) have varying conductivities and geometries.

Properties of Volume Conduction

• Linearity: Volume conduction is a linear process, meaning the superposition principle applies.
• Scalp Signals ≠ Source Signals: The electric potentials recorded at the scalp are not identical to the original neural signals due to attenuation and distortion during conduction.
• Weighted Summation: Each EEG sensor records a weighted sum of neural activity from multiple sources.
• Local Synchrony: Signals are strongest when local groups of neurons fire synchronously.
• Independence of Local Synchronies: Synchronized activity in different brain regions may be relatively independent of each other.
• Tissue Conductivity: The conductivity (or resistivity) of tissues determines how electric potentials propagate. At EEG frequencies, capacitive properties can typically be ignored.

Forward and Inverse Problems

Forward Problem:

• Definition: Calculating the scalp potential distribution generated by a known intracranial source configuration.
• Application: Used in simulations and source modeling to predict how a neural source would appear on the scalp.

Inverse Problem:

• Definition: Determining the location, strength, orientation, and type of neural generators from scalp-recorded signals.
• Challenge: There is no unique solution - an infinite number of source configurations can produce the same scalp potential.
• Solution: The inverse problem can be constrained using anatomical or physiological data (e.g., fMRI, structural MRI).

Summation of Neural Potentials

• Population Activity: The potential generated by a population of neurons is the sum of potentials from individual neurons.
• Synchronous and Regular Arrangement: For potentials to be detectable at a distance, neurons must be synchronously active and regularly arranged (e.g., pyramidal neurons in the cortex).

Mathematical Modeling of Potentials

Monopole Source:

• For a monopole in a homogeneous medium with conductivity \(\sigma\) (where \(\sigma = 1/\rho\) and \(\rho\) is resistivity), the potential \(V\) at distance \(r\) is:

\[ V = \frac{I}{4 \pi \sigma r} \]

where:
\(I\) is the current magnitude,
\(r\) is the distance from the source.

Dipole Source:

• For a dipole, the potential \(V\) at distance \(r\) (where \(r \gg d\), and \(d\) is the dipole separation) is:

\[ V = \frac{I d \cos(\theta)}{4 \pi \sigma r^2} \]

where:
\(I\) isthe magnitude of the dipole current source,
\(d\) is the distance between the dipole’s positive and negative poles
\(\theta\) is the angle between the dipole axis and the line connecting the dipole to the measurement point

Nonhomogeneous Media and Current Flow

Current Flow at Interfaces:

• When current flows between regions of different conductivity, the current density changes at the interface.
• Outward Bending: If the source is in a region of lower conductivity, current lines bend outward when entering a region of higher conductivity.
• Inward Bending: If the source is in a region of higher conductivity, current lines bend inward when entering a region of lower conductivity.

Models of Volume Conduction

• Homogeneous Sphere Model:
  • Assumes uniform conductivity within a spherical volume (e.g., brain).
  • Simplest model for estimating potential distributions.
• Multiple Sphere Model:
  • Two Planar Interfaces (e.g., brain-CSF and CSF-skull): Scalp potentials are approximately equal to those in an infinite homogeneous medium.
  • Five Regions (brain, CSF, skull, scalp, air) and Four Planar Interfaces: Scalp potentials are approximately one-fourth of those in an infinite homogeneous medium due to the low conductivity of the skull (about 1/80th that of brain or scalp).

Source Spread

Spatial Smearing: A small neural source in the brain spreads over a large area on the scalp due to volume conduction, reducing spatial resolution.

Spatiotemporal Integration

Single-Channel Representation

• Coverage Area: A single EEG channel represents the field potentials from approximately 10 cm² of the scalp surface.
• Limited Spatial Resolution: Due to volume conduction and the smearing effect of the skull and scalp, the signal recorded at a single channel is a spatially averaged representation of neural activity.
• This creates a “fish-eye lens” effect, where the relationship between the recorded signal and the underlying neuronal activity (primarily in superficial cortical layers) is indirect and distorted.

Challenges in Spatial Localization

• Superficial Layers: EEG primarily captures activity from superficial cortical layers (e.g., layers III and V of the neocortex), while deeper sources contribute less to the scalp signal.
• Volume Conduction Effects:
  • Neural activity from a small, localized brain region spreads out as it travels through the skull and scalp, resulting in a blurred or smeared signal across multiple EEG channels.
  • This makes it difficult to pinpoint the exact location of neural generators based on scalp recordings.
• Fish-Eye Scaling:
  • The spatial relationship between the source (neuronal activity) and the scalp signal is nonlinear, akin to looking through a fish-eye lens.
  • Activity from a small cortical area may appear spread out over a larger scalp region, while activity from a larger cortical area may appear compressed.

Temporal Integration

• Temporal Summation: EEG signals reflect the summation of neural activity over time, capturing synchronous oscillations and transient events (e.g., ERPs).
• Frequency-Dependent Effects:
  • Low-frequency activity (e.g., delta, theta) spreads more widely across the scalp due to volume conduction.
  • High-frequency activity (e.g., gamma) is more localized but harder to detect due to its lower amplitude and rapid attenuation.

Implications for EEG Analysis

• Source Localization: Advanced techniques like inverse modeling (e.g., dipole fitting, beamforming) are required to estimate the location and strength of neural sources from scalp EEG.
• Multichannel Analysis: Combining data from multiple EEG channels improves spatial resolution and helps disentangle overlapping sources.
• High-Density EEG: Using 64–256 electrodes enhances spatial sampling, reducing the “fish-eye” distortion and improving source localization accuracy.

EEG Signal Properties

Signal Amplitude and Units

• Amplitude Range: 0.1 to 100 μV per millisecond.

Variants of Recording Brain Electric Activity

Recording Method	Description
Electroencephalography (EEG)	Recording from the scalp surface. Non-invasive and widely used.
Intracranial EEG (iEEG)	Recording from within the brain using implanted electrodes.
Electrocorticography (ECoG)	Recording from the cortical surface. Higher spatial resolution than scalp EEG.
Stereoelectroencephalography (SEEG)	Recording from brain-implanted electrodes on thin rods. Used for precise localization.
Single Unit Recording	Recording from individual neurons using extracellular electrodes.
Intracellular Recording	Recording from inside a neuron using techniques like voltage clamp, patch clamp, or sharp electrodes.

Multidimensional Nature of EEG Signals

EEG signals are characterized by multiple dimensions:

• Time: Reflects the dynamic changes in neural activity over milliseconds to seconds.
• Space: Captured by multiple electrodes placed across the scalp or cortex.
• Frequency: Different frequency bands (e.g., delta, theta, alpha, beta, gamma) represent various brain states.
• Power: Indicates the strength of activity within specific frequency bands.
• Phase: Represents the timing and synchronization of neural oscillations.

EEG Signal Characteristics

• Non-Deterministic: EEG signals are not predictable with simple rules or formulas.
• No Special Characteristics: Unlike ECG, EEG lacks distinct, easily identifiable waveforms.
• Non-Stationary: The spectral properties of EEG signals change over time.
• Non-Linear: EEG signals exhibit complex, non-linear dynamics.
• Pseudo-Random: EEG signals are too complex to be described by explicit mathematical formulas.
• 3D Dynamic Structure: EEG represents the dynamic electric activity of the brain’s network.
• Cortical Correlates: EEG captures cortical activity influenced by subcortical structures (e.g., thalamus, dopaminergic system).

Limitations of EEG

• Localization: EEG is suboptimal for localizing specific brain functions.
• Long Processes: EEG is less suitable for analyzing processes longer than milliseconds (e.g., fMRI is better for slow hemodynamic changes).
• Source of Signal: Primarily from the cortex, modulated by subcortical structures like the thalamus.
• Deep Brain Structures: Contributions from deeper structures (e.g., thalamus, midbrain) to scalp EEG are typically minimal.

Synchrony and EEG Detection

• Synchrony Requirement: EEG detects activity when a large number of neurons fire near-synchronously.
  • External Events: Triggers cascades of neural processes (e.g., perception).
  • Internal Events: Triggers cascades of neural processes (e.g., “aha” moments).
  • Steady-State Firing: Neurons enter synchronized firing patterns (e.g., idle oscillations).
• Disorders of Synchrony: EEG can detect abnormalities in neural synchrony, such as those seen in epilepsy, Parkinson’s disease, or schizophrenia.