EEG Basics and ERPs: Comprehensive Notes

History and context
- Hans Berger discovered the EEG in the mid-1920s, leading to the development of the electroencephalogram as a tool to study brain electrical activity.
- Early uses focused on detecting sleep stages and epilepsy; patterns associated with wakefulness vs. sleep and seizures were foundational.
- Classic observations: wakeful, alert EEG shows high-frequency, low-amplitude activity, whereas deep sleep shows low-frequency, high-amplitude slow waves. Slow-wave sleep is the most unambiguous indicator of sleep.
- For a long time, EEG seemed limited to clinical neurology (sleep studies, epilepsy) and offered little insight into psychological processes. Later, signal processing and experimental design revealed psychological relevance.
EEG signals: characteristics and challenges
- EEG is a noisy, non-stationary signal.
- Noise sources (physiological and environmental):
- Physiological: cardiac activity (EKG), eye movements and blinks (EOG), muscle activity (EMG), sweat gland activity, etc.
- Environmental: electrical wiring and mains power (e.g., 50 Hz) and other ambient signals.
- Non-stationarity: the statistical properties of the EEG (e.g., frequency content) change over time; the signal is not predictable from moment to moment.
- Analogy: think of EEG as a piece of music where different instruments (frequencies) come in and out; a stationary signal would be all instruments playing a constant pattern, while a non-stationary signal has evolving frequency content.
- Practical implication: the neural signals related to psychology are very small in amplitude compared to background noise, making them hard to detect without clever analysis.
Time-domain representation and Fourier analysis
- A waveform is the EEG voltage as a function of time.
- Fourier's theorem: any complex waveform can be represented as the sum of simple sine waves with different frequencies, amplitudes, and phases:
 $X(t) = \sum{k=1}^{K} Ak \sin(2\pi fk t + \phik)$
- In practice, the contributions of each frequency can change over time (non-stationary). This leads to time-varying frequency analyses (neural oscillations).
- Intuition: each simple sine component is like a musical instrument; the brain signal is the orchestration of many such oscillations.
- Frequency-domain view (neural oscillations): brain regions may communicate through oscillatory activity at specific frequencies, reflecting inter-regional interactions.
- Alternative analysis approach: the time-domain signal can be averaged across trials to reveal consistent, stimulus-locked components (signal averaging).
Signal averaging and event-related potentials (ERPs)
- Technique: present a stimulus repeatedly (e.g., 100s or 500s of trials) and average the EEG epochs time-locked to stimulus onset.
- Rationale: non-stimulus-related activity and random noise tend to cancel out with averaging; stimulus-locked activity (ERP components) remains.
- Visual example stimulus: a checkerboard pattern shown on a computer screen; stimulus onset is time zero when the checkerboard reverses contrast.
- Pattern reversal evoked potential: pattern reversal (white/black inversion) induces a characteristic ERP.
- Brief aside: you can also generate other evoked potentials (SEP for somatosensory, AEP for auditory) by varying the sensory modality.
- The general term for these time-locked responses is ERPs; VEP is the ERP when the stimulus is visual.
Visual evoked potentials (VEP) and components
- VEPs are used to assess the visual pathway integrity (optic nerve, optic radiations, visual cortex).
- A typical VEP shows a time-locked sequence of peaks and troughs, often labeled as components (e.g., N1, P1, N2, P2, etc.).
- Labeling conventions and polarity:
- Some labs plot positive up; others plot negative up due to historical reasons (paper traces) or dipole orientation in cortex.
- Commonly, N1 is a negative deflection, P1 is a positive deflection, etc.
- For a given component, the latency is often used to identify it (e.g., P100 around 100 ms).
- Example nomenclature:
- N1, P1, N2, P2, etc. (N and P denote polarity; the number denotes the order/latency).
- In practice, you may also see component labels like C1 when polarity/consistency varies with electrode and stimulus location.
- Important timing markers:
- P100 (also called P1) ≈ 100 ms after stimulus
- N1 ≈ 150 ms after stimulus (negative deflection)
- P2 (often around 200–270 ms, sometimes annotated as P270 in literature)
- Practical observation: the back of the head often shows strong positive P100; the front shows the opposite polarity (e.g., N100) due to dipolar sources in the cortex.
- Dipole explanation: activity from aligned pyramidal cells creates a dipole; the orientation leads to frontal negativity and occipital positivity (or vice versa) depending on electrode location.
- Maximum scalp voltage does not reliably indicate the precise neural source location due to the inverse problem and dipole geometry.
Spatial sampling and topographic maps
- EEG systems commonly use 32, 64, or 128 channels; more channels provide better spatial resolution and scalp distribution maps.
- Spatial distribution reveals how the response varies across scalp locations and can indicate contralateral involvement (e.g., somatosensory evoked potentials when tapping a hand).
- Weather-map analogy: with many electrodes, you can interpolate to create a scalp voltage map similar to weather maps showing high/low activity areas.
- Practical note: 64 channels is often a sweet spot; increasing from 64 to 128 yields diminishing returns for some analyses.
- Example: P100 distributions peak at the back of the head; N1 may peak at the front; P270 can be concentrated at the back.
Inverse problem and source localization caveats
- The scalp voltage distribution is a mixture of signals from multiple brain sources.
- Inferring precise source locations from scalp data is mathematically ill-posed; multiple sources can produce similar scalp patterns.
- With strong assumptions (e.g., a single source, MRI-informed head model), localization can be reasonable within ~1 cm, but this is not guaranteed.
- Because of ill-posedness, EEG source localization relies on models and external information; different models can yield different solutions.
- Therefore, EEG is excellent for tracking temporal dynamics and scalp topography, but not a precise locator without modeling assumptions.
Multichannel and multifocal VEP (mfVEP): a more spatially resolved approach
- Concept: extend the same averaging principle to multiple visual field locations, not just one central checkerboard.
- Execution: present stimuli at many locations across the visual field (e.g., with wedges on a dartboard-like display) and perform time-locked averaging for each location.
- Pros: allows mapping of visual field function and pinpointing where along the optic pathway lesions affect specific parts of the visual field.
- Clinical example: multiple sclerosis (MS) lesions affecting the optic nerve or optic radiations can slow conduction, delaying VEP components at affected locations.
- Example data: in a healthy eye, P1 around 93 ms; in an optic neuritis eye, P1 around 120 ms; N1 around 133 ms in healthy eye vs 168 ms in affected location.
- mfVEP data are plotted for each location in space to reveal regional delays and to infer where along the visual pathway damage occurs.
Practical clinical applications and notes
- VEPs and ERPs have broad clinical utility in neuro-ophthalmology, neurology, and psychology research.
- The visual potential paradigm is used to diagnose optic nerve deficits, multiple sclerosis, glaucoma, and other visual deficits not explained by lens or retina alone.
- The pattern reversal paradigm is robust for evoking reliable visual responses and is a staple in neuro-ophthalmology.
- The same signal-averaging approach extends to other modalities (somatosensory ERP, auditory ERP) and even to studies of the brain’s expectation (omission ERP) when a stimulus is omitted after a series of regular pulses.
- In research, ERPs provide precise temporal information about when the brain processes specific events, even if exact source localization is uncertain.
- The lecturer notes that the same averaging technique will be used to explore psychology-related questions in later lessons, implying broad applicability beyond vision.
Summary of key takeaways
- EEG is a historically important, noninvasive measure of brain electrical activity with both clinical and research uses.
- Wakefulness vs. sleep and epilepsy yield characteristic EEG patterns; slow waves are diagnostic of deep sleep, while high-frequency activity dominates wakefulness.
- EEG is very noisy and non-stationary; brain signals are small relative to various physiological and environmental noises.
- Fourier analysis provides a frequency-domain view of EEG, which underpins the idea of neural oscillations and inter-regional communication.
- Time-domain signal averaging (ERP technique) isolates stimulus-locked brain responses from ongoing EEG noise.
- Visual evoked potentials (VEPs) reveal a sequence of components (N1, P1, N2, P2, P270, etc.) with characteristic latencies; labeling conventions vary across labs due to historical and practical reasons.
- Spatial sampling (32/64/128 channels) enables scalp topography and better inference about the distribution of cortical activity; the inverse problem makes precise source localization challenging.
- Multifocal VEP extends the method to map responses across the visual field, assisting in lesion localization in diseases like MS and optic neuritis.
- Clinical utility includes assessing optic nerve integrity, conduction delays due to demyelination, and visual pathway functionality.
- The topic will be revisited to address psychology-related questions using the same signal-averaging approach.
Notation and conventions to watch for
- Positive-up vs. negative-up conventions for ERP plots vary by lab and publication; always check the axis labeling before interpretation.
- N and P nomenclature (N1, P1, N2, P2, etc.) describes the polarity and order of deflections; occasionally C1 is used when polarity is inconsistent across conditions.
- When reporting latency, common markers include P100 (≈100 ms), N150 (≈150 ms), and later components like P270 (≈270 ms).
- For mfVEP, latency measurements (e.g., P1, N2) are compared across healthy and affected eyes to map regional deficits.
Small but useful analogies and examples from the lecture
- Astrophotography analogy for averaging: stacking multiple noisy images enhances real stars (signal) while noise averages out, yielding a clearer image of the stars. Similarly, averaging EEG trials enhances stimulus-locked responses (ERP) while non-stimulus noise cancels out.
- Weather map analogy for spatial mapping: more electrodes allow interpolating a detailed map of scalp voltages, just as more weather stations yield a better map of atmospheric conditions.
Quick refresher on equations (where applicable)
- Time-domain signal model (noise plus brain signal):
 $E(t) = B(t) + N(t)$
 where $E(t)$ is the recorded EEG, $B(t)$ is the brain-evoked signal, and $N(t)$ is background noise.
- ERP computation (signal averaging):
 $ERP(t) = \frac{1}{N}\sum{n=1}^{N} En(t)$
 where $E_n(t)$ is the EEG segment time-locked to stimulus onset for trial $n$ , and $N$ is the number of trials.
- Fourier decomposition (conceptual):
 $X(t) = \sum{k=1}^{K} Ak \sin(2\pi fk t + \phik)$
 representing how a complex EEG waveform can be decomposed into sine waves of frequencies $fk$ with amplitudes $Ak$ and phases $\phi_k$ .
Final note
- The lecturer plans to continue exploring psychology-related questions using signal averaging and ERPs in upcoming sessions, reinforcing how these methods bridge physiology and cognition.