2.3 Instrument Settings, Calibration & Differential Amplification

2.3 Instrument Settings, Calibration & Differential Amplification

Electroencephalography registers microvolt-level cerebral potentials (typically 10 μV to 200 μV) measured at the scalp in the presence of massive environmental electromagnetic noise (such as 120V/60Hz AC mains radiation, fluorescent lighting, and radiofrequency emissions). To isolate and accurately record these minute neurophysiological signals, modern LTM instruments depend on precision differential amplifiers, high-resolution analog-to-digital converters (ADCs), and digital filtering pipelines.

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1. Differential Amplification & Common Mode Rejection Ratio (CMRR)

The fundamental building block of every EEG recording channel is the differential amplifier. A differential amplifier features three electrical terminals: Input 1 (non-inverting/grid 1), Input 2 (inverting/grid 2), and Ground.

+-----------------------------------------------------------------------------+
|                      DIFFERENTIAL AMPLIFIER OPERATION                       |
|                                                                             |
|   Input 1 (V1) ---------\                                                   |
|                          \                                                  |
|                           (+)---\                                           |
|                                  [ DIFFERENTIAL STAGE ] ---> V_out          |
|                           (-)--/                                            |
|                          /                                                  |
|   Input 2 (V2) ---------/                                                   |
|                                                                             |
|   Patient Ground (Ref 0V) ---> Sets Common-Mode Baseline                    |
|                                                                             |
|   OUTPUT EQUATION:                                                          |
|   V_out = A_d * (V1 - V2) + A_cm * ((V1 + V2) / 2)                          |
|                                                                             |
|   CMRR = 20 * log10(|A_d| / |A_cm|)  --> Standard: >100 dB (100,000 : 1)    |
+-----------------------------------------------------------------------------+

Mathematical Principles of Differential Amplification

• Differential Gain ($A_d$): Amplifies the potential difference between Input 1 and Input 2 ($V_1 - V_2$).
• Common-Mode Gain ($A_{cm}$): Amplifies electrical signals that appear identically in magnitude and phase at both inputs ($V_{cm} = (V_1 + V_2) / 2$).
• Common Mode Rejection Ratio (CMRR): The mathematical ratio of differential gain to common-mode gain, expressed in decibels (dB):

$\text{CMRR} = 20 \times \log_{10}\left(\frac{|A_d|}{|A_{cm}|}\right)$

• Clinical Standard: ACNS guidelines mandate that clinical EEG amplifiers must possess a CMRR > 90–100 dB (a ratio exceeding 100,000:1), with modern digital systems frequently reaching 110 dB to 120 dB.

The Critical Role of Ground and Impedance Balance

• The Ground Electrode: The patient ground electrode does not serve as a recording reference; instead, it establishes an electrical common reference point between the patient's body and the amplifier's isolated zero-volt chassis. This allows the amplifier to measure and cancel common-mode environmental noise.
• Impedance Mismatch Destroys CMRR: High Common Mode Rejection operates effectively only when the source impedances at Input 1 and Input 2 are closely matched. If Input 1 has an impedance of 15,000 Ω while Input 2 is 1,000 Ω, environmental 60 Hz electromagnetic radiation couples unequally into the two leads. This transforms common-mode noise into a large differential voltage that cannot be cancelled by the amplifier, creating persistent 60 Hz artifact.

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2. ACNS Polarity Conventions & Deflection Rules

The American Clinical Neurophysiology Society (ACNS) establishes universal polarity display conventions that govern all clinical electroencephalographs worldwide.

+-----------------------------------------------------------------------------+
|                        ACNS POLARITY CONVENTIONS                            |
|                                                                             |
|   RULE 1: Input 1 is NEGATIVE relative to Input 2  ---> UPWARD Deflection   |
|   RULE 2: Input 1 is POSITIVE relative to Input 2  ---> DOWNWARD Deflection |
|   RULE 3: Input 2 is NEGATIVE relative to Input 1  ---> DOWNWARD Deflection |
|   RULE 4: Input 2 is POSITIVE relative to Input 1  ---> UPWARD Deflection   |
+-----------------------------------------------------------------------------+

Deflection Determination Matrix

Phase Reversal Analysis in Bipolar Chains

Because cortical epileptogenic spikes are surface-negative potentials generated by excitatory postsynaptic potentials (EPSPs) in apical dendrites of pyramidal neurons, two adjacent channels sharing the focus will deflect in opposite directions:

• Pointing Phase Reversal (↑ in Channel 1, ↓ in Channel 2): Identifies a surface-negative epileptogenic spike focus at the shared electrode.
• Diverging Phase Reversal (↓ in Channel 1, ↑ in Channel 2): Identifies a surface-positive transient at the shared electrode (e.g., Positive Occipital Sharp Transients of Sleep - POSTS, lambda waves, or positive spikes).

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3. Digital Filtering, Time Constants & Bandwidth

Analog and digital filters shape the frequency spectrum of the recorded EEG, attenuating unwanted non-cerebral noise while preserving physiological rhythms.

+-----------------------------------------------------------------------------+
|                        EEG FREQUENCY FILTER SPECTRUM                        |
|                                                                             |
|       LFF Cutoff (e.g., 1.0 Hz)                    HFF Cutoff (70 Hz)       |
|                 |                                          |                |
|   Attenuates    |       PASSBAND (Preserved EEG)           |   Attenuates   |
|   Slow Drift    |   Delta (0.5-4), Theta (4-8), Alpha (8-13),  Fast Muscle  |
|   (<1.0 Hz)     |   Beta (13-30), Gamma (30-70 Hz)         |   (>70 Hz)     |
|                 |                                          |                |
|   (Phase Lag)   |                                          |  (Phase Lead)  |
+-----------------------------------------------------------------------------+

High-Frequency Filter (HFF / Low-Pass Filter)

• Standard Clinical Setting: 70 Hz (with a roll-off slope typically 6 dB to 12 dB per octave).
• Cutoff Definition: The frequency at which signal amplitude is attenuated by 3 dB (representing a 30% reduction in voltage, leaving 70.7% of original amplitude).
• Effects of Altering HFF:
  • Lowering HFF to 35 Hz attenuates high-frequency muscle artifact, but blunts sharp epileptiform spikes, reduces spike amplitude, and introduces phase lead (shifts fast peaks slightly earlier in time).

Low-Frequency Filter (LFF / High-Pass Filter)

• Standard Clinical Setting: 0.53 Hz or 1.0 Hz.
• Cutoff Definition: The frequency at which slow-wave amplitude is attenuated by 3 dB (30% reduction).
• Time Constant (TC): The time (in seconds) required for a DC square-wave step voltage to decay to 37% ($1/e$) of its peak deflection.
• Mathematical Formula:

$\text{TC} = \frac{1}{2\pi \cdot f_{\text{LFF}}} \approx \frac{0.159}{f_{\text{LFF}}}$

• Filter-TC Relationships:
  • $\text{LFF} = 0.53\ \text{Hz} \rightarrow \text{TC} = 0.30\ \text{seconds}$
  • $\text{LFF} = 1.0\ \text{Hz} \rightarrow \text{TC} = 0.16\ \text{seconds}$
  • $\text{LFF} = 0.16\ \text{Hz} \rightarrow \text{TC} = 1.0\ \text{second}$
  • $\text{LFF} = 5.0\ \text{Hz} \rightarrow \text{TC} = 0.03\ \text{seconds}$
• Effects of Altering LFF:
  • Raising LFF to 5.0 Hz removes slow perspiration drift, but artificially diminishes cerebral delta slowing, distorts slow spike-wave complexes, and introduces phase lag (shifts slow peaks slightly later in time).

The 60 Hz Notch Filter (50 Hz International)

• Characteristics: An ultra-narrow band-stop filter designed to sharply attenuate signals between 59 Hz and 61 Hz.
• Proper Clinical Role: Should only be activated as a temporary viewing aid when 60 Hz noise cannot be remedied during recording.
• Dangers of Routine Notch Filtering: Masks failing electrode contacts, distorts fast spike morphology, alters gamma frequency rhythms, and induces ringing artifacts (artificial oscillatory ripples following sharp transients).

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4. Gain, Sensitivity & Dynamic Range

+-----------------------------------------------------------------------------+
|                        GAIN VS SENSITIVITY FORMULA                          |
|                                                                             |
|                      Voltage (microvolts, uV)                               |
|   Sensitivity (S) = --------------------------  --> Standard: 7 uV/mm       |
|                      Deflection (millimeters, mm)                           |
|                                                                             |
|   * Lower S number (e.g., 2 uV/mm) = HIGHER magnification (ECI / Coma)      |
|   * Higher S number (e.g., 20 uV/mm) = LOWER magnification (Hypsarrhythmia) |
+-----------------------------------------------------------------------------+

Sensitivity Relationships

$\text{Sensitivity} (\mu\text{V/mm}) = \frac{\text{Voltage} (\mu\text{V})}{\text{Deflection} (\text{mm})} \iff \text{Deflection} (\text{mm}) = \frac{\text{Voltage} (\mu\text{V})}{\text{Sensitivity} (\mu\text{V/mm})}$

• Standard Display Sensitivity: 7 μV/mm (a 50 μV signal produces a 7.14 mm deflection).
• High-Voltage EEG (Hypsarrhythmia / Severe Encephalopathy): Decrease display magnification by selecting 15 μV/mm, 20 μV/mm, or 30 μV/mm to prevent trace overlap and display clipping.
• Low-Voltage EEG / Electrocerebral Inactivity (ECI) Recording:
  • When an ECI study is ordered under an applicable local protocol, ACNS Guideline 6 technical practice uses sensitivity of at least 2 μV/mm for a minimum of 30 minutes, with long interelectrode distances and system-integrity checks. The 2023 AAN/AAP/CNS/SCCM brain-death guideline does not accept EEG as an ancillary test for brain death because scalp EEG does not assess brainstem function; the technologist follows the ordering physician, governing policy, and current law.

Analog-to-Digital Converter (ADC) Dynamic Range

Modern LTM systems utilize 16-bit to 24-bit ADCs. A 24-bit ADC divides the input voltage range into $2^{24} = 16,777,216$ discrete quantization levels. This enormous dynamic range prevents amplifier saturation during high-amplitude movement artifacts while preserving microvolt-level resolution without hardware gain adjustment.

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5. Digital Sampling Rates & Nyquist-Shannon Theorem

In digital EEG systems, continuous analog scalp voltages are sampled at discrete time intervals and converted into numerical values.

+-----------------------------------------------------------------------------+
|                    NYQUIST-SHANNON SAMPLING & ALIASING                      |
|                                                                             |
|   Continuous Analog Waveform  ---> [ Sampling Rate: fs ] ---> Digital Data  |
|                                                                             |
|   NYQUIST CRITERION:  fs >= 2 * f_max                                       |
|                                                                             |
|   Example: If highest brain frequency = 100 Hz:                             |
|   fs MUST be >= 200 Hz. If sampled at 120 Hz, the 100 Hz wave ALIASES       |
|   into an artificial, false 20 Hz delta/theta wave!                         |
|                                                                             |
|   PREVENTION: Analog Anti-Aliasing Low-Pass Filter before ADC digitizer     |
+-----------------------------------------------------------------------------+

The Nyquist Criterion

• Theorem: To accurately reconstruct an analog signal without distortion, the sampling frequency ($f_s$) must be at least twice the highest frequency component ($f_{\text{max}}$) present in the signal:

$f_s \ge 2 \cdot f_{\text{max}}$

• Nyquist Frequency: The theoretical maximum frequency that can be accurately represented ($f_{\text{Nyquist}} = f_s / 2$).
• Aliasing Artifact: If an input signal contains frequencies exceeding $f_s / 2$, these frequencies are improperly sampled and reflect back into the lower frequency spectrum, manifesting as false, lower-frequency waveforms (e.g., a 70 Hz myogenic transient sampled at 100 Hz appears as an artificial 30 Hz rhythm).
• Anti-Aliasing Filter: A steep analog low-pass hardware filter must be placed before the ADC to eliminate all frequency components above $f_s / 2$.

ACNS Sampling Rate Standards

• Minimum Clinical Standard: 256 Hz ($f_{\text{Nyquist}} = 128\ \text{Hz}$).
• Modern EMU Standard: 512 Hz to 1,024 Hz, ensuring precise morphology for high-frequency spikes and sharp transients.
• High-Frequency Oscillation (HFO) Recording: ≥ 2,048 Hz (or 5,000 Hz) to record ripples (80–250 Hz) and fast ripples (250–500 Hz) during invasive intracranial monitoring.

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6. Calibration Procedures (Square-Wave & Bio-Calibration)

Square-Wave Calibration (Instrument Calibration)

• Method: A precision DC calibration step voltage (e.g., 50 μV) is applied simultaneously across all amplifier channels.
• Verification Objectives:
  1. Gain Uniformity: Verifies that all channels produce identical vertical deflections (e.g., 7.14 mm at 7 μV/mm).
  2. Time Constant / Low-Frequency Response: Evaluates the exponential decay curve to verify matching LFF decay across all channels.
  3. High-Frequency Damping: Evaluates the rise time and sharp corners of the square wave to confirm matching HFF characteristics.

Bio-Calibration (Biological Calibration)

• Method: A single pair of scalp electrodes (traditionally Fp1-O2 or all electrodes connected to a common reference) is fed into every amplifier channel simultaneously.
• Verification Objectives:
  1. Confirms identical channel amplitude, phase alignment, and waveform morphology under actual patient biological input.
  2. Detects internal amplifier channel discrepancies, faulty digital montage mappings, or defective cable connectors prior to initiating the clinical recording.