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Technical Aspects of EEG

Interpreting EEG requires both the ability to recognize patterns and an understanding of the underlying physics and engineering principles. Although some of the concepts underlying the technical background of EEG are complex, most concepts which are relevant to clinical practice can be expressed using only simple equations. Unfortunately, the number of concepts required to understand how EEG works increases every year. The main reason for this is the digitization of recording. We all live in an analog world, in which measured quantities can take on an infinite number of positive or negative values. Several decades ago, this abruptly changed with the addition of substantial digital components to EEG equipment, which represent measurements using a limited number of possible discrete quantities and require computers to be integrated in the device. Digital components have been added in the amplifier, storage, and visualization stages as well as in the recording electrodes themselves in some recent investigational systems. Digital signal analysis has also changed the interpretation of EEG signals, with digital improvements to filters, digital remontaging, and the addition of automated detection and artifact removal. Although digital systems force the recorded signal to become discrete (potentially leading to loss of relevant information) and are slower than analog systems, their use is spreading throughout devices because they allow greater control on signal information flow, offer lower power consumption, and are less susceptible to noise.

ANALOG RECORDING

Basic Electrical Principles

The movement of electric charge in currents within the nervous system leads to the EEG signal. Electric charges exist with either positive or negative polarity and are found in packages of a particular unit size called “quanta,” such as the positive charge of one proton or the negative charge of one electron. Protons are usually fixed within atoms and cannot move, but some electrons from each atom, especially in certain materials, are free to move between atoms and their movement creates electrical current flow. Charges also create electrical fields which cause them to act at a distance upon other charges, with like charges repelling each other and opposite charges attracting. Electric current flows best through materials called conductors, which are mostly metals or water solutions. When electric current flows through a conductor, it also creates a magnetic field around it. The measurement unit for charge (Q) is the coulomb, which has the charge of 6.24 × 10¹⁸ electrons. Flow of electric current (I) is measured in amperes, also called “amps,” and is equal to the flow of one Coulomb of charge per second.

$\text{I}={\displaystyle \frac{dQ}{dt}}(dQ\text{is the change in Q; }dt\text{ is the change in time})$

Electric current does not flow very fast, with electrons moving only at an average speed of approximately 0.25 mm/sec, but the electric field spreads out within the conductor at the speed of light. This is similar to what happens in a pipe filled with water in which, when 2a small quantity of water is forced into one end of the pipe, the pressure increase within the water spreads very rapidly and a small quantity of water is immediately forced out of the other end of the pipe, despite the water itself in the pipe not having travelled far. Any changes to a magnetic field created by changes in the movement of electric charge also spread out from the conductor at the speed of light.

Electrical devices work by causing current to flow around in a circle, called a circuit. The voltage (V) is the amount of potential energy between two points in that circuit. The unit measure of V is the volt, which is the energy, measured in joules, which will be delivered per coulomb of charge when that charge passes between two points in the circuit. A common analogy to understand electric current flow is water flow to and from a water tank. The volume of water is equivalent to charge (Q), the rate of flow is equivalent to the current (I), and the voltage (V) is equivalent to the difference in the pressure of water between two points in the flow system (such as between the top of the water tank and the pipe in your home). Like an electric circuit, water delivery in a city runs in a circle, with water flowing down from the tank to various destinations from which it is eventually recollected and pumped back into the tank. But unlike water which usually flows only one way through pipes, electronic circuits are often designed to create current flow which alternates in direction very rapidly. A direct current (DC) is current which flows only in one direction. Alternating current (AC) rapidly switches direction of flow continuously.

The electrical resistance (R) is a measure of the difficulty of passing an electrical current through a conductor. Generally, the amount of current (I) is linearly proportional to the voltage and inversely linearly proportional to the resistance:

$\text{I}={\displaystyle \frac{\text{V}}{\text{R}}}(\text{This can also be represented as V}=\text{I}\times \text{R})$

The unit of measure for R is ohms (Ω), which equals 1 volt per ampere of current. A resistor is an electrical circuit element added to create an impediment to current flow, like a sponge or filter placed in a pipe to slow the flow of water. A material with a high R, such as rubber, is called an insulator. Conductance (G) is defined as the opposite of resistance such that G = 1/R. The human body predominantly consists of saltwater, which acts as a passive volume conductor, a relatively low R medium for electric current through which an electric field can spread easily throughout. This is the reason why signals generated in one area of the body (such as the heart) can be measured in completely different areas of the body (such as on the head or foot).

Two circuit elements serve to store electric charge, capacitors and inductors. Capacitors are devices used to store charge, consisting of one or more pairs of conductors (usually metal plates) separated by a thin insulator (Figure 1.1). A voltage source, such as a battery, pushes electrons (negative charge) onto one of the conductive plates, creating an electrical field which pushes electrons off the opposite plate, leaving positive charges behind. How much charge a capacitor can store, or its capacitance (C) is linearly proportional to the amount of charge stored in the capacitor (Q) and inversely linearly proportional to the voltage difference (V) between the two metal plate conductors.

$\text{C}={\displaystyle \frac{\text{Q}}{\text{V}}}$

The unit of measurement of capacitance is the farad (F), which equals the capacitance in which one coulomb of charge causes a potential difference across the capacitor of 1 volt. A capacitor will resist the flow of DC but will allow AC to “flow” through, although this AC flow is more of an illusion since charge just accumulates and leaves the two plates of the capacitor. This apparent “flow” of current across a capacitor is termed capacitive coupling.3

Inductors are electrical components that store energy in a magnetic field when electrical current is flowing through it. Typically an inductor consists of a coil of wire wrapped around a magnet (Figure 1.2). If the electric current flowing through the inductor decreases or stops, the magnetic field quickly collapses and induces a current in the coil which resists that decrease in current flow. In this way, an inductor resists changes in the current, therefore resisting AC but permitting DC. The strength of an inductor to perform this function is termed inductance (L) and its unit of measurement is a henry. In a circuit in which the current is decreasing at a constant rate of 1 ampere per second, an inductance of one henry results in the generation of one volt of potential difference across the inductor. This induced voltage, called the electromotive force, is directly proportional to the inductance (L) and directly proportional to the change in current (−dI). The change in current (−dI) is negative because the current is decreasing.

$V=\text{L}{\displaystyle \frac{-dI}{dt}}(dl\text{ is the change in current; }dt\text{ is the change in time})$

Often there are multiple circuit elements which store charge in an electrical circuit, and these sum in different ways depending on whether they are in series or in parallel, as described in Table 1.1.

4TABLE 1.1. Rules for combining resistors, inductors, and capacitors in electronic circuits

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	Resistors and Inductors	Capacitors
	$\begin{array}{c}\text{R}={\text{R}}_1+{\text{R}}_2+{\text{R}}_3\\ \text{L}={\text{L}}_1+{\text{L}}_2+{\text{L}}_3\end{array}$	${\displaystyle \frac{1}{\text{C}}}={\displaystyle \frac{1}{{\text{C}}_1}}+{\displaystyle \frac{1}{{\text{C}}_1}}+{\displaystyle \frac{1}{{\text{C}}_1}}$
	$\begin{array}{c}{\displaystyle \frac{1}{\text{R}}}={\displaystyle \frac{1}{{\text{R}}_1}}+{\displaystyle \frac{1}{{\text{R}}_2}}+{\displaystyle \frac{1}{{\text{R}}_3}}\\ {\displaystyle \frac{1}{\text{L}}}={\displaystyle \frac{1}{{\text{L}}_1}}+{\displaystyle \frac{1}{{\text{L}}_2}}+{\displaystyle \frac{1}{{\text{L}}_3}}\end{array}$	$\text{C}={\text{C}}_1+{\text{C}}_2+{\text{C}}_3$

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The fundamental circuit for understanding the analog components of neurophysiology recording is the resistor–capacitor (RC) circuit (Figure 1.3). The current flow in this circuit varies over time when a voltage change occurs.

Analog Amplifiers

The changes in the current in an AC electrical signal are sinusoidal, meaning they follow the shape of a sine wave. Many biological signals have a sinusoidal shape as well, and any time-varying signal can be broken down into a combination of sinusoidal waves of different frequencies and times of occurrence. One of the primary functions of neurophysiology instruments is to amplify a biological signal, which means to increase the 5power of the voltage and/or current of the time-varying electrical signal. Neurophysiology amplifiers are predominantly voltage amplifiers and therefore the output of the amplifier is measured in volts. The gain of an amplifier (G) is the factor by which the amplifier increases the amplitude of the input signal. A voltage amplifier with a G of 2, for example, outputs a signal with double the voltage of the input signal.

A simple amplifier with one channel has two input lines and two output lines. It amplifies the voltage potential difference between the two input lines (the input channel) to produce one output signal carried by two output lines (which are together called the output channel). These lines are usually wires and each input line is connected to an electrode on or in biologic tissue. Usually one input line is connected to a signal electrode, which is placed in a region of interest in the biologic tissue, and the other input line is connected to the reference electrode, which is placed in a location with relatively low noise. Biosignal recording equipment contain multichannel amplifiers made up of multiple single channel amplifiers, which permits recording from multiple signal electrodes. If a single reference electrode is connected to the second input of all of the amplifiers, this is called a referential recording setup. A ground electrode is also placed, usually on the forehead in EEG recording. The location of the referential electrode in EEG recording is usually chosen to be at the top of the head, at a distance from eye movement artifacts near the front of the head, muscle artifacts in the temporal regions, and the posterior dominant background rhythm in the posterior region. Figure 1.4 contains a diagram of the wiring of an amplifier system in a referential recording setup with two signal electrodes, one referential electrode and two amplifier output channels. This figure also shows the setup for bipolar recording, in which three electrodes are connected in a chain in which the middle electrode is connected to both amplifiers.

Because there is so much noise in the environment of neurophysiologic recordings, a special type of amplifier, called a differential amplifier, is used in neurophysiology recording equipment. This type of amplifier is essentially a combination of three amplifiers wired together. In the first stage of a differential amplifier, two amplifiers working in parallel amplify (a) the potential difference between the signal electrode and the patient ground electrode and (b) the potential difference between the reference electrode and the patient ground electrode. In the second stage, a third amplifier amplifies the difference between the outputs of the two first-stage amplifiers. A differential amplifier can be used for both a referential and a bipolar recording setup, but Figure 1.5 depicts only the referential setup.

Environment noise usually causes a voltage potential difference between the recording electrodes and the ground electrode, which is called the common mode signal, and this is of relatively similar magnitude among the recording channels. The differential signals are the voltage potential differences between each signal electrode and its reference electrode, which are the signals of interest. Differential amplifiers work to cancel out much of the common mode signal, a process is called common mode rejection, and to amplify the differential signals. The degree to which a differential amplifier rejects the common mode signal is called the common mode rejection ratio (CMRR). This is calculated using the amplification of the common mode signal, called the common mode gain (G_cm) versus the amplification of the referential signal, called the referential gain (G_d). This is usually expressed in the unit of decibels (dB), which expresses the ratio of two numbers (usually signal magnitude) on a logarithmic scale multiplied by a factor of 20.

$\text{CMMR}=20{\log }_{10}\left({\displaystyle \frac{{\text{G}}_{\text{d}}}{{\text{G}}_{\text{cm}}}}\right)$

An amplifier which reduces the common mode signal by a factor of 10,000 (10⁴) relative to the differential signals has a CMRR of 80 dB. Most modern biosignal amplifiers 6have a CMRR of over 100 dB. The entire bioamplifier system (consisting of multiple channel amplifiers) has a total input impedance (I_in) which can be calculated using a set of equations (not given here) which incorporate the total resistance, capacitance, and inductance of the amplifier as well as the frequency content of the AC signal. The I_in is designed to be as high as possible, in order to improve the performance of the amplifier. Most modern amplifiers have an I_in of 100 MΩ (100 megaohms) or more. But a high I_im is not sufficient to assure a high-quality recording. Each electrode has an impedance value as well, which is primarily due to skin resistance and electrode impedance (both capacitive and resistive). If there is a difference between the impedance of the electrodes, this can cause leakage of common mode signal into the output of the differential amplifiers. For this reason, it is not just important to keep the impedance of each electrode as low as possible, but also important to keep the impedance of each electrode within a similar range (such that a few electrodes don’t have significantly higher impedance than the other electrodes).

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