## Essentials of Electricity Reviewed

The cell membrane potential is seemingly ubiquitous in living cells. it is present in not only nerve and muscle cells but all the other cells from which recordings have ben made, including kidney and liver cells and even plant cells!

It is important to realize that a membrane potential is always a potential difference, i.e. the measurement is that of the voltage between two points-in this case, the inside of the cell with respect to the outside. it is impossible to measure the "potential" of a single point. (This obvious statement is necessary because it is surprisingly easy to lose sight of simple physical principles in a biological context!)

Although early extracellular measurements had indicated that the inside of the cell was negative with respect to the outside, a clear demonstration of the magnidute of the membrane potential was not possible until the development of the intracellular micropipett. Orignially used to stdy plant cells, the micropipette was adapted by Gram, Ling and Gerard to the study of animal tissue. Micropipettes are improbabl devices made by heating glass tubing and then ulling it rapidly ina longitudinal direction so that the diameter becomes very small while the ratio of wall thickness to lumens remains constant. These small electrodes can penetrate cell membranes, with the membrane sealing around the electrode tip after penetration so that the potential difference across the cell membrane can be recorded, apparently without significantly altering the properties of the impaled cell. Modern micropipettes can be used to study many cells, but they are still too large to penetrate the smaller dendrites and axons.

The magnitude of the cell membrane potential is about 90mV. This value an vary somewhat from cell to ell but is rarely over 100mV.

Question: What is 100 mV in volts?

Answer: 100 mV = 100 x 10^-3 Volts or 0.1 Volts

Thus the cell membrane potential is described as being about -90 mV, where the sign indicates the polarity of the inside of the cell with respect to the outside.

It is important to realize that a membrane potential is always a potential difference, i.e. the measurement is that of the voltage between two points-in this case, the inside of the cell with respect to the outside. it is impossible to measure the "potential" of a single point. (This obvious statement is necessary because it is surprisingly easy to lose sight of simple physical principles in a biological context!)

Although early extracellular measurements had indicated that the inside of the cell was negative with respect to the outside, a clear demonstration of the magnidute of the membrane potential was not possible until the development of the intracellular micropipett. Orignially used to stdy plant cells, the micropipette was adapted by Gram, Ling and Gerard to the study of animal tissue. Micropipettes are improbabl devices made by heating glass tubing and then ulling it rapidly ina longitudinal direction so that the diameter becomes very small while the ratio of wall thickness to lumens remains constant. These small electrodes can penetrate cell membranes, with the membrane sealing around the electrode tip after penetration so that the potential difference across the cell membrane can be recorded, apparently without significantly altering the properties of the impaled cell. Modern micropipettes can be used to study many cells, but they are still too large to penetrate the smaller dendrites and axons.

The magnitude of the cell membrane potential is about 90mV. This value an vary somewhat from cell to ell but is rarely over 100mV.

Question: What is 100 mV in volts?

Answer: 100 mV = 100 x 10^-3 Volts or 0.1 Volts

Thus the cell membrane potential is described as being about -90 mV, where the sign indicates the polarity of the inside of the cell with respect to the outside.

## Polarity and Magnitude of Cell Membrane Potential

Review of all of the basic ideas required to understand our treatment of membrane potentials and cell excitability.

## Physical and Chemical Background of Membrane Potentials

## Electronics

The basic ideas about electricity must be clear in your mind. A potential difference between two points (such as exists across the membrane) may cause a movement of charge.

The unit of charge is the coulomb (C), where 1 C = 6 x 10^18 electron charges; the flow of charge is called current, measured in amperes (A), where 1A = 1 C/s passing a given point.

Note that all currents may be said to travel in complete circuits. Of the many analytic elements used in the description of electrical circuits, there are only three whose properties need to be understood in order to follow the ideas presented on this page; batteries, resistors, and capacitors. The following sections review these elements.

Batteries: A battery (labeled E) may be defined as a device for storing potential chemical energy in such a way that the energy can become available to drive a current when the circuit between the battery poles is completed. In the ideal battery, the amount of chemical energy so stored is considered to be infinite, hence the potential should not be affected by the rate or duration of energy release. Thus, the battery symbol represents a constant-voltage source that is not affected by the actual amount of current flowing in the circuit.

Resistors. When a battery is attached to a resistor, a current flows in the circuit. Note: Although it is well known that currents in metallic conductors are a result of electron movements, throughout this course, the direction of current flow is presented as the direction of moement of positive particles. That is, current flows from the positive to the negative pole of the battery.

The relationship between the battery voltage, the size of the resistor, and the amount of current is given by Ohm's law:

I = E/R <=> E = IR <=> R = E/I

Where I = current, in amperes (A)

E = potential difference across the battery, in volts (V)

R = resistance in ohms (ohm symbol)

Question: If a 6V battery produces a 3A current, what is the value of R?

Resistance, as a concept, describes how effectively a circuit element "resists" flow of charge. In membrane physiology, often it is intuitively easier to invert this conceptand think in terms of the ease with which charge can pass across a cell membrane. We thus define conductance "g" as the reciprocal of resistance, with units of "reciprocal ohms." or mho (the word ohm spelled backward)

Thus g = 1/R and ohm's law can be written as I = gE

Note that here, for a constant E, current varies directly with conductance, when the variable conductance g increases I also increases. We use this relationship repeatedly when dealing with membrane currents in subsequent chapters.

A circuit involving two resistors in series with a battery is important in understanding much of what follows.

Such a voltage-divider circuit of two resistors in series is shown. Since the current must be the same through the two resistors in series, it sis easy to derive the following equation:

V1 = E (R1/R1+R2)

This equation shows that V1 is a fraction of the battery voltage E, as determined by the ratio of R1 to the total resistance.

It is instructive to see what happens to V1 and R1 is varies, given that E and R2 are constant. you ill find this of interest since an important part of the understanding of membrane potentials involves the change of a resistance in series with a battery. Therefore, lets look carefully at what happens. If R1 is very low, the V1 is almost zero, as you can readily see from where R1 / (R1 + R2) is almost zero. This is the situation when the two points on either side of R1 are connected by a very low-resistance path, such as a wire. This example verifies the simple fact that there can be no difference in potential between two points connected by a low resistance (high conductance).

If the resistance of R1 is raised until R1 = R2 then you can see from eq 3-4 that V1 = E/2 (the voltage of E is equally divided by the equal resistances.) This is the most obvious example of the voltage-divider aspects of this circuit.

Finally, if R, went to infinity (as would occur if R1 were an open switch) then V1 would go to E, no matter the value of R2.

When considering membrane potentials later, you will encounter the idea of the internal resistance of a battery.

The circuit of Fig 3-3 and Eq 3-4 can help you to understand the idea of internal resistance of a battery. You must realize that the battery symbol as defined previously cannot represent a real battery, because if the battery of Fig 3-1 were hooked up to a zero resisstance (a short circuit) the battery would produce (by Ohm's law) an infinite current! No real battery can do this. Therefore, the circuit diagram for a real battery connected to an external resistance must be diagrammed as shown in Figure 3-4. A moment's glance should tell you that you are familiar with this circuit, for it is the same as that in Figure 3-3 with the parts somewhat rearranged. The resistance R2 is now the internal resistance of the real battery, whose external terminals are at points A and B.

Now you can see how the internal resistance R2 helps you to understand the real battery. If the R1 resistance is made zero by shorting the battery, then the presence of R2 sitill limits the current to I = E/R2, rather than the infinite current of the "ideal" battery when short-circuited. A good battery (ne able to deliver current tno a low external resistance without significantly droppig its voltage has internal reisitance. As the battery becomes discharged, the internal resistance increases to the point at which the voltage drops noticeab ly. a light connected to a sdischarged mattery is dim)

In practice, batteries differ not only in voltage and internal resistance but also in their physical size A 12-V transistor battery is a small fraction of the bulk of a car attery. This difference reflects the total quantity of charge stored, as measured in ampere-hours.

You will see later that a small cell is like a small battery: it runs down more quickly if it cannot be recharged.

Capacitors. A capacitor is a device that can "store" charges on its plates, with the plates being closely spaced conductors separated by a nonconducting medium. Across a given capacitor, the amount of charge asymmetry is directly proportional to the applied voltage. This is given by

Q=CV where

Q = Quantity of charge, in coulombs

C = size of the capacitance, in farads

V = potential across the capacitor, in volts

The unit of charge is the coulomb (C), where 1 C = 6 x 10^18 electron charges; the flow of charge is called current, measured in amperes (A), where 1A = 1 C/s passing a given point.

Note that all currents may be said to travel in complete circuits. Of the many analytic elements used in the description of electrical circuits, there are only three whose properties need to be understood in order to follow the ideas presented on this page; batteries, resistors, and capacitors. The following sections review these elements.

Batteries: A battery (labeled E) may be defined as a device for storing potential chemical energy in such a way that the energy can become available to drive a current when the circuit between the battery poles is completed. In the ideal battery, the amount of chemical energy so stored is considered to be infinite, hence the potential should not be affected by the rate or duration of energy release. Thus, the battery symbol represents a constant-voltage source that is not affected by the actual amount of current flowing in the circuit.

Resistors. When a battery is attached to a resistor, a current flows in the circuit. Note: Although it is well known that currents in metallic conductors are a result of electron movements, throughout this course, the direction of current flow is presented as the direction of moement of positive particles. That is, current flows from the positive to the negative pole of the battery.

The relationship between the battery voltage, the size of the resistor, and the amount of current is given by Ohm's law:

I = E/R <=> E = IR <=> R = E/I

Where I = current, in amperes (A)

E = potential difference across the battery, in volts (V)

R = resistance in ohms (ohm symbol)

Question: If a 6V battery produces a 3A current, what is the value of R?

Resistance, as a concept, describes how effectively a circuit element "resists" flow of charge. In membrane physiology, often it is intuitively easier to invert this conceptand think in terms of the ease with which charge can pass across a cell membrane. We thus define conductance "g" as the reciprocal of resistance, with units of "reciprocal ohms." or mho (the word ohm spelled backward)

Thus g = 1/R and ohm's law can be written as I = gE

Note that here, for a constant E, current varies directly with conductance, when the variable conductance g increases I also increases. We use this relationship repeatedly when dealing with membrane currents in subsequent chapters.

A circuit involving two resistors in series with a battery is important in understanding much of what follows.

Such a voltage-divider circuit of two resistors in series is shown. Since the current must be the same through the two resistors in series, it sis easy to derive the following equation:

V1 = E (R1/R1+R2)

This equation shows that V1 is a fraction of the battery voltage E, as determined by the ratio of R1 to the total resistance.

It is instructive to see what happens to V1 and R1 is varies, given that E and R2 are constant. you ill find this of interest since an important part of the understanding of membrane potentials involves the change of a resistance in series with a battery. Therefore, lets look carefully at what happens. If R1 is very low, the V1 is almost zero, as you can readily see from where R1 / (R1 + R2) is almost zero. This is the situation when the two points on either side of R1 are connected by a very low-resistance path, such as a wire. This example verifies the simple fact that there can be no difference in potential between two points connected by a low resistance (high conductance).

If the resistance of R1 is raised until R1 = R2 then you can see from eq 3-4 that V1 = E/2 (the voltage of E is equally divided by the equal resistances.) This is the most obvious example of the voltage-divider aspects of this circuit.

Finally, if R, went to infinity (as would occur if R1 were an open switch) then V1 would go to E, no matter the value of R2.

When considering membrane potentials later, you will encounter the idea of the internal resistance of a battery.

The circuit of Fig 3-3 and Eq 3-4 can help you to understand the idea of internal resistance of a battery. You must realize that the battery symbol as defined previously cannot represent a real battery, because if the battery of Fig 3-1 were hooked up to a zero resisstance (a short circuit) the battery would produce (by Ohm's law) an infinite current! No real battery can do this. Therefore, the circuit diagram for a real battery connected to an external resistance must be diagrammed as shown in Figure 3-4. A moment's glance should tell you that you are familiar with this circuit, for it is the same as that in Figure 3-3 with the parts somewhat rearranged. The resistance R2 is now the internal resistance of the real battery, whose external terminals are at points A and B.

Now you can see how the internal resistance R2 helps you to understand the real battery. If the R1 resistance is made zero by shorting the battery, then the presence of R2 sitill limits the current to I = E/R2, rather than the infinite current of the "ideal" battery when short-circuited. A good battery (ne able to deliver current tno a low external resistance without significantly droppig its voltage has internal reisitance. As the battery becomes discharged, the internal resistance increases to the point at which the voltage drops noticeab ly. a light connected to a sdischarged mattery is dim)

In practice, batteries differ not only in voltage and internal resistance but also in their physical size A 12-V transistor battery is a small fraction of the bulk of a car attery. This difference reflects the total quantity of charge stored, as measured in ampere-hours.

You will see later that a small cell is like a small battery: it runs down more quickly if it cannot be recharged.

Capacitors. A capacitor is a device that can "store" charges on its plates, with the plates being closely spaced conductors separated by a nonconducting medium. Across a given capacitor, the amount of charge asymmetry is directly proportional to the applied voltage. This is given by

Q=CV where

Q = Quantity of charge, in coulombs

C = size of the capacitance, in farads

V = potential across the capacitor, in volts

**Engineering Principles**Recording and analyzing and interpreting electrical signals generated in the brain and by evoked potentials.

These signals are small! and surrounded by a variety of large electrical potentials originating in the environment.

Resolving true electrical brain activity requires three elements

These signals are small! and surrounded by a variety of large electrical potentials originating in the environment.

Resolving true electrical brain activity requires three elements

- good equipment
- meticulous recording technique
- improper technique may, in the worst case lead to injury of the patient from improper grounding or stray electrical currents

- informed interpretation of the data

Principles of Electricity

Standard is the recording of potential differences (voltage) between two points, one or both which are on the scalp.

Signals are movement of electrical charges in biological tissue.

Charge, is electronically quantized; approximation of (a continuously variable signal) by one whose amplitude is restricted to a prescribed set of values.

Standard is the recording of potential differences (voltage) between two points, one or both which are on the scalp.

Signals are movement of electrical charges in biological tissue.

Charge, is electronically quantized; approximation of (a continuously variable signal) by one whose amplitude is restricted to a prescribed set of values.

- it exists in units that correspond to the charge of elementary particles, such as protons and electrons
- the charge of a single electron is very small; in practice, much larger units of charge are used.

- usually denoted by I
- measured in units of amperes (A)
- 1 ampere of current represents a flow of 1 C of charge per second
- current flows when electrons move or in association with movement of negative ions or positive ions
- electron flow is more important in electronic devices
- ionic flow is more important in biological systems

- current flow is conventionally defined from positive to negative
- sodium Na+ ions moving from left to right (or chloride Cl- ions moving from right to left) would generate a positive current to the right

- electron flow is more important in electronic devices and ionic flow is more important in biological systems
- like charges repel and opposite charges attract
- a collection of freely moving charges will arrange itself in a uniform distribution so that
- positive and negative charges are as near to each other as possible
- positive-positive and negative-negative charge pairs are as far apart as possible

- other physical forces such as gravity, friction, magnetism, moving mass, and nuclear forces can oppose these electrical attractions and repulsions.
- this results in a separation of charges into more positive and negative areas.
- such a system stores electrical potential energy
- this energy is released when charges move to restore regional electrical neutrality
- the unit of energy in the MKS system is the joule (J)
- One joule, defined in terms of kinetic energy, is the energy required to accelerate a 1-kg mass by 1 m per square second over a distance of 1 m
- this is approximately equivalent to the energy a person would feel after dropping a lemon on his or her foot from waist high

- One joule, defined in terms of kinetic energy, is the energy required to accelerate a 1-kg mass by 1 m per square second over a distance of 1 m

- Voltage (V; or E for electromotive force) is defined as energy per unit charge
- one joule of energy is expended when 1 C of charge is moved across a potential difference of 1V
- voltages are always measured between two points in space
- it makes no more sense to say that a single point in an electrical circuit is 5 V than it does to say that a ball is "5m"
- in some circumstances the reference potential is called GROUND ("physical ground" in a discussion of the height of a ball or "electrical ground" in the case of a voltage difference).
- the precise meaning of electrical ground is elusive, because two places in the earth are rearely at identical potential with regard to any third point.
- nevertheless, potential differences between a circuit element and either ground rod typically are large in comparison with potential differences between two ground points

- a collection of freely moving charges will arrange itself in a uniform distribution so that

Examples of voltage and current for circuits of interest.

SystemLightening Hoover Dam Static From Carpet Household Light Bulb Car Battery Flashlight Battery Electrocardiogram Scalp Electroencephalography |
Volts100,000,000 50,000 2,000 110 12 1.5 0.0015 0.00005 |
Amps10,000 2,000 0.000001 1 200 0.6 0.00001 0.000001 |

- Impedance is a term used for the combined effects of resistance, capacitive reactance and inductive reactance
- Impedance can be significant in several aspects of EEG
- the most important of these is probably safety considerations
**dangerously low circuit impedances can allow high currents to pass through tissue with potentially disastrous consequences!**

****Impedance is also important in comparing amplitudes in different EEG channels.- High impedance (typically in a poorly affixed electrode) causes the EEG machine amplifiers to work improperly and distorts the resulting signal in that channel.
- Impedance is also an important factor in coupling the output of one amplification stage to another
- The EEG machine is designed so that electrodes should have impedances in the range of a few thousand ohms, whereas the input impedance of the machine is in millions of ohms
- If the impedance of the input is too low, the second stage may draw significant current from the primary stage and distort the measurement.
- Suppose for example that a 100 uV EEG signal is inputted into a circuit with a 1,000 ohm resister.
- Assume that the input impedance of the EEG machine is 10^6 ohms and therefore in a position to draw negligible current from the circuit
- Current through the circuit will be 0.1 nA
- In contrast, now suppose that the EEG machine has an input impedance of 1,000 ohms
- Total circuit impedance is now 2,000 ohms and current through the circuit is 50 nA
- Because of the low-input impedance, the output signal is attenuated and measured as 50 uV rather than 100 uV, as in the first case
- This illustrates that the high-input impedance of a good amplifier produces its output voltage largely independently of electrode impedance
- It is essentially a voltage divider with one resistance being MUCH larger than the other
- As a result of this design, the electrode impedance during normal EEG recording can vary by a factor of almost 10, with only minor alterations in the quality of the EEG
- Very high electrode impedances, which approach those of the EEG machine input cause the phenomenon called IMPEDANCE MISMATCH, which results in signal attenuation.

- Because of the low-input impedance, the output signal is attenuated and measured as 50 uV rather than 100 uV, as in the first case

- If the impedance of the input is too low, the second stage may draw significant current from the primary stage and distort the measurement.

- the most important of these is probably safety considerations

- Impedance can be significant in several aspects of EEG

Analog to Digital Converters

- The heart of a digital EEG machine is the analog-to-digital converter (ADC)
- This device usually consists of a circuit board installed in a computer and is composed of several conceptual parts
- a clock
- a voltmeter or series of voltmeters
- very rapidly accessible memory storage

- This device usually consists of a circuit board installed in a computer and is composed of several conceptual parts
- The signal from a single EEG channel is inputted into a corresponding channel in the ADC board
- the voltage across the input is measured and it's numerical value is written down in memory
- the clock ticks off a certain measures of time
- the process is repeated at regular intervals yielding a table of evenly spaced numbers
- the number of times per second that the voltage is measured is called the SAMPLE RATE and is measured in samples per second (HERTZ)

- the higher the sample rate, in general, the better the reproduction of the input signal
- ADC boards are measured according to their number of input channels; their throughput or the total number of samples per second that can be acquired by the entire device; and their resolution
- The throughput can usually be directed to and divided among any number of channels in the device.
- this number may be only one channel, if very fast sampling is required or the total number of channels available, depending on the application
- for example, if an ADC board has 32 input channels and a total throughput of 6,400 samples per second (6.4 kilohertz (kHz) it can sample each of 32 channels at a maximum of 200 Hz each
- the device could also sample two channels at 3.2 kHz each

- this number may be only one channel, if very fast sampling is required or the total number of channels available, depending on the application
- ADCs are also distinguished by their design for data sampling, including boards that sample each channel in turn and stagger them in time (it takes at least a few milliseconds to sample each channel), sample and hold devices that sample sequentially and then align data points in time and devices that sample all channels simultaneously
- another important characteristic of ADCs is their RESOLUTION or PRECISION
- this is a measure of how finely the voltage can be subdivided when measured
- this precision is measured in BITS, each bit being a place in a binary number
- the total number of voltage values that can be resolved is 2^n, where n is the number of bits
- if Vsubr is the maximum range of the board, then the input is resolved in steps whereby the change in V is Vsubr/2^n
- for example, if the board can resolve only two bits and is measuring on a scale of -100 to 100 uV, then there are 2^2 or four possible values for the EEG signal, each data point being rounded to the nearest 50 uV
- at this resolution, such a signal would look very rough, as measurements are rounded to the nearest 50 uV without any possible values in between
- this type of resolution is far different from the smooth lines drawn by pens on paper that are used with analog machines

- if Vsubr is the maximum range of the board, then the input is resolved in steps whereby the change in V is Vsubr/2^n

- BITS are used to measure resolution because the language of computers is BINARY numbers, in which each bit is a little electrical switch that is turned either on (a value of 1) or off (a value of 0)
- When these switches grouped together (usually in multiples of 8, 16, 32 or 64 at a time) they become binary numbers
- For example, in the number 101 in binary, the first place on the right has the decimal value of 1 * 1 = 1, the 0 in the middle (twos) place has the decimal value 0 * 2 = 0 and the 1 in the most leftward (fours) place has a decimal value of 1 * 4 = 4
- therefore the binary number 101 is equal to (1 * 4) + (0 * 2) + (1 * 1) = 5 in the decimal system

- ADC used in early digital EEG machines were eight-bit devices able to resolve EEG signals into 2^8 = 256 divisions
- therefore in a range -150 to +150 uV, steps of 300/256 uV or 1.17 uV can be resolved
- this initial resolution partially contributed to slow acceptance of these new devices because the tracings did not look as good as on paper
- most current EEG machines have 16 bit resolution and for an input range of =/- 15 uV can resolve 300/65,536 uV or 0.00457 uV

- of importance is that the input voltage (2,000 uV in this case) is not the actual input voltage that is divided up by the ADC
- rather, all brain activity, once brought into the machine, is amplified by a certain multiplier (called GAIN; the inverse of this is SENSITIVITY, the term commonly used to refer to controls to adjust amplitude on the EEG) that brings it into the standard input range of the ADC device (a typical range is =/- 5V)
- in the earlier case, recording =/- 1000 uV would require a gain of 5,000 to bring it to +/- 5