Resting Membrane Potential

All living cells generate an electrical potential across their membranes, with the intracellular region relatively negative compared with the extracellular region.²⁸ This potential difference across the cell membrane is referred to as the resting membrane potential. The development and maintenance of the resting membrane potential can be explained by a simple model.

We can partition a beaker into right and left halves with an impermeable membrane containing multiple closed potassium channels. Assume this membrane separates two different concentrations of a potassium chloride (KCl) solution with a 10-mM concentration on one side and 100-mmol/L concentration on the other (Figure 9-1).¹⁷ Potassium chloride in solution exists as positive potassium (K⁺) ions (cations) and negative chloride (Cl^–) ions (anions). A voltmeter (a device that detects potential differences) measuring the two solutions fails to detect a potential difference because there is a lack of physical continuity between the left and right halves of the beaker when the partition’s potassium channels are closed. In other words, the two solutions are electrically independent.

FIGURE 9-1 A beaker containing two different concentrations (10 mmol/L and 100 mM) of a potassium chloride (KCl) solution existing as potassium (K⁺) and chloride (Cl^–) ions. An impermeable partition containing closed potassium channels separates the two different concentration solutions. A voltmeter placed across the partition fails to register any voltage difference. If the partition is now made selectively permeable to just the potassium ions (potassium channels are opened), the concentration gradient difference will drive potassium ions into the lower-concentration side of the beaker until the electrical attraction from the accumulating negatively charged chloride ions prevents any further net K⁺ ion movement, thus establishing a dynamic equilibrium. At this point, a potential difference exists across the partition and represents the equilibrium potential.

(Redrawn from Dumitru D, Amato AA, Zwarts MJ: Electrodiagnostic medicine, ed 2, Philadelphia, 2002, Hanley & Belfus, with permission.)

If we now open the membrane’s potassium channels, K⁺ cations will flow “down” their concentration gradient from the high (100 mm/L) to low (10 mm/L) ion concentration side of the beaker (see Figure 9-1). The potassium ions will continue this directional flow until there is a balance between (1) the forces of the physical concentration gradient difference driving potassium to the lower-concentration region, and (2) the electrical gradient opposing this directional ion flow. Because there are only potassium channels, the negative chloride ions cannot pass through the membrane and remain on their respective sides of the beaker. As more and more positive potassium ions leave one side of the beaker, there begins to develop an unbalanced or “excess” amount of negative charges (Cl^–) on the high-concentration side of the beaker, with an equal buildup of “excess” positive charges (K⁺) on the other side of the beaker. The increasing net negative charge of the beaker half with the increasing number of unbalanced chloride ions begins to make it increasingly difficult for the positive potassium charges to leave the high-concentration side of the beaker. This is because the progressively building net negative charge increasingly attracts those remaining positive potassium ions. Similarly, a growing amount of positive potassium ions on the formerly low potassium concentration side of the beaker begin to increasingly repel additional potassium ions attempting to enter this side of the beaker.

At some point, the opposing electrical charges on the two sides of the beaker prevent any more potassium from leaving the beaker’s high-concentration side, even though there is still a higher potassium concentration on this side compared with the other. A balance is established between the ionic concentration forces driving potassium ions from the high- to low-concentration regions, and the electrical forces (positive repelling and negative attracting) tending to keep potassium ions in the more concentrated portion of the beaker. Any potassium ions that randomly enter the lower-concentration side of the beaker are balanced by other potassium ions similarly crossing in the opposite direction. The situation where balance between electrical and concentration forces exists is said to be a dynamic equilibrium. Placing a voltmeter across the partition measures a negative potential difference, as electrical continuity is now present between the halves of the beaker through the open potassium ion channels.

The above simple example can be applied to all cells in the body, and in particular to nerve and muscle cells. A nerve’s axon will be used as a prototypical example, although the same principles apply to muscle cells. The nerve cell is known to have a specialized cell membrane permeable primarily to potassium and chloride ions in the resting state, because of proteinaceous transmembranous ion channels rendering the membrane selectively permeable (i.e., semipermeable).³¹ The potassium channels are referred to as passive, because they are always open and permit the free flow of this ion. Contained within the axon but incapable of crossing the cell membrane are large, negatively charged protein molecules. This negative charge attracts potassium ions from outside the cell to enter through the passive potassium channels, resulting in a buildup of potassium ions within the axon. This process continues until there is so much potassium within the axon that the continued entry of more potassium ions is prevented by the high intracellular potassium concentration, even though all the negative charges have not yet been electrically balanced. This is because the force of the accumulated potassium ions’ concentration gradient now attempting to drive potassium out of the cell is just large enough to balance the intracellular anions’ electrical force attracting potassium ions into the cell.

Similar to the above beaker example, a dynamic equilibrium eventually develops between (1) intracellular negative charges attracting potassium ions, and (2) a high intracellular potassium concentration impeding further potassium ion entry. This dynamic equilibrium occurs at a point when the intracellular negative potential is reduced by the inflowing potassium ions to a value approximating –80 to –90 mV compared with the extracellular environment.

Nernst Equation

The above examples of beakers and cells can be expressed mathematically by simply stating that the net “work” of both the electrical gradient work (W_elec) and the concentration gradient work (W_con) is zero in the resting state (W_con + W_con = 0). This means that the work, or energy, of developing the concentration gradient (W_con) is balanced by, or equal but opposite to, that developed by the electrical gradient (W_elec) during the resting state: W_elec = –W_con. The negative sign is present to denote the “opposite” or balanced aspect of the work. The electrical work is expressed as W_elec = Z_iFE_m. The symbols designate specific aspects defining electrical ion work: Z_i is the ion’s charge, F is Faraday’s constant, and E_m is the transmembrane potential. The work required to move ions across the membrane can be expressed as the natural logarithm of the ionic concentration differences between the intracellular ([I]_i) and extracellular ([I]_e) ions. Universal gas (R) and temperature (T) constants are conversion factors necessary to balance units between all the variables. Substituting the above-noted variables into the balanced work equation results in the following equations:

This formula can be rearranged to find the potential at which the electrical work just balances the concentration work (i.e., the dynamic equilibrium or resting membrane potential) by solving the above equation for E_m

The above equation is more commonly known as the Nernst equation, and is a mathematical statement of the potential at which all the electrical and concentration forces are balanced in the cell’s resting state (i.e., the resting membrane potential).^28,31 By substituting the actual values for the different variables and using the more familiar base 10 logarithm, the equation converts to the more recognizable form. Also, the approximate concentration ratio of intracellular to extracellular potassium is 20:1. The Nernst equation then becomes:

Sodium Pump

Experimentation has shown that the Nernst equation predicts the resting membrane potential quite well with different extracellular potassium concentrations, as long as the potassium concentration is relatively high. When the extracellular potassium concentration is low, there is a deviation of the resting membrane potential from that predicted, with a less-negative potential achieved. This finding suggests that another ion (sodium: Na⁺) has some influence on the resting membrane potential. It turns out that sodium has a very high extracellular concentration compared with intracellular ion concentration, which results in small quantities of sodium ions leaking into the membrane through a few passive sodium channels present in the cell’s membrane. This relative impermeability of positive sodium ions, combined with a high extracellular but low intracellular sodium ion concentration, and the resulting electrical drive to enter the cell (negative inside), would tend to “run down” the cell resting membrane potential over time. Fortunately, the cell has developed a mechanism whereby this run down is prevented. Located within the cell membrane is an energy-dependent sodium-potassium pump that pumps in potassium ions and pumps out sodium ions in just the right ratio to match the sodium ions entering and the compensatory potassium ions exiting the cell. Two sodium ions are extruded for every three potassium ions taken into the cell. The sodium-potassium pump maintains the exact ionic balance necessary to sustain a stable resting membrane potential by maintaining this 2:3 ratio.

Goldman-Hodgkin-Katz Equation

An important modification of the Nernst equation is the inclusion of ion permeability as being the primary influence on the cell’s transmembrane voltage. The greater an ion’s permeability, the more likely it is to influence the transmembrane potential. This is because the equilibrium potential of the most permeable ion in effect becomes the cell’s resting membrane potential. The equation accounting for the different permeability (designated as “p” in the equation below) factors is known as the Goldman-Hodgkin-Katz equation^28,30,31:

In this equation, it can be seen that the cell’s transmembrane voltage (E_m) is primarily dependent on which ion has the greatest permeability. For example, in the resting state, the permeability of potassium is known to be relatively high because of non–voltage-gated potassium passive leak channels, while the permeability of sodium ions is very low. Chloride ions are distributed through chloride channels that are always open at the resting membrane voltage, and thus adjust to whichever ion’s permeability predominates between potassium and sodium as dictated by the net transmembrane potential. With a high potassium and low sodium permeability, the above equation simplifies to the Nernst equation; that is, potassium is the predominant ionic species, and E_m becomes –75 mV. If sodium permeability were to increase dramatically, then E_m would approach the sodium ion equilibrium potential of +55 mV. It would not quite reach this value because potassium and chloride ions continue to have some influence and would hold the maximum potential to a less positive (more negative) value of about +40 mV.

Action Potential Generation

In addition to the passive (always open) potassium ion channels and relatively few passive sodium ion channels, there are also sodium and potassium ion channels within nerve and muscle cell membranes modulated by transmembrane voltage differences. These channels are voltage-gated because they open and close depending on the transmembrane voltage.²⁵ Muscle and unmyelinated nerve contain both sodium and potassium voltage-gated channels. These voltage-gated sodium and potassium ion channels are closed at the resting membrane potential. If the transmembrane voltage changes toward a more depolarized direction (less negative) and reaches about 15 to 20 mV less negative than the resting membrane potential, the voltage-gated sodium channels open. This results in an increased permeability of the sodium ion, a process known as sodium activation. As noted above, the Goldman-Hodgkin-Katz equation predicts that the transmembrane potential shifts toward the sodium ion equilibrium potential. This massive shift in transmembrane potential is referred to as depolarization. After staying open for a short period, the sodium gates automatically close (sodium inactivation), with a return of the resting membrane potential again dictated by the resting state ion permeabilities (repolarization). In muscle and unmyelinated nerve membranes, a delayed opening of potassium voltage-gated channels occurs secondary to the depolarization and assists in repolarization.

Very few ions actually cross the membrane for sodium-induced depolarization or potassium-mediated repolarization. The region of membrane where there are large numbers of voltage-gated sodium channels in the open conformation acts as a so-called current sink for sodium ions to “sink,” or enter, the cell’s interior. This implies that a nearby source for the sodium ions must be present. The surrounding extracellular membrane region acts as the current source, thus permitting an ionic flow from the region surrounding the current sink. Sodium ions are thereby removed from the outside of the membrane surrounding the sink (making this region relatively more negative) and deposited on the inside of the cell (Figure 9-2). The newly introduced intracellular ions migrate to help neutralize some of the cell’s interior negative charges. This current flow, or charge transfer, from the extracellular to intracellular space is referred to as a local circuit current.¹⁷ The net effect of charge transfer is to make the cell’s interior less negative and exterior more negative, thereby shifting the transmembrane voltage in the more depolarized direction about the current sink. If the charge transfer is sufficient to depolarize the cell by approximately 15 to 20 mV, the membrane surrounding the sink is induced to permit sodium activation and hence undergo a significant depolarization. This process can then continue along the length of the cell.

FIGURE 9-2 A, Sodium (g_Na) and potassium (g_K) ion conductances are depicted over time resulting in an alteration of the transmembrane potential, creating an action potential. B, The spatial relationship of the sodium and potassium ion flux during an action potential is schematically depicted. Note the alteration of the transmembrane ionic potential differences corresponding to the depolarization and repolarization. C, Local circuit currents described the pathways of extracellular sodium ions entering the cell and then migrating longitudinally within the cell. D, Triphasic extracellular waveform associated with the intracellular monophasic action potential.

(Redrawn from Dumitru D, Amato AA, Zwarts MJ: Electrodiagnostic medicine, ed 2, Philadelphia, 2002, Hanley & Belfus, with permission.)

The above process creates an action potential spike at the original site of sodium activation. A mechanical, chemical, or electrical stimulus that causes the membrane potential to reach threshold over a localized region is all that is required to serve as the initiating stimulus of action potential generation. Once the process begins, it is self-sustaining as long as there are sufficient ion channels to repeat the depolarization process. The intracellular action potential is essentially a monophasic positive spike: –75 mV resting potential; +40 mV spike; return to resting –75 mV with sodium inactivation and potassium activation (see Figure 9-2). The membrane’s threshold value must be reached to generate the self-sustaining action potential that is the same at all regions of the membrane. This concept is referred to as the all-or-none phenomenon.

The nodes of Ranvier in myelinated nerves lack voltage-gated potassium channels and contain only voltage-gated sodium channels.^47,48 The action potential actually “jumps” from one node to the next, creating an efficient means of action potential propagation that is referred to as saltatory conduction. Repolarization in myelinated nerve does not require a delayed potassium current. As noted above, the resting membrane potential is restored once the permeability of sodium is reduced. Passive “back-leak” sodium and potassium currents are thought to mediate the discharge of the membrane’s capacitance, which accumulates over time with multiple action potential discharges.

Gender

Only a few studies have attempted to investigate the difference in nerve conduction studies between men and women.³ Noted is a slight increase in the antidromic sensory nerve amplitudes for both the median and ulnar nerves recorded from the digits in women. Also, women demonstrate a greater nerve conduction velocity (NCV) for upper and lower limb nerves compared with men. Both of these differences, however, are eliminated when one considers limb length and digit circumference (see below).⁴⁰

Aging

Several generalizations can be made regarding peripherally evoked sensory nerve action potentials (SNAPs) and aging. The conduction velocity demonstrates a consistent decline approximating 1 to 2 meters per second per decade.³⁶ The duration of SNAPs is about 10% to 15% longer in persons aged 40 to 60 years, and 20% longer in those aged 70 to 88 years, compared with persons aged 18 to 25 years.⁸ Compared with the 18- to 25-year-old group, the SNAP amplitude is one half and one third, respectively, for the 40- to 60-year-old and 70- to 88-year-old groups. The distal sensory latencies reveal a similar prolongation with age. There is a suggestion that the median and radial nerves do not demonstrate considerable alteration with age.¹⁹ At present, there is disagreement as to the magnitude of change in SNAP parameters induced by the aging process.

The results of aging on conduction velocity have been examined in a number of upper and lower limb nerves. Motor NCVs reveal similar changes to those described for sensory nerves. The newborn’s motor NCVs are about half of adult values, which are reached by 3 to 5 years of age.² After the age of 50 years, the conduction velocity of the fastest motor fibers progressively declines by approximately 1 to 2 m/s per decade. There is a concurrent increase in the distal motor latency and decrease in the motor response’s amplitude with advancing age. H-reflex latency demonstrates little alteration with aging in the healthy elderly.²⁰ The decrease in amplitude is difficult to ascertain clinically because of the wide range of normal H-reflex amplitudes and the central effects on amplitude that are difficult to control and quantify.

Digit Circumference

Females consistently demonstrate significantly higher antidromic SNAP amplitudes for the median and ulnar nerves recorded from the second and fifth digits.³ A negative linear correlation exists between finger circumference and amplitude for these two nerves. It is known that as the distance between the recording electrode and neural generator increases, the amplitude precipitously declines. Increasing the circumference of the finger displaces the electrode further from the nerve. Because men have significantly larger finger circumferences than women, this appears to explain the difference in SNAP amplitudes. There is no evidence that this difference is due to an intrinsic neural difference between male and female nerves.

Height

Several investigations have documented slower lower limb NCVs in taller compared with shorter individuals.^9,33 This difference is independent of the limb’s temperature or subject’s age. The etiology of this finding is unknown. Distal nerve tapering or an abrupt change in axon diameter has been speculated to account for this finding, but the exact etiology has not been definitively identified.^14,46

Temperature

Temperature is one of the most important factors influencing nerve conduction studies. As the temperature of the nerve is lowered, the amount of current required to generate an action potential increases. This decreased excitability is a direct temperature effect on the nerve’s action potential–generating mechanism at the nodes of Ranvier, and not a result of membrane resistance changes. The transmembrane resistance is not increased by a drop in temperature.^26,27 In addition to excitability, the configuration of an action potential is profoundly affected by a drop in temperature.

The action potential’s amplitude, rise time, and fall time all increase as the nerve’s temperature declines. The time required for the action potential of a cold nerve to reach its peak depolarization from the resting membrane level increases approximately 33%.³⁸ Similarly, the time necessary for the action potential to return to its resting level is also increased, but much more so than the rise time (69%). Because both the SNAP duration and the spike height increase, the area of the SNAP increases dramatically at lower temperatures.

The compound muscle action potential (CMAP) arising from cooled muscle tissue demonstrates similar changes as those noted for SNAPs. The CMAP amplitude, duration, rise time, and area all increase as the muscle’s temperature is reduced. Intramuscular recordings also reveal that those motor units in close proximity to the recording electrode are also increased in the same parameters noted above.

Temperature also has an impact on NCVs. Based on the prolongation of the rise and fall time noted above, it should be possible to infer the nerve’s response to cooling with respect to NCV. Because propagation is saltatory in myelinated nerves, decreased temperature results in an increase in the amount of time necessary to reach the action potential’s peak at each node of Ranvier, thereby slowing action potential propagation and reducing conduction velocity.

The first detailed investigation of temperature effects on NCV in human nerves revealed an NCV to temperature correlation of 2.4 m/s per °C for median and ulnar motor conduction.²⁴ With every 1° C drop in temperature, there was a 2.4 m/s decrease in the conduction velocity. Reductions in conduction velocity for upper limb motor nerve fibers have also been found to approximate a decrease of 4% or 5% per °C.^10,29 Correction factors using subcutaneous and intramuscular readings are equally correct, but it is more convenient and less painful to use surface measurements.²²

In the upper limb, the relationship between temperature and NCV has been investigated for the surface temperature range of 26° C to 33° C, measured at the midline of the distal wrist crease. Calculations reveal that for median motor and sensory nerves, NCV is altered 1.5 and 1.4 m/s per °C, respectively, while the distal latency for both nerves changes about 0.2 ms/°C.^21–23 The ulnar nerve demonstrated motor and sensory temperature relationships of 2.1 and 1.6 m/s per °C, respectively, and a distal motor and sensory latency correlation of 0.2 ms/°C.

Because of the profound effects of temperature on NCV, it is clear that reliable nerve studies require temperature control. A cool limb, irrespective of the ambient room temperature, can result in latencies, NCVs, and amplitudes that are not in the “normal” range. A normal limb study can yield results that are spuriously thought to be abnormal, but that are due only to the low temperature. This is an especially important issue when an abnormal nerve is being studied. Correction factors can be used for normal nerves, but serious questions remain about how abnormal nerves respond to temperature variations. Although applying a correction factor is less time-consuming than heating the limb, it is doubtful how accurately correction factors can be applied to abnormal nerves. Until more data are available regarding the best correction factor for diseased nerves, warming of the limb should be considered superior to using correction factors. The surface temperature approximating the recording electrodes should be at least 32° C in the upper limbs and 30 °C in lower limbs. Caution must be exercised when attempting to warm the limbs of patients with ischemic limbs, or those with altered sensation, to avoid injury.

Nerve Potentials

Sensory Nerve Action Potentials

Clinical Recordings

SNAPs can be obtained with either antidromic or orthodromic techniques.⁸ The term antidromic implies that the induced neural impulse propagates along the nerve in a direction opposite to its physiologic direction; for example, stimulating the median nerve at the wrist and recording the ensuing response from the second or third digit. A nerve will conduct an impulse proximally and distally from the point of stimulation by a depolarizing current. On the other hand, stimulating the median sensory fibers on the second digit and recording from the wrist is an example of an orthodromic technique. In orthodromic recordings, the sensory fiber impulses are detected at a site proximal to the stimulus as they travel physiologically from a distal to a more proximal region. Antidromically obtained SNAPs are usually larger and hence easier to assess, because the recording electrodes are in close proximity to the proper digital nerves than when a recording electrode is placed over the median nerve at the wrist for orthodromic techniques. Mixed nerve responses can have a component of both orthodromic and antidromic waveforms. For example, midpalm stimulations recorded at the wrist are a combination of orthodromic sensory and antidromic motor responses.

SNAP Configuration

Antidromic and orthodromic bipolar SNAP waveform recordings are typically biphasic rather than triphasic. The biphasic, negative-positive potential is a result of the bipolar recording technique and not a violation of volume conductor theory. Biphasic SNAP waveforms can best be understood by use of bipolar and referential recording montages for median nerve stimulation at the wrist (Figure 9-4).¹³ The median SNAP is indeed a triphasic waveform and conforms to the principles of volume conduction, but only appears biphasic because of the recording montage used.

FIGURE 9-4 The median nerve is stimulated at the wrist with an antidromic sensory recording montage. Active (a) and reference (r) are located on fingers as designated above. A, Bipolar recording with the commonly observed biphasic median nerve sensory nerve action potential (SNAP). B, The same active electrode location in (A) is referenced to the fifth digit, resulting in a triphasic SNAP. C, An active electrode placed on the fifth digit but referenced to the third digit permits one to observe what this electrode records when the median nerve is stimulated. An inverted triphasic potential of small magnitude is detected. It is inverted because of its connection to the inverting amplifier port. D, Electronically summating the potential recorded in (B) and (C) yields that recorded with a bipolar montage in (A).

(Redrawn from Dumitru D. Volume conduction: theory and application. In: Dumitru D, editor: Physical medicine and rehabilitation state of the art reviews: clinical electrophysiology, Philadelphia, 1989, Hanley & Belfus, with permission.)

It is also possible to predict the optimal interelectrode separation to maximize the biphasic potential’s amplitude in the bipolar recording.¹⁷ The critical factor in this instance is the rise time, baseline to negative peak, of the biphasic potential, because it is this parameter that defines the waveform’s maximum amplitude. The recording electrodes must be located at a distance greater than the action potentials’ spatial extent, represented by the rise time duration. The rise time of most SNAPs approaches 0.8 ms, which represents a longitudinal extent of 40 mm for an action potential conducting at 50 m/s (50,000 mm/1000 ms = D/0.8 ms; D = 40 mm). If the two recording electrodes are separated by a distance less than 40 mm, some similar information regarding the main peaks of the waveforms recorded by both recording electrodes (active and reference) results in mutual cancellation of data, producing a potential with a smaller amplitude. A portion of the nerve will be depolarizing under the reference electrode while still in some degree of depolarization under the active electrode. At interelectrode separations greater then 40 mm, the biphasic potential’s negative peak amplitude will no longer grow, but the terminal positive phase will enlarge slightly and might change its configuration. These findings can be demonstrated by varying the distance between recording electrodes and observing the ensuing results (Figure 9-5). In effect, as the recording distance decreases below 40 mm, the amplitude of the recorded waveform declines and the peak latency shortens.

FIGURE 9-5 The effect of interelectrode separation can be easily demonstrated by evoking an antidromic median sensory nerve action potential (SNAP) and progressively increasing the interelectrode separation between the active and reference electrode. The active electrode remains in the same location, while the reference electrode is sequentially displaced more distal on the digit. As can be seen, the SNAP amplitude increases, peak latency increases, and the onset latency remains the same.

(Redrawn from Dumitru D, Walsh NE: Practical instrumentation and common sources of error, Am J Phys Med Rehabil 67:55-65, 1988, with permission.)

Muscle Potentials