2.1 INTRODUCTION

In this chapter we consider the structure of nerve and muscle tissue and in particular their membranes, which are excitable. A qualitative description of the activation process follows. Many new terms and concepts are mentioned only briefly in this chapter but in more detail in the next two chapters, where the same material is dealt with from a quantitative rather than a qualitative point of view.

The first documented reference to the nervous system is found in ancient Egyptian records. The Edwin Smith Surgical Papyrus, a copy (dated 1700 B.C.) of a manuscript composed about 3500 B.C., contains the first use of the word "brain", along with a description of the coverings of the brain which was likened to the film and corrugations that are seen on the surface of molten copper as it cooled (Elsberg, 1931; Kandel and Schwartz, 1985).

The basic unit of living tissue is the cell. Cells are specialized in their anatomy and physiology to perform different tasks. All cells exhibit a voltage difference across the cell membrane. Nerve cells and muscle cells are excitable. Their cell membrane can produce electrochemical impulses and conduct them along the membrane. In muscle cells, this electric phenomenon is also associated with the contraction of the cell. In other cells, such as gland cells and ciliated cells, it is believed that the membrane voltage is important to the execution of cell function.

The origin of the membrane voltage is the same in nerve cells as in muscle cells. In both cell types, the membrane generates an impulse as a consequence of excitation. This impulse propagates in both cell types in the same manner. What follows is a short introduction to the anatomy and physiology of nerve cells. The reader can find more detailed information about these questions in other sources such as Berne and Levy (1988), Ganong (1991), Guyton (1992), Patton et al. (1989) and Ruch and Patton (1982).

2.2 NERVE CELL

2.2.1 The Main Parts of the Nerve Cell

The nerve cell may be divided on the basis of its structure and function into three main parts:

(1) the cell body, also called the soma;

(2) numerous short processes of the soma, called the dendrites; and,

(3) the single long nerve fiber, the axon.

These are described in Figure 2.1.

The body of a nerve cell (see also (Schadé and Ford, 1973)) is similar to that of all other cells. The cell body generally includes the nucleus, mitochondria, endoplasmic reticulum, ribosomes, and other organelles. Since these are not unique to the nerve cell, they are not discussed further here. Nerve cells are about 70 - 80% water; the dry material is about 80% protein and 20% lipid. The cell volume varies between 600 and 70,000 µm³. (Schadé and Ford, 1973)

The short processes of the cell body, the dendrites, receive impulses from other cells and transfer them to the cell body (afferent signals). The effect of these impulses may be excitatory or inhibitory. A cortical neuron (shown in Figure 2.2) may receive impulses from tens or even hundreds of thousands of neurons (Nunez, 1981).

The long nerve fiber, the axon, transfers the signal from the cell body to another nerve or to a muscle cell. Mammalian axons are usually about 1 - 20 µm in diameter. Some axons in larger animals may be several meters in length. The axon may be covered with an insulating layer called the myelin sheath, which is formed by Schwann cells (named for the German physiologist Theodor Schwann, 1810-1882, who first observed the myelin sheath in 1838). The myelin sheath is not continuous but divided into sections, separated at regular intervals by the nodes of Ranvier (named for the French anatomist Louis Antoine Ranvier, 1834-1922, who observed them in 1878).

Fig. 2.1.

Fig. 2.2.

2.2.2 The Cell Membrane

The cell is enclosed by a cell membrane whose thickness is about 7.5 - 10.0 nm. Its structure and composition resemble a soap-bubble film (Thompson, 1985), since one of its major constituents, fatty acids, has that appearance. The fatty acids that constitute most of the cell membrane are called phosphoglycerides. A phosphoglyceride consists of phosphoric acid and fatty acids called glycerides (see Figure 2.3). The head of this molecule, the phosphoglyceride, is hydrophilic (attracted to water). The fatty acids have tails consisting of hydrocarbon chains which are hydrophobic (repelled by water).

If fatty acid molecules are placed in water, they form little clumps, with the acid heads that are attracted to water on the outside, and the hydrocarbon tails that are repelled by water on the inside. If these molecules are very carefully placed on a water surface, they orient themselves so that all acid heads are in the water and all hydrocarbon tails protrude from it. If another layer of molecules were added and more water put on top, the hydrocarbon tails would line up with those from the first layer, to form a double (two molecules thick) layer. The acid heads would protrude into the water on each side and the hydrocarbons would fill the space between. This bilayer is the basic structure of the cell membrane.

From the bioelectric viewpoint, the ionic channels constitute an important part of the cell membrane. These are macromolecular pores through which sodium, potassium, and chloride ions flow through the membrane. The flow of these ions forms the basis of bioelectric phenomena. Figure 2.4 illustrates the construction of a cell membrane.

Fig. 2.3.

Fig. 2.4.

2.2.3 The Synapse

The junction between an axon and the next cell with which it communicates is called the synapse. Information proceeds from the cell body unidirectionally over the synapse, first along the axon and then across the synapse to the next nerve or muscle cell. The part of the synapse that is on the side of the axon is called the presynaptic terminal; that part on the side of the adjacent cell is called the postsynaptic terminal. Between these terminals, there exists a gap, the synaptic cleft, with a thickness of 10 - 50 nm. The fact that the impulse transfers across the synapse only in one direction, from the presynaptic terminal to the postsynaptic terminal, is due to the release of a chemical transmitter by the presynaptic cell. This transmitter, when released, activates the postsynaptic terminal, as shown in Figure 2.5. The synapse between a motor nerve and the muscle it innervates is called the neuromuscular junction. Information transfer in the synapse is discussed in more detail in Chapter 5.

Fig. 2.5.

2.3 MUSCLE CELL

There are three types of muscles in the body:

- smooth muscle,

- striated muscle (skeletal muscle), and

- cardiac muscle.

Smooth muscles are involuntary (i.e., they cannot be controlled voluntarily). Their cells have a variable length but are in the order of 0.1 mm. Smooth muscles exist, for example, in the digestive tract, in the wall of the trachea, uterus, and bladder. The contraction of smooth muscle is controlled from the brain through the autonomic nervous system.

Striated muscles, are also called skeletal muscles because of their anatomical location, are formed from a large number of muscle fibers, that range in length from 1 to 40 mm and in diameter from 0.01 to 0.1 mm. Each fiber forms a (muscle) cell and is distinguished by the presence of alternating dark and light bands. This is the origin of the description "striated," as an alternate terminology of skeletal muscle (see Figure 2.6).

The striated muscle fiber corresponds to an (unmyelinated) nerve fiber but is distinguished electrophysiologically from nerve by the presence of a periodic transverse tubular system (TTS), a complex structure that, in effect, continues the surface membrane into the interior of the muscle. Propagation of the impulse over the surface membrane continues radially into the fiber via the TTS, and forms the trigger of myofibrillar contraction. The presence of the TTS affects conduction of the muscle fiber so that it differs (although only slightly) from propagation on an (unmyelinated) nerve fiber. Striated muscles are connected to the bones via tendons. Such muscles are voluntary and form an essential part of the organ of support and motion.

Cardiac muscle is also striated, but differs in other ways from skeletal muscle: Not only is it involuntary, but also when excited, it generates a much longer electric impulse than does skeletal muscle, lasting about 300 ms. Correspondingly, the mechanical contraction also lasts longer. Furthermore, cardiac muscle has a special property: The electric activity of one muscle cell spreads to all other surrounding muscle cells, owing to an elaborate system of intercellular junctions.

Fig. 2.6.

2.4 BIOELECTRIC FUNCTION OF THE NERVE CELL

The membrane voltage (transmembrane voltage) (V_m) of an excitable cell is defined as the potential at the inner surface (F_i) relative to that at the outer (F_o) surface of the membrane, i.e. V_m = (F_i) - (F_o). This definition is independent of the cause of the potential, and whether the membrane voltage is constant, periodic, or nonperiodic in behavior. Fluctuations in the membrane potential may be classified according to their character in many different ways. Figure 2.7 shows the classification for nerve cells developed by Theodore Holmes Bullock (1959). According to Bullock, these transmembrane potentials may be resolved into a resting potential and potential changes due to activity. The latter may be classified into three different types:

Pacemaker potentials

2. Transducer potentials across the membrane, due to external events. These include generator potentials caused by receptors or synaptic potential changes arising at synapses. Both subtypes can be inhibitory or excitatory.

3. As a consequence of transducer potentials, further response will arise. If the magnitude does not exceed the threshold, the response will be nonpropagating (electrotonic). If the response is great enough, a nerve impulse (action potential impulse) will be produced which obeys the all-or-nothing law (see below) and proceeds unattenuated along the axon or fiber.

Fig. 2.7.

2.5 EXCITABILITY OF NERVE CELL

If a nerve cell is stimulated, the transmembrane voltage necessarily changes. The stimulation may be

After stimulation the membrane voltage returns to its original resting value.

If the membrane stimulus is insufficient to cause the transmembrane potential to reach the threshold, then the membrane will not activate. The response of the membrane to this kind of stimulus is essentially passive. Notable research on membrane behavior under subthreshold conditions has been performed by Lorente de Nó (1947) and Davis and Lorente de Nó (1947).

If the excitatory stimulus is strong enough, the transmembrane potential reaches the threshold, and the membrane produces a characteristic electric impulse, the nerve impulse. This potential response follows a characteristic form regardless of the strength of the transthreshold stimulus. It is said that the action impulse of an activated membrane follows an all-or-nothing law. An inhibitory stimulus increases the amount of concurrent excitatory stimulus necessary for achieving the threshold (see Figure 2.8). (The electric recording of the nerve impulse is called the action potential. If the nerve impulse is recorded magnetically, it may be called an action current. The terminology is further explicated in Section 2.8 and in Figure 2.11, below.)

Fig. 2.8.

2.6 THE GENERATION OF THE ACTIVATION

The mechanism of the activation is discussed in detail in Chapter 4 in connection with the Hodgkin-Huxley membrane model. Here the generation of the activation is discussed only in general terms.

The concentration of sodium ions (Na⁺) is about 10 times higher outside the membrane than inside, whereas the concentration of the potassium (K⁺) ions is about 30 times higher inside as compared to outside. When the membrane is stimulated so that the transmembrane potential rises about 20 mV and reaches the threshold - that is, when the membrane voltage changes from -70 mV to about -50 mV (these are illustrative and common numerical values) - the sodium and potassium ionic permeabilities of the membrane change. The sodium ion permeability increases very rapidly at first, allowing sodium ions to flow from outside to inside, making the inside more positive. The inside reaches a potential of about +20 mV. After that, the more slowly increasing potassium ion permeability allows potassium ions to flow from inside to outside, thus returning the intracellular potential to its resting value. The maximum excursion of the membrane voltage during activation is about 100 mV; the duration of the nerve impulse is around 1 ms, as illustrated in Figure 2.9. While at rest, following activation, the Na-K pump restores the ion concentrations inside and outside the membrane to their original values.

Fig. 2.9.

2.7 CONCEPTS ASSOCIATED WITH THE ACTIVATION PROCESS

Some basic concepts associated with the activation process are briefly defined in this section. Whether an excitatory cell is activated depends largely on the strength and duration of the stimulus. The membrane potential may reach the threshold by a short, strong stimulus or a longer, weaker stimulus. The curve illustrating this dependence is called the strength-duration curve; a typical relationship between these variables is illustrated in Figure 2.10. The smallest current adequate to initiate activation is called the rheobasic current or rheobase. Theoretically, the rheobasic current needs an infinite duration to trigger activation. The time needed to excite the cell with twice rheobase current is called chronaxy.

Accommodation and habituation denote the adaptation of the cell to a continuing or repetitive stimulus. This is characterized by a rise in the excitation threshold. Facilitation denotes an increase in the excitability of the cell; correspondingly, there is a decrease in the threshold. Latency denotes the delay between two events. In the present context, it refers to the time between application of a stimulus pulse and the beginning of the activation. Once activation has been initiated, the membrane is insensitive to new stimuli, no matter how large the magnitude. This phase is called the absolute refractory period. Near the end of the activation impulse, the cell may be activated, but only with a stimulus stronger than normal. This phase is called the relative refractory period.

The activation process encompasses certain specifics such as currents, potentials, conductivities, concentrations, ion flows, and so on. The term action impulse describes the whole process. When activation occurs in a nerve cell, it is called a nerve impulse; correspondingly, in a muscle cell, it is called a muscle impulse. The bioelectric measurements focus on the electric potential difference across the membrane; thus the electric measurement of the action impulse is called the action potential that describes the behavior of the membrane potential during the activation. Consequently, we speak, for instance, of excitatory postsynaptic potentials (EPSP) and inhibitory postsynaptic potentials (IPSP). In biomagnetic measurements, it is the electric current that is the source of the magnetic field. Therefore, it is logical to use the term action current to refer to the source of the biomagnetic signal during the action impulse. These terms are further illustrated in Figure 2.11.

Fig. 2.10.

Fig. 2.11.

2.8 CONDUCTION OF THE NERVE IMPULSE IN AN AXON

Ludvig Hermann (1872, 1905) correctly proposed that the activation propagates in an axon as an unattenuated nerve impulse. He suggested that the potential difference between excited and unexcited regions of an axon would cause small currents, now called local circuit currents, to flow between them in such a direction that they stimulate the unexcited region.

Although excitatory inputs may be seen in the dendrites and/or soma, activation originates normally only in the soma. Activation in the form of the nerve impulse (action potential) is first seen in the root of the axon - the initial segment of the axon, often called the axon hillock. From there it propagates along the axon. If excitation is initiated artificially somewhere along the axon, propagation then takes place in both directions from the stimulus site. The conduction velocity depends on the electric properties and the geometry of the axon.

An important physical property of the membrane is the change in sodium conductance due to activation. The higher the maximum value achieved by the sodium conductance, the higher the maximum value of the sodium ion current and the higher the rate of change in the membrane voltage. The result is a higher gradient of voltage, increased local currents, faster excitation, and increased conduction velocity. The decrease in the threshold potential facilitates the triggering of the activation process.

The capacitance of the membrane per unit length determines the amount of charge required to achieve a certain potential and therefore affects the time needed to reach the threshold. Large capacitance values, with other parameters remaining the same, mean a slower conduction velocity.

The velocity also depends on the resistivity of the medium inside and outside the membrane since these also affect the depolarization time constant. The smaller the resistance, the smaller the time constant and the faster the conduction velocity. The temperature greatly affects the time constant of the sodium conductance; a decrease in temperature decreases the conduction velocity.

The above effects are reflected in an expression derived by Muler and Markin (1978) using an idealized nonlinear ionic current function. For the velocity of the propagating nerve impulse in unmyelinated axon, they obtained

(2.1)

where v = velocity of the nerve impulse [m/s]

i_{Na max} = maximum sodium current per unit length [A/m]

V_th = threshold voltage [V]

r_i = axial resistance per unit length [W/m]

c_m = membrane capacitance per unit length [F/m]

A myelinated axon (surrounded by the myelin sheath) can produce a nerve impulse only at the nodes of Ranvier. In these axons the nerve impulse propagates from one node to another, as illustrated in Figure 2.12. Such a propagation is called saltatory conduction (saltare, "to dance" in Latin).

The membrane capacitance per unit length of a myelinated axon is much smaller than in an unmyelinated axon. Therefore, the myelin sheath increases the conduction velocity. The resistance of the axoplasm per unit length is inversely proportional to the cross-sectional area of the axon and thus to the square of the diameter. The membrane capacitance per unit length is directly proportional to the diameter. Because the time constant formed from the product controls the nodal transmembrane potential, it is reasonable to suppose that the velocity would be inversely proportional to the time constant. On this basis the conduction velocity of the myelinated axon should be directly proportional to the diameter of the axon. This is confirmed in Figure 2.13, which shows the conduction velocity in mammalian myelinated axons as linearly dependent on the diameter. The conduction velocity in myelinated axon has the approximate value shown:

v = 6d (2.2)

where v = velocity [m/s]

d = axon diameter [µm]

Fig. 2.12.

Fig. 2.13.

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where	v	= velocity of the nerve impulse [m/s]
	i_{Na max}	= maximum sodium current per unit length [A/m]
	V_th	= threshold voltage [V]
	r_i	= axial resistance per unit length [W/m]
	c_m	= membrane capacitance per unit length [F/m]