Abstract
Voltage-gated Na + channels exhibit three states: closed activatable, open activated, and closed inactivatable. At resting membrane potentials, about 75% of the channels are in the closed activatable state. Depolarizing the axon membrane causes the activatable channels to open, allowing Na + to move along a voltage and concentration gradient, which further depolarizes the membrane and results in a propagated action potential. At the nerve terminal, neurotransmitters are released by the invading action potential to act on cell receptors adjacent to the terminal or systemically if the transmitter is released into the blood.
Regulated current pulses are the preferred method of electrically activating a nerve because the induced field remains constant during the stimulus pulse. When voltage pulses are used, the injected current is a function of electrode–tissue impendence and the current decays with time, meaning that the excitatory field decays with time.
Cathodic currents are more effective in initiating propagating action potentials on axons because depolarizing currents are more concentrated near the electrode. Depolarizing currents are more widely distributed when anodic stimulation is applied, which means that larger currents must be used to reach threshold depolarization with anodic stimuli. Short-duration high-amplitude stimuli require less charge to initiate a propagated action potential than do low-amplitude long-duration stimuli. In general, less charge injection generates fewer electrochemical reaction products and draws less power.
The effect of an applied stimulus is always greater on larger-diameter axons than on smaller-diameter axons, because internodal spacing is greater in larger axons than it is in smaller ones. The effect of the applied stimulus is always greater on axons that are closer to the electrode than on axons farther from the electrode. This means that when a cathodic stimulus is applied to an axon, the threshold for activation of larger fibers will lower than that required to activate smaller fibers, if they are at the same distance from the electrode.
Driving the electrode interface potential anodically can result in loss of electrode metal and the creation of metallic salts that are powerful oxidizing agents. To avoid oxidizing the electrode, the amount of charge injected in the anodic phase may be limited by using imbalanced biphasic pulses or lower charge injection with balanced biphasic stimuli.
Keywords
Action potential, Electrical stimulation, Electrochemistry, Transmembrane potential, Voltage-gated ion channel
Outline
Overview 71
Some Basic Concepts 72
Resting Potential Across the Axon Membrane 72
Voltage-Gated Ion Channels 72
Action Potentials 73
Electrically Generating Action Potentials 73
Choosing the Duration of the Stimulus 75
Electrochemistry of Stimulating Electrodes 76
Electrode Behavior Under Pulsed Conditions 78
How Stimulus Waveform Choices Affect Tissues 81
Current–Voltage Stimulation 82
References 82
In the context of neuromodulation and neuroprosthetics, electrical stimulation is applied to restore function to people who are unable to move, see, or hear or to alter behavior such as seen in a variety of disorders of motor, sensory, and cognitive function. Guidelines have evolved during the past 50 years or so on ways to apply electrical stimulation, so that the neural response does not diminish with repeated application. These guidelines include the choices of current rather than voltage pulses, biphasic rather than monophasic pulses, and charge-balanced rather than charge-imbalanced pulses. The material presented in this chapter is intended to be an explanation of these guidelines and to provide a basis for forming informed decisions on stimulation systems.
Overview
When electrical currents are delivered to the nervous system to elicit or inhibit neural activity, two things can happen. First, the current creates a potential field that can alter the state of the voltage-gated ion channels, proteins that are embedded in the membranes of neural elements. Second, electrochemical reactions can occur at the electrode–tissue interface. Altering the state of voltage-gated ion channels can initiate or suppress a propagated action potential, which, in turn, effects the release of neurotransmitter at the terminal end of the axons. Uncontrolled electrochemical reactions, at the electrode–tissue interface, can cause damage to the electrode or injury to target tissues.
There are three primary ideas that one must keep in their mind when thinking about neuromodulation. The science behind clinical applications such as effecting movement or sensation has been well developed, and these principles are essential to understand for safe and effective delivery of electrical stimulation to neural tissue.
First , electrical activation of the nervous system is more than causing paralyzed limbs to move, sound sensations in the deaf individual, and visual sensations in a blind person. It is about controlling and targeting release of neurotransmitters.
Second , the science underpinning electrical activation technology is the knowledge of voltage-gated ion channels, particularly the voltage-gated Na + channel.
Third , the electrode is the business end of any neural prostheses. What happens at the electrode–tissue interface can determine the long-term viability of a device.
Using these three concepts as a foundation, one can more easily understand the rationale for making decisions about choices for stimulation parameters and how these choices affect the utility and longevity of a device intended to modulate the behavior of neural circuits or activate the nervous system to restore function.
Some Basic Concepts
An electrode forms the interface between the neuromodulation hardware and the targeted nervous tissue. Electrical stimulation is achieved by connecting two opposite poles of a stimulus source to the tissue. Conventional current flows from the positive pole of a stimulus source to the negative pole, while electrons (negative charges) flow in the opposite direction.
Anode and Cathode : The electrode at which oxidation reactions occur (increased positive valence or electron removal) is defined as the anode, and the electrode at which reduction occurs (decreased positive valence or electron gain) is defined as the cathode.
Voltage and Current : Neuromodulation is effected by application of electrical charge to the tissues. Voltage is a measure of the energy carried by the charge, being the “energy per unit charge” (volts), while current is the rate of flow of charge (amperes).
Stimulus Characteristics : Electrical charge applied to effect stimulation of neural tissue can be characterized temporally by its voltage or current. The basic element of applied charge, a voltage or current pulse, is defined by its duration (pulse width), amplitude (volts or amperes), and shape (rectangular, triangular, or sinusoidal). The repetition rate of individual pulses is the stimulus frequency or pulse rate. Sets of pulses followed by silent intervals can provide patterned temporal stimulation, and may also be modulated by frequency or amplitude.
Electrode Characteristics : The size (area) of the electrode tissue interface determines the charge and current density of the applied stimulus, which decrease with increasing electrode area. The current intensity varies inversely with the square of the distance from the electrode.
Effect of Axon Diameter : The effects of an applied electrical field are greater on larger diameter axons because they have a longer separation between nodes of Ranvieŕ. The effect can be either depolarization or hyperpolarization. Smaller-diameter axons require higher stimulus amplitudes for the generation of action potentials than do larger-diameter axons.
Nerve Depolarization/Excitation : When the transmembrane potential of an axon is decreased to a level where sufficient numbers of voltage-gated Na + channels are switched from the resting excitable state to an active state, it causes a propagated action potential to be initiated. This state change occurs when a net transmembrane current occurs, flowing from the inside to the outside of the axon and is usually caused by the application of a cathodic stimulus applied near the site of excitation.
Nerve Hyperpolarization : When the transmembrane potential is increased from the resting state (becoming more negative), the voltage-gated Na + channels are less likely to be gated into the active state. This state change occurs when the net transmembrane current is negative, flowing from the outside of the cell to the inside of the cell, and is usually caused by the application of an anodic stimulus applied near the site of hyperpolarization.
Resting Potential Across the Axon Membrane
Three major ions are separated across an axon membrane at rest. 1
1 Calcium, Ca 2+ , is also a major ion that is in higher concentration outside the neuron. It will not be considered for the purposes of this discussion.
The concentrations of Na + and Cl − are much higher in the extracellular space than in the intracellular space, while K + is higher on the inside compared with the extracellular space. The resting potential of the membrane is about −70 mV, inside with respect to the outside, which is close to the Nernst potential 22 Equilibrium potential of the ionic electrochemical gradient across the membrane.
for both K + and Cl − , a value determined by the difference in ion concentration between the two sides of the membrane. K + and Cl − concentrations determine resting potential across the nerve membrane. The resting nerve membrane is poorly permeable to Na + . The Na + Nernst potential is about +55 mV, which drives an inward current flow during an action potential.Voltage-Gated Ion Channels
Voltage-gated ion channels are a class of transmembrane proteins that are activated by changes in electrical potential difference across the cell membrane ( ). Voltage-gated sodium ion channels (Na v ) can have three possible states: closed-activatable, activated (open and conducting), and closed-inactivatable. Na v channels are made up of 1800 to 4000 amino acids with four transmembrane repeat domains. The molecules of the protein interact with each other and surrounding molecules to form a structure that defines its function. Each of the four transmembrane domains contains a voltage-sensitive α helix that is displaced in the open or conduction state ( ). The linker between the III and IV repeat domains acts as a ball and chain to fold up into the channel opening to block Na + from moving through the channel in the inactivatable state. When a channel opens, Na + moves from outside the membrane, through the channel, to the inside following both a concentration gradient and a voltage gradient. Shortly after the channel opens, it becomes energetically favorable for the linker between the III and IV repeats to move into the opening and block further Na + movement ( ).
The opening of Na v is a stochastic process that is potential dependent, meaning that as the transmembrane potential increases, the probability increases for a resting channel to transition to a conduction state. In the conduction state, each Na v channel acts as a current source when the channel opens, permitting Na + to move from the outside to the inside and depolarize the membrane. The Na v channel density is about 2000 channels/μm 2 in the nodes of Ranvieŕ. By convention, the potential across a membrane is defined as inside with respect to outside, giving rise to the resting potential, which is about −70 mV. Also, positive current flow is defined as positive charge moving from inside to outside; therefore, Na + moving from outside to inside is a negative current.
At resting membrane potentials, some channels are opening and closing, and about 75% of the Na v are in an activatable state, meaning they can be opened, and 25% are in the inactivatable state, with the linker between the III and IV repeat blocking Na + flow through the channel. K + outflow keeps the membrane potential from drifting, and a Na + -K + pump maintains equilibrium concentrations and membrane potentials. If the membrane potential were to be hyperpolarized, made more negative, the fraction of channels in the activatable state would increase, approaching 100% at −100 mV.
Action Potentials
Na + movement from the outside to the inside depolarizes, or raises the transmembrane potential. Na v are concentrated at nodes of Ranvieŕ, so there are tens of thousands of channels involved in generating an action potential at a single node. When a large number of Na v open, in short succession, more Na + moves in than K + moves out of the membrane and the membrane potential moves positively. This in turn increases the probability that activatable Na v will open, meaning many miniature current sources act in close succession to depolarize the nerve membrane, driving the potential from about −70 mV to approximately +20 mV or higher. This rapid change in membrane potential is recognized as the “all-or-none” action potential. Because all Na v close shortly after opening and transition to the inactivatable state, Na + movement is terminated and K + movement from inside to outside the membrane restores the membrane potential to the resting state.
A propagated action potential is created when the transient change in membrane potential at one node of Ranvieŕ gives rise to a potential difference inside the axon between that node and an adjacent node. The transient depolarization causes positive charge to move to the next adjacent node of Ranvieŕ, which depolarizes the adjacent node causing activatable Na v to open in short succession, and the process continues to the terminal end of the axon where a neurotransmitter is released to act on an adjacent cell or to act systemically when released into the blood.
Electrically Generating Action Potentials
Charge can be neither created nor destroyed, which is a fundamental law of physics. However, charge can be separated, and when it is separated, there exists a potential difference to recombine the charge. The magnitude of the potential difference is inversely proportional to the separation distance. With these ideas in mind, two points need to be kept in mind in the following discussion. First , at resting membrane potentials charge is separated across a nerve membrane, more positive charge outside and more negative charge inside. Second , if we provide a pathway to inject charge, we must provide a pathway to remove it, and if charge flows into a cell, it flows out of the cell somewhere else. Charge flow, per unit time, is defined as current. As current flows in a resistive medium, like tissue, a potential difference arises along the pathway it follows. Locations where the more charge is flowing have a higher potential gradient compared with points where less charge is flowing.
Consider now that we have placed two electrodes in the same conductive tissue space, occupied by an axon, and that one of the electrodes, the stimulating electrode, is much closer to the axon than the other electrode. The distant electrode will be referred to as the return or indifferent electrode. Current injected into the tissue at the stimulating electrode disperses as it moves away from the injection site, the current density 3
3 Charge flow per unit area.
being highest near the injection site. This means that the potential difference between equally spaced points closer to the injection site will be higher than the potential difference for similarly spaced points farther from the injection site.When a cathodic current pulse of 100-μs duration is applied to the stimulating electrode, negative charge is injected into the tissue at the highest current density close it. The negative charge injected counters the positive charge outside the membrane and the negative charge inside the axon moves away from the membrane. A negative charge moving away from the inside of the membrane is effectively the same as a positive charge moving from the inside to the outside of the membrane. This is called a capacitive current. In other words, the membrane capacitance is discharged by the stimulus pulse. So, what has happened is that the cathodic pulse has the effect of driving a positive current from the inside of the axon to the outside of the axon with the bulk of the current flowing through the node of Ranvieŕ that is closest to the stimulating electrode. Inward flowing current is distributed over the nodes adjacent to the stimulating electrode. The magnitude of the current density is lowered, by more than half, at nodes flanking the node of Ranvieŕ nearest to the stimulating electrode. Current flow through the relevant nodes is illustrated in Fig. 6.1 .
Current flowing out of the node of Ranvieŕ closest to the stimulating electrode reduces the potential across the membrane at this location, and Na v , in this patch of membrane, will have an increased probability of transitioning from the closed-activatable state to the open-conduction state, allowing Na + to move to the inside of the membrane and further lowering the transmembrane potential. If the net Na + inflow exceeds that net K + outflow, a regenerative action potential will follow with all activatable Na v opening at that node, setting the scene for a propagated action potential along the axon and cause the release of a neurotransmitter at the terminal end.
When the depolarizing current is insufficient to open enough Na v channels before K + flows out to repolarize the membrane, it is unable to generate an action potential. This would be termed a subthreshold stimulus.
If an anodic pulse, rather than the cathodic pulse, is delivered, the current flow through the respective nodes of Ranvieŕ is reversed. The inward current flow at the node nearest the electrode causes the transmembrane potential to increase (hyperpolarize), and this will not generate an action potential. However, at the flanking nodes, positive current exits the membrane, which causes depolarization, and may potentially trigger an action potential. Note, however, that the exiting current is distributed over many nodes rather than a single node as in the case of the cathodic pulse. For an action potential to be created with an anodic pulse, the current pulse would need to be substantially higher in magnitude than is required for a cathodic pulse. Thus, the rule of thumb that the threshold for generating a propagated action potential in peripheral nerves is lower for a cathodic pulse than for an anodic pulse.
The change in transmembrane potential, resulting from an applied stimulus, can be described mathematically and is given by the second spatial difference of the electric field along the axon, also referred to as the activation function.
V e , n − 1 − 2 V e , n + V e , n + 1
Propagated action potentials can occur following the termination of a prolonged period of membrane hyperpolarization. This phenomenon is labeled “anodic break,” suggesting that the action potential occurred as a result of the lagging edge of the anodic pulse. Actually, the membrane is made hyperexcitable during the hyperpolarization period. During the period of anodic polarization, the number of channels in the activatable state is moved from 75% to a much larger fraction, approaching 100%. When the anodic pulse is terminated the membrane potential moves back to resting potential, Na v channels open as the 25% fraction in the inactivatable state is reestablished. When Na + flow inward through Na v channel opening is not countered by K + outflow, sufficient depolarization can occur to initiate a propagating action potential.
Choosing the Duration of the Stimulus
It is well known and accepted that larger stimulus amplitudes are required for shorter pulse durations to initiate a propagated action potential. This is known as the strength–duration characteristic or relationship. An example is shown in Fig. 6.2A . As the stimulus duration increases, the amplitude required to initiate a propagated action potential asymptotically approaches a minimal value, called the rheobase current, I r . This curve can be fitted to a mathematical expression, the Hill equation.
I th = I r 1 − e ( − PD t c ) ln 2
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