Static Electric Charge And Electric Fields

Physical objects may acquire an electric charge when they have a net excess or deficit of electrons relative to the number of protons. When the number of electrons exceeds the number of protons, the object is said to have a negative charge, whereas a net deficit of electrons results in the object acquiring a positive charge. An electrically charged object is surrounded by an electric field such that charged objects act at a distance on other objects having similar or opposite charge. The strength of the electric field is related to the magnitude of its charge. A gravitational field also acts at a distance, but an electric field has an important difference, polarity. Thus, electric fields have directionality with the convention that field lines are drawn away from positively charged and toward negatively charged objects. The electric fields surrounding charged objects interact with each other such that the presence of two electrically charged objects results in a force that either attracts the two objects (if they have opposite charges) or repels the two objects (if they have the same qualitative charge). This attractive or repulsive force acts at a distance, not requiring that the charged objects be in contact, and the attractive or repulsive force (F) is given by Coulomb’s law:

where Q₁ and Q₂ are the magnitude of the charges (measured in coulombs), r is the distance separating the charged objects, and k is a constant equal to with ε being the permittivity of free space. According to Coulomb’s law, the force attracting or repelling charged objects increases with the magnitude of charge and decreases with the square of the distance that separates them.

Electric Circuit

An electric circuit is an electric charge–conducting pathway that ends at its beginning. For electric circuits involved in myocardial stimulation by pacemakers or ICDs, the voltage difference in the circuit is provided by a battery. The difference in voltage generated by the battery results in a flow of charge (current) from the pulse generator through the conductors in the leads, electrodes, extracellular electrolytes, cell membranes with highly regulated transmission of charged ions in both directions through the membrane, and intracellular ions and charged molecules. As current flows through the complete electric circuit, the net voltage change must be zero (Kirchoff’s voltage law). Thus, the electromotive force (voltage) generated by the battery (an increase in potential energy) must be completely dissipated (a decrease in potential energy) as current flows through all the elements of the circuit to end at the battery.

Electric circuits in the clinical practice of pacing have multiple elements, including the pulse generator battery, the lead conductor(s), the electrodes, the myocardium, and blood within the great veins and cardiac chambers. All these elements introduce opposition to the flow of current.

Electrode Polarity

All defibrillator and pacemaker electric circuits have both a positively charged electrode (the anode) and a negatively charged electrode (the cathode). The negatively charged cathode is typically the tip electrode on a pacing lead. Electrons from the pulse generator flow through the cathode-tissue interface and return to the anode, which may be located on a pacing lead or the pulse generator casing.

The terminology used for electrode polarity may be confusing as applied to lead electrodes and the electrodes of a battery. The electrode in a battery at which oxidation occurs (e.g., oxidation of lithium to yield Li⁺ plus an electron, e⁻) is the battery anode. The battery anode, by continuing oxidation, furnishes electrons to the circuit external to it. Therefore, in contradistinction to the terminology used for pacing leads, the terminal of the battery where electrons are provided to the circuit is the battery anode. From the battery anode, electrons flow through the circuitry and eventually enter the pacemaker lead electrode that is in contact with the myocardium. This electrode, receiving electrons from the pulse generator and furnishing electrons to the tissue, is the lead cathode. The return electrode located in the heart or on the pulse generator casing is the lead anode. It collects electrons from the tissue and returns them through the pulse generator circuitry to the positive electrode of the battery, the battery cathode, where reduction occurs (e.g., I₂ + 2e⁻ yields 2I⁻). The consistency in the terminology is that, when oxidation occurs, it occurs at an anode, and in the circuitry, an anode connects to a cathode that subsequently connects to another anode, and so on.

Opposition to Flow of Electric Current

In cardiac pacing and defibrillation, several elements in the electric circuit oppose the flow of electric current. As current flows through some of these elements, such as the conductor wires in the leads and pulse generator, the opposition to current flow results in energy being lost as heat. These elements are known as ohmic, and the opposition to current flow is called resistance (R). The instantaneous voltage developed across a perfect resistor is linearly proportional to the instantaneous current flow through the resistor. If a steady voltage across the resistor is represented by V, the current by I, and an unchanging resistance by R, the relationship is expressed as follows in Ohm’s law:

In reality, when all the elements of a cardiac pacing circuit are considered, these factors are much more complex than can be represented by Ohm’s law alone. These other factors include capacitance and inductance. For calculations involving a pulsed (e.g., pacemaker stimulus) or an alternating current (AC) circuit that contain reactive elements (e.g., electrodes in contact with electrolytes), the term impedance (Z) must be used in place of resistance. Impedance is a vector sum of resistance (R) and reactance (X). The following sections discuss the major components of reactance.

Capacitance

As mentioned earlier, current can be carried in different ways. Electrolyte is used as a generic term for the electrically conductive extracellular and intracellular fluids near pacemaker or defibrillator electrodes and elsewhere in the heart and blood vessels. The electrolyte conducts ions but not electrons. The difference between the conduction of electric currents by electrolytic fluids and the flow of electrons over metal wires is crucial to pacing. Because a negatively charged pacing electrode in contact with the endocardium is surrounded by blood and interstitial fluid, positively charged ions move toward that electrode during a pacing stimulus. This results in the phenomenon of polarization, which develops rapidly and dissipates slowly after the end of the stimulus. The opposite effect occurs on the positively charged anode. This effect of ions moving to oppose the flow of electric current has the effect of a capacitor in the circuit.

A capacitor is an object that stores energy in an electric field by holding positive charges apart from closely approximated negative charges. A capacitor requires a material or space between the layers of negative and positive charges that is normally nonconducting (the dielectric). A cell membrane, although leaky, acts as a capacitor by separating the negatively charged inside of the cell from the more positively charged outside. Cell membranes have very high capacitance per unit area of cell membrane. The interface between a pacing electrode and the charged electrolytes that surround the electrode at its surface in the myocardial tissue acts, in part, as a capacitor. The terms Helmholtz capacitor and Helmholtz capacitance are used in this chapter for capacitor-like effects that occur at pacemaker and defibrillator electrode-electrolyte interfaces.

Capacitance (C) is the term that specifies, for a given voltage applied across a capacitor, how much electrical charge (Q) can be stored by the capacitor. If V represents a steady voltage applied across the capacitor, then Q = CV. (If E is used instead of V as the symbol for electric potential, the relationship may be expressed as Q = CE.) The unit for capacitance is the farad. One farad is the capacitance of a capacitor that, on being charged to 1 volt, will have stored 1 coulomb of charge. Again, a coulomb is the amount of charge delivered by 1 ampere flowing for 1 second. Coulombs delivered can be expressed as follows:

in which Q_t is the total charge delivered between time 0 and time t, and i_t is the instantaneous current at each time segment between time 0 and time t. The integral is the net area under the instantaneous current-versus-time plot.

Inductance

When an alternating current flows through a wire, a magnetic field surrounding the wire is induced. An inductor is an object that stores or releases energy in or from a changing magnetic field. The voltage difference across an inductor is proportional to the rate of change of current flowing through the inductor. Energy is stored during the formation of the magnetic field and is released when the magnetic field decreases or disappears. Inductance is the term that specifies the relationship between the voltage across an inductor and the rate of change of current traversing the inductor. The magnitude of the inductance can be represented by the symbol L. If V_t represents the instantaneous voltage across the inductor, and i_L represents the instantaneous current flowing through the inductor, the relationship is given by the following equation:

Note that the voltage across the inductor is directly proportional to the rate of change of current flowing through the inductor. Cell membrane currents have some of the current- and voltage-versus-time characteristics of an inductance in parallel with a capacitance.¹ These inductance-like effects are related to the timing and magnitude of potassium ions moving into and out of the cell.²

Reactance (Capacitance and Inductance)

For reactive elements connected in series, net reactance is the scalar sum of inductive reactance (positive in the mathematical complex plane) and capacitive reactance (negative in complex plane). Pure reactance values depend on the rates of change of current and voltage, whereas pure resistance values do not. Phenomena of this type are caused by differences in the timing of the peaks (phase angles) of the voltages or currents in the various reactive components. These reactive effects can be important in biventricular pacing threshold measurements (see later discussion). The component of reactance that is most relevant to both pacing electrodes and cell membranes is capacitance, with inductance being much less important. For example, the cardiac action potential spreading throughout the heart generates a changing magnetic field that transiently stores a very small amount of energy. However, the changing magnetic field generated by spread of the action potential is so small that it is not clinically significant except in the research setting.³

For circuits with resistance R, capacitance C, and inductance L in series, where q_t represents the charge accumulated across the capacitance at any time t, and where the current through these combined elements at time t is i_t, the voltage V_t at time t is described by the following equation:

(remembering that and that the voltage across a capacitor at time t is ).

These equations indicate that, for an instantaneous current i_t, the instantaneous voltage across the series circuit is the sum of the effects at that instant in time of the resistance, capacitance, and inductance of the circuit. Note especially that the instantaneous effects are highly related to the net amount of charge, , that has accumulated in the capacitor from time 0 to the instantaneous time t. The equations show that the capacitance effect on the voltage decreases as the capacitance increases. This has clinical relevance in that, for example, the polarization voltage that interferes with autosensing pulse generators decreases as the electrode capacitance increases.

The Phospholipid Bimembrane

Living cells maintain or regenerate a difference in electric potential across the cell membrane. Excitable tissues such as myocardium respond to electrical stimulation of one or more cells with a wave of electrical depolarization—a transient reversal of the voltage gradient across the membrane—that can propagate from cell to cell. Excitable cells respond to a relatively small applied change in electric potential difference across the cell membrane by triggering a series of biochemical and biophysical events (described later). These depolarization events result in myocyte contraction. Depolarization propagates along excitable cell membranes, as in the transmission of an action potential along a squid axon, and from myocyte to myocyte through gap junctions.

Cell Membrane Characteristics

Cell membrane characteristics are major determinants of tissue excitability. The membrane of the cardiac myocyte is composed principally of phospholipids, cholesterol, and proteins.⁴ The membrane phospholipids have a charged polar headgroup and two long hydrocarbon chains arranged as shown in Figure 1-1. The cell membrane comprises two layers of phospholipids with their hydrophobic aliphatic chains oriented toward the central portion of the bilayer membrane and their polar headgroup regions toward the outside boundaries of the membrane. Because the membrane is composed of two layers of phospholipids, the polar regions of the phospholipid molecules interface with the aqueous environments inside and outside the cell. The lipid-soluble hydrocarbon chains are forced away from the aqueous phase to form a nonpolar interior.

Figure 1-1 The phosphomembrane bilayer of a cardiomyocyte contains ion channels and structures that maintain distinct ion concentrations inside and outside of the cell. Charge pumps maintain an ion concentration gradient across the membrane while ion channels allow for charge in the form of ions to pass through the membrane. The ion current flow causes changes in transmembrane potential and cardiac activation.

Determinants of the Resting Transmembrane Potential

Relatively large gradients of individual ion concentrations exist across the cardiac cell membrane.⁵ The gradient of sodium ions (Na⁺) across the membrane is approximately 145 millimoles per liter (mmol/L) outside to 10 mmol/L inside. In contrast, the potassium ion (K⁺) concentration outside the cell is approximately 4.5 mmol/L, whereas the inside concentration is 140 mmol/L. In the absence of a cell membrane, both Na⁺ and K⁺ would rapidly move in a direction determined by the concentration gradient. The diffusion force tending to move K⁺ out of and Na⁺ into the cell is proportional to the concentration gradients of those ions. The potential energy attributable to the diffusion force (PE_d) tending to move K⁺ out of the cell is given by the following equation:

[1-1]

where R is the gas constant, T is the absolute temperature, ln is the natural logarithm operator, [K⁺]_i is the concentration of potassium ion inside the cell, and [K⁺]_o is the concentration of potassium ion outside the cell. If the ratio of [K⁺]_i to [K⁺]_o is large, the potential energy across the membrane is large. For each ion species, the difference in concentration between the inside and the outside of the cell results in that ion’s contribution to the difference in electric potential across the cell membrane.

In resting cardiac cells, the intracellular cytoplasm has a measured potential of about −90 millivolts (mV), relative to the extracellular fluid. This electric force tends to move positively charged ions such as K⁺ and Na⁺ to the inside of the cell and negatively charged ions such as chloride (Cl⁻) to the outside of the cell in proportion to the potential gradient. The potential energy attributable to the electric force (PE_e) tending to move K⁺ into the cell is expressed as follows:

[1-2]

where z here is the valence (the number of positive or negative electrical charges) of the ion, F is the Faraday constant (96,500 coulombs/equivalent), and V_m is the transmembrane potential difference (transmembrane voltage, measured in millivolts). During equilibrium, the total of the potential energies from diffusion and electric forces is zero, and no net ionic movement occurs. Therefore, the sum of Equation 1-1 and Equation 1-2 may be set to zero. This yields the Nernst equation, which describes (in measurable electrical units) the potential that must exist for a single ionic species, here K⁺, to be in equilibrium across the membrane of a resting cardiac cell:

[1-3]

or, in log base 10 terms,

Using known values for extracellular K⁺, V_m(K⁺) = −90 mV. When Equation 1-3 is solved using Na⁺ concentrations, a V_m(Na⁺) of +50 mV is obtained. Therefore, it is the equilibrium potential for potassium ion (not sodium ion) that is the major factor responsible for the resting transmembrane potential. This suggests that the resting membrane is more permeable to K⁺ than to Na⁺.

To calculate the transmembrane potential when multiple ionic species exist in different concentrations across the membrane, the Goldman constant field equation (modified by Hodgkin and Katz⁶) is used:

[1-4]

where P_K+, P_Na+, and P_Cl− are the cell membrane permeabilities for the respective ions. At physiologic concentrations, this equation yields a transmembrane potential of −90 mV (the equilibrium potential for K⁺). Equation 1-4 describes how resting potentials vary as sodium and potassium ion concentrations are changed. Because there is a passive leak of charged ions through the membrane, the resting potential would not exist at the level of −90 mV unless it were actively maintained. This is accomplished by two active transport mechanisms that exchange Na⁺ ions for K⁺ and calcium (Ca²⁺) ions.

One might ask: with all the potassium ions and other positively charged ions in the cell, and with a relatively small amount of negatively charged chloride ions in the cell, how can the interior of the cell be negative with respect to the outside? The answer is that an array of intracellular organic and inorganic anions inside the cell—molecules that do not cross the membrane—carry net negative charges sufficient to make the overall balance of charge negative.

Voltage-Gated Channels

Voltage-gated channels open in response to an applied electric potential. The source of this voltage can be an action potential propagated from an adjacent cell or the electric field of an artificial pacemaker electrode. If depolarization of the membrane exceeds a threshold voltage, an action potential is triggered, resulting in a complex cascade of ionic currents flowing across the membrane into and out of the cell. As a result of this flow of charge across the membrane, the potential gradient across the membrane changes in a characteristic pattern of events that produce the cardiac action potential (Fig. 1-3).

Figure 1-3 Microelectrode recording of transmembrane potential (V_m) from left ventricular endocardium of human heart.

In phase 0 (depolarization), sodium ions (Na⁺) rapidly enter the cell through fast channels. In phase 1, the initial repolarization is primarily the result of activation of a transient outward potassium ion (K⁺) current and inactivation of the fast Na⁺ current. In phase 2 (plateau), the net current is very small, although the individual Na⁺, Ca²⁺, and K⁺ currents are about an order of magnitude larger. Phase 3 (final repolarization) completes the cycle, with the Na⁺-K⁺ pump bringing the membrane potential to a stable point at which inward and outward currents are again in balance. During phase 4, the cell is polarized and gradually undergoes slow depolarization.

(From Stokes K, Bornzin G: The electrode-biointerface [stimulation]. In Barold SS [ed]: Modern cardiac pacing. Mt. Kisco, NY, Futra, 1985, pp 33-78.)

Selective membrane-bound proteins (ion channels) determine the passive transmembrane flux of an individual ion species. The transmembrane currents determine or influence cellular polarization at rest, action potential depolarization and repolarization, conduction, excitation-contraction coupling, and myofibril contraction. The channels that regulate transmembrane conductance of Na⁺ and Ca²⁺ are voltage gated. The sodium channel is a large protein molecule composed of approximately 1830 amino acids.¹⁰ It contains four internally homologous repeating domains, believed to be arranged around a central water-filled pore lined with hydrophilic (“water-loving”) amino acids. It is estimated that there are 5 to 10 Na⁺ channels per square micrometer (µm²) of cell membrane. When an alteration changes the membrane potential to about −70 to −60 mV (the threshold potential), four to six positively charged amino acids move across the membrane in response to the change in electric field. This causes a change in the conformations of the channel proteins, resulting in opening of the channel. After a single Na⁺ channel changes to the open conformation, about 10⁴ Na⁺ ions enter the cell. On depolarization of the membrane, the Na⁺ channels remain open for less than 1 millisecond (msec). After rapid depolarization of the membrane, the Na⁺ channel again changes to the closed conformation. In addition to the Na⁺ channel, specialized proteins are suspended in the cell membrane that have differential selectivity for K⁺, Ca²⁺, and Cl⁻ ions, with much different time constants for activation and inactivation.

Sinoatrial and Atrioventricular Nodal Cells

In contrast to Purkinje fibers and working myocardial cells, sinoatrial (SA) and atrioventricular (AV) nodal cells are characterized by no true resting potential. Following repolarization, the transmembrane potential of the nodal cells reach a minimum of approximately −60 mV. The SA and AV nodal cells have a slow, inward, depolarizing, combined Na⁺/K⁺ current known as the “funny” current (I_f). These I_f channels open and cause the transmembrane potential to rise slowly until Ca²⁺ channels are activated and an action potential is generated. The rate of this rise in transmembrane potential is affected by factors such as autonomic nervous stimulation and hormones.

In these nodal structures, depolarization is primarily mediated by inward Ca²⁺ conductance through specialized Ca²⁺ channels. There are two types of Ca²⁺ channels in the mammalian heart. The L-type channels are the major voltage-gated pathway for entry of Ca²⁺ into the myocyte, and they are heavily modulated by catecholamines.¹¹ The T-type channels contribute to spontaneous depolarization of the cell associated with automaticity (pacemaker currents). The pore of the Ca²⁺ channel has a functional diameter of about 0.6 nanometers (nm), larger than that of the Na⁺ channels (0.3-0.5 nm).¹² The selectivity for Ca²⁺ is high, up to 10,000-fold greater than that for Na⁺ or K⁺. The key elements are high-affinity binding sites for Ca²⁺, positioned along a single file pore. “Elution” of a Ca²⁺ ion occurs when another Ca²⁺ ion enters and is selectively bound.

In normal situations, the SA node has the most pronounced automaticity and highest spontaneous firing rate in the heart. If the SA node is not functioning properly, however, or if block develops between the SA node and the AV node, the AV node will display pacemaker activity at a slightly slower rate than the SA node. In the absence of a pacemaker signal from the AV node, Purkinje fibers will activate at an even slower rate than either the SA or the AV node.

Maintenance of Resting Membrane Potential

The resting membrane potential is maintained by the pumping of Na⁺ ions out of the cell and K⁺ ions into the cell. The Na⁺,K⁺—adenosine triphosphatase (ATPase) pump moves three Na⁺ ions out of the cell in exchange for two K⁺ ions moved into the cell.^13–15 The basic unit of the Na⁺,K⁺-ATPase protein (pump) consists of one alpha (α-) and one beta (β-) subunit. The α-subunit is large (1016 amino acids) and spans the entire membrane, whereas the β-subunit is a smaller glycoprotein. There appear to be about 1000 pump sites/µm² of cardiac cell membrane. The fully activated pump cycles about 50 to 70 times per second (interval of 15-20 msec/cycle). Similarly, the Na⁺-Ca²⁺ pump moves three Na⁺ ions out of the cell in exchange for one Ca²⁺ ion.^16,17 Therefore, both transport mechanisms result in the net movement of one positive charge out of the cell, polarizing the membrane and maintaining a negatively charged interior. The function of both exchange mechanisms depends on the expenditure of energy in the form of high-energy phosphates and is susceptible to interruptions in aerobic cellular metabolism (e.g., during ischemia).

The Cardiac Action Potential

When the voltage gradient across the membrane of a myocyte decreases so that the inside of the cell becomes less negatively charged with respect to the outside of the cell, a critical transmembrane voltage difference is reached, the threshold voltage. At threshold, the cell membrane suddenly undergoes a further depolarization that is out of proportion to the intensity of the applied stimulus. This abrupt change in the potential across the membrane is the start of a cascade of inward and outward currents that together are known as an action potential.¹⁸

The cardiac action potential is an enormously complex event and consists of five phases¹⁹ (see Fig. 1-3): phase 0, the upstroke phase of rapid depolarization; phase 1, the overshoot phase of initial rapid repolarization; phase 2, the plateau phase; phase 3, the rapid repolarization phase; and phase 4, characterized by a slow, spontaneous depolarization of the membrane in cells with spontaneous pacemaker activity, until the threshold potential is again reached and a new action potential is generated.

Phase 4: Automaticity and the Conduction System

Automaticity is the property of certain cells by which they are able to initiate an action potential spontaneously. It has been known for centuries that the heart can exhibit spontaneous contraction even when completely denervated. Leonardo da Vinci observed that the heart could “move by itself.”²⁴ William Harvey reported that pieces of the heart could “contract and relax” separately.²⁵ Many cells within the specialized conduction system have the potential for automaticity.

Not all parts of the heart, however, possess this property. In fact, cells in different areas of the heart have different transmembrane potentials, thresholds, and action potentials. Fast responses are characteristic of ordinary working ventricular muscle cells and His-Purkinje fibers, with resting membrane potentials of −70 to −90 mV and rapid conduction velocities. Normal SA and AV nodal cells have slow responses, with resting potentials of −40 to −70 mV and slow conduction velocities. Cells, or group of cells, with the fastest rate of spontaneous membrane depolarization during phase 4 are the first to reach threshold potential and initiate a propagated impulse. Therefore, cells with the steepest slope in phase 4 become the heart’s natural pacemaker. Ordinary working myocardial cells usually are not automatic.

Normally, depolarization is initiated at the SA node.^26,27 Figure 1-4 shows action potentials from different types of cardiac cells.²⁸ Rather than maintaining a stable resting membrane potential, the repolarization of the action potential is followed by a slow depolarization from about −71 to −54 mV, the threshold required to initiate another action potential. This slow, spontaneous depolarization drives cardiac automaticity and is related to a specialized current (I_f). In the case of AV nodal cells, the fast upstroke is carried predominantly by an inward Ca²⁺ current. Repolarization is caused by delayed activation of the K⁺ current. The balance of inward and outward currents determines the net “pacemaker” current and is finely regulated by both adrenergic and cholinergic neurotransmitters. In the presence of AV block or abnormal SA nodal function, AV junctional cells in the region of the proximal penetrating bundle usually assume the role of pacemaker at rates slower than that of the sinus node. In the absence of disease in the AV junction, the escape rhythm occurs with a frequency that is about 67% of the sinus rate.²⁹

Figure 1-4 Action potentials from different cell types in the heart.

Specialized pacemaker and conduction cell types have distinct action potential characteristics. Activation times for a normal heartbeat demonstrate the spread of activation throughout the whole heart. AV, Atrioventricular.

(From Malmivuo J, Plonsey R: Bioelectromagnetism: principles and applications of bioelectric and biomagnetic fields. New York, 1995, Oxford University Press.)

Myocardial Cell Electrical Properties

A single Purkinje fiber typically has an internal resistance that is two to three times greater than that of blood. The specific membrane resistance of a Purkinje fiber is on the order of 10⁴ ohms–square centimeter (Ω-cm²). The time constant of the surface membrane is on the order of 10 msec, and the membrane capacity is about 1 microfaraday (µF)/cm². Gap junctions are intercellular channels that provide a pathway for electrical communication between myocytes. Their diameter is about 2 nm and length about 12 nm. Gap conductance is voltage sensitive.³² Under pathologic conditions, such as severe hypoxia or ischemia, gap junctions will not function normally.

Single-Cell Excitation by Electrical Stimulus

The basic principle underlying cardiac pacing is the ability of an externally applied voltage difference to generate a self-propagating wavefront of cardiac depolarization in the heart. This wavefront is the result of propagation of action potentials across the myocardium, a process that involves the opening and closing of ion channels in the membrane.

In reality, an applied external electrical stimulus initiates cardiac excitation as a result of passive effects on the transmembrane potential. This is a result of a change in potential that is induced in the extracellular space. Because of the relatively high impedance between cells across the membrane and through the gap junctions compared with the lower impedance path through the extracellular space, relatively small amounts of current pass through the cell membrane. When an external stimulus is applied, the potential within the intracellular space does not vary appreciably over the length and width of a cardiac myocyte (Fig. 1-5). However, near the stimulating electrode, the extracellular stimulus causes a field gradient to develop in the extracellular space. The transmembrane voltage (V_m) is equal to the difference in potential inside the cell (V_i) minus the potential outside the cell in the extracellular space (V_e), so a change in extracellular potential with little change in intracellular potential across the length of the cell results in a net difference in V_m. This is represented as follows:

Figure 1-5 Response of a cardiomyocyte to electric field.

Relatively little current passes through the relatively high impedance cell membrane. A, Cardiomyocite exposed to extracellular electric field. The intracellular voltage (V_i) is relatively low impedance and thus does not vary from one side of the cell to the other while the extracellular voltage (V_e) drops from one end of the cell to the other. B, Transmembrane potential (V_m) is defined as V_m = V_i − V_e, so the left side of the cell is hyperpolarized by the external field while the right side of the cell is depolarized. If the extracellular field gradient is large enough, the right-sided portion of the cell may reach threshold and initiate an action potential that may activate the entire cell and spread to adjacent cells through gap junctions.

(From Dosdall DJ, Fast VG, Ideker RE: Mechanisms of defibrillation. Annu Rev Biomed Eng. 12:233-258, 2010.)

Thus, as considered along the length of a cardiac myocyte, one end has a more negative transmembrane potential than the other. This leads to a net hyperpolarization of the cell on one end and depolarization on the other end. The induced change in V_m has the capacity to open voltage-gated ion channels within the cardiac cell membrane. Voltage-gated Na⁺ channels are opened by a decrease in V_m. If an external stimulus is strong enough to cause V_m on the depolarized side of the cell to rise above the threshold to activate the inward Na⁺ channels, the influx of Na⁺ ions rapidly leads to further depolarization of the cell and initiates an action potential. This action potential spreads to adjacent cells by passing ions through gap junctions and raising V_m in adjacent cells, and initiating an active response through the activation of Na⁺ channels.

Factors Determining Capture by an Electrical Stimulus

In order for an electrical stimulus to stimulate (capture) myocardium, it must be applied with sufficient amplitude, for a sufficient duration (measured in milliseconds), at a time when the myocardium is electrically excitable. Many clinical factors determine whether a stimulus of given amplitude will result in capture, including proximity of the electrode to the myocardium, pathology of the underlying cardiac tissue, size and shape of the electrode, and effects of drugs and hormones, as well as electrolytes. For routine clinical practice, the most important factor is that the lead must be positioned close to well-functioning myocardium in a secure manner. (It is also important that the lead does not stimulate the diaphragm or the phrenic nerve, that it is at a site that results in good hemodynamic function, and that the location does not allow the electrode to bump other electrodes.) After adequate lead positioning, the strength-duration relation is the next most important consideration.

Current Density, Electric Field Gradient, and Propagation of Depolarization

There are two approaches to thinking about how an electrical stimulus induces a self-propagating wavefront of depolarization within myocardium. The current density approach considers the magnitude of current flowing through a given mass of myocardium between the stimulating electrodes and finds this to be the critical factor required to induce a regenerative wavefront of depolarization. From this point of view, the stimulation threshold is a function of current density (amperes/cm²) in the excitable myocardium underlying the electrode.^33–36 The electric field approach holds that the critical factor affecting myocardial depolarization is the magnitude of the electric field gradient (volts/cm in viable tissue) that is induced in the myocardium beneath the stimulating electrode.^37,38 These approaches are fundamentally the same in that there is a mathematical relationship between the electric field gradient and the current density at the stimulating electrode.

Because reactance as well as resistance is present, Ohm’s law in this context must be stated in terms of impedance, as follows:

[1-5a]

where v is the stimulus voltage, i is the current, and z is the impedance to current flow. Note that each of these is a vector. Also note that z varies with current density at the electrode (because of interface properties), with direction of current flow (anisotropy), and with domain (extracellular or intracellular).

The total energy of the pacing stimulus is determined by the applied voltage, the current, and the duration of the stimulus, as follows:

[1-5b]

where J_t is the energy delivered (expressed in joules) from time zero to time t during the pulse, v_t is the voltage, and i_t is the current at the electrode at instantaneous time t during the pulse. This equation indicates that the total energy delivered during the pulse is proportional to the area under a curve. The curve is formed in the vertical dimension by the instantaneous product of voltage and current applied to the electrode, and in the horizontal dimension by the time elapsing during the pulse. When the time t reaches the programmed pulse duration, the pulse ends. The area under the curve then represents the electrical energy transferred during the time span of the pulse. The equation can easily be solved in real time with a small digital computer, provided that continuous phasic measurements of the voltage and current in the wire going to the electrode are available. (Note that this equation has blood flow and pressure energy analogs.³⁹)

For pacemakers in almost all clinical situations, it is more practical and very reasonable to calculate the energy delivered by a constant-voltage pulse through a pacemaker electrode by means of an approximation. The assumptions are that (1) the voltage during the pulse really is constant and (2) the current flowing is linearly related to the voltage. Because neither is quite true, the questions become (1) whether the information obtained proves useful and (2) to what degree it can be misleading. If the assumptions are close to being correct, the following equation can be approximately correct and useful:

where J is the energy delivered, V is the “constant” voltage, I is the current, R is the resistance, and t is the stimulus duration. This equation indicates that the total energy delivered can be estimated by multiplying the voltage reading displayed on the pacing systems analyzer (PSA) by the current reading on the PSA and multiplying that product by the stimulus duration. Alternatively, the voltage reading can be squared, then divided by the resistance reading, and the quotient multiplied by the stimulus duration. The virtue in this calculation is that ordinary equipment can provide a quick, approximate determination of the total energy delivered per stimulus. In clinical practice, however, the usual range of good or acceptable values for pacing threshold current and voltage is known, and there is rarely a need to calculate the delivered energy.

The stimulation threshold of isolated cardiac myocytes depends on their orientation within an electric field. The threshold is lowest when the myocytes are oriented parallel to the field and highest when the axis of the myocytes is perpendicular to the field.⁴⁰ It is clear that myocardial stimulation may be induced with anodal or cathodal stimulation, or both, although with somewhat different characteristics. Various investigators have used several different parameters to express stimulation threshold, including current (mA), potential (V), energy (J), charge (Q), pulse width (t, msec), and voltage multiplied by stimulus duration (V-sec).^41–47 For the purposes of this chapter, the myocardial stimulation threshold for pacing is defined as the minimum stimulus amplitude at any given pulse width required to consistently achieve myocardial depolarization outside the heart’s refractory period.⁴⁸ Stimulation thresholds measured with a constant-voltage (CV) generator are stated in volts, and those of a constant-current (CI) generator are stated in milliamperes (mA). Note that a true constant-voltage generator may yield a slightly different stimulation threshold than the pseudoconstant-voltage generators in ordinary use.

Why must an electrical pacing stimulus rely on propagation in myocardium rather than directly exciting the entire heart? With the magnitude of a stimulus generated by a pacemaker pulse generator, the electric field gradient and ion current density near the electrode are great enough to trigger an action potential only extremely close to the electrode. Unless propagation of the local depolarization occurs, no cardiac contraction will result.

In contrast to cardiac pacing with direct production of only local depolarization and dependence on self-propagation of depolarization, defibrillation involves direct depolarization or hyperpolarization of a large portion of the heart. This is necessary to provide at least the minimum local voltage gradient required to produce depolarization over major portions of the myocardium. To do so requires a stimulus intensity that is much greater than that required for pacing⁴⁹ (see Chapter 2 for a thorough discussion of defibrillation).

Electric Potential Gradients and Currents for Stimulation and Defibrillation

When the electric field exceeds approximately 1 V/cm in the extracellular space during diastole, myocardial stimulation (capture) results. The electric field must be achieved only in the area of several dozen cells and may be achieved typically with less than 0.5 mA. When the electric field strength is increased to 6 V/cm, ventricular fibrillation may occur if the stimulus is applied during the vulnerable period (approximately the peak of the T wave). An area where the voltage gradient is at least 6 V/cm must be achieved at a distance of 1 cm from the electrode. To accomplish this, a current of approximately 20 mA is required to initiate ventricular fibrillation. This same field strength (6 V/cm) is also required to interrupt ventricular fibrillation (defibrillation). However, defibrillation requires the minimum field intensity to be approximately 6 V/cm at almost all points in the myocardium. In order to achieve this minimum electric field gradient at the same instant over the entire heart, a very large shock current, typically more than 10 A, must be applied. This current is thousands of times greater than the current required for pacing.⁴⁹

When a pacemaker pulse is applied, electrically excitable myocytes respond with a wave of depolarization followed by repolarization in the myocardium. Depolarization of a small, local group of myocytes begins the self-propagating process. The initial depolarization adjacent to the electrode produces a potential gradient great enough at neighboring myocytes to result in their depolarization. The process is a self-regenerating mechanism that requires time to spread, and once established, it is largely independent of the distance from the stimulating electrode.

Defibrillation is largely accomplished by providing an extremely large potential gradient between the defibrillation electrodes. This produces, at one instant within local myocardium everywhere in the heart, at least a 6 V/cm gradient. In contrast, pacing is accomplished by providing a gradient of approximately 1 V/cm or less at a local site and relies on self-propagation to spread the depolarization process throughout the myocardium.

Virtual Electrode Effect

Virtual electrodes are important because they can serve as sites that initiate or prevent depolarization of myocytes.⁵⁰ Newton and Knisley⁵¹ defined virtual electrodes as “experimentally observed regions of large delta Vm that arise distant from the stimulating electrode.” “Delta Vm” (ΔV_m) here represents the change in voltage difference across the myocyte membrane during application of the stimulation current.

A virtual electrode can be described as a collection of charge predominately of one sign at a site away from a regular electrode. If, in an electrically neutral solution, ions of one charge sign are moved away by an electric field, a relative excess of ions of the other charge sign will be left or will move in the opposite direction. For example, if the regular electrode is paced with a negative-going stimulus, a site elsewhere in the tissue (i.e., not at this physical electrode) may become transiently positive and alter the transmembrane potentials of cells at that site.^52–55 In cardiac tissue, a virtual electrode can occur as an effect of anisotropy after a defibrillation shock and can initiate refibrillation. A virtual electrode may also result from ion redistribution patterns in a nonanisotropic medium. In anisotropic tissue, charge redistribution produced by a physical electrode can have a “dog bone” shape.⁵⁶

The virtual electrodes occur at sites where ions flow into or out of cells by crossing the cell membrane. An applied unipolar stimulation current flows into some cells while simultaneously flowing out of others, thus producing negative and positive virtual electrodes at different locations. In an anisotropic medium, a cathodal pulse produces a virtual electrode with a dog bone shape oriented perpendicular to cardiac fibers and containing a large ΔV_m, and a pair of virtual electrodes containing negative ΔV_m at locations along the fibers. Theoretical models have shown that this effect can be attributed to unequal tissue anisotropy in the intracellular and extracellular spaces; that is, intracellular current at a given location favors the longitudinal direction 10 to 1, whereas extracellular current favors the longitudinal direction only 3 to 1 (Knisley, personal communication, 2005). Knisley and Pollard⁵⁷ studied the effects of electrode-myocardial separation on cardiac stimulation of rabbit hearts in conductive solution. The electrode-myocardial separation altered the spatial distribution of ΔV_m and increased the pacing threshold.

In regard to electrode-myocardial tissue separation, Shepard et al.,⁵⁸ during 1980s transthoracic defibrillator implantation procedures, sewed the electrodes used for rate sensing onto the outer surface of the pericardium. Sensing voltages were normal. Pacing thresholds of these electrodes measured were high (3.7 ± 1.9 mA and 4.5 ± 2.19 V at 0.5-msec stimulus duration), as would be expected both from current density considerations and from Knisley’s findings. The initial impedance was 1209 ± 383 Ω, and the chronic impedance was 1550 ± 358 Ω at a median follow-up time of 964 days. The thresholds had by then decreased to 3.8 ± 2.07 V and 2.7 ± 1.8 mA. The transpericardial distance from underlying myocardium did result in high initial pacing thresholds (and in the special distribution of ΔV_m near the electrodes). However, the long-term tissue reaction of pericardium and underlying myocardium to the presence of these electrodes was not detrimental in terms of threshold evolution.

Virtual electrodes normally exist near an electrode when a pacing pulse is applied. Nikolski and Sambelashvili,⁵⁹ studying Langendorff-perfused rabbit hearts, found that stimuli of magnitude five times threshold produced “make” or stimulus-onset excitation from virtual cathodes, whereas near-threshold stimuli produced “break” or stimulus-termination excitation from virtual anodes.

In studying how cardiac tissue damage at an electrode results in a pacing threshold increase, Sambelashvili et al.⁶⁰ found that the virtual electrode effect was destroyed by very strong (40 mA, 4 msec, biphasic, 240/min) pacing pulses applied for 5 minutes. Fluorescent optical mapping showed that decrease or loss of the virtual electrode polarization was associated with pacing threshold increase. Propidium iodide staining showed tissue damage within an area about 1 mm in diameter surrounding the electrode.

Another view of the effect of strong stimuli as just described is that local tissue damage at a pacing electrode increases the distance from the electrode to normal myocytes. Because electric field strength and current density decrease with distance from the electrode, an increase in pacing stimulus amplitude applied to the electrode is necessary to restore the stimulus current density to the pacing threshold level of myocytes at the outer edge of the damaged tissue.

Anodal and Cathodal Stimulation

The polarity of a stimulus can be cathodal or anodal. In determining how an artificial electrical stimulus interacts with cardiac cells to initiate this self-propagating wavefront, the mechanism of excitation of cardiac tissue by an electrical stimulus depends on the polarity, strength, and duration of the stimulus. Cardiac excitation may occur immediately adjacent to the electrode by direct stimulation or at a distance from the electrode through virtual electrode effects. The two mechanisms by which electric current stimulates cardiac excitation close to electrodes are cathodal make and anodal break. Virtual electrodes cause cardiac excitation by cathodal break and anodal make phenomenon.

Cathode make excitation occurs adjacent to a cathode from the high current density immediately surrounding the electrode. Current flows in the extracellular space and causes hyperpolarization and depolarization of opposite ends of the cell, as shown in Figure 1-5. Current also passes through the cell membrane and causes an increase in V_m that exceeds the threshold for fast Na⁺ channels to activate. Excitation spreads outward from the central excitation site in an elliptical shape because of tissue anisotropy (Fig. 1-6). Cathode make occurs on the rising edge of the stimulation pulse (Fig. 1-7, A).

Figure 1-6 Action potentials are initiated by cathodal and anodal excitation.

Excitation make and break phenomena occur under and near electrodes. Cathodal make occurs when the excitation current directly excites the tissue under the electrode. Anodal break occurs under the excitation electrode on termination of the stimulating pulse.

(From Antoni H: Electrical properties of the heart. In Reilly JP, editor: Applied bioelectricity: from electrical stimulation to electropathology. New York, 1998, Springer, p 160.)

Figure 1-7 Computer simulation of four types of excitation with stimulating electrode (black rectangle).

Cathode make (A), anode make (B), cathode break (C), and anode break (D) excitation are shown at various times; columns are time (t) in milliseconds. In A and B, t = 0 when the stimulation pulse turns on, and in C and D, t = 0 when the stimulation pulse is turned off.

(From Wikswo JP, Roth BJ: Virtual electrode theory and pacing. In Efimov IR, Kroll MW, Tchou PJ, editors: Cardiac bioelectric therapy: mechanisms and practical implications. New York, 2009, Springer Science, pp 283-330.)

An anode tends to hyperpolarize cells immediately adjacent to the electrode, but virtual cathodes form on both sides of the central anode. Anode make excitation causes activation to spread on both sides of the central hyperpolarized region until the excitation merges into a single wavefront and spreads elliptically (Fig. 1-7, B). The threshold for stimulation with cathode make is typically higher than for anode make because the virtual cathodes that form at a distance from the central anode are weaker and have less depolarizing power than the direct effects of a central cathode.

Cathode break excitation occurs when the stimulating pulse is turned off (Fig. 1-7, C). While the stimulation pulse is turned on, the tissue under the stimulating electrode is depolarized, and the fast Na⁺ channels open and then become unexcitable. Propagation of the excitation is repressed somewhat by the virtual anodes on either side. On termination of the stimulating pulse, the virtual anodes disappear, and excitation spreads from the active tissue under the electrode to the hyperpolarized regions under the virtual anodes. Because the tissue under the virtual anodes was hyperpolarized, the Na⁺ channels are fully excitable, and the excitation wavefront spreads rapidly through the area previously covered by virtual anodes. Cathode make occurs at a lower threshold than cathode break and is not observed unless tissue is refractory when the stimulation pulse commences but becomes excitable during the pulse. If the tissue has recovered by the time the pulse turns off, cathode break may occur.

If the tissue is unexcitable surrounding an anode at the beginning of a stimulation pulse, anode break excitation may result from a mechanism similar to that of cathode break. Excitation may be initiated by the termination of the excitation pulse (Fig. 1-7). Hyperpolarization directly below the anode causes the Na⁺ channels to become excitable. Depolarization from the virtual cathodes then rapidly propagates into the hyperpolarized region under the anode (Fig. 1-7, D). The virtual cathodes are relatively weak compared to the hyperpolarizing effect of the anode, but the activation spreads from the depolarized region into the hyperpolarized region because the cell membrane has a nonlinear response by which hyperpolarization decays more rapidly than does depolarization. Because anode break relies on virtual cathodes to initiate excitation in recently recovered tissue, however, this mechanism of excitation has the highest threshold of all, the make or break excitation mechanisms.

Anode and cathode make and break phenomenon have been detected in computer models and verified in animal experiments.^54,61 Optical mapping techniques with voltage-sensitive dye have been particularly useful in illuminating these mechanisms of stimulation.

Chronaxie, Rheobase, Energy, and Pulse Duration Thresholds

The intensity of an electrical stimulus (measured in volts or milliamperes) that is required to capture the atrial or ventricular myocardium depends on the duration of the stimulus.^62,63 The historical background and the relations between the various electrical factors have been reviewed, further studied, and clearly stated by Blair,⁶⁴ and by Geddes⁶⁵ for electrode-electrolyte interface function and models.

The interaction of stimulus amplitude and stimulus duration (pulse width) defines the strength-duration curve (Fig. 1-8). Lapique described this exponential relationship of stimulus intensity (current), I, and pulse duration, t, as follows:

Figure 1-8 Relationships between chronic ventricular canine constant-voltage strength-duration curves expressed in terms of potential (V), charge (µC), and energy (µJ) for a tined unipolar lead with an 8-mm², polished, ring-tip electrode. Thresholds are measured at the point of gain of capture. Rheobase is the current or voltage threshold to the right that is independent of pulse width. Chronaxie is the pulse width at twice the rheobase.

(From Stokes K, Bornzin G: The electrode-biointerface [stimulation]. In Barold SS, editor: Modern cardiac pacing. Mt Kisco, NY, Futura, 1985, pp 33-78.)

[1-5c]

where I_rh is the rheobase current, e is the mathematical constant 2.718, and τ is the membrane time constant.

The voltage or current amplitude required for endocardial stimulation has an exponential relation to the pulse duration, with a relatively flat curve at durations of longer than 1 msec and a rapidly rising curve at durations of less than 0.25 msec. Because of this fundamental property, a stimulus of short pulse duration must be of much greater intensity to capture the myocardium than a longer-duration pulse. Conversely, increasing the pulse width to longer than 1 msec has minimal influence on the intensity of the stimulus that is required for capture. Therefore, if one defines the stimulation threshold in terms of pulse amplitude without also specifying the pulse duration, important information is neglected. Similarly, specifying the capture threshold in terms of pulse duration can be misleading if the stimulus amplitude setting is omitted or unknown.

In 1892, Hoorweg⁶⁶ used a voltage source, a galvanometer, and low-leakage capacitors to conduct quantitative stimulation studies. He found that the voltage at which a capacitor must be charged to cause depolarization of nerves and muscles is an inverse function of the capacitance of the capacitor, as follows:

[1-6]

In this experimentally determined equation, V_c is the threshold voltage to which a capacitor of capacitance C must be charged to produce stimulation on discharge. R is the resistance of the circuit through which the capacitor is discharged, and a and b are coefficients that vary with the specimen (tissue) tested. Here, the experimentally determined constant a has the dimension amperes and the constant b has the dimension ampere-seconds. (The capacitance can be derived from the equation

where C is the capacitance, Q is the charge on either conductor, and V is the magnitude of the potential difference across the capacitor; the capacitance has the dimension ampere-seconds [or coulombs] per volt; 1 coulomb per volt = 1 farad). Hoorweg determined that there was only one specific capacitance value for which the threshold charge was a minimum. He also determined that the threshold charge was a linear function of the stimulus duration, “intersecting the y-axis above zero.” However, Hoorweg did not have the capability to measure thresholds at very short pulse durations. In reality, the threshold charge increases toward infinity as the pulse duration approaches zero.

In 1901, Weiss⁶⁷ reported that the threshold charge required for stimulation increases linearly with stimulus duration. He called this relationship the “formule fondamentale.” If I represents the magnitude of the current, t is the stimulus duration, and a and b are constants determined by analyzing the data, Weiss found that:

[1-7]

Or, because = Q, the charge in the capacitor at threshold stimulus duration t, Q = at + b. For a constant-current stimulus, this can be stated in words as threshold charge requirement = a amperes times t seconds + b, where b is a constant with dimensional units of ampere-seconds. The values of the constants a and b vary with the tissue tested.

The left-hand side of Equation 1-7 indicates that the charge delivered into the electrode is, for a constant current, the magnitude of the current multiplied by the duration of the current. The right-hand side states that the charge required to stimulate at threshold is a minimum of b ampere-seconds plus the product of the current level a and the stimulus duration t. Weiss⁶⁷ noted that, for various stimulus durations tested, the quantity of charge required to initiate depolarization remained constant.

The statement that the threshold charge requirement does not change with stimulus duration is true only within a limited range. The limitation leads to the concept of rheobase, as stated in 1909 by Lapique;⁶⁸ when pulse duration is increased beyond a limited range, the current requirement does not decrease further. The charge delivered continues to increase as pulse duration is increased. Lapique called this minimum current the rheobase, or the lowest stimulus current that continues to capture the heart when the stimulus duration is made extremely long. In this situation, further increases in stimulus duration no longer reduce the magnitude of current required to stimulate the heart.

Note from Equation 1-7 that the ratio a/b has the dimensions/amperes divided by (ampere-seconds); this expression reduces in dimensions to the reciprocal of the stimulus duration. Lapique called the time seen in the a/b ratio the chronaxie, specified in seconds. Chronaxie time experimentally turns out to be approximately the threshold pulse duration at twice rheobase amplitude, and it has become defined as such; this is illustrated in Figure 1-8. Note again that rheobase is specified in terms of current, and chronaxie is specified in terms of time.

Lapique⁶⁹ determined that stimulation at the chronaxie pulse width approaches the minimum threshold energy. Therefore, the two most important reference points on a current or voltage strength-duration curve are rheobase and chronaxie. Obtaining a true rheobase typically requires pulse widths of 10 msec or greater. For clinical purposes, rheobase can be approximately measured at pulse widths of 1.5 to 2 msec. The value obtained may be slightly greater than the true rheobase. Therefore, the chronaxie stimulus duration obtained by setting the stimulus current at twice the approximate rheobase current and then finding the minimum stimulus duration that will result in capture is slightly low. In a time-saving, useful, and reasonable clinical sense, one may empirically set the stimulus duration at a value determined from experience, such as 0.4 to 0.5 msec and then determine the current and voltage thresholds. Safety factor allowances of current and voltage are then added or subtracted based on the patient’s current and projected clinical status (see later discussion).

The goal is to find the combination of pacing threshold stimulus current, voltage, and pulse width that results in minimal charge drain from the pulse generator battery at normal pulse rates. Figure 1-8 shows that, for capture to be accomplished, the least charge was required at the shortest pulse duration (0.1 msec in the figure), but the least energy was required at about 0.3-msec stimulus duration. A very short pulse duration puts thresholds close to the steeply ascending limb of the voltage or current curve, where slight fluctuations can risk loss of capture. For this reason, Irnich^70,71 recommended that chronaxie, or the pulse duration slightly to the left of chronaxie, is the most efficient pulse duration for both pacing and defibrillation. In most cases, the pulse duration at chronaxie or slightly greater appears to represent the best overall compromise between adequate safety and generator longevity. One also considers the expected stability or instability of the patient’s status, patient compliance, and follow-up arrangements, both short and long term.

Pacing thresholds can also be specified in terms of only energy (microjoules, µJ) or only pulse duration (milliseconds). However, reliance on specifications in either of these units alone can be misleading. Doing so discounts that, regardless of the pulse duration or energy used, the heart cannot be stimulated unless the stimulus amplitude exceeds the rheobase current.⁷²

For example, if rheobase is achieved with a pulse amplitude of 0.5 V and 10 msec, the pulse at this point on the strength-duration curve will have 5 µJ of energy (current × voltage × time) with a 500-Ω lead (1 mA × 0.5 V × 10 msec = 5 µJ). A 0.4-V, 20-msec pulse on a 500-Ω lead has 6.4 µJ of energy (28% greater than the “threshold” energy at 10 msec) but will not result in cardiac capture. Increasing the pulse duration to 100 msec at 0.4 V results in 32 µJ of energy (540% greater than “threshold” energy at 10 msec) but will still not capture the heart, for the same reason. No matter how far the pulse duration is extended (with increased energy), the myocardium will not be captured unless the stimulus amplitude is at least as great as the rheobase value. Therefore, calculation of the energy threshold at very long pulse durations does not provide clinically useful information.⁷³

Coates and Thwaites⁷⁴ studied the strength-duration curve in 229 patients with 325 leads. The mean atrial chronaxie (n = 101) was 0.24 ± 0.07 msec, and the mean ventricular chronaxie (n = 224) was 0.25 ± 0.07 msec. Mean atrial and ventricular rheobase values were 0.51 ± 0.2 V and 0.35 ± 0.14 V, respectively. Because the pulse generators were set at factory-nominal pulse durations of 0.45 to 0.50 msec, the authors concluded that pacing was suboptimal from the efficiency point of view. They pointed out that battery drain would be reduced by programming pulse duration to the chronaxie value and then programming the voltage to double the chronaxie value. In a study of excitability of rat atria during postnatal development up to 120 days, Gurjao de Godoy et al.⁷⁵ found that atrial rheobase decreased with animal age and was altered by electric field orientation. Atrial chronaxie increased only with age. The clinician might keep in mind that the chronaxie is influenced not only by electrode material, size, and stimulation mode, but also by clinically varying biochemical factors. Certainly, marked variations in pacing threshold, either up or down, do occur months and years after implantation in some children and adults.⁷⁶

As stated earlier, on the left side of the chronaxie point of the strength-duration curve, the current and voltage rise rapidly as stimulus duration decreases. At pulse durations greater than chronaxie, the slope of the strength-duration curve gradually flattens. Small changes in stimulus amplitude are then less likely to result in loss of capture, especially if the threshold has increased because of a pathophysiologic condition. This increased safety comes at the cost of decreased battery life.

Practical Application to Threshold Measurement

To determine the strength-duration relationship, the clinician must measure the stimulation threshold at specific amplitudes and pulse durations. However, the result obtained varies somewhat with the method used. Usually the threshold, as measured at a specific stimulus duration (e.g., 0.5 msec), will be slightly higher when the stimulus amplitude is gradually being increased than being decreased. The threshold can also be measured by holding the output voltage constant and changing the stimulus duration. The stimulation threshold then is defined as the lowest-amplitude pulse duration that results in consistent capture of the myocardium. Only the threshold measured in this way can be clinically useful, as noted earlier. It also can be deceptive, because the strength-duration curve is not linear.

For example, if the pulse duration threshold is 0.5 msec at an amplitude of 2 V, reprogramming the pacemaker stimulus to a pulse duration of 1 or even 1.5 msec would provide a very small margin of safety (Fig. 1-9). Instead, doubling the stimulus amplitude to 4 V at a pulse duration of 0.5 msec would provide an adequate margin of safety. In contrast, consider that, in this same patient, the pulse duration threshold is 0.15 msec at a pulse amplitude of 3.5 V. Increasing the pulse width to 0.45 msec would also provide an adequate safety margin. The reason that a threefold increase in pulse width is not adequate in the first example but is acceptable in the second relates to the location of the threshold stimulus on the strength-duration curve.

Figure 1-9 Programming of pulse amplitude and pulse duration based on analysis of the strength-duration curve in a patient evaluated at the time of pulse generator replacement (6 years after lead implantation). The rheobase voltage was 1.4 V, and the chronaxie pulse width (PW) was 0.30 msec. Note that the stimulation threshold, determined by decreasing the stimulus amplitude at a constant pulse duration of 0.5 msec, was about 2 V (point A). Doubling of the PW on the relatively flat portion of the strength-duration curve (point B) provides little safety margin for ventricular capture. In contrast, consider a threshold value on the steeply ascending portion of the strength-duration curve (point C). Doubling of the pulse amplitude doubles the safety margin on this portion of the curve, but it lies very close to the curve (point D). An appropriate setting for the chronic pacing pulse might be achieved by doubling the pulse amplitude from point A to point E. Also note that a similar programmed setting would have been obtained had the pulse duration been tripled from point C. Thus, the shape of the strength-duration curve has an important influence on the choice of the amplitude and duration of the pacing pulse.

Consideration of programming the pulse generator to twice the voltage threshold found at the chronaxie pulse duration is only a starting point. Determination of the safety margin necessary for any particular patient depends on several physiologic factors, as discussed next.

Capture Hysteresis (Wedensky Effect)

The threshold stimulus amplitude measured by decreasing the voltage or current until loss of capture occurs is sometimes less than that determined by increasing the stimulus intensity from below threshold until gain of capture occurs. This hysteresis-like phenomenon is the Wedensky effect,⁷⁷ the effect of subthreshold stimulation on the subsequent suprathreshold stimulation when the stimulus amplitude is being increased (Fig. 1-10).

Figure 1-10 Pacing thresholds determined by gradually incrementing and decrementing the pulse amplitude until gain and loss of capture, respectively, are demonstrated in a patient with complete atrioventricular block. The pacing threshold was determined at cycle lengths of 2000, 1500, 1000, 750, and 500 msec and with a constant pulse duration of 2.0 msec. To prevent variation in cycle length during incrementing and decrementing pulse amplitudes, a backup pulse was delivered at 25 msec. Note that the threshold values determined in this manner, with increments and decrements of the stimulus amplitude, are similar. Therefore, the Wedensky effect may be marginal when the pacing cycle length is maintained at a constant value.

Langberg et al.⁷⁸ observed no demonstrable capture hysteresis at pacing cycles longer than 400 msec. They concluded that the Wedensky effect was related to asynchronous pacing in the relative refractory period when incrementing the stimulus intensity, versus the synchronous late-diastolic stimulation when decrementing the stimulus amplitude until loss of capture.

Swerdlow et al.⁷⁹ showed in a study of 40 patients that cardiovascular collapse occurs at AC current levels less than the ventricular fibrillation current threshold. The continuous capture threshold for AC current is less than the capture threshold for a single ordinary pacing stimulus. The authors suggested that continuous capture at low levels of AC current requires a cumulative effect of subthreshold stimuli; this is a variation of the Wedensky effect. The safety standard for 60-hertz (Hz) current leakage longer than 5 seconds should be 20 microamperes (µA) or less to avoid intermittent capture.

Effect of Pacing Rate on Stimulation Threshold

Hook et al.⁸⁰ reported a significant increase in ventricular pacing threshold in 10 of 16 patients at 400 msec and in 15 of 16 at 300 msec (relative to a pacing cycle length of 600 msec). The phenomenon was not observed at every trial (e.g., 12 of 72 trials at 400 msec). The patients were all candidates for ICDs, and 9 of 12 were receiving antiarrhythmic drugs. The leads were bipolar: a pair of epicardial corkscrews in 11 patients and endocardial screw-in lead in five patients.

The atrial stimulation threshold has also been shown to vary as a function of pacing rate.^81,82 Katsumoto et al.⁸³ reported that 29 of 36 patients exhibited constant-current atrial pacing threshold energy and current variations as a function of pacing rate in the range of 60 to 120 beats per minute (bpm). The pacing was done with activated vitreous carbon electrodes.

Kay et al.⁸⁴ found significant human atrial threshold changes as a function of pacing rate (125-300 bpm) using constant-voltage stimulation. They found a significant increase in rheobase voltage (Fig. 1-11), chronaxie, and minimum threshold energy at pacing rates greater than 225 bpm using platinized (low-polarizing) unipolar electrodes. They also determined strength-interval curves and found no correlation between atrial effective refractory period and rheobase voltage, chronaxie, or rate-dependent changes in either of these values. They concluded that the phenomenon is probably related to the “opposing effects of decreasing cycle length on the action potential duration and the slope of the strength-interval curve. Thus, if the pacing interval shortens to a greater extent than the refractory period and pacing stimuli are delivered during the ascending limb of the strength-interval curve (the relative refractory period), the diastolic threshold will increase.”⁸⁴

Figure 1-11 Effect of pacing rate on atrial rheobase voltage in patients.

The rheobase voltage increases significantly for pacing rates greater than 225 beats/min (values shown as mean ± SEM).

(From Kay GN, Mulholland DH, Epstein AE, Plumb VJ: Effect of pacing rate on human atrial strength-duration curves. J Am Coll Cardiol 15:1618-1623, 1990.)

The increase in stimulation threshold with increasing stimulation rate probably has minimal implications for bradycardia pacing. It is important for antitachycardia pacing, however, because threshold must be measured at rates required to interrupt the arrhythmia. In addition, the safety factors used with antitachycardia pacemakers must be based on thresholds measured at the clinically appropriate rates, rather than during pacing at resting rates.

Conductor Resistance and Conduction Losses

Energy dissipation in the lead from the pulse generator to the electrode is proportional to the square of the current. To minimize charge drain from the battery, low lead resistance and low current are desirable. Because the purpose of a pacing stimulus is to produce high current density at the electrode-electrolyte interface in the heart, the ideal situation is to deliver a low current from a very small surface area of electrode. If high current density (current magnitude divided by the plane area of the myocardium touched by the electrode) can be obtained with a small, high-impedance electrode, the current drained from the battery will be less than with lower impedance.

At pacing threshold, a certain current density exists. If the interface area is made smaller, the current can be reduced equivalently and the same current density maintained. Minimizing the current needed for stimulation requires an optimal combination of interface area, current density, surface material and structure of the electrode, and increased impedance from making the electrode interface area smaller. An increase in impedance made to reduce current drain from the battery should be accomplished by making changes in the electrode, not by increasing the resistance of the wires to and from the pacemaker.

Impedance at Electrode-Tissue Interface

The resistance (ohmic polarization) of the stimulating electrode is inversely and exponentially proportional to the size of the electrode and the temperature and conductivity of the tissue.^85,86 For practical purposes, in vivo temperature and conductivity are essentially constant. Decreasing the geometric surface area of the electrode, as illustrated in Figure 1-13, is a way to increase the current density at the electrode for any given level of output current from the pulse generator.

Figure 1-13 Leading-edge ohmic polarization or electrode resistance of chronic canine ventricular leads (12 weeks after implantation) measured with a Medtronic Model 5311 pacing systems analyzer as a function of the unipolar cathode’s geometric surface area.

Each data point was obtained from a population of animals testing one lead design. The study included 323 animals and 48 lead models.

Size reduction alone, however, has the negative effect of increasing polarization impedance. In effect, the Helmholtz capacitance at the interface is decreased by reducing the area of the electrode. One remembers from the equation

that the voltage v_t across the Helmholtz capacitance at the electrode is proportional to the accumulated charge and inversely proportional to the capacitance. If the electrode contact area with the tissue is made smaller to increase the current density and nothing else is changed, the capacitance will be decreased. For a given applied charge, that action will increase the Helmholtz capacitance voltage, because of the inverse relationship between the voltage and the capacitance.

For a given electrode material (as a first approximation), capacitance (C) is a function of the interface surface area (A_i):

[1-8]

where e is the dielectric constant of the Helmholtz double layer and d is its thickness. Because e and d are essentially constants in vivo, the capacitance of the electrode varies as a function of the interface surface area.

How does one obtain a very large surface area to contact the tissue and not use a large-diameter electrode? Initially, this was accomplished by making the electrodes porous.^87–89 Microporous electrodes, such as activated carbon or platinized platinum, have a higher real surface area.^90,91 The capacitance of microporous surfaces is greater than that of porous surfaces and still greater than that of polished surfaces. Fractal-surface electrodes have been best at meeting the requirements of very small geometric areas and large Helmholtz interface areas at the same time.

Another approach to the problem of decreasing polarization is to use a material that supplies its own majority charge carriers. An example is the silver–silver chloride (Ag/AgCl) electrode in chloride solution. The majority carrier, in this case Cl⁻, cannot be depleted; Cl⁻ evolves at the cathode and is formed at the anode. Therefore, voltage across the electrode interface has a waveshape (waveform) essentially identical to that of the applied constant current, and the electrode is “nonpolarizing.” Unfortunately, no clinically usable, nonpolarizing (charge-carrier supplying) electrode material seems available for permanent implantation. Ag/AgCl electrodes, for example, are not used for permanent pacing because the anode erodes and the AgCl eventually dissolves from the cathode.^92,93

The ideal, practical stimulating electrode is made of a corrosion-resistant, biocompatible material with small geometric size and very high interface surface area, which gives it the characteristics of very high capacitance and a lower polarization voltage.

Reactance and Charge Movement at Electrode-Electrolyte Interface

The electrode and the tissue act not as pure resistances but as reactances that change the time relationships between voltage and current when a pacemaker or defibrillator pulse is applied. The only elements of almost-pure resistance in the pacemaker circuit external to the pulse generator are the lead wires.

When the pacing pulse begins, several events occur almost immediately. Electron motion in the lead wires and electrodes must result in ion motion in the interstitial fluid. The electric field between the electrodes results in (1) reversible or irreversible oxidation-reduction processes occurring at the interface between the electrode and the electrolyte, and/or (2) the electrode-tissue interface’s acceptance of current without charge crossing the interface. In the latter case, the interface acts as a capacitor. Figure 1-14 shows the result is the sequence of events. The leading-edge voltage/current ratio is referred to as ohmic polarization. The increasing charge on the Helmholtz capacitor results in increasing opposition to further current inflow. The figure shows this as polarization overvoltage. The rates of voltage and current change depend on rates of ion movement within the electrolyte. These in turn depend on the mass and charge of ion species, species interactions and concentrations, and the applied electric field. The result is that lead wire current and voltage are not linearly related. The circuit is reactive. The vector combination of this reactance and the resistive elements (e.g., lead wires) make up the impedance faced by the pulse generator output.

Figure 1-14 The effect of polarization (upper diagram) has been separated from the capacitively coupled constant-voltage pacing pulse (lower diagram) to help clarify the electrical manifestation of electrode polarization. At the leading edge of the pulse, polarization is essentially zero. With time (pulse duration), the voltage resulting from polarization (sometimes called polarization overvoltage, V_p) increases. When the pacing pulse is shut off, polarization overvoltage decays exponentially as a result of diffusion.

(From Stokes K, Bornzin G: The electrode-biointerface [stimulation]. In Barold SS, editor: Modern cardiac pacing. Mt Kisco, NY, Futura, 1985, pp 33-78.)

Charge Conduction and Transmembrane Potential Changes in Cardiac Pacing and Defibrillation

The directed motion of electric charge is the result of electric field gradients. Currents at pacemaker or defibrillator electrodes and within the heart can be considered in several categories, including (1) ion movement currents external to cells, within cells, and across cell membranes, and (2) charge separation currents that bring opposing charges to the electrode-electrolyte interface and membrane intracellular-extracellular interfaces, without charge actually crossing the interface. The latter currents are capacitive, charging the Helmholtz capacitor at the electrode and changing the voltage difference across the cell membrane before it depolarizes.

In 1969, Otto Schmidt⁹⁵ described biologic information processing using the concept of “interpenetrating domains.” In the heart, two domains of charge flow exist: extracellular and intracellular. The two domain pathways are different in their anisotropic characteristics, and they are interwoven. Current passes from one domain to the other through cell membranes. Bidomain theory and studies are based on the concept that at every point in the heart, there are two electric potential vectors, one intracellular and one extracellular. Mathematically, each domain is continuous and occupies the entire domain. Membrane current leaves one domain and enters the other at the same coordinates. The analytical and experimental work from these concepts has provided insight about depolarization wavefront passage over the myocardium, current flow directions in relation to wavefront direction, and virtual electrode formation.^96–99

Roth⁹⁹ showed that stimulation of myocytes by application of a defibrillation shock can result in transmembrane voltage (V_m) changes by four mechanisms: (1) direct polarization of the tissue, as described by cable theory (see later discussion); (2) production of virtual anodes and cathodes, as described by bidomain models with unequal anisotropy ratios of the intracellular and extracellular spaces; (3) polarization of the tissue secondary to change in orientation of cardiac fibers (curving); and possibly, (4) polarization of individual cells or groups of cells because of a sawtooth electric potential effect. Sawtooth alterations in potential may result from resistive discontinuities introduced by intercellular gap junctions. Plonsey and Barr¹⁰⁰ predicted the occurrence of sawtooth effects in 1986. Under what circumstances and to what degree, if any, the sawtooth effect might become important in fibrillation or defibrillation is uncertain.^101–103

Electrical Charge Movement in Wires and in Tissue

Whether contraction of a myocyte occurs when a pacemaker pulse is applied is a function of several factors: (1) the amplitude, waveform, and duration of ion flow in the extracellular tissue resulting from the electric field gradient produced by the pulse; (2) the state of the preexisting voltage difference from the outside to the inside of the cell (degree of polarization or depolarization of the cell membrane); and (3) the biochemical state of the cell.

Irnich^104,105 discussed fundamental laws of electrostimulation in 1990, then three myocardial stimulation theorems in 2002, introduced by George Weiss 100 years earlier: (1) the pacing threshold, as measured by the voltage-time product of the stimulus, is a linear function of the pulse duration; (2) there is a minimum of the delivered threshold energy requirement that depends on the pulse duration; and (3) pulse shape plays no role in electrostimulation. The third theorem is a concept with clinically apparent limitations and requires some interpretation,^106,107 as discussed later.

Capacitance and Polarization

When an electric field is applied to an electrode, the interface with the surrounding tissue stores electric charge separated by charge sign, thereby acting as a capacitor. A capacitor requires a finite amount of time to charge or discharge to any specified voltage. The relationship between the voltage across a pure capacitor at any time t, when i represents the instantaneous current flow and the capacitance has magnitude C (measured in farads), is

and the instantaneous current i entering or leaving the capacitor is

where dv/dt represents the rate of change of the voltage across the capacitor. The amount of charge stored, , is directly proportional to the net area under the curve of instantaneous current entering and leaving the capacitor plotted against time. Note also that, for a given amount of charge, the voltage across the capacitor is inversely proportional to the capacitance. A perfect capacitor with no energy loss in storage or discharge is described by these equations.

Neither cell membranes nor man-made capacitors are perfect capacitors. In nonperfect capacitors, some energy is dissipated in the capacitor during storage or discharge. Pacemaker and defibrillator electrodes act as imperfect capacitors by means of the Helmholtz double-layer effect (described later).

The capacitance of canine myocytes in isosmotic solution is about 175 picofarads (pF). Cell membrane capacitance is about 0.01 microfarad (µF) per square millimeter of membrane surface area.¹⁰⁸ The capacitance of pacemaker electrodes has been reported to range from 0.2 µF/mm² (smooth surface) to 40 µF/mm² (fractal-surface electrode). The area of pacemaker tip electrodes is usually in the range of 4 to 10 mm². Therefore, the capacitance might be 200 µF or more. The time constant for a 200-µF capacitor C discharging through a 500-Ω resistor R is R × C, or 100 msec. This means that the voltage across the capacitor, or across an ideal electrode-electrolyte interface, if the capacitance were a truly constant 200 µF and the interface impedance 500 Ω, would on discharge decrease from its maximum level to 37% of maximum in 100 msec.

Figure 1-15 shows the Helmholtz capacitance and Warburg impedance in a schematic representation of a typical pacing configuration. These effects are caused by the electrode/tissue interface and the conversion of electric charge from electron flow to ion flow.

Figure 1-15 Equivalent circuit representation of an electrode-electrolyte interface, including the Helmholtz capacitance and the Warburg impedance.

(Modified from Rodman JE: Solution, Surface and solid state assembly of porphyrins [PhD thesis]. Cambridge, University of Cambridge, 2000, Fig 4.6.)

Figure 1-16 demonstrates the decay of the Helmholtz capacitance following a constant current pulse. After termination of the pacing pulse, the voltage decays slowly toward baseline, but does not reach it before the second pulse is delivered. If the impedance between the positive and negative sockets of the pulse generator were made to go to very high impedance when the pacemaker pulse ends, almost no current would flow in the catheter wires between pulses. The Helmholtz capacitor at the electrode would discharge mainly through resistive components in the electrode-electrolyte interface. In that case, when the constant-current stimulus stops, the voltage measured across the catheter pins would keep the same polarity and would decay slowly rather than go to zero precipitously.

Figure 1-16 Slow decay of pacing catheter lead voltage between biphasic stimulus phases.

The plot shows current (top trace) and induced voltage (lower trace) from a Bloom stimulator delivered between the pacing tip of an Endotak catheter and a “hot can” electrode in saline. At the end of each phase, the voltage measured at the pulse generator terminals initially goes rapidly toward zero but then, partway toward zero, it begins to change only slowly. This is the effect of discharge of the Helmholtz capacitor into the surrounding electrolyte. This voltage response between phases is a function of the rates of ion movement in the electrolyte.

Figure 1-16 also illustrates this decay by an electronic circuit simulation during pacing of a fibroblast cell culture through a bipolar cardiac catheter. The top trace shows a biphasic constant-current pulse with 3 msec between the end of the initial, negative phase and the beginning of the positive phase. The duration of each phase is 1 msec. The pulse generator circuit here goes to a high impedance rather than a low impedance when each phase ends. The bottom trace shows the voltage response. At the end of each phase, the voltage measured at the pulse generator terminals initially goes rapidly toward zero but, partway toward zero, it begins to change only slowly. This is the effect of the Helmholtz capacitor discharging into the surrounding electrolyte, and it is a function of the rates of ion movement at that time during the discharge cycle.

Biphasic Stimulus Effect

Of great interest is the effect of decreasing the delay time between the end of the first and the beginning of the second phase. Compare Figure 1-16 with Figure 1-17. When the stimulus is biphasic with almost no delay (here about 10 µsec) between phases, the slow decay of voltage at the end of the first phase is aborted by the beginning of the second, opposite-polarity phase. The amplitude and duration of the voltage decay after the second phase are each less when the second phase occurs immediately rather than being delayed by 3 msec. In practical terms, because of Helmholtz effects, electrical activity continues to occur at and near the electrode after the stimulating pulse stops. Details of the activity depend on the stimulus (uniphasic or biphasic), delay time between phases, characteristics of each phase, and the action of the pulse generator output circuit when the stimulus stops (high impedance, low impedance, or recharge pulse). The electrical activity also depends on the characteristics of the electrode (e.g., geometric vs. electrical surface area), the ionic solution, and the tissue.

Figure 1-17 Effect of near-zero delay between phases on voltage response to biphasic constant-current pulse.

This plot was made under the same conditions as Figure 1-16, except that the delay between phases was decreased from 3 msec to approximately 100 µsec. When the stimulus is biphasic with almost no delay between phases, the slow decay of voltage at the end of the first phase is aborted by the beginning of the second, opposite-polarity phase.

Capacitance, Polarization, and True Impedance

When using an ordinary pacing systems analyzer, one thinks of impedance as a voltage/current ratio. If reactance is present, as it is at a pacemaker or defibrillator electrode because of the Helmholtz capacitance effect, the voltage/current ratio as seen on the PSA can be deceptive (see Biventricular Pacing). Because of the charging and discharging of the Helmholtz capacitor at the electrode-electrolyte interface, the applied voltage and resultant current are not linearly related. Therefore, the circuit is reactive, and impedance rather than resistance is the correct measure of opposition to current flow (see earlier discussion).

There are practical problems in easily measuring true impedance during implantation procedures. In most clinical circumstances, however, the voltage/current ratio provides a reasonable estimate of the load into which the pulse generator is working, which is a major factor in determining current drawn from the battery.

Charge Grouping and Polarization

When an electrical stimulus is applied to the heart, the negatively charged cathode in contact with the myocardium attracts positively charged ions in the extracellular space. Likewise, the positively charged anode attracts negatively charged ions. This grouping phenomenon is known as polarization. The word “polarization” in this chapter has the following meanings:

Capacitance Effect of Helmholtz Double Layer

About 1879, Helmholtz suggested that a layer of ions (inner Helmholtz layer) is attracted to the surface of a charged electrode, and that this layer is bounded on its nonelectrode side by a layer of oppositely charged ions (outer Helmholtz layer) in the solution.¹⁰⁹ This interface acts as a capacitor. Helmholtz assumed for this model that no electron transfer reactions occur at the electrode and that the electrode environment is only an electrolyte. These (and more complicated charge redistributions) occur because of attraction and repulsion interactions between an electrode held at a given electric potential (e.g., 2 V negative during 0.5-msec pacemaker pulse) and the ions and charged molecules in the interstitial fluid. The charge placed on the electrode, by electrostatic attraction, forces the accumulation of a polarized water layer and a second layer of hydrated, oppositely charged ions adjacent to the electrode surface. The oppositely charged ions come from the electrolyte. The interface at the electrode becomes an electrical double layer. This is in effect a charged capacitor.¹¹⁰

However, the actual interface is not a simple double layer. The Helmholtz model does not take into account other factors, such as absorption on the surface, thermal buffeting, and interaction between solvent dipole moments and the electrode. Models more complicated than the Helmholtz include the Gouy-Chapman and Gouy-Chapman-Stern.¹¹¹ These models have dissimilar shapes for the plot of electric potential variation with distance from the electrode. The layers have relatively high dielectric constants and form an interface that behaves electrically like a capacitor (C_c and C_a in Fig. 1-18). In a semiconductor or in localized regions of an electrolyte, an excess of positive or of negative charge may be present. If the excess is of positive charge carriers, the positive carriers are the majority carriers and the negative charge carriers the minority carriers. An excess of negative carriers makes these the majority and the positive carriers the minority.

Figure 1-18 Simplified equivalent circuit for cardiac pacemaker.

T⁻ and T⁺ are, respectively, the negative (cathode) and positive (anode) terminals of the implanted pulse generator (IPG; in a unipolar device, T⁺ is inside the can). The direction of current flow is shown with i₀. R_W⁻ is the resistance of the conductor wire leading to the distal tip of the lead (cathode), whereas R_W⁺ is that of the wire leading to the bipolar lead’s proximal ring electrode or the unipolar pulse generator’s can. R_t is the resistance of the tissue between the bipolar lead’s two electrodes, or the lead tip to the pulse generator can in a unipolar system. R_c is the ohmic polarization of the cathode, whereas R_a is that of the bipolar anode or unipolar generator can. C_c is the capacitance of the cathode, and C_a is that of the anode (can). The equivalent circuit is the same for unipolar and bipolar systems, but the values for some of the components differ.

The second layer of the double layer is formed of hydrated ions and more water (Fig. 1-19). In physiologic electrolytes, the ions include Na⁺ and Cl⁻ in major concentrations (majority carriers). Other ions present in lower concentrations (minority carriers) include hydronium (H₃O⁺), hydroxyl (OH⁻), and phosphate (HPO₄²⁻).

Figure 1-19 Hypothesized structure of the Helmholtz double layer.

At the left is an uncharged cathodic electrode interface. When the electrode is charged, a layer of surface hydration develops (region A). Region B contains a second, more loosely held hydration layer with hydrated ions. Based on electrostatic considerations, layer B has a high dielectric constant, approaching that of pure water. It has a thickness of less than 10 Å. Region C represents bulk solution.

(From Stokes K, Bornzin G: The electrode-biointerface [stimulation]. In Barold SS, editor: Modern cardiac pacing. Mt Kisco, NY, Futura, 1985, p 63.)

The ions attracted to or repelled from the electrode during the electrical stimulation pulse make up a separation of charge in the tissue electrolyte. When the pacemaker pulse is applied as a negative voltage to the electrode, electrons accumulate in the electrode. Reversible reactions may form metal-oxide complexes on the surface of the electrode. A primary water layer forms on the electrode. Positive ions surrounded by water molecules—a water shell—make a secondary water layer. This accumulation of positive ions in the electrolyte near the electrode unbalances local electrolyte charge neutrality. Secondary ion rearrangements occur in great complexity, with several names for the various processes.

When the pacemaker pulse stops, the ions, being no longer attracted to or repelled from the electrode (depending on the polarity of the electrode and of the ions), are forced by their charges to rearrange themselves back toward their original, more electrically neutral positions (determined by random motion) in the electrolyte near the electrode. Ion rearrangement is not as fast as the transmission of an electric potential in a wire. The result is that, after a pacemaker or defibrillator pulse stops, the Helmholtz capacitor acts as if it were a temporary battery of declining voltage discharging itself into the tissue. The decaying voltage gradient in the tissue persists long enough to be detected by a pacemaker or defibrillator and may be great enough to interfere with sensing in autocapture devices in some situations. Other factors being equal, the voltage decay duration is greater and the polarization voltage is less when the electrode surface area is great versus small.

Electrode-Electrolyte Interface Processes

At equilibrium, an electrode in a solution will have, relative to a reference electrode, a potential that depends on the composition of the electrode, the composition of the solution, and other factors such as temperature.¹¹² When a pacemaker pulse is applied, the electrode is forced to a different electric potential. This new potential forces ion flow to occur in the vicinity of the electrode. Ion secondary rearrangements occur distally. The net ion drift near the electrode is in a direction that will produce a new equilibrium, a balance of charge across the interface.

At least two types of processes involving ion flow occur at the interface between a pacemaker or defibrillator electrode and tissue. First, oxidation-reduction reactions, which can be reversible or irreversible, involve electron movement across the interface and constitute faradic current. The second process, nonfaradic current, occurs without transfer of electrons across the interface. It consists of electron flow in or out of the electrode itself and a flow of ions in various layers or “clouds” toward or away from the interface. This nonfaradic process is similar to charging or discharging an electrical capacitor, but at an electrode in electrolyte, there is directed electron drift in or out of the electrode and directed ion drift within the electrolyte. The ion flow and the electron flow each constitute an electric current, yet no charge crosses the interface.

Away from the electrode in the body of the electrolyte, the electric potential gradient causes ions to move away from or toward the electrode region, depending on their charge. Ion mobility characteristics, concentration gradients, and temperature gradients also affect ion movement. In the heart the process is more complicated than in an electrolyte solution alone, because of the anisotropic properties of the extracellular and intracellular domains.

Optimizing Impedance for Minimum Battery Consumption

The effects of high impedance on the pacing system vary with the cause and location. The manner of resistance distribution in the system can produce different effects, increasing or decreasing the efficiency of the stimulating pulse. To clarify these issues, one needs to examine the leads and the electrode-tissue interface impedance and conduction losses.

A clinically useful electrode does not waste energy in mini–heat production or in undesirable chemical reactions, and it also has a low pacing threshold. Therefore, the electrode should have minimal energy loss in the lead wires, minimal energy loss in moving ions in the electrolyte during charge and discharge of the Helmholtz capacitance, and high current density at the electrode, allowing depolarization of the membranes of nearby myocytes with less lead current than would otherwise be needed.

All these factors influence the impedance as seen at the pulse generator. Note that fibrous tissue formation around an electrode does not necessarily increase the impedance but does increase the pacing threshold. (For further discussion of these issues, see Clinical Aspects of Myocardial Stimulation by Pacemakers.)