电子工程师手册（英文版六）：ch113

Reilly, J.P., Geddes, L.A., Polk, C. “Bioelectricity” The Electrical Engineering Handbook Ed. Richard C. Dorf Boca Raton: CRC Press LLC, 2000 113 Bioelectricity 113.1 Neuroelectric Principles Electrical Model for Nerve Excitation 113.2 Bioelectric Events Origin of Bioelectricity?Law of Stimulation?Recording Action Potentials?The Electrocardiogram (ECG)?Electromyography (EMG)?Electroencephalography (EEG)?Magnetic (Eddy- Current) Stimulation 113.3 Application of Electric and Magnetic Fields in Bone and Soft Tissue Repair History?Devices for Bone and Cartilage Repair?Soft Tissue Repair and Nerve Regeneration?Mechanisms and Dosimetry 113.1 Neuroelectric Principles J. Patrick Reilly Natural bioelectric processes are responsible for nerve and muscle function. These processes can be affected by externally applied electric currents that are intentionally introduced through medical devices or unintentionally introduced through accidental exposure (electric shock). A thorough treatment of this topic is given in Reilly [1992]. Externally applied electric currents can excite nerve and muscle cells. Muscle can be stimulated directly or indirectly through the nerves that enervate the muscle. Thresholds of stimulation of nerve are generally well below thresholds for direct stimulation of muscle. An understanding of neuroelectric principles is a valuable foundation for investigation into both sensory and muscular responses to electrical stimulation. Figure 113.1 illustrates functional components of sensory and motor (muscle) neurons. The illustrated nerve fibers are myelinated, i.e., covered with a fatty layer of insulation called myelin and having nodes of Ranvier where the myelin is absent. The conducting portion of the nerve fiber is a long, hollow structure known as an axon. The axon plus myelin sheath is frequently referred to as a nerve fiber, or neuron. Bundles of neurons are called nerves. The body is equipped with a vast array of sensors (receptors) for monitoring its internal and external environment. Electrical stimulation generally involves the somatosensory system, i.e., the system of receptors found in the skin and internal organs. Other specialized receptors include those in the visual and auditory systems and chemical receptors by which neurons communicate with one another. The somatosensory receptors can be classified as mechanoreceptors, thermoreceptors, chemoreceptors, and nociceptors. Numerous specializations of mechanoreceptors respond to specific attributes of mechanical stim- ulation. Thermoreceptors are specialized to respond to either heat or cold stimuli. Nociceptors are unresponsive until the stimulus reaches the point where tissue damage is imminent and are usually associated with pain. Many nociceptors are responsive to a broad spectrum of noxious levels of mechanical, heat, and chemical stimuli. The muscles are equipped with specialized receptors to monitor and control muscle movement and posture. Figure 113.1 illustrates a pacinian corpuscle, which responds to the onset or termination of a pressure stimulus applied to the skin. J. Patrick Reilly Metatec Associates L. A. Geddes Purdue University C. Polk University of Rhode Island ? 2000 by CRC Press LLC When a sensory receptor is stimulated, it produces a voltage change called a generator potential. The generator potential is graded: if you squeeze a pacinian corpuscle, for example, it produces a voltage; if you squeeze it harder, it produces a greater voltage. The generator potential initiates a sequence of events that leads to a propagating action potential (a “nerve impulse” in common parlance). The functional boundary of the biological cell is a thin (about 10 nm) bimolecular lipid and protein structure called a membrane. Electrochemical forces across the membrane regulate chemical exchange across the cell. The medium within the cell (the plasm) and outside the cell (the interstitial fluid) is composed largely of water containing various ions. The difference in the concentration of ions inside and outside the cell causes an electrochemical force across the cell membrane. The membrane is a semipermeable dielectric that allows some ionic interchange. Under conditions of electrochemical equilibrium (no net force in either direction), the membrane will attain a potential described by the Nernst equation (113.1) where [S] i and [S] o represent the concentrations of ionic substance S inside and outside the cell, R is the universal gas constant, T is absolute temperature, F is the Faraday constant (number of coulombs per mole of charge), and Z is the valence of substance S. Using the values R = 8.31 J/mol K, T = 310 K, F = 96,500 C/mol, and Z = +1 (for a monovalent cation), converting to the base 10 logarithm, and expressing V m in millivolts, we obtain (113.2) FIGURE 113.1 Functional components of (a) motor and (b) sensory neurons. Arrows indicate the direction of information flow. Signals are propagated across synapses via chemical neurotransmitters and elsewhere by membrane depolarization. Synapses are inside the spinal column. The sizes of the components are drawn on a distorted scale to emphasize various features. V RT FZ S S m o i = ln [] [] V S S m o i =61log [] [] ? 2000 by CRC Press LLC In a quiescent state, nerve and muscle cells maintain a membrane potential typically around –60 to –90 mV, with the inside of the cell negative relative to the outside. Two ions that are involved in the electrical response of nerve and muscle are Na + and K + . The concentration of these ions inside and outside the cell dictates the Nernst potential according to Eq. (113.2). Example concentrations in mM/cm 3 for a nerve axon would be [Na + ] i = 50, [Na + ] o = 460, [K + ] i = 400, and [K + ] o = 10. The Na + potential is found to be around +60 mV; the K + potential is found to be somewhat more negative than the resting potential. Obviously, the cell maintains in a state of electrochemical disequilibrium. The energy that maintains this force is derived from the metabolism of the cell—a dead cell will eventually revert to a state of equilibrium. Considering the transmembrane potential (?100 mV), and its small thickness (?10 nm), the electric field across the membrane is enormous (?10 MV/m). The membrane is semipermeable; that is, it is a lossy dielectric which allows the passage of certain ions. The ionic permeability varies substantially from one ionic species to another. The ionic channels in the excitable membrane will vary their permeability in response to the transmembrane potential; this property distinguishes the excitable membrane from the ordinary cellular membrane, and it supports propagation of nerve impulses. The electrodynamics of the excitable membrane of unmyelinated nerves were first described in detail in the Nobel prize work of Hodgkin and Huxley [1952]. This work was later extended to the myelinated nerve mem- brane by Frankenhaeuser and Huxley [1964]. Figure 113.2 illustrates an electrical model of the Hodgkin-Huxley membrane, which consists of nonlinear conductances for Na + and K + and a linear leakage ele- ment. The potential sources shown in the diagram are the Nernst potentials for the particular ions as given by Eq. (113.2). The capacitance term C m is formed by the dielectric membrane separating the conductive media on either side. The conductances g Na and g K apply to Na + and K + channels; the conductance g L is a general “leakage” channel that is not specific to any particular ion. The g Na and g K conductivities are highly dependent on the voltage applied across the membrane as described by a set of nonlinear differential equations. When the membrane is in the resting state, g Na << g K , and the membrane potential moves toward the Nernst potential for Na + . In this depolarized state, the membrane is said to be excited. The transition between the resting and excited condition of the membrane occurs rather abruptly when the membrane potential has been depolarized by roughly 15 mV. After excitation, the ionic channel conduc- tances vary again, causing the membrane to revert back to its resting potential. The duration of the excited state lasts roughly 1 ms. The progression of the membrane voltage during the period of excitation and recovery is termed an action potential. After the membrane has been excited, it cannot be reexcited until a recovery period, called the refractory period, has passed. Figure 113.3 illustrates the processes that support the propagation of an action potential. Consider that point A on the axon is depolarized. The local depolarization causes ionic transfer between adjacent points on the axon, thus propagating the region of depolarization. If depolarization were initiated from an external electrical source on a resting membrane at point A, an action potential would propagate in both directions away from the site of stimulation. The body’s natural condition, however, is to initiate an action potential at the terminus of the axon, which then propagates in only one direction. Electrical Model for Nerve Excitation Myelinated fibers have much lower thresholds of excitation than unmyelinated fibers. Accordingly, the myelinated fiber is an appropriate choice for electrical stimulation studies. FIGURE 113.2Hodgkin-Huxley membrane model. FIGURE 113.3Spread of the depolarization wave front along an axon. Depolarization occurring in region A results in charge transfer from the adjacent regions. ? 2000 by CRC Press LLC Figure 113.4 illustrates an electrical model for myelinated nerve as originally formulated by McNeal [1976]. The myelin internodes are treated as perfect insulators and the nodes as individual circuits consisting of capacitance C m and an ionic conductance term. The nodes are interconnected through the internal axon medium by conductances G a . The current flowing in the biological medium creates voltage disturbances V e,n at the exterior of the nodes. The current emanating from the nth node is the sum of capacitive and ionic currents described by (113.3) where C m is the membrane capacitance at the node, V n is the transmembrane potential, I i,n is the total ionic current, and V i,n is the internal voltage. In this expression, V n is taken relative to the resting potential, such that V n = 0 applies to the membrane resting potential. The ionic current flux is the sum of individual ionic terms (similar to the representation in Fig. 113.4), I i,n = pdW(J Na + J K + J L + J P ) (113.4) where the J terms are ionic current densities as described by a set of nonlinear differential equations developed by Frankenhaeuser and Huxley [1964] for a myelinated nerve membrane. Other relationships are (113.5) C m = c m pdW (113.6) where d is the axon diameter at the node, r i is the resistivity of the internal axon medium, L is the internodal distance, W is the nodal gap width, and c m is the membrane capacitance per unit area. The relationship between the axon diameter d and the fiber diameter D (including myelin) is d ? 0.7D. The voltage V n across the membrane is V n = V i,n – V e,n (113.7) where V i,n and V e,n are the internal and external nodal voltages with reference to a distant point in the conducting medium outside the axon. Substituting Eq. (113.7) into (113.3) results in FIGURE 113.4Equivalent circuit model for electrical excitation of myelinated nerve fiber. The membrane conductance G m is described by nonlinear ionic conductances, similar to the representation in Fig. 113.2. C dV dt IGVVV m n in a in in in += + +,,–,, (– ) 11 2 G d L a i = p r 2 4 ? 2000 by CRC Press LLC (113.8) For application to an unmyelinated fiber, Eq. (113.8) may be analogously expressed in continuous form as (113.9) where V and V e are membrane voltage and external voltage, respectively, at longitudal position x. Equation (113.9) can be derived from first principles, or can be obtained from (113.8) by substituting C m = c m pdDx, G a = pd 2 /(4r i Dx), G m = g m pdDx, where d is the fiber diameter, Dx is the longitudinal increment, r i is the axoplasm resistivity (in Wcm) internal to the fiber, c m is capacitance per unit area, and g m is conductance times unit area. Continuous and discrete spatial derivatives are connected by ? 2 V/ ?x 2 ? (V n–1 – 2V n + V n+1 )/Dx 2 ; ? 2 V e /?x 2 ? (V e,n–1 – 2V e,n + V e,n+1 )/Dx 2 ; t m is the member time constant given by c m /g m ; l is the membrane space constant given by l = (r m /r i ) 1/2 = (dr m /4r i )) 1/2 , and r m is the membrane specific resistance (in Wcm 2 ). An additional relationship is I i,n = V/G m . If one treats l as a constant, then (113.9) describes the membrane response only during its sub-threshold (linear) phase. For membrane depolarization approaching the threshold of excitation, membrane conductance of ionic constituents becomes highly nonlinear, as noted above — it is this nonlinear behavior that leads to nerve excitation. The left-hand side of Eq. (113.9) is the so-called cable equation that was developed by Oliver Heaviside over 100 years ago in connection with the analysis of the first transatlantic telegraphy cable. The right-hand side is a driving function due to the external field in the biological medium. For additional information on cable theory as applied to the excitable membrane, the reader is directed to Jack et al. [1983]. One conclusion that can be drawn from Eqs. (113.8) and (113.9) is that a second spatial derivative of voltage (or equivalently a first derivative of the electric field) must exist along the long axis of an excitable fiber in order to support excitation. Nevertheless, excitation is possible in a locally constant electric field where the fiber is terminated or where it bends. The orientation change or the termination creates the equivalent of a spatial derivative of the applied field. Stimulation at “ends and bends” can be the dominant mode of excitation in many cases. The external voltages in Eq. (113.8) are dependent on the distribution of current within the biological medium. For a point electrode in an isotopic medium, for instance, we can determine these voltages by (113.10) where r n is the distance between the stimulating electrode and the nth node and r e is the resistivity of the external medium. For a uniform current density flowing in a direction parallel to the fiber axis, the external voltages are determined by V e,n = V e,1 + ELn (113.11) where V e,1 is a reference voltage at the terminal node, L is the internodal distance, n is the node number, and E is the electric field in the medium. The electric field is related to current density by J = Es, where s = 1/r e is the conductivity of the medium and J is the current density. Since the response of the electrical model is independent of V e,1 , we may assume V e,1 = 0 for convenience in Eq. (113.11). The internodal distance L is proportional to fiber diameter D through the relationship L/D ? 100. Other fiber diameter relationships are expressed in Eqs. (113.5) and (113.6). Because of these relationships, thresholds of electrical stimulation will vary inversely with fiber diameter. The distribution of myelinated nerve diameters found in human peripheral nerve or skeletal muscle typically ranges from 5 to 20 mm. dV dt C GV V V V V V I n m a n n n en en en in =++-+ ++ 1 22 11 1 [( – )– ] –,,, t ? l ? ? l ? ? m e V dt V x V V x – 2 2 2 2 2 2 += V I r en e n , = r p4 ? 2000 by CRC Press LLC Figure 113.5 illustrates the response of the myelinated nerve model of Fig. 113.4 to a rectangular current stimulus [Reilly et al., 1985]. The example is for a small cathodal electrode that is 2 mm radially distant from a 20-mm fiber and directly above a central node. The transmembrane voltage DV is scaled relative to the resting potential. The solid curves show the response at the node nearest the stimulating electrode. Response a is for a pulse that is 80% of the threshold current, b is at threshold, and c is 20% above threshold. The threshold stimulus pulse in this example has an amplitude I T of 0.68 mA. Response a is similar to that of a linear network with a parallel resistor and capacitor and charged by a brief current pulse. Responses b and c demonstrate the highly nonlinear response of the excitable membrane. The dashed curves in Fig. 113.5 show the membrane response to a threshold stimulus at the three nodes adjacent to the one nearest the stimulating electrode. The time delay implies a propagation velocity of 43 m/s, which is typical of a 20-mm fiber. The membrane response seen in curves b through f illustrates the action potential described earlier. The action potential is typically described as an “all-or-nothing” response; that is, its amplitude is not normally graded—either the axon is excited, or it is not. The threshold current needed for excitation is highly dependent on its duration and waveshape. A common format for representing the response of a nerve is through strength-duration curves, i.e., the plot of the threshold of excitation versus the duration of the stimulating current. We can determine the threshold of excitation by “titrating” the stimulus current between a threshold and no-threshold condition. Figure 113.6 illustrates strength-duration curves derived from the myelinated nerve model described previ- ously under the same conditions applying to Fig. 113.5. Three types of stimulus current apply to Fig. 113.6: a monophasic constant current pulse, a symmetric biphasic rectangular current, and a single cycle of a sine wave. The phase duration indicated on the horizontal axis applies to the initial cathodal half cycle for the two biphasic waves. Stimulus magnitude is given in terms of peak current on the right vertical axis and in terms of the charge in a single monophasic phase of the stimulus on the left vertical axis. The charge is computed by Q = It p for the rectangular waveforms and Q = (2/p)It p for the sinusoidal waveforms (I is threshold current and t p is phase duration). FIGURE 113.5Response of myelinated nerve model to rectangular monophasic current of 100 ms duration, 20-mm diameter fiber, point electrode 2 mm from central node. Solid lines show response at node nearest electrode for three levels of current. I T denotes threshold current. Dashed lines show propagated response at next three adjacent nodes for a stimulus at threshold. (Source: J. P. Reilly, V. T. Freeman, and W. D. Larkin, “Sensory effects of transient electrical stimulation—Eval- uation with a neuroelectric model,” IEEE Trans. Biomed. Eng., vol. BME-32, no. 12, pp. 1001–1011, ? 1985 IEEE.) ? 2000 by CRC Press LLC The solid curve labeled “current” is of the type that is most often represented as a strength-duration curve. For this curve, the minimum threshold current occurs for long-stimulus durations and is called the rheobasic current, or simply rheobase. The duration consistent with twice the rheobase is called the chronaxie. The solid curve in Fig. 113.6 labeled “charge” gives the area under the rectangular current pulse. The threshold charge is a minimum for short-duration stimuli. Mathematical curve fits to the strength-duration curves for monophasic rectangular stimuli are (113.12) and (113.13) where I T is threshold current, Q T is threshold charge, I o is the minimum threshold current for long-duration stimuli, Q o is the minimum threshold charge for short-duration stimuli, and t e is an experimentally determined strength-duration time constant. It is readily shown that chronaxie = t e ln 2 = 0.693t e in this formulation. Values of I o and Q o vary considerably with experimental parameters such as electrode size and location and the size of the neuron. Values of t e also vary considerably with experimental conditions: a value around 250 ms is typical for both sensory and motor nerve excitation via cutaneous electrodes, and values around 125 ms are observed for stimulation of axons by small electrodes. Much longer time constants are associated with direct stimulation of muscle cells. FIGURE 113.6Strength/duration relationships derived from the myelinated nerve model: current thresholds and charge thresholds for single-pulse monophasic and for single-cycle biphasic stimuli with initial cathodal phase, point electrode 2 mm distant from 20 mm fiber. Threshold current refers to the peak of the stimulus waveform. Charge refers to a single phase for biphasic stimuli. (Source: J. P. Reilly, V. T. Freeman, and W. D. Larkin, “Sensory effects of transient electrical stimula- tion—Evaluation with a neuroelectric model,” IEEE Trans. Biomed. Eng., vol. BME-32, no. 12, pp. 1001–1011, ? 1985 IEEE.) I I e T o te = 1 1– –/t Q Q t e T o e te = / – –/ t t 1 ? 2000 by CRC Press LLC The current reversal of a biphasic stimulus can reverse a developing action potential that was elicited by the initial phase. As a result, a biphasic pulse may have a higher threshold than a monophasic pulse as suggested by the biphasic thresholds in Fig. 113.6. The degree of biphasic threshold elevation is magnified as the stimulus duration is reduced. A sinusoidal current is a special case of a biphasic stimulus. Sinusoidal threshold response can be represented by strength-frequency curves, as shown by the solid curves in Fig. 113.7 for the myelinated nerve model. Several experimental curves have been included in the figure; these have been shifted vertically to facilitate comparisons. Notice that the myelinated nerve model predicts a lower threshold for stimulation by a continuous sine wave as compared with a single cycle. The strength-frequency curve follows a U-shaped function, with a minimum at mid frequencies and an upturn at both low and high frequencies. At low frequencies the slow rate of change of the sinusoid prevents the membrane capacitance from building up a depolarizing voltage because membrane capacitance is coun- teracted by membrane leakage. This process describes the neural property known as accommodation, i.e., the adaptation of a nerve to a slowly varying or constant stimulus. The high-frequency upturn occurs because of the canceling effects of a current reversal on the membrane voltage change. An empirical fit to strength- frequency curves is I t = I o K H K L (113.14) where I t is the threshold current, I o is the minimum threshold current, and K H and K L are high- and low-frequency terms, defined, respectively, as (113.15) and FIGURE 113.7Strength-frequency curves for sinusoidal current stimuli. Dashed curves are from experimental data. Solid curves apply to myelinated nerve model. Experimental curves have been shifted vertically to facilitate comparisons. K f f H e a = ? è ? ? ? ÷ é ? ê ê ù ? ú ú 1–exp– – ? 2000 by CRC Press LLC (113.16) where f e and f o are constants that determine the points of upturn in the strength-frequency curve at high and low frequencies, respectively. An upper limit of K L ￡ 4.6 is assumed for Eq. (113.16) to account for the fact that excitation may be obtained with finite dc currents. An empirical fit of Eqs. (113.15) and (113.16) to the mylinated nerve model thresholds indicates that a = 1.45 for a single-cycle stimulus and a = 0.9 for a continuous stimulus; b = 0.8 regardless of stimulus duration. The value of I o will depend on various conditions of stimulation, including the size of the electrode, its location on the body, and the location of the stimulated nerve. With continuous sinusoidal stimulation, it is possible to produce a series of action potentials that are phase- locked to the individual sinusoidal cycles, as noted in Fig. 113.8. This makes the sinusoidal stimulus much more potent than a single pulse of the same phase duration. This potency is a consequence of the fact that perceived magnitude for neurosensory stimulation and muscle tension for neuromuscular stimulation both increase with the rate of action potential production. Defining Terms Action potential:A propagating change in the conductivity and potential across a nerve cell’s membrane; a nerve impulse in common parlance. Axon: The conducting portion of a nerve fiber—a roughly tubular structure whose wall is composed of the cellular membrane and which is filled with an ionic medium. Chronaxie:The minimum duration of a unidirectional square-wave current needed to excite a nerve when the current magnitude is twice rheobase. FIGURE 113.8Model response to continuous sinusoidal stimulation at 500 Hz. The lower panel depicts the response to a stimulus current set at threshold level (I T ) for a single-cycle stimulus. Upper panels show responses for stimulation 20 and 50% above the single-cycle threshold. (Source: J. P. Reilly, V. T. Freeman, and W. D. Larkin, “Sensory effects of transient electrical stimulation—Evaluation with a neuroelectric model,” IEEE Trans. Biomed. Eng., vol. BME-32, no. 12, pp. 1001–1011, ? 1985 IEEE.) K f f L o b = ? è ? ? ? ÷ é ? ê ê ù ? ú ú 1–exp– – ? 2000 by CRC Press LLC Fiber, nerve: A single nerve cell; a neuron—classified on the presence or absence of myelin. Myelinated nerve cells have diameters typically in the range 2 to 20 mm and conduction velocities of 5 to 120 m/s; unmyelinated nerves have diameters from 0.3 to 1.3 mm and conduction velocities of 0.6 to 2.3 m/s. Fiber lengths may be up to 1 m. The term nerve usually refers to a bundle of nerve fibers. Membrane: The functional boundary of a cell. Nerve cells possess membranes that are excitable by virtue of their nonlinear electrical conductance properties (see Action potential). Myelinated nerve: A nerve fiber insulated with a fatty substance called myelin and having periodically exposed nodes of Ranvier. Neuron: A nerve cell. Sensory neurons carry information from sensory receptors in the peripheral nervous system to the brain; motor neurons carry information from the brain to the muscles. Refractory period: A period of time after the initiation of an action potential during which further excitation is impossible (absolute refractory period) or requires a greater stimulus (relative refractory period). Rheobase: The minimum current necessary to cause nerve excitation—applicable to a long-duration current (e.g., several milliseconds). Strength-duration curve: A curve expressing the functional relationship between the threshold of excitation of a nerve fiber and the duration of a unidirectional square-wave electrical stimulus. References B. Frankenhaeuser and A. F. Huxley, “The action potential in the myelinated nerve fiber of Xenopus laevis as computed on the basis of voltage clamp data,” J. Physiol., vol. 171, pp. 302–315, 1964. A. L. Hodgkin and A. F. Huxley, “A quantitative description of membrane current and its application to conduction and excitation in nerve,” J. Physiol., vol. 117, pp. 500–544, 1952. J. J. B. Jack, D. Noble, and R. W. Tsien, Electric Current Flow in Excitable Cells, Oxford: Clarendon Press, 1983. D. R. McNeal, “Analysis of a model for excitation of myelinated nerve,” IEEE Trans. Biomed. Eng., vol. BME- 22, pp. 329–337, 1976. J. P. Reilly, V. T. Freeman, and W. D. Larkin, “Sensory effects of transient electrical stimulation—Evaluation with a neuroelectric model,” IEEE Trans. Biomed. Eng., vol. BME-32, no. 12, pp. 1001–1011, 1985. J. P. Reilly, Electrical Stimulation and Electropathology, New York: Cambridge University Press, 1992. Further Information For further information, the reader is directed to the references listed at the end of this chapter. Additional references are: R. Plonsey and R.C. Barr, Biolectricity—A Quantitive Approach, New York: Plenum, 1988. W. Agnew and D. McCreery, Neural Prostheses, Englewood Cliffs, N.J.: Prentice-Hall, 1990. E.R. Kandel, J.H. Schwartz, and T. M. Jessell (Eds.), Principles of Neural Science, 3rd ed., New York: Elsevier, 1991. Several journals treat engineering applications of neuroelectric principles, such as IEEE Transactions on Biomedical Engineering, Medical and Biological Engineering and Computing, and Annals of Biomedical Engineering. Of the many conferences treating bioelectric responses, one having a broad range of applications is the IEEE Annual Conference on Engineering in Medicine and Biology. 113.2 Bioelectric Events L. A. Geddes Bioelectric signals are exploited for the diagnostic information that they contain. Such signals are often used to monitor and guide therapy. Although all living cells exhibit bioelectric phenomena, a small variety produce potential changes that reveal their physiological function. The most familiar bioelectric recordings are the electrocardiogram, ECG (which reflects the excitation and recovery of the whole heart), the electromyogram, EMG (which reflects the activity of skeletal muscle), and the electroencephalogram, EEG (which reflects the activity of the outer layers of the brain, the cortex). The following paragraphs will describe (1) the origin of ? 2000 by CRC Press LLC ? 2000 by CRC Press LLC MEDICAL CARDIAC PACEMAKER Wilson Greatbatch Patented October 9, 1962 #3,057,356 An excerpt from Greatbatch’s patent application: The primary object of this invention is to provide an improved artificial cardiac pacemaker for restoring satisfactory heart rhythm to a heart which is functioning inadequately due to conduction defects in the auricular-ventricular bundle. Another object of this invention is to provide an artificial cardiac pacemaker requiring low power con- sumption, so that battery operation is feasible for long uninterrupted periods without battery replacement. Another object of this invention is to provide an artificial cardiac pacemaker which may be directly connected to the surface of the ventricle of the heart. A still further object of this invention is to provide an artificial cardiac pacemaker which is constructed from materials compatible to the body environment and is of such an electrical and mechanical configuration, that permanent implantation of the device within the human body is both feasible and practical. Greatbatch’s pacemaker was the first to be compact enough and use such low power that it could be implanted within the body and run for five years before requiring battery replacement. Wilson Greatbatch, Inc. is a leading producer of pacemaker batteries and other medical products. (Copyright ? 1995, DewRay Products, Inc. Used with permission.) all bioelectric phenomena; (2) the nature of the electrical activity of the heart, skeletal muscle, and the brain; and (3) the characteristics of instrumentation used to display these events. Origin of Bioelectricity Cell membranes resemble charged capacitors operating near the dielectric breakdown voltage. Assuming a typical value of 90 mV for the transmembrane potential and a membrane thickness of 100 ?, the voltage gradient across the membrane is 0.9 ′ 10 5 V/cm. A typical value for the capacitance is about 1 mF/cm 2 . The transmembrane charge is the result of a metabolic process that creates ionic gradients with a high concentration of potassium ions (K + ) inside and a high concentration of sodium ions (Na + ) outside. There are concentration gradients for other ions, the cell wall being a semipermeable membrane that obeys the Nernst equation (60 mV/decade concentration gradient for univalent ions). The result of the ionic gradient is the transmembrane potential that, in the cells referred to earlier, is about 90 mV, the interior being negative with respect to the exterior. Figure 113.9 illustrates this concept for a cylindrical cell. The transmembrane potential is stable in inexcitable cells, such as the red blood cell. However, in excitable cells, a reduction in transmembrane potential (either physiological or induced electrically) results in excitation, characterized by a transmembrane ion flux, resulting from a membrane permeability change. When the trans- membrane potential is reduced by about one-third, Na + ions rush in; K + ions exit slightly later while the cell depolarizes, reverse polarizes, then repolarizes. The resulting excursion in transmembrane potential is a prop- agated action potential that is characteristic for each type of cell. In Fig. 113.10 are shown the action potentials of (A) a single cardiac ventricular muscle cell, (C) a skeletal muscle cell, and (E) a nerve cell. In (B) and (D), the ensuing muscular contractions are shown. An important property of the action potential is that it is propagated without decrement over the entire surface of the cell, the depolarized region being the stimulus for adjacent polarized regions. In contractile cells it is the action potential that triggers release of mechanical energy as shown in Figs. 113.10(B) and (D). Law of Stimulation Although action potentials are generated physiologically, it should be obvious that excitable cells can be made to respond by the application of a negative pulse of sufficient current density (I) and duration (d) to reduce the transmembrane potential to a critical value by removing charge, thereby reducing the membrane potential to the threshold potential (TP), as shown in Fig. 113.9. The law of stimulation is I = b/(1 – e –d /t), where b is the threshold current density for an infinitely long-duration pulse and t is the cell membrane time constant, being different for each type of excitable tissue. Figure 113.11 is a plot of the threshold current (I) versus duration (d) for mammalian cardiac muscle, sensory receptors, and motor nerve. This relationship is known as the strength-duration curve. FIGURE 113.9 (A) Typical charged membrane, (B) its equivalent circuit, and (C) action potential resulting from a stimulus I of duration d. ? 2000 by CRC Press LLC Recording Action Potentials Action potentials of single excitable cells are recorded with transmembrane electrodes (micron diameter) only in research studies. When action potentials are used for diagnostic purposes, extracellular electrodes are used that are both large and distant from the population of cells which become active and recover. The depolarization FIGURE 113.10 The action of (A) cardiac muscle and (B) its contraction, (C) skeletal muscle and (D) and its contraction. The action potential of nerve is shown in (E). FIGURE 113.11 The strength-duration curve for heart, sensory receptors, and motor nerve. I is the stimulus current, b is the rheobasic current, and t is the membrane time constant. The stimulus duration is d. ? 2000 by CRC Press LLC and repolarization processes send small currents through the conducting environmental tissues and fluids, resulting in a time-varying potential field. Appropriately placed electrodes allow recording the electrical activity of the bioelectric generators. However, the waveforms of such recordings are vastly different from those of the transmembrane action potentials shown in Fig. 113.10. By using cable theory, it is possible to show that such extracellular recordings resemble the second derivative of the excursion in transmembrane potential [Geddes and Baker, 1989]. Despite the difference in waveform, extracellular recordings identify the excitation and recovery processes very well. The Electrocardiogram (ECG) Origin The heart is two double-muscular pumps. The atria pump blood into the ventricles, then the two ventricles contract. The right ventricle pumps venous blood into the lungs, and the left ventricle pumps oxygen-rich blood into the aorta. Figure 113.12 is a sketch of the heart and great vessels, along with genesis of the ECG. The ECG consists of two parts: the electrical activity of the atria and that of the ventricles. Both components have an excitation wave and a recovery wave. Within the right atrium is a specialized node of modified cardiac muscle, the sinoatrial (SA) node, that has a spontaneously decreasing transmembrane potential which reaches the threshold potential (TP), resulting in self-excitation (Fig. 113.12, upper left). Therefore the SA node is the cardiac pacemaker, establishing the heart rate. The SA node action potential stimulates the adjacent atrial muscle, completely exciting it and giving rise to the first event in the cardiac cycle, the P wave, the trigger for atrial contraction. Atrial excitation is propagated to another specialized node of tissue in the base of the ventricles, the atrioventricular (AV) node, the bundle of His and the Purkinje fibers. Propagation of excitation over the ventricles gives rise to the QRS, or simply the R wave, which triggers ventricular contraction. Meanwhile during the QRS wave, the atria recover, giving rise to the T p wave, following which the atria relax. The T p wave FIGURE 113.12Genesis of the ECG. The SA node is the pacemaker, setting the rate. Excitation is propagated from the atria to the AV node, then to the bundle of His, and to the ventricular muscle via the Purkinje fibers. The SA node has a decreasing membrane potential that reaches the threshold potential (TP), resulting in spontaneous excitation (inset). ? 2000 by CRC Press LLC is not ordinarily seen in the ECG because it is obscured by the ventricular QRS wave. During the QRS wave the ventricles contract, then relax following their recovery potential, the T wave; Fig. 113.12 summarizes this sequence. Ordinarily the T p wave is not visible. However, if the propagation of excitation from the atria to the ventricles is blocked, the T p wave can be seen. Figure 113.13 is a record of the ECG from a limb lead and a recording from a lead within the right atrium in a subject with transient AV block. Note that the sharp P wave in the atrial lead coincides with the P wave in the limb recording and that the atrial lead shows both P and T p waves, easily identified during AV block. Clinical Significance From the foregoing it can be seen that the ECG is only a timing signal; there is no dynamic information in its amplitude. Nonetheless, by observing the orderly P-QRS-T sequence it is possible to determine if the excitatory and recovery processes in the heart are functioning normally. Disturbances in the orderly timing of the cardiac cycle are elegantly displayed by the ECG. For example, each atrial excitation may not be delivered to the AV node. AV block exists when there is less than a 1/1 correspondence between the P and QRS complexes (Fig. 113.13). Figure 113.14(1) shows a normal ECG and Fig. 113.14(2) illustrates a 2/1 AV block with two P waves for each QRS-T complex. Complete AV block exists when none of the atrial excitations reach the AV node, as shown in Fig. 113.14(3). In this case the ventricles developed their own rhythm, which was slow; cardiac output is low, and in such a situation an artificial pacemaker must be implanted. For many reasons, the atria develop a rapid rate called atrial tachycardia or supraventricular tachycardia. A very rapid atrial rate is designated atrial flutter [Fig. 113.14(4)]. With both atrial tachycardia and flutter, the atrial contractions are coordinated, although the ventricular pumping capability is reduced owing to inadequate filling time. The ventricles are driven at a rapid rate, and cardiac output is low. Atrial fibrillation is an electrical dysrhythmia in which all the atrial muscle fibers are contracting and relaxing asynchronously and there is no atrial pumping. This dysrhythmia [Fig. 113.14(5)] causes the ventricles to be excited at a very rapid and irregular rate. Cardiac output is reduced, and the pulse is rapid and irregular in force and rate. If the propagation of excitation in the ventricles is impaired by damage to the bundle of His, the coordination of excitation and contraction is impaired and reveals itself by a widening of the QRS wave, and often a notch is present; Fig. 113.14(6) illustrates right (RBBB) and left (LBBB) bundle-branch block. These waveforms are best identified in the chest (V) leads. All parts of the heart are capable of exhibiting rhythmic activity, there being a rhythmicity hierarchy from the SA node to the ventricular muscle. In abnormal circumstances the atria and ventricles can generate spontaneous beats. Such ectopic excitations do not ordinarily propagate normally, and therefore the ECG waveforms are different. Figure 113.14(7) illustrates ventricular ectopic beats in which the first (l) Q-S,T wave arose at the apex and the second (2) R-S,T wave arose at the base of the ventricles. The coupled (bigeminus) FIGURE 113.13Lead 2 ECG and an atrial lead. In the center of the record AV block was produced, showing the P waves in lead 2 and the P and T p waves in the atrial lead. ? 2000 by CRC Press LLC beat usually produces no arterial pulse because of inadequate time for filling of the ventricles and poor coordination of the contraction. The ventricles may become so excitable that they develop a rapid rhythm called ventricular tachycardia, as shown in Fig 113.14(8). In this situation the pumping capability is diminished owing to the high rate that impairs filling and to impaired coordination of contraction. Ventricular fibrillation is a condition in which all of the ventricular muscle fibers contract and relax independently and asynchronously. Pumping ceases and cardiac output falls to zero. The ECG [Fig. 113.14(9)] exhibits rapid oscillations of waxing and waning amplitude at a rate of 800 to 1500 per minute. Ventricular fibrillation is lethal unless the circulation is restored within a few minutes, first by cardiopulmonary resuscitation (CPR) and then by electrical defibrillation. The latter technique employs the delivery of a substantial pulse of current through the heart applied directly or with transchest electrodes. Figure 113.15 illustrates ventricular tachycardia (left), ventricular fibrillation (center), and defibrillation (right), with the restoration of pumping. When a region of the ventricles is deprived of its coronary artery blood supply, the cells in this region lose their ability to generate action potentials and to contract. These cells remain depolarized while they are dying and do not contribute to genesis of the QRS-T complex. Instead, there appears a shift in the portion of the FIGURE 113.14ECG waveforms. FIGURE 113.15The electrocardiogram (ECG) and blood pressure during ventricular tachycardia (left), which progressed to ventricular fibrillation (center). A strong transchest shock was applied to defibrillate the ventricles that resumed pumping with the tachycardia returning (right). ? 2000 by CRC Press LLC ECG between the S and T waves, i.e., there is an S-T segment shift. This is the cardinal sign of a myocardial infarction (heart attack) and is almost always accompanied by chest pain (angina pectoris). Figure 113.14(10) illustrates the ECG in myocardial infarction. Whether the S-T segment displacement is up (1) or down (2) depends on the region of the ventricles injured, as well as the lead used to record the ECG. ECG Leads The spread of excitation and recovery over the atria and ventricles varies in direction with time. Therefore, excitation and recovery are vectors, and the location of body-surface electrodes is important. For this reason, standard electrode sites have been adopted, as shown in Fig. 113.16. There are three standard limb leads, three augmented (a) limb leads, and six chest (V) leads, the latter being monopolar. The reference for the monopolar chest leads is the centerpoint of three resistors (r), each joined to one of the limb electrodes. The right leg is used to ground the subject. Each lead “sees” a different region of the heart. The use of so many leads allows quick and easy identification of the direction of propagation of excitation (and recovery) by merely inspecting the amplitudes of the waveforms in the various leads. If excitation (or recovery) travels orthogonal to a lead axis, the net amplitude will be zero or very small. If excitation (or recovery) travels parallel to a lead axis, the amplitude of the wave will be maximum. Figure 113.16 illustrates the amplitudes of the P, QRS, and T waves for the 12 ECG leads. Note that leads 1, 2, 3, aVR, aVL, and aVF identify the vector projections in the frontal plane. Leads V 1–6 identify the vector components in a quasi-horizontal plane. There are normal values for the amplitudes and durations for the P, QRS, and T waves as well as their vectors. The interested reader can find more on ECG in the many handbooks on this subject. Two good, recently published texts are by Chou [1991] and Phillips and Feeney [1990]. FIGURE 113.16The limb and chest (V) leads. ? 2000 by CRC Press LLC Instrumentation Standards of performance evolved from recommendations by the American Medical Association in 1950 and the American Heart Association in 1954 and 1967. These recommendations have been collected and expanded into an American National Standard, published by the Association for the Advancement of Medical Instrumen- tation (AAMI) [1991]. The title of the document is “Diagnostic Electrocardiographic Devices.” This document not only lists all the performance and labeling requirements, but also provides useful information on testing ECGs and should be consulted by those contemplating construction of an ECG. Only some of the highlights of the standard will be presented here. The ECG is displayed by a direct-writing pen that employs a heated stylus writing on thermosensitive paper. Two chart speeds are used, 25 and 50 mm/s. The rulings on the paper represent 40 ms when the standard speed (25 mm/s) is used. The amplitude sensitivity is 10 mm for a 1-mV input signal. The sinusoidal frequency response extends from 0.05 to 100 Hz for the 30% attenuation points. The input stage is a differential amplifier with an input impedance in excess of 2.4 MW The common-mode rejection ratio (CMRR) is measured with a 20-V (rms) 60-Hz generator with an output impedance of 51,000 W connected in series with a 10-pF capacitor. The 60-Hz CMRR should be in excess of 5000. The maximum dc leakage current through any patient electrode is 0.2 mA. Electromyography (EMG) The electrical activity of skeletal muscle is monitored to assess the integrity of the motor nerve that supplies it and to evaluate recovery of the motor nerve following injury to it. The EMG is also characteristically altered in many degenerative muscle diseases. Although muscle action potentials can be detected with skin-surface electrodes, a monopolar or bipolar needle electrode is used in clinical EMG. The electrical activity is displayed on an oscilloscope screen and monitored aurally with a loudspeaker. Contraction of Skeletal Muscle The functional unit of the muscular system is the motor unit, consisting of a nerve cell located within the spinal cord, its axon (nerve fiber), and the group of muscle fibers that it innervates, as shown in Fig. 113.17. Between the nerve fiber and the muscle fibers is the myoneural junction, the site where acetylcholine is liberated and transmits excitation to the muscle fibers. The number of muscle fibers per nerve fiber is called the innervation ratio, which ranges from 1:1 to about 1000:1; the former ratio is characteristic of the extraocular muscles, and the latter is typical for the postural muscles. A single stimulus received by the nerve fiber physiologically, or a single stimulus delivered to it electrically, will cause all the innervated muscle fibers to contract and relax; this response is called a twitch. Figure 113.10(C) and (D) illustrates the relationship between the muscle action potential and twitch. Note that the action potential is almost over before contraction begins and the contraction far outlasts the duration of the action potential. FIGURE 113.17The functional unit of the muscular system, the motor unit, consisting of a nerve cell located within the spinal cord, its axon, and the muscle fibers that it innervates. ? 2000 by CRC Press LLC If multiple stimuli are delivered to a single motor-nerve fiber with an increasing frequency, the twitches fuse into a sustained (tetanic) contraction whose force is much more than that of a twitch. This occurs because each action potential liberates contractile energy. The critical fusion frequency depends on the type of muscle, but in general it is about 25 to 40 per second. The force developed by a whole muscle consisting of thousands of motor units is graded in two ways: (l) by the frequency of nerve impulses in each nerve fiber and (2) by the number of motor units that are activated. Clinical EMG When the electrical activity of skeletal muscle is examined for diagnostic purposes, an insulated needle electrode, bare only at the tip [Fig. 113.18(A)], is inserted into the muscle and paired with a skin-surface electrode. Another skin-surface electrode is used to ground the subject. Occasionally a coaxial needle electrode [Fig. 113.18(B)] or a bipolar hypodermic needle electrode [Fig. 113.18(C)] is used. In the latter case the outer sleeve is used as the ground. A high-gain, differential amplifier, oscilloscope, and loudspeaker are used, as shown in Figure 113.18(D). In a normal subject at rest, the electrical activity monitored during insertion of the needle electrode consists of a short burst of muscle action potentials displayed on the oscilloscope and heard in the loudspeaker. These action potentials are called insertion potentials and subside quickly in the normal muscle. When the muscle is at rest, there is no electrical activity (electrical silence). If the muscle is contracted voluntarily, the frequency of action potentials increases with the force developed by the muscle. However, there is no linear or constant relationship between these two events. Each action potential, called a normal motor-unit potential, lasts a few milliseconds to the first zero crossing, as shown in Fig. 113.18(E). There is considerable art associated with placing the exploring electrode. If the electrode tip is not adjacent to contracting muscle fibers, the sound of the action potential is muffled and electrode adjustment is required. The same is true for detecting fibrillation potentials (see below). If the nerve cell in the spinal cord or the nerve fiber supplying a muscle is damaged, the muscle cannot be contracted voluntarily or reflexly (by tapping the tendon) and is therefore paralyzed. In the absence of thera- peutic intervention and with the passage of time, the nerve beyond the damaged site dies and the muscle fibers start to degenerate. In about 2 1/2 to 3 weeks in humans, the individual muscle fibers start to contract and relax spontaneously and randomly, producing short-duration, randomly occurring action potentials called FIGURE 113.18Equipment used for electromyography. (A) Needle electrode, (B) hypodermic monopolar and (C) bipolar electrodes, (D) the recording apparatus, (E) skeletal muscle action potential, and (F) fibrillation potential. ? 2000 by CRC Press LLC fibrillation potentials [Fig. 113.18(F)], which are displayed on the oscilloscope screen and heard as clicks in the loudspeaker. Although there is electrical activity, the muscle develops no net force. The fibrillation potentials persist as long as there are viable muscle fibers. In such a denervated muscle, insertion of the needle electrode elicits a vigorous train of short-duration insertion potentials that resemble fibrillation potentials with a fre- quency of about 1 to 10 per second. If the damaged ends of the nerve are brought together surgically, the central end of the nerve will start to grow slowly and reinnervate the muscle. Gradually the fibrillation potentials disappear, although the muscle is still not able to be contracted. Long before there is visible evidence of muscle contraction, if the subject is presented with the EMG display and asked to contract the affected muscle, primitive muscle action potentials can be elicited. With the passage of time, the fibrillation potentials disappear and there is electrical silence at rest and primitive (nascent) motor-unit activity occurs with voluntary contraction. Later when reinnervation is complete, only normal motor-unit potentials are present with voluntary contraction and electrical silence at rest. The EMG is also used to diagnose some degenerative muscle and related nerve disorders. Myotonia is a degenerative disease of muscle fibers in which the muscle relaxes poorly. Insertion of the needle electrode elicits an intense burst of insertion potentials that sound like a thunderstorm in the loudspeaker. A similar response is obtained by tapping the muscle. When relaxation does occur, there is electrical silence. Voluntary contraction produces normal action potentials along with shorter-duration action potentials from the diseased muscle fibers. Myasthenia gravis is a disease in which there is impairment of transmission of acetylcholine across the myoneural junctions to the muscle fibers. As a result, muscle contraction cannot be sustained. Because the muscle fibers are normally innervated, there are no fibrillation potentials. With voluntary contraction, normal action potentials occur, and if the disease is severe, the action potentials decrease in frequency as the force of contraction decreases and soon sustained muscle contraction cannot be maintained. Muscular dystrophy is a degenerative disease of muscle fibers in which there is atrophy of some fibers, swelling in others, and an increase in sarcolemmal and connective tissue with the deposition of fat. Insertion of the needle electrode elicits a vigorous burst of short-duration, high-frequency action potentials. Typically at rest there are no fibrillation potentials. With voluntary contraction, the action potentials are short in duration, high in frequency, and produce a whirring sound in the loudspeaker. As fatigue supervenes, the frequency and amplitude decrease. The reader who is interested in obtaining more information on EMG will find it in books by Cohen and Brumlik [1969] and Marinacci [1955]. Both contain a wealth of clinical information. Instrumentation As yet there is no American National Standard for EMG, although steps are being taken in this direction. As shown in Fig. 113.18, the EMG is displayed in two ways: (1) visually with an oscilloscope and (2) aurally with a loudspeaker. Both are needed to enable acquisition and analysis of the EMG. Buchtal et al. [1954] stated that the principal frequency components for the human EMG require a bandwidth of 1 Hz to 10 kHz. It has been found that a time constant of about 50 ms is satisfactory, which corresponds to a low-frequency –3-db point of 3 Hz. For needle electrodes with a tip diameter of 0.1 mm or larger, the input impedance (one side to ground) should not be lower than that of a 500-kW resistor in parallel with less than 25-pF capacitance. Smaller-area electrodes require a higher input impedance [Geddes et al., 1967]. The cable used to connect the needle electrode to the amplifier should not add more than 250 pF to the input capacitance. The common- mode rejection ratio (CMRR) should be in excess of 5000. Electroencephalography (EEG) The electrical activity of the brain can be recorded with electrodes on the scalp, on the exposed brain, or inserted into the brain. The latter method is used in research studies. When recordings are made with brain-surface (cortex) electrodes, the recording is called an electrocorticogram (ECoG). With scalp electrodes, the recording is designated an electroencephalogram (EEG) that is displayed by direct-inking pens using a chart speed of 3 cm/s. Typically 8 to 12 channels are recorded simultaneously. ? 2000 by CRC Press LLC Although the brain consists of about 10 l4 neurons, the EEG reflects the electrical activity of the outer layer, the cortex, which is the seat of consciousness. The type of electrical activity depends on the location of the electrodes and the level of alertness. The frequency and amplitude are profoundly affected by alertness, drows- iness, sleep, hyperventilation, anesthesia, the presence of a tumor, head injury, and epilepsy. The clinical correlation between cerebral disorders and the voltage and frequency spectra is well ahead of the physiological explanations for the waveforms. Recording Technique Both bipolar [Fig. 113.19(A)] and monopolar [Fig. 113.19(B)] techniques are used. With monopolar record- ing, one side of each amplifier is connected to a reference electrode, usually on the earlobe. With bipolar recording, the amplifiers are connected between pairs of scalp elec- trodes in a regular order. With both types of recording, one-half the number of channels is connected to elec- trodes on the opposite side of the head. In this way, the electrical activity from homologous areas of the brain can be compared at a glance. With the bipolar method illustrated in Fig. 113.19(A), abnormal activity located under electrode X will be revealed as a phase reversal in adjacent channels. With monopolar recording using the earlobe reference elec- trode [Fig. 113.19(B)] the abnormal activity under elec- trode X will be largest in the channel connected to that electrode and smaller in the adjacent channels. In clinical EEG, 21 electrodes are applied to the scalp in what is known as the 10-20 system. This array was established by the International Federation of EEG Soci- eties in 1958. The 10-20 system employs skull landmarks as reference points to locate the electrodes. The Normal EEG In the normal resting adult, the EEG displays a fluctuating electrical activity having a dominant frequency of about 10 Hz and an amplitude in the range of 20 to 200 mV. This activity is called the alpha rhythm and ranges in frequency from about 8 to 12 Hz, being most prominent in the occipital and parietal areas. It may occupy as much as half the record. The alpha rhythm increases in fre- quency with age from birth and attains its adult form by about 15 to 20 years. The alpha rhythm is most prominent when the eyes are closed and in the absence of concen- tration. Opening the eyes, engaging in patterned vision, or performing such cerebral activity as mental arithmetic diminishes or abolishes the alpha rhythm. Figure 113.20 presents a good example of this phenomenon. Although the alpha rhythm is the most prominent electrical activity, other frequencies are present. For example, there is a considerable amount of low-voltage, high-frequency (beta) activity ranging from 18 to 30 Hz. It is usually found in the frontal part of the brain. However, the normal electroencephalogram contains waves of various frequencies (in the range of 1 to 60 Hz) and amplitudes, depending on the cerebral state. To establish communication among electroencephalographers, a terminology has been developed to describe waveforms and their frequencies; Table 113.1 presents a glossary of these terms. FIGURE 113.19Methods of recording the EEG. (A) The bipolar and (B) the monopolar method. Note how abnormal activity under electrode X is revealed by the two techniques. ? 2000 by CRC Press LLC Drowsiness and sleep affect the normal EEG profoundly. Figure 113.21 illustrates the typical changes that occur as a subject goes to sleep. With drowsiness, the higher-frequency activity which is associated with alertness or excitement and the alpha rhythm that dominates the waking record in the relaxed state are replaced by a characteristic cyclic sequence of changes which constitute the focus of a new specialty devoted to sleep physiology, in which the EEG is used to identify different stages of sleep. Rapid, deep breathing (hyperventilation) at a rate of 30 per minute for about 3 min reduces the partial pressure of carbon dioxide in the blood which reduces cerebral blood flow. A typical EEG response consists of large-amplitude, bilaterally synchronous, frontally prominent waves with a frequency of 4 to 7 per second. The frequency usually decreases with increasing hyperventilation. The lack of bilateral symmetry is an indication of abnormality. Anesthesia dramatically alters the EEG in a manner that depends on the type and amount of anesthetic given. Despite differences among anesthetic agents, some important similarities accompany anesthesia. The first change is replacement of the alpha rhythm with low-voltage high-frequency activity that accompanies the analgesia and delirium stages. Thus the EEG resembles that of an alert or excited subject, although the subject is not appropriately responsive to stimuli; usually the response is excessive and/or inappropriate. From this point on, the type of EEG obtained with deepening anesthesia depends on the type of anesthetic. However, when a deeper level of anesthesia is reached, the EEG waveform becomes less dependent on the type of anesthetic. Large-amplitude low-frequency waves begin to dominate the record, and with deepening anesthesia their frequency is reduced and they begin to occur intermittently. With very (dangerously) deep anesthesia, the record is flat (i.e., isoelectric). Complicating interpretation of the EEG in anesthesia are the effects of hypoxia, hypercapnia, and hypoglycemia, all of which mimic deep anesthesia. FIGURE 113.20The EEG of a relaxed human subject with eyes closed and open. Note that the record is dominated with alpha rhythm (8–12 Hz) when the eyes are closed. (Source: Derived in part from M.A.B. Brazier, The Electrical Activity of the Nervous System, London: Sir Isaac Pitman & Sons, Ltd., 1951. With permission.) TABLE 113.1EEG Waveform Terminology Waveform Frequency, Hz Conditions Alpha 8–12 Parietal-occipital, associated with the awake and relaxed subject, prominent with eyes closed. Beta 18–30 More evident in frontal-parietal leads, seen best when alpha is blocked. Delta 1–3.5 Associated with normal sleep and present in children less than 1 year old, also seen in organic brain disease. Theta 4–7 Parietal-temporal, prominent in children 2 to 5 years old. Sleep spindle (sigma) 12–14 Waxing and waning of a sinusoidal-like wave having the envelope that resembles a spindle, seen during sleep. Lambda Transient Visually evoked, low-amplitude, occipital wave, resulting from recognition of a new visual image. Spike and wave ca. 3 Sharp wave (spike) followed by rounded wave associated with petit mal epilepsy. FIGURE 113.21The EEG of a subject going to sleep. ? 2000 by CRC Press LLC Clinical EEG The EEG plays a valuable role in identifying intracranial pathology. The clinical utility relies on recognition of patterns of frequency, voltage, and waveform. Localization of abnormal areas is provided by the multiple scalp electrodes and recording channels. The EEG has its greatest value as an aid in the diagnosis and differentiation of the many types of epilepsy, a condition in which groups of neurons in the brain become hyperexcitable and, depending on their location, produce sensory, motor, and/or autonomic manifestations. The epilepsies associated with cortical lesions are often detected by the scalp EEG. The EEG in epileptics is usually abnormal between, as well as during, attacks. The EEG provides information on the location of the area (or areas) of abnormal neuronal activity. Petit mal epilepsy is characterized by a tran- sient loss (few to 20 s) of conscious thought, although motor activity may continue. Often there are eye movements and blinking. The EEG shows a characteristic 3 per second spike-and- wave pattern [Fig. 113.22(A)]. Psychomotor epi- lepsy is characterized by sensory hallucinations and abnormal thoughts, often with stereotyped behavior. During the attack, the subject is stupor- ous and the EEG [Fig. 113.22(B]) has a charac- teristic pattern. Jacksonian, or motor, epilepsy starts in a specific area of the motor cortex and is preceded by an aura, a characteristic sensation perceived by the subject. The convulsion starts with localized muscle twitching that often starts in the face, hand, arm, then spreads over the entire body as a generalized convulsion; Fig. 113.22(C) shows the onset of a convulsion. Con- sciousness is lost during and for a short time after the fit. The EEG provides information on the origin of the abnormal discharge in the motor cortex. Grand mal epilepsy is characterized by a contraction all the muscles (tonic phase), then jerking (clonic phase). Conscious- ness is lost, and the subject is in a coma for some time following the attack. The EEG [Fig. 113.22(D)] shows high-voltage, high-frequency waves that progress over the entire cortex. Traumatic epilepsy results from injury to the brain. It is believed that contraction of scar tissue acts as a stimulus to adjacent nerve cells which discharge rhythmically, the excitation spreading to a grand mal convul- sion. The EEG provides information on the origin of the abnormal discharge. Tumors are associated with low-frequency (delta) waves. However, other intracranial lesions also produce slow waves. Although the EEG can identify the location of tumors, usually it cannot differentiate between brain injury, infection, and vascular accident, all of which produce low-frequency waves. Interpretation of the EEG always includes other clinical information. For those wishing to delve deeper into EEG, additional information can be found in most textbooks of medical physiology. The three-volume Atlas of EEG, authored by Gibbs and Gibbs [1952], contains a wealth of information on EEG in epilepsy and includes a vast array of eight-channel EEGs. Instrumentation The American EEG Society [1986] published guidelines for the performance of EEG machines. The guidelines recommended a minimum of eight channels. Chlorided silver disks or gold electrodes, adhered to the scalp with collodion, are recommended; needle electrodes are not. A chart speed of 3 cm/s is standard, and a recording sensitivity of 5 to 10 mV/mm is recommended. The frequency response extends from 1 to 70 Hz for the –3-dB points. Evoked Potentials With the availability of signal averaging using a digital computer, it is possible to investigate the integrity of the neural pathways from peripheral sense organs to the cortex by using appropriate stimuli (e.g., clicks, light FIGURE 113.22EEG waveforms in epilepsy: (A) petit mal, (B) psychomotor, (C) Jacksonian, and (D) grand mal. ? 2000 by CRC Press LLC flashes, or current pulses). Usually the stimulus consists of a few hundred to about 1000 pulses, averaged to produce the somatosensory-evoked potential (SSEP). Likewise, it is possible to evaluate the integrity of the neural pathways from the motor cortex to peripheral muscles by applying multiple short-duration current pulses to scalp electrodes and recording nerve and/or muscle action potentials with skin-surface electrodes. Such recordings are called motor-evoked potentials (MEPs). With both SSEPs and MEPs, the largest responses appear on the opposite side of the body from the stimulus. Because the responses are in digital form, they can be written out in hard-copy format. With SSEPs, the response consists of many waves occurring at various times after the stimulus. To permit close examination of the various waveforms, several displays are presented, each with a different time axis. Figure 113.23 presents a sketch of the neural pathways from the periphery to the cortex, showing the topographic distribution of sensation along the cortex using the homunculus created by Penfield, described in detail in 1968. Also shown in Fig. 113.23 is a typical SSEP obtained by stimulating the median nerve with skin-surface electrodes connected to an isolated (i.e., not grounded) stimulator output circuit. Note the remarkably low amplitude of the responses that were obtained by averaging the response to 240 stimuli. Note also that the first display showed the responses from 0 to 50 ms and the second display presented the responses in the 0- to 400-ms interval. FIGURE 113.23Pathways from the peripheral sense organs to the cortex and the topographical distribution of sensation along the cortex with Penfield’s homunculus. Also shown are the stimulating electrodes on the wrist and the SSEPs recorded from the contralateral cortex. (Source: SSEPs redrawn from T. W. Picton, “Evoked cortical potentials, how? what? and why?,” Am. J. EEG Technol., vol. 14, no. 4, pp. 9–44, 1974. With permission.) ? 2000 by CRC Press LLC Figure 113.24 shows the motor pathways from the motor cortex to a typical muscle. The cortical motor areas are represented by Penfield’s homunculus. A train of 250 stimuli were applied between electrodes on the scalp and in the mouth. The motor-evoked potentials were recorded with skin-surface electrodes over the spinal column. The MEP of a patient in whom the muscles were paralyzed is also shown in Fig. 113.24. Because the muscles were paralyzed, the MEPs shown in the figure represent action potentials in the spinal cord. Note the prominent peaks at 7 and 14 ms. These peaks provide information on the path taken by the nerve impulses initiated in the motor cortex. Although there is no ANSI standard for evoked-potential recording, the American EEG Society [1986] published guidelines for equipment performance and recording techniques. This information should be con- sulted by those contemplating entry into this field. Magnetic (Eddy-Current) Stimulation When scalp electrodes are used to stimulate the brain, there is considerable skin sensation under the electrodes owing to the high perimeter current density [Overmeyer et al. 1979]. It has been found that sufficient eddy current can be induced in living tissue by discharging an energy-storage capacitor into an air-cored coil placed on the skin. This mode of stimulation is almost without skin sensation; by some it is called “ouchless stimulation” FIGURE 113.24Neural motor pathways from the cortex to a typical muscle. The motor areas are represented by Penfield’s homunculus. A train of 240 stimuli delivered to the motor cortex provided the average MEP detected with electrodes placed over the spinal column in this patient to whom a muscle paralytic drug was given; therefore the MEPs are from the spinal cord. (Source: Redrawn from Levy et al., 1984, and Penfield and Rasmussen, 1968.) ? 2000 by CRC Press LLC and it can be used to stimulate the brain, peripheral nerves, and the heart. The parameters associated with eddy-current stimulation are kiloamperes, Teslas/sec, milliohms, microhenries, microseconds, and low damp- ing. Because the forces on the coil conductors are very large, special care is required in fabricating such coils. Stimulators With magnetic (eddy-current) stimulation, three circuits and two coil geometries are used. The simplest circuit is illustrated in Fig. 113.25, which shows a capacitor (C) being discharged into the stimulating coil (L). The induced current (i) is proportional to the rate of change (di/dt) of the coil current (i). The resistance (R) in the entire circuit is low and the coil current is an underdamped sinusoid. The tissue is stimulated by the induced current density J = k(de/dx)/r, where de/dx is the induced voltage gradient, r is the tissue resistivity, and k is a constant that depends on coil geometry and target distance. The effective stimulus duration (d) is from the onset of the induced current to the first zero crossing as shown in Fig. 113.25. Typical durations (d) range from 20 to 200 msec. When the damping is low, the multiple pulses of induced current can elicit responses, providing the period is longer than the refractory period of the tissue being stimulated. Note that the capacitor voltage falls to zero and the capacitor must be recharged to deliver the next stimulus. The second type of eddy-current stimulator employs energy recovery and is shown in Fig. 113.26. The charged capacitor (C) is discharged into the stimulating coil (L) by triggering a silicon-controlled rectifier (SCR). By placing a diode across the SCR as shown, some of the energy stored in the magnetic field can be recovered to recharge the capacitor. In this way, the power supply need only deliver a modest amount of current to restore the charge on the capacitor. FIGURE 113.25Simplest type of magnetic (eddy-current) stimulator and coil and induced current waveforms. FIGURE 113.26Magnetic (eddy-current) stimulator that recovers energy stored in the magnetic field. ? 2000 by CRC Press LLC With the circuits shown in Figs. 113.25 and 113.26, it is necessary to use non-polarized capacitors. When a long-duration pulse is desired, it is more practical to employ electrolytic capacitors because of their high energy storage per unit of weight. When employing electrolytic capacitors, it is necessary to prevent reverse charging. To achieve this goal, a diode (D) and a series current-limiting resistor (Rz) are placed across the capacitor, as shown in Fig. 113.27. The resulting induced current waveform is shown on the right. Stimulating Coils Air-cored coils are used because all known ferromagnetic materials saturate at the high flux densities used with eddy-current stimulation. Two types of coils are used: (1) annular and (2) coplanar, sometimes called figure eight, osculating, or butterfly. Most coils are annular in shape and the radius is chosen on the basis of the distance to the target tissue to be stimulated. Nyenhuis et al. [1991] analyzed the factors pertaining to the optimum design of such annular coils and calculated the mag- netic-field energy and ohmic heating. They found that the mag- netic field energy exhibits a broad minimum when the coil outer radius is between two and five times the target distance. Ohmic heating in the coil decreases as the radius of the coil increases. Increasing annular width results in a small reduction in field energy and coil heating; thin coils (small height) reduce the field energy but increase heating. A reasonable compromise between efficiency and coil size is a coil with an outer diameter that is twice the distance between the coil surface and the underlying target tissue to be stimulated and whose height and annular width are 0.2 and 0.6 that of the mean radius, respectively. The induced electric field gradient (de/dx) is maximum at the perimeter of an annular coil. Weissman and Epstein [1992] plot- ted the electric field induced in a saline volume conductor due to an annular coil; Fig. 113.28a is the result which shows a maximum over the perimeter of the coil. Eddy-current stimulation is very energy inefficient when com- pared to direct tissue stimulation with electrodes. To improve the efficiency, investigators have sought strategies to concentrate (focus) the magnetic field without the use of ferromagnetic mate- rial. Ueno et al. [1988] introduced what they called the figure-of- eight coil of the type shown in Fig. 113.29 in which the current in the conductors where the two coils touch is in the same direction, thereby concentrating the field. Note that the currents in the two coils are in opposite directions; hence the magnetic fields (B1, B2) are in opposite directions. With this coil configuration and current direction, the induced electric field is a maximum over the site where the coils touch, as shown in Fig. 113.28b. Although the use of a pair of coils increases the efficiency of magnetic stimulation, it makes coil placement more critical. FIGURE 113.27Method of using a diode (D) and current-limiting resistor (Rz) to avoid reverse polarity on the energy- storage capacitor (C). FIGURE 113.28 Induced electric field (de/dx) for a single annular coil (a) and for a pair of coplanar annular coils (b). (Redrawn from [Weissman and Epstein 1992]). ? 2000 by CRC Press LLC Figure 113.30a shows a commercially available annular coil and Fig. 113.30b shows the figure-of-eight (Butterfly?) coil. These coils can be used for stimulating the brain or peripheral nerve. Proper location of the coil with respect to the target tissue is essentials (see Fig. 113.28 for locations of maximum de/dx). Many types of excitable tissue can be stimulated by eddy current. Geddes et al. [1991] investigated its use to produce inspiration in humans by stimulating both phrenic nerves at the base of the neck. The phrenic nerves cause the diaphragm to contract, thereby producing inspiration. By using two series-connected pairs of coplanar coils, each pair angled at 150°, current pulses at 25/sec were delivered from a 50 mF capacitor charged FIGURE 113.29Current (I) and magnetic field (B) direction in the coplanar (figure-of-eight) coil. FIGURE 113.30 Commercially available coils for magnetic (eddy-current) stimulation. (Courtesy of Cadwell, Kennewick, WA 99336). FIGURE 113.31Magnetically induced inspiration (M) produced by a train of eddy-current stimuli applied to both phrenic nerves with two pairs of coplanar coils at the base of the neck. S = spontaneous breaths. ? 2000 by CRC Press LLC to 1200 volts, the magnetically induced inspiration (M) of 900 mL shown in Fig. 113.31 was produced. To make this record, the subject first hyperventilated, then stopped breathing and the magnetic stimulator was turned on for about 1 sec. The breaths marked S are spontaneous breaths with a volume of 400 mL. Cardiac muscle has been stimulated to contract with single pulses of eddy current. The first to achieve this feat was Bourland et al. [1990] who applied a coplanar coil to the left chest of an anesthetized dog. Blood pressure and the electrocardiogram were recorded and the heart was stopped by right vagal stimulation, during which time a pulse of current was delivered to the coplanar coils and a ventricular contraction was produced, showing an inverted QRS wave in the ECG and a blood-pressure pulse. That it is difficult to stimulate the heart with a pulse of eddy current can be assessed by the parameters of the stimulator used by Bourland et al. [1990] which employed a 682 mF capacitor, charged to 9900 volts, and discharged into the 220 mH coplanar coil assembly. The peak current was 17,000 amps and the stored energy was 33,421 joules. The duration of the induced current pulse was 690 msec. This stimulator was used by Mouchawar et al. [1992], who reported mean current and energy thresholds for cardiac stimulation in the range of 9200 amps and 11,850 joules. From the foregoing it is clear that the ventricles can be caused to contract with pulses of eddy current. However, if it is desired to pace at 60/min. (1/sec), the power needed is 11.85 kilowatts, hardly a practical value for domestic or hospital use. Summary and Conclusion Although eddy-current stimulation of excitable tissue is quite popular now, the first report was by d’Arsonval [1896], who reported seeing bright flashes in the visual field (phosphenes) when the head was placed in a coil carrying 30 amperes of 42 Hz current (see Geddes translation [1991]). It is now known that stimulation of the retinal receptors in the eye produces such phosphenes. Magnetic stimulation is largely used to excite nerve cells in the brain and spinal cord. The diagnostic information is contained in the time between the stimulus and the response (action potential). The same measure is used when peripheral nerve is stimulated. A major advantage of magnetic stimulation is that no electrodes are required and the skin need not be exposed to apply the stimuli. However, the main advantage is that the skin sensation is very mild. A major disadvantage is the high energy needed to induce sufficient eddy current density to achieve stimulation. When repetitive pulses are required, the power drawn by the magnetic stimulator may require a 60-Hz AC energy source of 220 or 440 volts. Moreover, with repetitive stimulation, coil heating becomes a problem. The avail- ability of magnetically permeable materials that saturate at several orders of magnitude above presently available materials would be of benefit to the field of magnetic (eddy-current) stimulation. This section has focused only on the three most prominent bioelectric events, those of the heart, skeletal muscle, and brain. The eye, ear, sweat glands, and many types of smooth muscle produce action potentials that are used for their diagnostic value, as well as being the subject of on-going research. The reader interested in delving deeper into this field can find such information in a book by Geddes and Baker [1989]. Defining Terms Atrophy: Wasting of cells deprived of nourishment. Autonomic:That part of the nervous system which controls the internal organs. Ectopic beat: A heart beat that originates from other than the normal site. Hypocapnia:A condition of reduced carbon dioxide in the blood. Hypoxia:A reduced amount of oxygen. Magnetic stimulation:Eddy current stimulation. Metabolic process:The method by which cells use oxygen and produce carbon dioxide and heat. Myocardial infarction:A heart attack in which a region of the heart muscle is deprived of blood and soon dies. Occipital:The back of the brain. Parietal: The side of the brain. ? 2000 by CRC Press LLC Related Topic 2.1 Step, Impulse, Ramp, Sinusoidal, Exponential, and DC Signals References American EEG Society, “Guidelines in EEG and evoked potentials,” Amer. J. Clin. Neurophysiol., vol. 3 (Suppl.), 1986. Association for the Advancement of Medical Instrumentation (AAMI), Diagnostic ECG Devices, ANSI-AAMI Standard EC-101-1991. J.D. Bourland, G.A. Mouchawar, J.A. Nyenhuis, et al., “Transchest magnetic (eddy-current) stimulation of the dog heart,” Med. Eng. Comput. March, pp. 196–198, 1990. F. Buchtal, C. Guld, and P. Rosenflack, “Action potential parameters of normal human muscle and their dependence on physical variables,” Acta Physiol. Scand,. vol. 32, pp. 200–220, 1954. T-C. Chou, Electrocardiography in Clinical Practice, 3d ed. Philadelphia: W. B. Saunders, 1991. H.L. Cohen and F. Brumlik, Manual of Electromyography, New York: Hoeber Medical Division, Harper & Row, 1969. A. d’Arsonval, “Dispositifs pour la mesure des courants alternatifs de toutes frequences,” C. R. Soc. Biol. (Paris), vol. 2, pp. 450–451, 1896. L.A. Geddes, “The history of magnetic stimulation,” J. Neurophysiol., vol. 8, no. 1, pp. 3–9, 1991. L.A. Geddes, L.E. Baker, and M. McGoodwin, “The relationship between electrode area and amplifier input impedance in recording muscle action potentials,” Med. Biol. Eng. Comput., vol. 5, pp. 561–568, 1967. L.A. Geddes and L.E. Baker, Principles of Applied Biomedical Instrumentations, 3rd ed., New York: Wiley, 1989. L.A. Geddes, G. Mouchawar, J.D. Bourland, and J. Nyenhuis, “Inspirations produced by bilateral electro- magnetic, cervical phrenic nerve stimulation in man,” IEEE Trans. Biomed. Eng., vol. 30, no. 10, pp. 1047–1048, 1991. F.A. Gibbs and E.L. Gibbs, Atlas of Electroencephalography, London: Addison-Welsey, 1952. International Federation of EEGSocieties, J. Knott, Chairman, EEGClin. Neurophysiol., vol. 10, pp. 378–380, 1958. International Federation for Electroencephalography and Clinical Neurophysiology, EEG. Clin. Neurophysiol., vol. 10, pp. 371–375, 1958. W.J. Levy, D.H. York, M. McCaffery, and F. Tanzer, “Evoked potentials from transcranial stimulation of the motor cortex in humans,” Neurosurgery, vol. 15, no. 3, pp. 287–302, 1983. A.A. Marinacci, Clinical Electromyography, Los Angeles: San Lucas Press, 1955. G.A. Mouchawar, J.D. Bourland, J.A. Nyenhuis, et al., “Closed-chest cardiac stimulation with a pulsed magnetic field,” Med. Biol. Eng. Comput., March, pp. 162–168, 1992. J.A. Nyenhuis, G.A. Mouchawar, J.D. Bourland, and L.A. Geddes, “Energy considerations in the magnetic (eddy- current) stimulation of tissues,” IEEE Trans. Magn., vol. 27, no. 1, pp. 680–687, 1991. K.M. Overmeyer, J.A. Pearce, and D.P. DeWitt, “Measurement of temperature distributions at electrosurgical dispersive electrode sites,” Trans. ASME, J. Biomech. Eng., vol. 101, pp. 66–72, 1979. W. Penfield and T. Rasmussen, The Cerebral Cortex of Man, New York: Hafner, 1968. R.E. Phillips and M.K. Feeney, The Cardiac Rhythms: A Systematic Approach to Interpretation, 3rd ed., Phila- delphia: W. B. Saunders, 1990. T.W. Picton, “Evoked cortical potentials, how? what? and why?,” Am. J. EEG Technol., vol. 14, no. 4, pp. 9–44, 1974. S. Ueno, T. Tashiro, and K. Harada, “Localized stimulation of neural tissues in the brain by means of a paired configuration of time-varying magnetic fields,” J. Appl. Phys., vol. 64, no. 10, pp. 5862–5866, 1988. J.D. Weissman and C.M. Epstein, “Magnetic stimulation of the nervous system,” Am. J. EEG Technol., vol. 32, pp. 127–146, 1992. ? 2000 by CRC Press LLC 113.3 Application of Electric and Magnetic Fields in Bone and Soft Tissue Repair C. Polk History As early as 1962 in the United States [Bassett and Becker, 1963], and even earlier—1957—in Japan [Fukada and Yasuda, 1957] it was shown that electric potential differences appear across both living and dead bone subjected to mechanical stress. Bassett and Becker observed that these stress-generated electrical signals decayed very slowly in comparison with similarly initiated signals in piezoelectric crystals and concluded [Bassett and Becker, 1963] that piezoelectric phenomena “while probably present, were not the sole cause of these potentials.” Later analysis and experiments established that the observed signals were primarily due to ion displacement within the porous regions and multiple fluid-filled channels present in all bone. The early observations already suggested that direct application of an externally generated voltage might have an effect on bone development. This was shown to be the case by Bassett et al. [1964] who found that a dc current of the order of 1 mA (corresponding to a current density of approximately 0.01 A/m 2 ) produced massive osteogenesis near the cathode when electrodes were implanted into the femur of living dogs. Having shown that application of a dc electric field to nonexcitable, connective tissue cells can produce effects similar to those elicited by mechanical stress, Bassett and his co-workers realized that clinical exploitation of these phenomena would require surgical implantation of electrodes with attendant danger of infection. They proceeded therefore to explore whether noninvasive, inductive coupling that gave waveforms similar to those endogenously produced by mechanical stress could lead to beneficial bone development. In 1974 they reported favorable results obtained with pulsed electromagnetic fields on dogs [Bassett et al., 1964]. Signals of this type have generally been identified as PEMF (pulsed electromagnetic field) in the orthopedics/electrical stimulation community for the last 20 years and have been applied successfully in a large number of cases for the repair of nonunions [Grossling et al., 1992]. In Germany relatively large-amplitude, low-frequency (<20 Hz) sinusoidal magnetic fields have been used for both bone repair and wound healing [Kraus, 1984]. Although the noninvasive PEMF treatment for nonunions (fractures that fail to heal) became—at least in the United States—the most widely used clinical application of subradio frequency fields, several investigators pursued the application of dc electric fields through implanted electrodes and the application of higher- frequency currents through electrode contacts placed on the skin surface to enhance bone repair [Brighton et al., 1979]. At the same time mostly laboratory investigations, in vitro and on animals, explored the application of all three modalities—PEMF, implanted dc electrodes, and higher-frequency coupling through skin elec- trodes—to produce blood vessel regeneration (angiogenesis), soft tissue healing, nerve repair or regeneration, and regression of tumors. Claimed to be useful in edema and pain management and for acceleration of wound repair is pulsed radio frequency (PRF), mainly the diathermy frequency of 27.12 MHz assigned by the FCC, at an average power level that should usually produce only very moderate tissue heating [Kloth and Ziskin, 1996; Markov, 1995]. Motivated by the suggested clinical applications, a large number of basic science investi- gations have been initiated, and are continuing today, with the object of understanding the mechanisms through which low-intensity electric and magnetic fields affect cells and living tissue. Some of these are reviewed briefly in the subsection Mechanisms and Dosimetry. Devices for Bone and Cartilage Repair In the United States medical devices are approved for clinical use only after it has been shown to the satisfaction of the U.S. Food and Drug Administration (FDA) that they are not only safe, but also effective. This is a much more stringent requirement than the mere demonstration of safety demanded presently in most European countries (although some EEC countries are considering moving toward approval criteria that are similar to those used in the United States). The United States laws governing the sale of medical devices for clinical use are also much more restrictive than the controls over implementation of new surgical procedures that involve only informal medical peer review. Even organized multi-patient clinical trials require not more than approval ? 2000 by CRC Press LLC by a local hospital-based institutional review board. The FDA Office of Device Evaluation does approve some new devices, after careful review, for clearly limited clinical trials. However, information on such limited, temporary approval is not made available. Table 113.2 therefore shows only those devices which are presently (July 1, 1996) approved and does not include experimental systems which may be undergoing currently limited clinical trials. Some of the latter are discussed further on, based only on information furnished by manufacturers or available from the published medical literature. The devices listed in Table 113.2 are approved for one of three applications: the treatment of nonunions (fractures that have failed to heal after standard treatment involving setting and stabilization with casts), congenital pseudoarthroses [Bassett, 1984], and promotion of spinal fusion. Although many animal experi- ments (and possibly a few human trials, especially in Europe) have evaluated the application of electric or magnetic fields for acceleration of fresh fracture healing and for reversal of osteoporosis, no devices are currently approved in the United States for these purposes. Classified by electrical and mechanical characteristics, the devices in Table 113.2 are either: 1.Noninvasive: a.Generating time-varying magnetic fields applied by coils to the affected body part (A, B, C, D, and H). b.Generating time-varying electric fields applied through skin-surface electrodes (capacitively coupled) (E). 2.Invasive: dc applied from an implanted battery (F, G). TABLE 113.2Electrical Bone Growth Stimulators Approved by the U.S. FDA as of July 1, 1996 Manufacturer FDA “PMA” Number* Text FDA Docket Number Device Indications Technology Approved References Electro-Biology, Inc. EBI Bi-OsteoGen/Bone Nonunion; Noninvasive November A P790002 Healing System** congential pulsed electro- 1979 B 80M-0057 pseudoarthroses; magnetic field failed fusions (PEMF) American Medical Physio-Stim Nonunions Noninvasive February C Electronics, Inc. (excluding PEMF 1986 P850007 vertebrae and 86M-013B flat bones) American Medical Spinal-Stim To promote spinal Noninvasive February D Electronics, Inc fusion as an adjunct PEMF 1990 P850007 to surgery or as nonop- 90M-0067 erative treatment when 9 months have elapsed since the last surgery Biolectron, Inc. Orthopak BGS Nonunions (excluding Noninvasive/cap- February E P850022; 86M-0139 Device vertebrae and flat bones) acitively coupled 1986 Electro-Biology, Inc. Orthogen/Osteogen Nonunion of long bones Implantable dc January F P790005; 80M-0254 1980 Electro-Biology, Inc. P850035 87M-0174 SpF Implantable Spinal Fusion Stimulator? Spinal fusion adjunct Implantable dc April 1987 G SpF-4 (original); SpF-2 (S5); SpF-2T, 4T (S6); SpF-XL (S13) OrthoLogic P910066 OrthoLogic 1000 Nonunions (excluding vertebrae and flat bones) Noninvasive PEMF March 1994 *These numbers are useful when calling the U.S. FDA (Dockets Management Branch) to obtain summary of safety and effectiveness of particular devices. **Originally designed Bi-Osteogen Systems 204. ?Originally Osteostim HS 11. ? 2000 by CRC Press LLC A signal typical for some PEMF (A, C, D) devices is illustrated in Fig. 113.32. Part A shows the magnetic field versus time and Part B the corresponding electric field induced into a linear, isotropic medium. The waveform shown on Part B can be measured by a probe coil having a sufficiently large number of turns. The frequency spectrum of the electric field is shown in Fig. 113.33. Signals used by the different manufacturers are protected by patents, and FDA approval is for particular signal param- eters within specified tolerances on time and amplitude. The pseudoarthro- sis signal used by Electrobiology, Inc. (EBI) (B in Table 113.2) consists of single pulses repeated at a rate of 72 pps rather than the pulse bursts illustrated in Figs. 113.32 and 113.33. Each magnetic field pulse increases from zero to 3.5 mT in 380 ms and then decreases slowly to zero in approx- imately 4.5 ms. The signals that are now in use have evolved considerably from those employed in the initial studies, and some have little resemblance to the endogenous electrical signals elicited by mechanical stress. The PEMF signals employed by the various manufacturers in the United States and Europe can have several different pulse shapes, rise and decay times, pulse widths, pulse repetition rates, and amplitudes. Since it has been shown (see Mechanisms and Dosimetry) that all these variables can have a profound effect on the biological action of a particular signal, it is essential that reports on effectiveness or lack of effectiveness of PEMF give an exact description of the signal which was used. Unfortunately the medical liter- ature is replete with examples where this information is either incomplete or completely absent. Details of shape, orientation, and location of the application coil or coils are also important, since these parameters, together with pulse amplitude and shape, determine the nature of the magnetic and electric field at the location of the injured tissue. If the amplitude of the axially directed magnetic flux density B is constant over some region of radius R within the cross section of a circular cylinder, the induced electric field is (113.17) provided the material of the cylinder is electrically homogeneous and isotropic. In Eq. (113.17) r < R is the distance from the center of the cylinder and f ^ is a unit vector in the circumferential direction. For magnetic fields varying sinusoidally as B 0 cos wt, = wB 0 (r/2) sin wt f ^ .Since most biological objects are neither homogeneous nor isotropic, the actual induced electric fields at various points in the tissue or cells may deviate substantially from the values given by Eq. (113.17) [Polk and Song, 1990; Van Amelsfort, 1990]. Equation (113.17) is useful only for estimating the spatial average value of the induced electric field, which depends in the bone environment on the point-to-point variation of the electrical properties of muscle, fat, cartilage, periosteum (outer bone membrane), and bone marrow. Current pulses of the PEMF devices are usually produced by the discharge of capacitor banks controlled by a timing network. The applicator coil cannot be interchanged among different devices because its inductance and resistance are a part of the discharge network. While earlier bone growth stimulators employed Helmholtz coil-pair arrangements, most present devices have single coils which can be custom-shaped for particular limbs. Figure 113.34 shows a typical system sold by EBI. This unit is driven by rechargeable batteries, and the control unit (shown in Fig. 113.34) includes an elapsed-time clock to measure the total time of stimulation of the fracture being treated. A typical treatment time can be between 2 and 10 h/day over a period of 6 months. The so-called capacitively coupled device (E in Table 113.2) generates a continuous sine wave at a frequency of 60 kHz. The total current through the skin contains a not negligible conduction component since conductive contact is made between the applicator electrodes and the skin that represents a “leaky” capacitor. Electric fields produced at the tissue level by this device are between 1 and 50 V/m [Pollack and Brighton, 1989]. These levels FIGURE 113.32A typical PEMF signal (signal A of Table 113.2). (A) Magnetic field versus time. (B) Elec- tric field (μ ?B/?t) versus time. Sig- nal consists of 15 pulse bursts per second. Each burst is 4.5 ms long and contains 20 pulses. In each pulse the magnetic field increases from 0 to approx. 2 mT during 200 ms, decreases to 0 again during 23 ms, and is equal to 0 for 2 ms before the next 225-ms sequence begins. E B t r = ? è ? ? ? ÷ – ? ? ? f 2 E ? 2000 by CRC Press LLC FIGURE 113.33 Electric field spectrum *E(w)* of signal in Fig. 113.32 as measured by the output from an air-core coil (0.6 cm mean diameter, 65 turns). (A) 10 Hz to 1 kHz (50 mV full scale); (B) 4 to 40 kHz (1 mV full scale). FIGURE 113.34 PEMF applicator and control unit and implantable dc stimulating device (battery with wire electrode) manufactured by Electrobiology, Inc. (systems A and G of Table 113.2). (Photograph courtesy of Electrobiology, Inc.) ? 2000 by CRC Press LLC are very much higher than the average amplitude of the electric fields produced in tissue by PEMF devices and also higher than the instantaneous peak values produced by some of the PEMF systems. It is interesting to note here that in vitro experiments with truly capacitively coupled fields showed enhancement of bone cell prolif- eration at very much lower amplitude (10 –5 V/m) when the frequency of the continuous sine wave was 10 Hz rather than 60 kHz [Fitzsimmons et al., 1986]. The most recent addition to FDA approved non-invasive systems (H in Table 113.2) employs a sinusoidally time varying 76.6 Hz, 40 mT field superimposed on a DC field of 20 mT. Possible reasons for using this AC/DC “resonance” combination are discussed in the Mechanisms and Dosimetry section. An invasive (implantable) dc device (F, G in Table 113.2) is also shown on Fig. 113.34. The small (approx- imately 4 ′ 2 ′ 0.5 cm) titanium case contains a long-life battery that is connected to it. The case acts as the anode, and two (shown) or four titanium wires act as the cathode. The amplitude of the continuous current is between 5 mA (for some spinal fusion applications) and 20 mA (for nonunion of long bones). The cathodes are placed at the location where bone growth is to be enhanced, for example, at the vertebrae that are surgically fused, while the case is placed in a convenient location at some distance from the bone. Treatment details and success rates, in comparison with surgical procedures without use of dc stimulation, are discussed in the medical literature [Nerubay et al., 1986]. Although not used or approved for use in the United States, the German “Magnetodyn” system [Kraus, 1984] is interesting not only because it employs sinusoidal magnetic fields between 2 and 20 Hz but also because it relies on metallic implants that are used for fixation of the bone to act as the “secondary” of a “transformer” whose primary is the external applicator. Sometimes an implanted pickup coil (“secondary”) is connected to fixation bars or to screws (electrically insulated from the bars) on each side of a pseudoarthrotic gap. With this system, peak electric fields of 40 V/m and current densities of 5 A/m 2 have been produced in the gap. A PEMF signal (similar to B in Table 113.2) has also been used experimentally to arrest osteonecrosis (bone death possibly due to vascular impairment or toxic agents) of the femoral head. Application for 8 h/day over 12 months gave substantially better results than the standard surgical (decompression) treatment [Aaron and Steinberg, 1991]. Soft Tissue Repair and Nerve Regeneration No electric or magnetic system to aid nerve regeneration or soft tissue repair is approved by the FDA at the present time for nonexperimental therapy. However, considerable animal and in vitro experimentation in this country and abroad suggests the clinical usefulness of electric currents for soft tissue repair [Canaday and Lee, 1991] and possibly also to enhance repair of nerve fibers that have sustained crush or transsection injury [Ito and Bassett, 1983; Siskin et al., 1990]. Since there is a great variety of soft tissue pathologies that could respond to electric or magnetic fields, the volume of application in this area could in the future become larger than in orthopedics, provided field-tissue and field-cell interactions become better understood and clinical benefits for specific injuries and diseases are established. A pulsed radio frequency (PRF) device sold in the U.S. by Electropharmacology, Inc., of Pompano Beach, FL, produces 27.12 MHz pulses of 65 microsecond duration. Pulse repetition rates can be selected between 80 and 600 pps and peak output power is adjustable between 174 and 363 watts. Thus, the highest possible average power delivered into the 9-in. diameter inductive applicator is 14.16 watt. (“Inductive” applicator means that the applicator is designed to make the ratio of electric to magnetic field in its immediate vicinity much less than the 377 W wave impedance of free space; thus, the magnetic field is maximized in the “near field” region). Coupling to living tissue at 27.12 MHz without impedance matching is rather poor [Polk, 1995]. If it is assumed that only 20% of the 14.16 W average power is absorbed by the tissue, application for the recommened treatment period of 30 min would correspond to an energy transfer of 1.2 kilocalories. If the mass of the local region to which this energy is applied is of the order of 2 kg, this would correspond to a temperature increase of 0.6°C in the absence of cooling by blood circulation or convection. In any case, although “the PRF modality was originally reported as a non-thermal biophysical treatment of infections” [Ginsberg, 1934; Markov and Pilla, 1995], the device is likely to produce at least moderate tissue heating when applied with maximum output settings. The Electropharmacology “MRT Softpulse Model 912” is marketed for clinical use in the U.S. under FDA rules which permit continued sale of ? 2000 by CRC Press LLC devices that are substantially equivalent to older equipment (in this case “Diapulse”) in use before the enactment of present FDA rules. Beneficial effects of time-varying electric fields in wound healing are most likely related to promotion of angiogenesis. Wound healing consists of several stages, the first being inflammation, when changes in vascular permeability occur; infiltration of leucocytes and macrophages takes place; and cells migrate, synthesize gran- ulation tissue, collagen, and proteoglycans, and initiate formation of capillaries. This is followed by transitional repair and remodeling phases. Electrical currents are probably only important in the first two stages [Canaday and Lee, 1991] and the experimental clinical trials performed thus far involve therapy for inflammation. One was a double-blind study of persistent rotator cuff tendinitis [Binder et al., 1984] that showed beneficial effects of a PEMF very similar to the pseudarthrosis signal used by EBI (B in Table 113.2, described above in previous section). Cuff tendinitis is probably due to partial interruption of blood supply to the rotator cuff tendons of the shoulder by compression of vessels between adjacent bones. Another double-blind study [Ieran et al., 1990] employing a PEMF signal indicated beneficial effects in the treatment of skin ulcers. Other clinical trials [Bentall, 1986] and animal experiments involved irradiation of wounds with pulsed high and very high frequencies between 3 and 44 MHz, at power levels from 73 mW to 15 W, employing pulse widths between 65 and 100 ms and pulse repetition frequencies between 200 Hz and 1 kHz. A commonly used animal model for wound healing is the McFarlane skin flap involving partial excision of a rectangular skin section on the back of the rat. Survival of the flap depends mainly on blood supply, with vascularization of the skin flap being an indirect measure of treatment success. The EBI signal shown on Fig. 113.33 (A in Table 113.2) is reported to have decreased skin flap necrosis when exposure was for 6 h/day for 3 days, while exposure for 18 h on the first day after injury had no observable effect [Luce and Bryant, 1986]. Exposure with a triangular, symmetric and almost continuous magnetic field (18-ms triangular pulse, followed by 2-ms pause) at a frequency of 50 Hz (8-mT peak to peak value) produced a significant increase in wound contraction in rats (in comparison with controls) who were exposed to the field for 30 min immediately after surgery and for the same period thereafter every 12 h. In an effort to determine what type of signals are most beneficial for the acceleration of wound healing, skin flap necrosis was observed under exposure to sinusoidal magnetic fields at constant ?B/?t of 0.5 T/s using frequencies of 20, 72, and 500-Hz [Sisken and Herbst, 1990]. While signals at 20 and 72 Hz significantly decreased necrosis after 7 days, the 500-Hz signal was ineffective. Very soon after some types of bone injury and pathology were first treated with PEMF, the effects of PEMF on peripheral nerve regeneration became subjects of investigation. Improved neural function that appeared as an unintended “side effect” in the clinical treatment of nonunions led Kort et al. [1980] to a systematic investigation of PEMF effects on neural regeneration in rats. Other investigators employed other animal models and also compared PEMF with direct current as agents for neural regeneration. More recent work [Siskin et al., 1990] employed a PEMF signal consisting of 20-ms pulses at a repetition rate of 2 pulses per second with exponential rise and decay times of, respectively, 0.5 and 1 ms. Amplitudes were 0.3 mT for experiments with crush lesions of the sciatic nerve in rats and 0.05 mT for stimulation in vitro of neurite outgrowth in dorsal root ganglia. Estimated values for the mean induced electric field pulses were 5 mV/m in the animal experiments and 0.7 mV/m in the 60-mm-diameter culture dishes of the in vitro work. Stimulation for 2 h per day of the in vitro cultures produced approximately 50% enhancement of neurite outgrowth in comparison with controls after 2 days. The in vivo experiments using the 0.3-mT pulse produced “a 22% increase in the rate of regeneration relative to controls” as measured by a standardized test of reflex response. A very interesting observation was that animals exposed to the 0.3-mT field for 4 h/day for 7 days prior to the crush injury, who received no treatment after injury, responded similarly to those treated postinjury. Analysis of extracts from sciatic nerve segments after sacrifice of the animals showed that treatment with PEMF changed the molecular weight distribution of synthesized polypeptides. A report on a very limited (13 subjects) clinical trial [Ellis, 1987] of spinal nerve stimulation in para- and quadriplegics employing pulsed electric current introduced by needle electrodes produced “encouraging results” in terms of increased sensory perception and motor function. The signal obtained from a Chinese multipurpose therapy apparatus was described as follows: “The pulsed-wave generator produced a biphasic wave form of 2 ms duration with an initial slow positive deflection followed by an 80-ms rise time to its maximal negative deflection and subsequent asymptotic decay. This wave shape was pulsed in ramped bursts of 200 pulses per ? 2000 by CRC Press LLC second for 1.5 s with 0.75 s rest time before the next ramped burst. Peak-to-peak voltages of approximately 30 V were common, and current flow was on the order of 1 mA.” The diathermy frequency of 27.12 MHz used for PRF therapy has also been employed, with ELF amplitude modulation, to induce sleep. At least one double blind study [Reite et al., 1994] has shown the effectiveness for this purpose of “Low Energy Emission Therapy” (LEET). In this application, the 27.12 MHz carrier is period- ically amplitude modulated with a 42.7 Hz sine wave for 3 s and then interrupted for 1 s during a 15-min treatment period. The signal is applied by means of an electrically conducting mouthpiece in direct contact with the oral mucosa. “The estimated local SAR (“specific absorption rate”) is less than 10 W/kg in the oral mucosa and 0.1 to 100 mW/kg in brain tissue, with high SAR values only in the conduction area between tongue and mouth piece” [Reite et al., 1994]. The RF electrical field strength in the fluid surrounding neurons is calculated to be in the range of the ELF electrical fields generated by normal brain activity. No information is available on either positive or negative long term health effects, if any, due to treatment with this device. Mechanisms and Dosimetry Although clinical effects of electric currents, PEMF, and sinusoidal electric and magnetic fields are well docu- mented, and although some specific biochemical results have been obtained in vitro or in animal experiments that suggest explanation of bone and soft tissue effects, the mechanism of field-to-cell or field-to-protein transduction is presently not understood. As a consequence, optimum “dose” (what field magnitude for how long) and optimum waveshapes or frequencies for particular clinical applications are unknown, and dosimetry relies largely on trial and error methods. It is known that electrokinetic or streaming potentials rather than piezoelectricity make the principal contribution to electric potentials generated by mechanically stressed bone [Gross and Williams, 1982; Lavine and Grodzinsky, 1987]. Thus potential differences appear when mechanical loading displaces fluid that contains “counterions” which normally reside opposite ions fixed to cell or intercellular matrix surfaces. These potentials are likely to play a role in intercellular signaling and in bone as well as cartilage and soft tissue development. While the original intent of electrical bone therapy was to simply mimic endogenously generated fields, a much wider range of signals was found to be clinically useful. Furthermore it was found later that some weak ionic currents (?5 ′ 10 –2 A/m 2 ) [Levine and Grodzinsky, 1987] appear endogenously without mechanical stress and that extremely weak sinusoidal electric fields can produce profound effects on cells in vitro. For example, both cell number and phosphotase activity in monolayers of osteoblasts (bone forming cells) was significantly affected by a magnetically induced (1.8 mT) 30 Hz electrical field estimated to be 0.6 mV/m [McLeod et al., 1993]. Sinusoidally alternating fields between 50 and 300 Hz, as small as 0.6 mV/m, were shown to affect ATP splitting activity of the membrane enzyme Na, K-ATPase [Blank and Soo, 1992]. A 60-Hz magnetic field of 1.2 NT was reported to inhibit the oncostatic action of the hormone melatonin on estrogen positive human breast cancer cells (“MCF-7”) in vitro [Liburdy et al.]. Calcium metabolism was affected significantly in mitogen-activated lymphocytes by a 4-mT, 16-Hz magnetic field (in the presence of a 23.4-mT dc magnetic field) that induced an average electric field of about (2) 10 –5 V/m [Yost and Liburdy, 1992]. Sinusoidal 15-Hz magnetic fields at the 0.5-mT level, giving an estimated mean electric field in the affected tissue of less than 10 –3 V/m, significantly affected cartilage development in immature rats [Ciombor et al., 1991]. It is likely that the mechanism involved when direct currents are directly applied to injured bone (or other tissue) differs from the transduction sequence which must be acting when low-intensity alternating fields are employed. Even the 5-mA continuous current of the implantable devices (F, G in Table 113.2) when distributed over an (estimated) 5-cm 2 area corresponds to a steady electric field of 1 V/m in bone tissue of 0.01-S/m conductivity. This value is large compared with the average (but not the peak) fields induced by some PEMF devices and very large compared with the average fields induced in tissue by other PEMF devices [Rubin et al., 1989] or the mV/m ELF sinusoidal fields that affect cartilage and bone development [Ciomber et al., 1991; McLeod and Rubin, 1990]. For example, if one assumes a mean radius of 4 cm for a particular human bone fracture, one obtains from Eq. (113.17) the electric field values between 0.18 and 1.74 V/m shown on Table 113.3. When electrodes are implanted, as for the dc signals, chemical reactions at the electrodes may play a role in bone and cartilage formation. For example, the reaction at a stainless steel cathode involves consumption of dissolved oxygen and increase in local pH [Lavine and Grodzinsky, 1987]. ? 2000 by CRC Press LLC If the mechanism of interaction were to involve simple charge transfer by the applied electric field, it would be useful to compare the magnitude of the charge transferred by a single pulse, within a specified volume, with the random charge fluctuation due to thermal excitation during the pulse. An equation due to Einstein [1956] gives the mean square value of the charge fluctuation dq in terms of Boltzmann’s constant k, the absolute temperature T, the conductance G of the current-carrying region, and the observation time t: <dq 2 > = 2GkTt (113.18) It is then easy to find the electric field required to transfer during time t a charge at least equal to dq over the length of a conductance of volume v (v = length ′ cross-sectional area) and uniform conductivity s. One obtains (113.19) Assuming bone tissue with conductivity 10 –2 S/m, a physiological temperature of 37°C, an interaction volume of 10 –14 m 3 (about equal to the volume of a cell with 10-mm radius), and an observation time of 200 ms equal to the duration of the positive pulse of device A, one obtains from Eq. (113.19) a minimum value of 6.6 V/m. Unless v and s can be assumed to be much larger, this would indicate that the values given in Table 113.3 should be below thermal noise. If one considers, instead of charge transfer over some as yet unknown path, the voltage induced by the applied field across the membrane of the idealized spherical cell with 10-mm radius, and compares the energy of the repetitive pulse below 100 Hz—where biological action apparently occurs [McLead and Rubin, 1990]—with the thermal noise voltage given by <V 2 n >= 4kTR (Df ) (113.20) where (Df) is the bandwidth and R the transmembrane resistance, one finds again that the electric field due to the PEMF devices would be at best only marginally above thermal noise. The induced electric fields of the in vitro experiments mentioned above are also clearly below thermal noise. It is possible to obtain somewhat better signal-to-noise ratios if one considers either larger interaction volumes (assuming electrical phenomena involving the intercell volume), elongated cells, or cells connected by gap junctions [Polk, 1992]. It is also important to note that in the extremely inhomogeneous biological system, the actual electric field at a particular point can be considerably larger or smaller than its spatial average. Nevertheless very substantial improvement of signal-to-noise ratios would require signal averaging and limi- tation of bandwidth by resonance phenomena [Weaver and Astumian, 1990; Adair, 1991]. Weak steady and time-varying magnetic fields could also be detected above thermal equilibrium noise by ferrimagnetic single- domain particles that have recently been detected in the human brain [Kirschvink et al., 1992]. In addition, the applicability of Eqs. (113.18) and (113.20) is questionable, because living systems are often far from thermal equilibrium. For example, only mitogen-stimulated—and not quiescent—lymphocytes are affected by weak electric and magnetic fields [Yost and Liburdy, 1992]. Also, some molecules inside cells may at times be involved in systematic and guided rather than random thermal motion [Hoffman, 1992]. Several attempts have been made to construct theoretical models that would explain narrowband resonances in biological systems. Experiments to confirm or reject these hypotheses have thus far given ambiguous results. TABLE 113.3 Electric Field (V/m) Induced by PEMF Signals at Radius of 4 cm into Electrically Uniform Medium; B Perpendicular to Plane in which Radius is Defined Positive Peak Negative Peak Average of Rectified Signal PEMF device A (Table 113.2, Figs. 113.25, 113.26) 0.2 1.74 0.024 PEMF device B (Table 113.2) 0.18 0.015 (1.4) 10 –4 E kT vt 3 ? è ? ? ? ÷ 2 12 s / ? 2000 by CRC Press LLC One theory assumes that ion transfer through cell membranes is affected by cyclotron resonance [Liboff and McLeod, 1988]. It is based on the fact that the cyclotron resonance frequency w c = 2pf c of several physiologically important ions of charge Q and mass m, in the steady magnetic field B 0 of the earth, falls into the ELF range: (113.21) For example, the Ca 2+ ion has a resonance frequency of 16 Hz in a dc field of 21.0 mT. However, it has been pointed out that the collision frequency in the physiological environment would be very much larger than the cyclotron frequency and would therefore wipe out any resonance motion, that the usually hydrated ions would have a total mass larger than m, and that the energy gain caused by an alternating field of frequency w c (as in a cyclotron) would require an orbital radius larger by many orders of magnitude than a typical cell radius [Polk, 1986]. Another theory postulates that the binding of Ca 2+ to the protein calmodulin (ubiquitous in all verte- brates) should be affected by magnetic fields at frequencies w c and w c /n (where n is an integer) [Lednev, 1991; Adair, 1992]. This mechanism involves Zeeman splitting at ELF, due to B 0 , of infrared vibrational modes that are chemically or thermally excited. Some experiments showing a resonant cell response at the frequency given by (113.21) could not be replicated, while others were performed only over a very narrow frequency range. Nevertheless, apparently successful attempts have been made to stimulate bone cell proliferation at these field combinations [Fitzsimmons et al., 1991]. The “Orthologic” device (H in Table 113.2) employs an experimentally determined and apparently clinically useful combination of a 20 mT static field with a 40 mT 76.6 Hz alternating field. This frequency lies near the fifth harmonic (76.2 Hz) of the calcium ion resonance frequency given by Eq. (103.21); however, since the device is always used in the presence of the geomagnetic field of the order of 50 mT, the total DC magnetic field parallel to the 76.6 Hz field can have any value between 0 and 70 mT which would essentially eliminate unique determination of a 76.6 Hz “resonance”. To clarify the sequence of biological events that occurs when PEMF signals are applied to developing bone, the following in vivo experiment was performed [Aaron et al., 1989]. Twenty-five milligrams of demineralized rat bone matrix in powdered form was implanted along the thoracic musculature of immature rats. This powder recruits cells from the surrounding tissue leading to formation of cartilage within 6 to 10 days; thereafter progressive calcification occurs, leading to formation of fibrous particles by days 12 to 14 and formation of a small bone (“ossicle”). These developments were compared in a large number of paired rats, with equal numbers unexposed and exposed (8 h/day) to the PEMF signal illustrated on Figs. 113.32 and 113.33 (A in Table 113.2). Estimates of the mean electric fields in the exposed tissues give values equal to about one-fourth of those listed on line 1 in Table 113.3. Chemical and histological analysis of ossicles harvested from animals, sacrificed on every second day, showed that exposure to this PEMF signal at the applied level significantly increased both rate and quantity of cartilage formation and enhanced maturation of the subsequent bone. The experimenters concluded that field exposure either enhanced recruitment or proliferation of cartilage precursor cells, increased differentiation of precursor to cartilage cells, or accelerated maturation of cartilage cells. Getting even closer to fundamental events at the cellular level, both signals A and B (Table 113.2) were used to expose cultured mouse bone cells and mouse skin fibroblasts, as well as explanted mouse pineal cells in organ culture [Luben, 1993]. In all three cases various chemical procedures were employed to examine “beta- adrenergic receptors.” These are cell surface protein strands that span the cell membrane and emerge from it; they mediate cell response to agents such as epinephrine (= adrenaline) or norepinephrine through so-called G proteins which act essentially as molecular amplifiers at the interior surface of the cell. Other G proteins are involved in the response to growth factors. The arrangement of the exposure coils and culture plates was such as to give mean electric fields equal to about one-tenth of the values shown in Table 113.3. Exposures were of 4 h duration. Specific types of G proteins were stimulated by the A signal, others by the B signal. The total number of binding sites on the cells was not affected, but the affinity of the receptors for specific hormones was changed, suggesting a change in receptor conformation. It is interesting to compare this work, which employed peak values of the order of 10 –2 V/m and time average values not greater than 2 (10 –3 ) V/m, with w c QB m = 0 ? 2000 by CRC Press LLC other in vitro experiments showing effects on enzyme activity at the cell surface by ELF sinusoidal fields between 5 (10 –4 ) V/m and 30 V/m [Blank, 1992]. Related experiments at higher field intensities and the theory of field effects on catalysis [Robertson and Astumian, 1991] also show that electric field action at the exterior of the cell surface can be translated via enzyme-catalyzed chemical reactions to the cell interior. Defining Terms Angiogenesis: Formation of blood vessels. ATPase: An enzyme that converts adenosine triphosphate (ATP) to adenosine diphosphate (ADP); energy released thereby spontaneously in hydrolysis is used to drive an energy requiring reaction such as one producing muscle movement. Capacitively coupled fields or currents: Fields applied to the affected limb by electrodes touching the skin (the current from the electrodes has both displacement and conduction components). Chondrogenesis: Formation of cartilage. Exponential decay time t d : Defined by B = B 0 exp(–t/t d ) Exponential rise time t r : Defined by B = B 0 [1 – exp(–t/t r )] G protein: Guanine nucleotide-binding protein, serves to couple receptors to cell membrane-associated enzymes for purposes of signal transduction. LEET: Low energy emission therapy. Nonunion: Bone fracture that fails to heal within normally expected period with conventional management. Osteoblast: A bone-forming cell. Osteonecrosis: Death of bone within a living vertebrate. PEMF: Pulsed electromagnetic field. PRF: Pulsed radio frequency. Pseudoarthrosis: Formation of a pseudojoint in a broken or not completely formed bone (usually of con- genital origin). Receptor: Large protein molecule that usually protrudes from, and is embedded in, the membrane of a eucaryotic (nucleus-containing) cell. The part of the receptor outside the cell binds only to selected molecules that then cause chemical activity of proteins bound to the end at the cell interior. Activity continues as long as a single molecule (for example, of a hormone, the first “messenger”) is bound to the exterior part, and many molecules of a “second messenger” are released on the cell interior. Streaming potential: Potential difference produced when liquid pressure displaces “counterions” that are normally held by electrostatic forces near ions of the opposite sign embedded in the surface of a stationary material. Related Topic 35.1 Maxwell Equations References R.K. Aaron, D.M. Ciombor, and J. Grant, “Stimulation of experimental endochondral ossification by low-energy pulsing electromagnetic fields,” J. Bone and Mineral Research, vol. 4, no. 2, pp. 227–233, 1989. R.K. Aaron and E. Steinberg, “Electrical stimulation of the femoral head,” Seminars in Arthroplasty, vol. 2, no. 3, pp. 214–224, 1991. K.R. Adair, “Constraints on biological effects of weak extremely low frequency electromagnetic fields,” Physical Review A, pp. 1039–1048, 1991. R.K. Adair, “Criticism of Lednev’s mechanism for the influence of weak magnetic fields on biological systems,” Bioelectromagnetics, vol. 13, pp. 231–235, 1992. C.A.L. Bassett and R.O. Becker, “Generation of electric potentials by bone in response to mechanical stress,” Science, vol. 13, p. 1063, 1963. ? 2000 by CRC Press LLC C.A.L. Bassett, R.J. Pawluk, and R.O. Becker, “Effects of electric currents on bone in vivo,” Nature, vol. 204, p. 652, 1964. C.A.L. Bassett, R.J. Pawluck, and A.A. Pilla, “Augmentation of bone repair by inductively coupled electromag- netic fields,” Science, vol. 184, pp. 575–577, 1974. C.A.L. Bassett, “Biology of fracture repair, nonunion and pseudoarthrosis,” in Compilations of Fracture Man- agement, H.R. Gossling and S.L. Pillsbury (eds.), New York: J. B. Lippincott, 1984, pp. 1–8. R.H.C. Bentall, “Low level pulsed radiofrequency fields and the treatment of soft-tissue injuries,” Bioelectro- chemistry and Bioenergetics, vol. 16, pp. 531–548, 1986. A. Binder, G. Parr, B. Hazelman, and S. Fitton-Jackson, “Pulsed electromagnetic field therapy of persistent rotator cuff tendinitis. A double-blind controlled clinical assessment,” Lancet, pp. 695–698, March 31, 1984. M. Blank, “Na, K-ATPase function in alternating electric fields,” FASEB Journal, vol. 6, pp. 2434–2438, April 1992. M. Blank and L. Soo, “Threshold for inhibiting of Na,K-ATPase by ELF alternating currents”, Bioelectromagnetics, 13, 329–333, 1992. C.T. Brighton, Z.B. Friedenberg, and J. Black, “Evaluation of the use of constant direct current in the treatment of nonunion,” in Electrical Properties of Bone and Cartilage, C.T. Brighton, J. Black, and S.R. Pollack (eds.), New York: Grune and Stratton, 1979, pp. 519–545. D.J. Canaday and R.C. Lee, “Scientific basis for clinical applications of electric fields in soft tissue repair,” in Electromagnetics in Medicine and Biology, C.T. Brighton and S.R. Pollack (eds.), San Francisco: San Francisco Press, 1991, pp. 275–280. D.M. Ciombor, R. Aaron, H. Fisher, C. Polk, D. Gautreau, and D. Cherlin, “Effect of 15 Hz Sinusoidal Magnetic Field on Cartilage Development In Vivo Depends Non-Linearly on Duration of Daily Stimulation,” Project Resumes, The Annual Review of Research on Biological Effects of 50 and 60 Hz Electric and Magnetic Field, U.S. Dept. of Energy, Office of Energy Management, 1991, p. P-8. A. Einstein, in Investigation on the Theory of Brownian Movement, M.R. Furth and A.D. Cowper, (eds.), New York: Dover Publications, 1956 (originally published 1905 in German), p. 33. W. Ellis, “Pulsed subcutaneous electrical stimulation in spinal cord injury,” Bioelectromagnetics, vol. 8, pp. 159–164, 1987. R.J. Fitzsimmons, J. Farley, W.R. Adey, and D.J. Baylink, “Embrionic bone matrix formation is increased after exposure to a low amplitude capacitively coupled electric field in vitro,” Biochimica et Biophysica Acta, vol. 882, pp. 51–56, 1986. R. Fitzsimmons, D. Baylink, F.P. Magee, and A.M. Weinstein, “Electromagnetic field stimulated bone cell proliferation” (Abstract), J. Bone and Mineral Research, vol. 6 (Supplement 1), August 1991. E. Fukada and I. Yasuda, “On the piezoelectric effect in bone,” J. Phys. Soc. Japan, vol. 12, p. 1158, 1957. A.J. Ginsberg, “Ultrashort radiowaves as a therapeutic agent”, Med. Record, 140, 651–653, 1934. H.R. Gossling, R.A. Bernstein, and J. Abbott, “Treatment of ununited tibial fractures, a comparison of surgery and pulsed electromagnetic fields (PEMF),” Orthopaedics, vol. 15, no. 6, pp. 711–719, 1992. D. Gross and W.S. Williams, “Streaming potential and the electromechanical response of physiologically moist bone,” J. Biomechanics, vol. 15, pp. 227–295, 1982. M. Hoffman, “Motor molecules on the move,” Science, vol. 256, pp. 1758–1760, June 26, 1992. M. Ieran, S. Zaffuto, M. Bagnacani, M. Annovi, A. Moratti, and R. Cadossi, “Effect of low frequency pulsing electromagnetic fields on skin ulcers of venous origin in humans: A double-blind study,” J. Orthop. Research, vol. 8, no. 2, pp. 276–282, 1990. H. Ito and C.A.L. Bassett, “Effect of weak, pulsing electromagnetic fields on neural regeneration in the rat,” Clinical Orthopaedics, vol. 181, pp. 283–290, 1983. J.L. Kirschvink, A. Kobayashi-Kirschvink, and B.J. Woodford, “Magnetic biomineralization in the human brain,” Proc. Natl. Acad. Sci. USA, vol. 89, 1992. L.C. Kloth and M.C. Ziskin, “Diathermy and pulsed radio frequency radiation”, chapt. 8 in Thermal Agents in Rehabilitation, 3rd ed., S.L. Michlovitz, Ed. Philadelphia: F.A. Davis Co., 1996. J. Kort, H. Ito, and C.A.L. Bassett, “Effects of pulsing electromagnetic fields on peripheral nerve regeneration,” J. Bone Joint. Surg. Orthop. Trans., vol. 4, p. 238, 1980. ? 2000 by CRC Press LLC W. Kraus, “Magnetfeld Therapie und magnetisch induzierte Elektrostimulation in der Orthop?die,” Orthop?de, vol. 13, pp. 78–92, 1984. L.S. Lavine and A.J. Grodzinsky, “Electrical stimulation of repair of bone,” J. Bone Joint Surgery, vol. 69, no. 4, pp. 626–630, 1987. V.V. Lednev, “Possible mechanism for the influence of weak magnetic fields on biological systems,” Bioelectro- magnetics, vol. 12, pp. 71–75, 1991. A.R. Liboff and B.R. McLeod, “Kinetics of channelized membrane ions in magnetic fields,” Bioelectromagnetics, vol. 9, pp. 39–51, 1988. R.P. Liburdy, T.R. Sloma, R. Sokolic, and P. Yaswen, “ELF magnetic fields, breast cancer, and melatonin: 60 Hz fields block melatonin’s oncostatic action on ER+ breast cancer cell proliferation”, J. Pineal Research, 14, 89–97. R.A. Luben, “Effects of low energy electromagnetic fields on signal transduction by G protein linked receptors,” in Electricity and Magnetism in Biology and Medicine, San Francisco: San Francisco Press, pp. 57–62, 1993. E.A. Luce and G.C. Bryant, “Dose-response of electromagnetic field current in rat skin flap survival,” Trans. Bioelectrical Repair and Growth Society, vol. 6, p. 72, 1986. M.S. Markov, “Electric current and electromagnetic field effects on soft tissues: Implications for skin and wound healing”, Wounds, 15(3), 94–110, 1995. M.S. Markov and A.A. Pilla, “Electromagnetic field stimulation of soft tissues: Pulsed radio frequency treatment of post-operative pain and edema”, Wounds, 7(4), 143–151, 1995. K.J. McLeod and C.T. Rubin, “Frequency specific modulation of bone adaptation by induced electric fields,” J. Theor. Biol., vol. 145, pp. 385–396, 1990. K.J. McLeod, H.J. Donahue, P.E. Levin, M.-A. Fontaine, and C.T. Rubin, “Electric fields modulate bone cell function in a density dependent manner”, J. Bone Mineral Res., 8(8), 977–984, 1993. J. Nerubay, B. Marganit, J.J. Bubis, A. Tadmar, and A. Katznelson, “Stimulation of bone formation by electrical current on spinal fusion,” Spine, vol. 11, p. 167, 1986. C. Polk, “Physical mechanisms by which low-frequency magnetic fields can affect the distribution of counterions on cylindrical biological cell surfaces,” J. Biol. Phys, vol. 14, pp. 3–8, 1986. C. Polk and J.H. Song, “Electric fields induced by low frequency magnetic fields in inhomogeneous biological structures that are surrounded by an electric insulator,” Bioelectromagnetics, vol. 11, pp. 235–249, 1990. C. Polk, “Dosimetric extrapolations across biological systems: dosimetry of ELF magnetic fields,” Bioelectro- magnetics, vol. 13 (S1), 1992. C. Polk, “Introduction”, Fig. 11, p 5 in Biological Effects of Electromagnetic Fields, 2nd ed., C. Polk and E. Postow, Eds., Boca Raton, FL: CRC Press, 1995. S.R. Pollack and C.T. Brighton, “Dosimetry in electrical stimulation,” Trans. Bioelectric Repair and Growth Society, vol. IX, p. 40, 1989. M. Reite, L. Higgs, J.-P. Lebet, A. Barbault, C. Rossel, N. Kuster, U. Dafni, D. Amato, and B. Pasche, “Sleep inducing effect of low energy emission therapy”, Bioelectromagnetics, 15, 67–75, 1994. B. Robertson and R.D. Astumian, “Frequency dependence of catalyzed reactions in a weak oscillating field,” J. Chem. Phys., vol. 94, pp. 7414–7419, 1991. C.T. Rubin, K.J. McLeod, and L.E. Lanyon, “Prevention of osteoporosis by pulsed electromagnetic fields,” J. Bone and Joint Surgery, vol. 71A, no. 3, pp. 411–418, 1989. B.F. Sisken and E. Herbst, “Wound healing: electrical and electromagnetic fields,” Proc. 12th Ann. Intern. Conf. IEEE Engineering in Medicine and Biology Society, vol. 4, no. 5, p. 1533, 1990. B.F. Sisken, M. Kanje, G. Lundborg, and W. Kurtz, “Pulsed electromagnetic fields stimulate nerve regeneration in vitro and in vivo,” Restorative Neurology and Neuroscience, vol. 1, pp. 303–309, 1990. A.M.J. Van Amelsfort, An Analytical Algorithm for Solving Inhomogeneous Electromagnetic Boundary-Value Problems for a Set of Coaxial Circular Cylinders, Eindhoven, The Netherlands: James Clerk Maxwell Foundation, 1990. J.C. Weaver and R.D. Astumian, “The response of living cells to very weak electric fields: the thermal noise limit,” Science, vol. 247, pp. 459–562, January 26, 1990. M.G. Yost and R.P. Liburdy, “Time-varying and static magnetic fields act in combination to alter calcium signal transduction in the lymphocyte,” FEBS, vol. 296, no. 2, pp. 117–122, 1992. ? 2000 by CRC Press LLC Further Information W.R. Adey, “Electromagnetic fields, cell membrane amplification, and cancer promotion,” in Extremely Low Frequency Electromagnetic Fields: The Question of Cancer, B.W. Wilson, R.G. Stevens, and L. E. Anderson (eds.), Columbus, Ohio: Battelle Press, 1990, pp. 211–249. C.A.L. Bassett, “Bioelectromagnetics in service of medicine,” Bioelectromagnetics, 13:7–17, 1992. Bioelectromagnetics, the bi-monthly (formerly quarterly) journal of the Bioelectromagnetics Society. Published by Wiley-Liss, New York, since 1980. J. Black, Electrical Stimulation, New York: Praeger, 1987. M. Blank (ed.), Electricity and Magnetism in Biology and Medicine, San Francisco: San Francisco Press, 1993. C. Branden and J. Tooze, Introduction to Protein Structure, New York: Garland Publishing, 1991. C.T. Brighton, J. Black, and S. Pollack (eds.), Electrical Properties of Bone and Cartilage, New York: Grune and Stratton, 1979. C.T. Brighton and S.R. Pollack (eds.), Electromagnetics in Medicine and Biology, San Francisco: San Francisco Press, 1991. C. Polk and E. Postow, CRC Handbook of Biological Effects of Electromagnetic Fields, (second edition) Boca Raton, Fla.: CRC Press, 1996. Transactions of the Bioelectric Repair and Growth Society. Vols. I through XI. Published annually since 1980 by the Bioelectric Repair and Growth Society, Dresher, Pennsylvania. ? 2000 by CRC Press LLC