《电子工程师手册》学习资料（英文版）ch113 Bioelectricity.pdf

113 Bioelectricity 113. 1 Neuroelectric Principles Electrical Model for Nerve Excitation 113.2 Bioelectric Events J. Patrick Reilly Origin of Bioelectricity. Law of Stimulation. Recording Action Potentials. The Electrocardiogram(ECG). Electromyograph (EMG). Electroencephalography (EE magnetic(Eddy- L. A. Geddes Current) Stimulation 113.3 Application of Electric and Magnetic Fields in Bone and Soft Tissue Repa C. Polk History. Devices for Bone and Cartilage Repair. Soft Tissue pair and Nerve Regeneration. Mechanisms and Dosimetry 113.1 Neuroelectric Principles Patrick reilly Natural bioelectric processes are responsible for nerve and muscle function. These processes can be affected by xternally applied electric currents that are intentionally introduced through medical devices or unintentional 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 ntil 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. C 2000 by CRC Press LLC

© 2000 by CRC Press LLC 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 (EddyCurrent) 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 stimulation. 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 Vm 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 = 61 log [ ] [ ]

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 H M/cm for a nerve axon would be (Nat 50, (Na*.= 460, [K'li=400, and [K*.= 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 nembrane 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 theOutside Nobel prize work of Hodgkin and Huxley [1952]. This Membrane work was later extended to the myelinated nerve mem- c 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 EK ment. The potential sources shown in the diagram ar the Nernst potentials for the particular ions as given by Eq (113.2). The capacitance term Cm is formed by the dielectric membrane separating the conductive media on FIGURE 113.2 Hodgkin-huxley membrane model either side. The conductances &Na and &x apply to Na* and K+ channels; the conductance gt is a general"leakage"channel that is not specific to any particular ion. The &Na and gx 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, &Na < &k, and the membrane potential moves toward the Nernst potential for Nat. 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 tances vary again, causing the membrane to revert back to its resting potentia the ionic channel conduc- the membrane potential has been depolarized by roughly 15 mV. After excitatie 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 FIGURE 113.3 Spread of the depolarization wave Myelinated fibers have much lower thresholds of excitation front along an axon. Depolarization occurring in than unmyelinated fibers. Accordingly, the myelinated fiber region A results in charge transfer from the adjacent is an appropriate choice for electrical stimulation studies. regions e 2000 by CRC Press LLC

© 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/cm3 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 (ª100 mV), and its small thickness (ª10 nm), the electric field across the membrane is enormous (ª10 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 membrane 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 element. The potential sources shown in the diagram are the Nernst potentials for the particular ions as given by Eq. (113.2). The capacitance term Cm is formed by the dielectric membrane separating the conductive media on either side. The conductances gNa and gK apply to Na+ and K+ channels; the conductance gL is a general “leakage” channel that is not specific to any particular ion. The gNa and gK 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, gNa << gK, 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 conductances 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 113.2 Hodgkin-Huxley membrane model. FIGURE 113.3 Spread 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 Cm and an ionic conductance term. The nodes are interconnected through the internal axon medium by conductances Ga. The current flowing in the biological medium creates voltage disturbances Ve,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 Cm is the membrane capacitance at the node, Vn is the transmembrane potential, Ii,n is the total ionic current, and Vi,n is the internal voltage. In this expression, Vn is taken relative to the resting potential, such that Vn = 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), Ii,n = pdW(JNa + JK + JL + JP) (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) Cm = cmpdW (113.6) where d is the axon diameter at the node, ri is the resistivity of the internal axon medium, L is the internodal distance, W is the nodal gap width, and cm is the membrane capacitance per unit area. The relationship between the axon diameter d and the fiber diameter D (including myelin) is d ª 0.7D. The voltage Vn across the membrane is Vn = Vi,n – Ve,n (113.7) where Vi,n and Ve,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 113.4 Equivalent circuit model for electrical excitation of myelinated nerve fiber. The membrane conductance Gm is described by nonlinear ionic conductances, similar to the representation in Fig. 113.2. C dV dt m I G V V V n + = i n, a i n, – i n, + i n, + ( – ) 1 1 2 G d L a i = p r 2 4