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Impedance Measurement of the Electrical Structure of Skeletal Muscle

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Abstract

The sections in this article are:

1 Methods and Techniques
1.1 Microelectrode Techniques
1.2 Analysis of Sinusoidal Data
1.3 Impedance Analysis With Fourier Techniques
1.4 Instrumentation Noise
1.5 Manipulation of Impedance Data
1.6 Theory and Curve Fitting
1.7 Electrical Models of the T System
1.8 Necessity for Morphometry
2 Results of Impedance Measurements
2.1 Impedance Measurements of Normal Frog Fibers
2.2 Other Preparations of Skeletal Muscle
2.3 Impedance Measurements of Muscle Fibers in Various Conditions
2.4 Comparison With Other Results
3 Discussion
3.1 Impedance Measurements of Nonlinearities
3.2 Other Methods
Figure 1. Figure 1.

A: simple circuit with 2 different values of series resistance. Other panels show response of the circuit plotted in different ways. B: transient response to a step function of current (1 μA) applied at time 0. Dashed line, response with 100‐Ω series resistance, is a vertical displacement of response with no series resistance (solid line). Therefore these responses are hard to tell apart and are hard to use to measure the series resistance. C: magnitude of impedance of circuit measured with sinusoidal currents of the frequency shown on the abscissa. The effect of a series resistance is upward displacement of the curve without change in shape. D: plot of imaginary part of the impedance vs. real part of the impedance. Although frequency is not an explicit variable, variation of frequency and the subsequent variation in the real and imaginary parts of the impedance produce the curve. Again the effect of a series resistance is a simple translation of the curve without change in shape. E: phase angle between sinusoidally applied current and voltage. Effects of series resistance are substantial, making it easy to measure series resistance.

Figure 2. Figure 2.

A: lumped approximation to properties of 1 cm2 of surface membrane and associated T system of frog skeletal muscle with 2 different values of series resistance indicated. B: transient response of lumped circuit to a step function of applied current. Tiny difference between the 2 curves makes measurement of series resistance difficult from transient responses. C: magnitude of the response to sinusoidal currents of different frequencies. Effect of series resistance is small, making measurement difficult. D: a plot of imaginary vs. real part of the impedance. Effects of series resistance and of the 1‐μF capacitor are hard to see in this plot. E: phase angle between sinusoidally applied current and voltage. Effects of series resistance are substantial, making it easy to measure series resistance.

Figure 3. Figure 3.

Three sinusoids show effects of digital sampling. Samples taken at 8/s (filled circles) from a sinusoid of 4‐Hz frequency are the same as samples taken from a sinusoid of 0 Hz (i.e., DC). Thus samples taken at this rate cannot distinguish between the 2 sinusoids—the sinusoids are said to be aliases of one another. Similarly samples taken at 5/s (open circles) from a sinusoid of 1‐Hz frequency cannot be distinguished from samples from a sinusoid of 8 Hz; they also are aliases. Aliasing is a direct consequence of sampling. Once digital samples are taken, aliases cannot be distinguished. Precautions can be taken before sampling to minimize problems of aliasing.

Figure 4. Figure 4.

Idealized filter response shown in a log‐log plot. Ordinate is the gain in dB. Frequency at which the gain is −3 dB is shown as Bw; frequency at which the gain is down −A dB is shown as FA = kBw. Filters recommended for use in impedance measurements have more complicated responses, with ripple in the pass band (DC to Bw), nonlinear dependence on frequency, and a finite amount of gain in any range of frequencies. All these features of practical filters are introduced to allow a very steep dependence of gain on frequency, i.e., as small a value of k as possible.

Figure 5. Figure 5.

Optimal relation between sampling rate, bandwidth, and folding frequency. All signals above Bw contain aliased energy. Adjustment of the folding frequency to halfway between Bw and FA allows closest approach of FA to Bw without introduction of aliased energy below Bw. This adjustment maximizes bandwidth and fraction of usable frequency points. Linear plot is used for convenience. Filter is shown with a limiting gain at high frequencies to be more realistic.

Figure 6. Figure 6.

Instrumentation noise in the output signal. Transfer function H(f) might be impedance of a muscle fiber. Input x(t) is applied current. Noise‐free measurements of x(t) are assumed to be available. Pure output y(t) is voltage that would be measured in the absence of instrumentation noise. Noise n(t) is noise introduced by voltage‐recording amplifier and associated electronic devices. Noisy output ŷ(t) is the sum of pure output and noise; ŷ(t) is the best available estimate of membrane voltage. Transfer function should be estimated from estimates Ĝxy(f) and Ĝxx(f) of cross‐power and power spectra, respectively. Those estimates should be the mean of cross power and power recorded from k blocks of data, as indicated. Cross power and power of each block of data are determined from the Fourier transforms X(f) and Y(f) of signals x(t) and y(t), respectively. *Complex conjugate. Other estimates of the transfer function (e.g., made by dividing the power spectra and then averaging) lead to incorrect results, as discussed by Bendat and Piersol 10.



Figure 1.

A: simple circuit with 2 different values of series resistance. Other panels show response of the circuit plotted in different ways. B: transient response to a step function of current (1 μA) applied at time 0. Dashed line, response with 100‐Ω series resistance, is a vertical displacement of response with no series resistance (solid line). Therefore these responses are hard to tell apart and are hard to use to measure the series resistance. C: magnitude of impedance of circuit measured with sinusoidal currents of the frequency shown on the abscissa. The effect of a series resistance is upward displacement of the curve without change in shape. D: plot of imaginary part of the impedance vs. real part of the impedance. Although frequency is not an explicit variable, variation of frequency and the subsequent variation in the real and imaginary parts of the impedance produce the curve. Again the effect of a series resistance is a simple translation of the curve without change in shape. E: phase angle between sinusoidally applied current and voltage. Effects of series resistance are substantial, making it easy to measure series resistance.



Figure 2.

A: lumped approximation to properties of 1 cm2 of surface membrane and associated T system of frog skeletal muscle with 2 different values of series resistance indicated. B: transient response of lumped circuit to a step function of applied current. Tiny difference between the 2 curves makes measurement of series resistance difficult from transient responses. C: magnitude of the response to sinusoidal currents of different frequencies. Effect of series resistance is small, making measurement difficult. D: a plot of imaginary vs. real part of the impedance. Effects of series resistance and of the 1‐μF capacitor are hard to see in this plot. E: phase angle between sinusoidally applied current and voltage. Effects of series resistance are substantial, making it easy to measure series resistance.



Figure 3.

Three sinusoids show effects of digital sampling. Samples taken at 8/s (filled circles) from a sinusoid of 4‐Hz frequency are the same as samples taken from a sinusoid of 0 Hz (i.e., DC). Thus samples taken at this rate cannot distinguish between the 2 sinusoids—the sinusoids are said to be aliases of one another. Similarly samples taken at 5/s (open circles) from a sinusoid of 1‐Hz frequency cannot be distinguished from samples from a sinusoid of 8 Hz; they also are aliases. Aliasing is a direct consequence of sampling. Once digital samples are taken, aliases cannot be distinguished. Precautions can be taken before sampling to minimize problems of aliasing.



Figure 4.

Idealized filter response shown in a log‐log plot. Ordinate is the gain in dB. Frequency at which the gain is −3 dB is shown as Bw; frequency at which the gain is down −A dB is shown as FA = kBw. Filters recommended for use in impedance measurements have more complicated responses, with ripple in the pass band (DC to Bw), nonlinear dependence on frequency, and a finite amount of gain in any range of frequencies. All these features of practical filters are introduced to allow a very steep dependence of gain on frequency, i.e., as small a value of k as possible.



Figure 5.

Optimal relation between sampling rate, bandwidth, and folding frequency. All signals above Bw contain aliased energy. Adjustment of the folding frequency to halfway between Bw and FA allows closest approach of FA to Bw without introduction of aliased energy below Bw. This adjustment maximizes bandwidth and fraction of usable frequency points. Linear plot is used for convenience. Filter is shown with a limiting gain at high frequencies to be more realistic.



Figure 6.

Instrumentation noise in the output signal. Transfer function H(f) might be impedance of a muscle fiber. Input x(t) is applied current. Noise‐free measurements of x(t) are assumed to be available. Pure output y(t) is voltage that would be measured in the absence of instrumentation noise. Noise n(t) is noise introduced by voltage‐recording amplifier and associated electronic devices. Noisy output ŷ(t) is the sum of pure output and noise; ŷ(t) is the best available estimate of membrane voltage. Transfer function should be estimated from estimates Ĝxy(f) and Ĝxx(f) of cross‐power and power spectra, respectively. Those estimates should be the mean of cross power and power recorded from k blocks of data, as indicated. Cross power and power of each block of data are determined from the Fourier transforms X(f) and Y(f) of signals x(t) and y(t), respectively. *Complex conjugate. Other estimates of the transfer function (e.g., made by dividing the power spectra and then averaging) lead to incorrect results, as discussed by Bendat and Piersol 10.

References
 1. Adrian, R. H., and W. Almers. Membrane capacity measurements on frog skeletal muscle in media of low ion content. J. Physiol. London 237: 573–604, 1974.
 2. Adrian, R. H., W. K. Chandler, and A. L. Hodgkin. The kinetics of mechanical activation in frog muscle. J. Physiol. London 204: 207–230, 1969.
 3. Adrian, R. H., L. L. Costantin, and L. D. Peachey. Radial spread of contraction in frog muscle fibres. J. Physiol. London 204: 231–257, 1969.
 4. Adrian, R. H., and L. D. Peachey. Reconstruction of the action potential of frog sartorius muscle. J. Physiol. London 235: 103–131, 1973.
 5. Almers, W. Gating currents and charge movements in excitable membranes. Rev. Physiol. Biochem. Pharmacol. 82: 95–190, 1978.
 6. Asami, K., T. Hanai, and N. Koizumi. Dielectric approach to suspensions of ellipsoidal particles covered with a shell in particular reference to biological cells. Jpn. J. Appl. Physiol. 19: 359–365, 1980.
 7. Barry, P. H., and R. H. Adrian. Slow conductance changes due to potassium depletion in the transverse tubules of frog muscle fibers during hyperpolarizing pulses. J. Mem.br. Biol. 14: 243–292, 1973.
 8. Baylor, S. M., and W. K. Chandler. Optical indications of excitation‐contraction coupling in striated muscle. In: Biophysical Aspects of Cardiac Muscle, edited by M. Morad and M. Tabatabai. New York: Academic, 1978, p. 207–228. (Proc. Cardiac Muscle Symp., May 1977, Shiraz, Iran.)
 9. Baylor, S. M., W. K. Chandler, and M. W. Marshall. Studies in skeletal muscle using optical probes of membrane potential. In: Regulation of Muscle Contraction Coupling, edited by A. D. Grinnell and M. A. B. Brazier. New York: Academic, 1981, p. 97–127.
 10. Bendat, J. S., and A. G. Piersol. Random Data: Analysis and Measurement Procedures. New York: Wiley‐Interscience, 1971.
 11. Bendat, J. S., and A. G. Piersol. Engineering Applications of Correlation and Spectral Analysis. New York: Wiley‐Interscience, 1980.
 12. Bezanilla, F., and P. Horowicz. Fluorescence intensity changes associated with contractile activation in frog muscle stained with Nile Blue‐A. J. Physiol. London 246: 709–735, 1975.
 13. Blinks, J. R. Influence of osmotic strength on cross‐section and volume of isolated single muscle fibres. J. Physiol. London 177: 42–57, 1965.
 14. Brigham, E. O. The Fast Fourier Transform. Englewood Cliffs, NJ: Prentice‐Hall, 1974.
 15. Brillinger, D. R. Time Series: Data Analysis and Theory. New York: Holt, Rinehart & Winston, 1975.
 16. Carter, G. C. Coherence Estimation. New London, CT: Naval Underwater Systems Center, 1981.
 17. Chandler, W. K., R. F. Rakowski, and M. F. Schneider. Effects of glycerol treatment and maintained depolarization on charge movement in skeletal muscle. J. Physiol. London 254: 285–316, 1976.
 18. Chandler, W. K., and M. F. Schneider. Time‐course of potential spread along a skeletal muscle fiber under voltage clamp. J. Gen. Physiol. 67: 165–184, 1976.
 19. Clausen, C., and J. Fernandez. A low‐cost method for rapid transfer function measurements with direct application to biological impedance analysis. Pfleugers Arch. 390: 290–295, 1981.
 20. Cohen, L. B., and B. M. Salzberg. Optical measurement of membrane potential. Rev. Physiol. Biochem. Pharmacol. 83: 36–88, 1978.
 21. Cole, K. S. Membranes, Ions and Impulses: A Chapter of Classical Biophysics. Los Angeles: Univ. of California Press, 1968.
 22. Conti, F., B. Neumcke, W. Nouner, and R. Stampfli. Conductance fluctuations from the inactivation process of sodium channels in myelinated nerve fibres. J. Physiol. London 308: 217–239, 1980.
 23. Cooper, G. R., and C. D. McGillem. Methods of Signal and System Analysis. New York: Holt, Rinehart & Winston, 1967.
 24. Costantin, L. L. Contractile activation in skeletal muscle. Prog. Biophys. Mol. Biol. 29: 197–224, 1975.
 25. Costantin, L. L. Activation in striated muscle. In: Handbook of Physiology. The Nervous System, edited by J. M. Brookhart and V. B. Mountcastle. Bethesda, MD: Am. Physiol. Soc., 1977, sect. 1, vol. I, pt. I, chapt. 7, p. 215–259.
 26. Desoer, C. A., and E. S. Kuh. Basic Circuit Theory. New York: McGraw‐Hill, 1969.
 27. Dormer, K. J. Fundamental Tissue Geometry for Biologists. New York: Cambridge Univ. Press, 1980.
 28. Dulhunty, A. F., and C. Franzini‐Armstrong. The relative contribution of the folds and caveolae to the surface membrane of frog skeletal muscle fibres at different sarcomere lengths. J. Physiol. London 250: 513–539, 1975.
 29. Eisenberg, B. R., and R. S. Eisenberg. Selective disruption of the sarcotubular system in frog sartorius muscle. J. Cell Biol. 39: 451–467, 1968.
 30. Eisenberg, B. R., and R. S. Eisenberg. The T‐SR junction in contracting single skeletal muscle fibers. J. Gen. Physiol. 79: 1–19, 1982.
 31. Eisenberg, B. R., and A. Gilai. Structural changes in single muscle fibers after stimulation at a low frequency. J. Gen. Physiol. 74: 1–16, 1979.
 32. Eisenberg, B. R., R. T. Mathias, and A. Gilai. Intracellular localization of markers within injected or cut frog muscle fibers. Am. J. Physiol. 237 (Cell Physiol. 6): C50–C55, 1979.
 33. Eisenberg, R. S. The equivalent circuit of single crab muscle fibers as determined by impedance measurements with intracellular electrodes. J. Gen. Physiol. 50: 1785–1806, 1967.
 34. Eisenberg, R. S., V. Barcilon, and R. T. Mathias. Electrical properties of spherical syncytia. Biophys. J. 25: 151–180, 1979.
 35. Eisenberg, R. S., and P. W. Gage. Ionic conductances of the surface and transverse tubular membranes of frog sartorius fibers. J. Gen. Physiol. 53: 279–297, 1969.
 36. Eisenberg, R. S., and E. A. Johnson. Three dimensional electrical field problems in physiology. Prog. Biophys. Mol. Biol. 20: 1–65, 1970.
 37. Eisenberg, R. S., and R. T. Mathias. Structural analysis of electrical properties. Crit. Rev. Bioeng. 4: 203–232, 1980.
 38. Eisenberg, R. S., R. T. Mathias, and J. L. Rae. Measurement, modelling and analysis of the linear electrical properties of cells. Ann. NY Acad. Sci. 303: 342–354, 1977.
 39. Endo, M. Entry of fluorescent dyes into the sarcotubular system of the frog muscle. J. Physiol. London 185: 224–238, 1966.
 40. Falk, G., and P. Fatt. Linear electrical properties of striated muscle fibres observed with intracellular electrodes, Proc. R. Soc. London Ser. B 160: 69–123, 1964.
 41. Fatt, P., and B. Katz. An analysis of the end‐plate potential recorded with an intracellular electrode. J. Physiol. London 115: 320–370, 1951.
 42. Fishman, H. M., D. Poussart, and L. E. Moore. Complex admittance of Na+ conduction in squid axon. J. Membr. Biol. 50: 43–63, 1979.
 43. Franzini‐Armstrong, C. Studies of the triad. II. Penetration of tracers into the junctional gap. J. Cell Biol. 49: 196–203, 1971.
 44. Franzini‐Armstrong, C. Structure of sarcoplasmic reticulum. Federation Proc. 39: 2403–2409, 1980.
 45. Franzini‐Armstrong, C., J. E. Heuser, T. S. Reese, A. P. Somlyo, and A. V. Somlyo. T‐tubule swelling in hypertonic solutions. A freeze substitution study. J. Physiol. London 283: 133–140, 1978.
 46. Franzini‐Armstrong, C., R. A. Venosa, and P. Horowicz. Morphology and accessibility of the “transverse” tubular system in frog sartorius muscle after glycerol treatment. J. Membr. Biol. 14: 197–212, 1973.
 47. French, A. S., and E. G. Butz. Measuring the Wiener kernels of a nonlinear system using the fast Fourier transform algorithm. Int. J. Control 17: 529–539, 1973.
 48. Freygang, W. H., Jr., S. I. Rapoport, and L. D. Peachey. Some relations between changes in the linear electrical properties of striated muscle fibers and changes in ultrastructure. J. Gen. Physiol. 50: 2437–2458, 1967.
 49. Gage, P. W., and R. S. Eisenberg. Action potentials, after potentials, and excitation‐contraction coupling in frog sartorius fibers without transverse tubules. J. Gen. Physiol. 53: 298–310, 1969.
 50. Gilai, A. Electromechanical coupling in tubular muscle fibers. II. Resistance and capacitance of one transverse tubule. J. Gen. Physiol. 67: 343–367, 1976.
 51. Gonzalez‐Serratos, H. Inward spread of activation in vertebrate muscle fibres. J. Physiol. London 212: 777–799, 1971.
 52. Gould, S. J. Hen's teeth and horse's toes. Nat. Hist. 89: 24–28, 1980.
 53. Hanai, T., K. Asami, and N. Koizumi. Dielectric theory of concentrated suspensions of shell spheres in particular reference to the analysis of biological cell suspensions. Bull. Inst. Chem. Res. Kyoto Univ. 57: 297–305, 1979.
 54. Hannan, E. J. Multiple Time Series. New York: Wiley, 1970.
 55. Hille, B., and D. T. Campbell. An improved Vaseline gap voltage clamp for skeletal muscle fibers. J. Gen. Physiol. 67: 265–293, 1976.
 56. Hodgkin, A. L., and A. F. Huxley. A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. London 117: 500–544, 1952.
 57. Hodgkin, A. L., and S. Nakajima. The effect of diameter on the electrical constants of frog skeletal muscle fibres. J. Physiol. London 221: 105–120, 1972.
 58. Hodgkin, A. L., and S. Nakajima. Analysis of the membrane in frog muscle. J. Physiol. London 221: 121–136, 1972.
 59. Huxley, A. F., and R. E. Taylor. Local activation of striated muscle fibres. J. Physiol. London 144: 426–441, 1958.
 60. Jack, J. J. B., D. Noble, and R. W. Tsien. Electric Current Flow in Excitable Cells. Oxford, UK: Oxford Univ. Press, 1975.
 61. Kay, S. M., and S. L. Marple. Spectrum analysis: a modern perspective. Proc. IEEE 69: 1380–1418, 1981.
 62. Kirsch, G. E., R. A. Nichols, and S. Nakajima. Delayed rectification in the transverse tubules. J. Gen. Physiol. 70: 1–21, 1977.
 63. Koopmans, L. H. The Spectral Analysis of Time Series. New York: Academic, 1974.
 64. Lam, H. Y. Analog and Digital Filters: Design and Realization. Englewood Cliffs, NJ: Prentice‐Hall, 1979.
 65. Magrab, E. B., and D. S. Blomquist. The Measurement of Time‐Varying Phenomena. New York: Wiley 1971.
 66. Marmarelis, P. Z., and V. Z. Marmarelis. Analysis of Physiological Systems: The White‐Noise Approach. New York: Plenum, 1978.
 67. Marmarelis, V. Z. A single‐record estimator for correlation functions of nonstationary random processes. Proc. IEEE 69: 841–842, 1981.
 68. Masry, E., and M. C. Lui. A consistent estimate of the spectrum by random sampling of the time series. SIAM J. Appl. Math. 28: 793–810, 1975.
 69. Mathias, R. T., L. Ebihara, M. Lieberman, and E. A. Johnson. Linear electrical properties of passive and active currents in spherical heart cell clusters. Biophys. J. 36: 221–242, 1981.
 70. Mathias, R. T., R. S. Eisenberg, and R. Valdiosera. Electrical properties of frog skeletal muscle fibers interpreted with a mesh model of the tubular system. Biophys. J. 17: 57–93, 1977.
 71. Mathias, R. T., R. A. Levis, and R. S. Eisenberg. Electrical models of excitation contraction coupling and charge movement in skeletal muscle. J. Gen. Physiol. 76: 1–31, 1980.
 72. Mathias, R. T., J. L. Rae, and R. S. Eisenberg. Electrical properties of structural components of the crystalline lens. Biophys. J. 25: 181–201, 1979.
 73. Mathias, R. T., J. L. Rae, and R. S. Eisenberg. The lens as a non‐uniform syncytium. Biophys. J. 34: 61–83, 1981.
 74. Mobley, B. A., and B. R. Eisenberg. Sizes of components in frog skeletal muscle measured by methods of stereology. J. Gen. Physiol. 66: 31–45, 1975.
 75. Mobley, B. A., J. Leung, and R. S. Eisenberg. Longitudinal impedance of skinned frog muscle fibers. J. Gen. Physiol. 63: 625–637, 1974.
 76. Mobley, B. A., J. Leung, and R. S. Eisenberg. Longitudinal impedance of single frog muscle fibers. J. Gen. Physiol. 65: 97–113, 1975.
 77. Nakajima, S., and J. Bastian. Membrane properties of the transverse tubular system of amphibian skeletal muscle. In: Electrobiology of Nerve, Synapse, and Muscle, edited by J. P. Reuben, D. P. Purpura, M. V. L. Bennett, and E. R. Kandel. New York: Raven, 1976, p. 243–268.
 78. Nakajima, S., Y. Nakajima, and J. Bastian. Effects of sudden changes in external sodium concentration on twitch tension in isolated muscle fibers. J. Gen. Physiol. 65: 459–482, 1975.
 79. Nakajima, S., Y. Nakajima, and L. D. Peachey. Speed of repolarization in glycerol treated frog muscle fibres. J. Physiol. London 234: 465–480, 1973.
 80. Nastuk, W. L., and A. L. Hodgkin. The electrical activity of single muscle fibers. J. Cell. Comp. Physiol. 35: 39–73, 1950.
 81. Nicolaysen, K. The spread of the action potential through the t‐system in hagfish twitch muscle fibers. Acta Physiol. Scand. 96: 29–49, 1976.
 82. Oppenheim, A. V., and R. W. Schafer. Digital Signal Processing. Englewood Cliffs, NJ: Prentice‐Hall, 1975.
 83. Palm, G., and T. Poggio. The Volterra representation and the Wiener expansion: validity and pitfalls. SIAM J. Appl. Math. 33: 195–216, 1977.
 84. Palm, G., and T. Poggio. Wiener‐like system identification in physiology. J. Math Biol. 4: 375–381, 1977.
 85. Papoulis, A. Probability, Random Variables and Stochastic Processes. New York: McGraw‐Hill, 1965.
 86. Papoulis, A. Signal Analysis. New York: McGraw‐Hill, 1977.
 87. Patkay, J. D., F. Chu, and H. A. Wiggers. Front‐end design for digital signal analysis. Hewlett‐Packard J. 29: 9–13, 1977.
 88. Peachey, L. D., and R. H. Adrian. Electrical properties of the transverse tubular system. In: Structure and Function of Muscle (2nd ed.), edited by G. Bourne. New York: Academic, 1972, vol. I, p. 1–30.
 89. Peskoff, A. Electrical potential in cylindrical syncytia and muscle fibers. Bull. Math. Biophys. 41: 183–193, 1979.
 90. Peskoff, A., and R. S. Eisenberg. Interpretation of some microelectrode measurements of electrical properties of cells. Annu. Rev. Biophys. Bioeng. 2: 65–79, 1973.
 91. Portnoff, M. Time‐frequency representation of digital signals and systems based on short‐time Fourier analysis. IEEE Trans. Acoust. Speech Signal Process. 28: 55–69, 1980.
 92. Poussart, D., L. E. Moore, and H. M. Fishman. Ion movements and kinetics in squid axon. I. Complex admittance. Ann. NY Acad. Sci. 303: 355–379, 1977.
 93. Rabiner, L. R., and R. W. Schafer. Digital Processing of Speech Signals. Englewood Cliffs, NJ: Prentice‐Hall, 1978.
 94. Sachs, F., and P. Specht. Fast microelectrode headstage for voltage clamp. Med. Biol. Eng. Comput. 19: 316–320, 1981.
 95. Schanne, O. F., and E. Ruiz‐P.‐Ceretti. Impedance Measurements in Biological Cells. New York: Wiley‐Interscience, 1978.
 96. Schetzen, M. The Volterra and Wiener Theories of Nonlinear Systems. New York: Wiley‐Interscience, 1980.
 97. Schetzen, M. Nonlinear system modeling based on the Wiener theory. Proc. IEEE 69: 1557–1573, 1981.
 98. Schneider, M. F. Linear electrical properties of the transverse tubules and surface membrane of skeletal muscle fibers. J. Gen. Physiol. 56: 640–671, 1970.
 99. Sigworth, F. J. Covariance of nonstationary sodium current fluctuations at the node of Ranvier. Biophys. J. 34: 111–133, 1981.
 100. Somlyo, A. V. Bridging structures spanning the gap at the triad of skeletal muscle. J. Cell Biol. 80: 743–750, 1979.
 101. Somlyo, A. V., H. Shuman, and A. P. Somlyo. Elemental distributions in striated muscle and the effects of hypertonicity. J. Cell Biol. 74: 828–857, 1977.
 102. Suzuki, K., V. Rohlicek, and E. Fromter. A quasi‐totally shielded, low capacitance glass microelectrode with suitable amplifiers for high frequency intracellular potential and impedance measurements. Pfluegers Arch. 378: 141–148, 1978.
 103. Takashima, S., and H. P. Schwan. Passive electrical properties of squid axon membrane. J. Membr. Biol. 17: 51–68, 1974.
 104. Valdiosera, R., C. Clausen, and R. S. Eisenberg. Measurement of the impedance of frog skeletal muscle fibers. Biophys. J. 14: 295–315, 1974.
 105. Valdiosera, R., C. Clausen, and R. S. Eisenberg. Circuit models of the passive electrical properties of frog skeletal muscle fibers. J. Gen. Physiol. 63: 432–459, 1974.
 106. Valdiosera, R., C. Clausen, and R. S. Eisenberg. Impedance of frog skeletal muscle fibers in various solutions. J. Gen. Physiol. 63: 460–491, 1974.
 107. Vergara, J., F. Bezanilla, and B. M. Salzberg. Nile blue fluorescence signals from cut single muscle fibers under voltage or current clamp conditions. J. Gen. Physiol. 72: 775–800, 1978.
 108. Weiner, D. D., and J. F. Spina. Sinusoidal Analysis and Modeling of Weakly Nonlinear Circuits: With Application to Nonlinear Interference Effects. New York: Van Nostrand Reinhold, 1980.
 109. Zampighi, G., J. Vbrgara, and F. Ramon. On the connection between the transverse tubules and the plasma membrane in frog semitendinosus skeletal muscle. Are caveolae the mouths of the transverse tubule system? J. Cell Biol. 64: 734–740, 1975.

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Robert S. Eisenberg. Impedance Measurement of the Electrical Structure of Skeletal Muscle. Compr Physiol 2011, Supplement 27: Handbook of Physiology, Skeletal Muscle: 301-323. First published in print 1983. doi: 10.1002/cphy.cp100111