Rigorous green's function formulation for transmembrane potential induced along a 3-D infinite cylindrical cell

IEEE Transactions on Biomedical Engineering

Volumn 49, Issue 12 I, 2002, Pages 1491-1503

  Livshitz, Leonid M ^a   Einziger, Pinchas D ^a   Mizrahi, Joseph ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

Functional electrical stimulation; Green's function; Infinite cylinder; Membrane boundary conditions; Transmembrane potential (TMP)

Indexed keywords

CELLS; ELECTROMAGNETIC FIELD EFFECTS; FIBERS; GREEN'S FUNCTION;

FUNCTIONAL ELECTRICAL STIMULATION;

BIOMEDICAL ENGINEERING;

ANALYTICAL PARAMETERS; ARTICLE; ELECTROMAGNETIC FIELD; ELECTROSTIMULATION; EXCITATION; LITERATURE; MATHEMATICS; MEMBRANE POTENTIAL; OSCILLATION; PREDICTION;

AXONS; COMPUTER SIMULATION; ELECTRIC CONDUCTIVITY; ELECTRIC STIMULATION; ELECTROMAGNETIC FIELDS; EXTRACELLULAR SPACE; MEMBRANE POTENTIALS; MICROELECTRODES; MODELS, NEUROLOGICAL; NERVE FIBERS, UNMYELINATED; NEURAL CONDUCTION; SENSITIVITY AND SPECIFICITY;

EID: 0346666972     PISSN: 00189294     EISSN: None     Source Type: Journal    
DOI: 10.1109/TBME.2002.805479     Document Type: Article

References (21)

1. J. Bernhardt and H. Pauly, "On the generation of potential differences across the membranes of ellipsoidal cells in an alternating current," Biophysik, vol. 10, pp. 89-98, 1973.
2. R. S. Eisenberg and E. A. Johnson, "Three-dimensional electrical field problem in physiology," Prog. Biophys. Mol. Biol., vol. 20, pp. 1-65, 1970.
3. A. Peskoff, "Green's function for Laplace equation in an infinite cylindrical cell," J. Math. Phys., vol. 15, no. 12, pp. 2112-2120, 1974.
4. O. Sten-Knudsen, "Is muscle contraction initiated by internal current flow," J. Physiol., vol. 151,. pp. 363-384, 1960.
5. J. J. B. Jack, D. Noble, and R. W. Tsien, Electric Current Flow in Excitable Cells. Oxford, U.K.: Claredon, 1988, pp. 99-129.
6. D. R. McNeal, "Analysis of a model for excitation of myelinated nerve," IEEE Trans. Biomed. Eng., vol. BME-23, pp. 329-337, Apr. 1976.
7. F. 71 R Rattay, Electrical Nerve Stimulation. New York: Springer-Verlag, 1990.
8. E.N. Warman, W. M. Grill, and D. M. Durand, "Modeling the effects of electric fields on nerve fibers: Determination of excitation thresholds," IEEE Trans. Biomed. Eng., vol. 39, pp. 1244-1254, Dec. 1992.
9. C. M. Zierhofer, "Analysis of a linear model for electrical stimulation of axons-Critical remarks on the 'activating function concept'," IEEE Trans. Biomed. Eng., vol. 48, pp. 173-184, Feb. 2001.
10. J. P. Reilly, Applied Bioelectricity. New York: Springer-Verlag, 1998.
11. R. H. Adrian, "Electrical properties of striated muscle," in Handbook of Physiology, L. Peachy, Ed. Bethesda, MD: Amer. Phys. Soc., 1983, ch. 10, Skeletal Muscle, sec. X, pp. 275-300.
12. R. W. P. King and T. T. Wu, "Electric field induced in cells in the human body when this is exposed to low-frequency electric field," Phys. Rev. E, vol. 58, no. 2, pp. 2363-2369, 1998.
13. A. M. Weinberg, "Green's function in biological potential problem," Bull. Math. Biophys., vol. 4, pp. 107-115, 1942.
14. J. D. Jackson, Classical Electodynamics, 3rd Ed. New York: Wiley, 1999.
15. I. S. Gradstein and I. M. Ryzhik, Table of Integrals, Series, and Products. New York: Academic, 1965.
16. R. Plonsey and R. E. Barr, "Electric field stimulation of excitable tissue," IEEE Trans. Biomed. Eng., vol. 42, pp. 329-336, Apr. 1995.
17. H. S. Carslaw, Mathematical Theory of the Conduction of Heat in Solids. New York: Dover, 1945.
18. L. M. Livshitz, P. D. Einziger, and J. Mizrahi, "Current distribution in skeletal muscle activated by FES: Image-series formulation and isometric recruitment curve," Ann. Biomed. Eng., vol. 28, pp. 1218-28, 2000.
19. L. M. Livshitz, J. Mizrahi, and P. D. Einziger, "Interaction of array of finite electrodes with layered biological tissue: Effect of electrode size and configuration," IEEE Trans. Neural Syst. Rehab. Eng., vol. 9, pp. 355-361, Aug. 2001.
20. J. Ruohonen, M. Panizza, J. Nilsson, P. Ravazzani, F. Grandori, and G. Tognola, "Transverse-field activation mechanism in magnetic stimulation of peripheral nerves," Electroenceph. Clin. Neurophys., vol. 101, pp. 167-174, 1996.
21. V. Schnabel and J. J. Struijk, "Calculation of electric fields in a multiple cylindrical volume conductor induced by magnetic coils," IEEE Trans. Biomed. Eng., vol. 48, pp. 78-86, Jan. 2001.