Hybrid finite element method for describing the electrical response of biological cells to applied fields

IEEE Transactions on Biomedical Engineering

Volumn 54, Issue 4, 2007, Pages 611-620

  Ying, Wenjun ^a   Henriquez, Craig S ^b  

^a USA   (United States)

^b DUKE UNIVERSITY   (United States)

Author keywords

Field stimulation; Hybrid finite element method; Interface problem; Laplace equation; Transmembrane potential

Indexed keywords

ALGORITHMS; CELL MEMBRANES; DIFFERENTIAL EQUATIONS; ELECTRIC FIELD EFFECTS; FINITE ELEMENT METHOD; INITIAL VALUE PROBLEMS; LAPLACE EQUATION; RUNGE KUTTA METHODS;

ELECTRIC FLUX; FIELD STIMULATION; INTERFACE PROBLEMS; MEMBRANE CURRENTS; TRANSMEMBRANE POTENTIALS;

CELL PROLIFERATION;

ACTION POTENTIAL; ALGORITHM; ARTICLE; CELL MEMBRANE; CHANNEL GATING; DYNAMICS; ELECTRIC ACTIVITY; FINITE ELEMENT ANALYSIS; GEOMETRY; INTEGRATION; MATHEMATICAL MODEL; MEMBRANE CURRENT; STIMULUS RESPONSE;

ANIMALS; CELL MEMBRANE; CELL PHYSIOLOGY; COMPUTER SIMULATION; DOSE-RESPONSE RELATIONSHIP, RADIATION; ELECTRIC STIMULATION; ELECTROMAGNETIC FIELDS; FINITE ELEMENT ANALYSIS; HUMANS; MEMBRANE POTENTIALS; MODELS, BIOLOGICAL; RADIATION DOSAGE;

EID: 33947525299     PISSN: 00189294     EISSN: None     Source Type: Journal    
DOI: 10.1109/TBME.2006.889172     Document Type: Article

References (48)

1. L. M. Mir, M. F. Bureau, J. Gehl, R. Rangara, D. Rouy, J. M. Caillaud, P. Delaere, D. Branellec, B. Schwartz, and D. Scherman, "High-efficiency gene transfer into skeletal muscle mediated by electric pulses," Proc. Nat. Acad. Sci. USA, vol. 96, no. 8, pp. 4262-4267, 1999.
2. E. Neumann, S. Kakorin, and K. Toensing, "Fundamentals of electroporative delivery of drugs and genes," Bioelectrochem. Bioenerg., vol. 48, no. 1, pp. 3-16, 1999.
3. G. Sersa, T. Cufer,M. Cemazar,M. Rebersek, and R. Zvonimir, "Electrochemotherapy with bleomycin in the treatment of hypernephroma metastasis: case repeat and literature review," Tumori, vol. 86, no. 2, pp. 163-165, 2000.
4. T. Ashihara, T. Yao, T. Namba, M. Ito, T. Ikeda, A. Kawase, S. Toda, T. Suzuki, M. Inagaki, M. Sugimachi, M. Kinoshita, and K. Nakazawa, "Electroporation in a model of cardiac defibrillation," J. Cardiovasc. Electrophysiol, vol. 12, no. 12, pp. 1393-1403, 2001.
5. H. Fricke, "The electric permittivity of a dilute suspension of membrane-covered, ellipsoids," J. Appl. Phys., vol. 24, pp. 644-646, 1953.
6. H. P. Schwan, "Electrical properties of tissue and cell suspensions," Adv. Biol. Med. Phys., vol. 5, pp. 147-209, 1957.
7. T. Kotnik and D. Miklavcic, "Analytical description of transmembrane voltage induced by electric fields on spheroidal cells," Biophys. J., vol. 79, no. 2, pp. 670-679, 2000.
8. J. Gimsa and D. Wachner, "Analytical description of the transmembrane voltage induced on arbitrarily oriented ellipsoidal and cylindrical cells," Biophys. J., vol. 81, no. 4, pp. 1888-1896, 2001.
9. B. Valic, M. Golzio, M. Pavlin, A. Schatz, C. Faurie, B. Gabriel, J. Teissie, M. P. Rols, and D. Miklavcic, "Effect of electric field induced transmembrane potential on spheroidal cells: theory and experiment," Eur. Biophys. J., vol. 32, no. 6, pp. 519-528, 2003.
10. D. C. Lee and W. M. Grill, "Polarization of a spherical cell in a nonuniform extracellular electric field," Ann. Biomed. Eng., vol. 33, no. 5, pp. 603-615, 2005.
11. R. Susil, D. Semrov, and D. Miklavcic, "Electric field induced transmembrane potential depends on cell density and organization," Electro. Magnetobiol., vol. 17, no. 3, pp. 391-399, 1998.
12. M. Pavlin, N. Pavselj, and D. Miklavcic, "Dependence of induced transmembrane potential on cell density, arrangement and cell position inside a cell system," IEEE Trans. Biomed. Eng., vol. 49, no. 6, pp. 605-612, Jun. 2002.
13. D. A. Stewart, T. R. Gowrishankar, K. C. Smith, and J. C. Weaver, "Cylindrical cell membranes in uniform applied electric fields: validation of a transport lattice method," IEEE Trans. Biomed. Eng., vol. 52, no. 10, pp. 1643-1653, Oct. 2005.
14. C. S. Peskin, "Numerical analysis of blood flow in the heart," J. Comput. Phys., vol. 25, pp. 220-252, 1977.
15. R. J. LeVeque and Z. Li, "The immersed interface method for elliptic equations with discontinuous coefficients and singular sources," SIAM J. Numer. Anal., vol. 31, no. 4, pp. 1019-1044, 1994.
16. D. Semrov and D. Miklavcic, "Numerical modeling for in vivo electroporation," in Electrochemotherapy, Electrogenetherapy and Transdermal Drug Delivery: Electrically Mediated Delivery of Molecules to Cells, M. J. Jaroszeski, R. Heller, and R. Gilbert, Eds. Totowa, NJ: Humana, 1999, pp. 63-81.
17. R. C. Penland, D. M. Harrild, and C. S. Henriquez, "Modeling impulse propagation and extracellular potential distributions in anisotropic cardiac tissue using a finite volume element discretization," Comput. Visual. Sci., vol. 4, pp. 215-226, 2002.
18. S. Zozor, O. Blanc, V. Jacquemet, N. Virag, J. M. Vesin, E. Pruvot, L. Kappenberger, and C. S. Henriquez, "A numerical scheme for modeling wavefront propagation on a monolayer of arbitrary geometry," IEEE Trans. Biomed. Eng., vol. 50, no. 44, pp. 412-420, Apr. 2003.
19. L. J. Leon and F. A. Roberge, "A new cable model formulation based on Green's theorem," Ann. Biomed. Eng., vol. 18, no. 1, pp. 1-17, 1990.
20. _, "A model study of extracellular stimulation of cardiac cells," IEEE Trans. Biomed, Eng., vol. 40, , no. 12, pp. 1307-1319, Dec. 1993.
21. K. R. Foster and A. E. Sowers, "Dielectrophoretic forces and potentials induced on pairs of cells in an electric field," Biophys. J., vol. 69, no. 3, pp. 777-784, 1995.
22. E. C. Fear and M. A. Stuchly, "Modeling assemblies of biological cells exposed to electric fields," IEEE Trans. Biomed. Eng., vol. 45, no. 10, pp. 1259-1271, Oct. 1998.
23. _, "Anovel equivalent circuit model for gap-connected cells," Phys. Med. Biol., vol. 43, no. 6, pp. 1439-1448, 1998.
24. A. Ramos, A. Raizer, and J. L. Marques, "A new computational approach for electrical analysis of biological tissues," Bioelectrochemistry, vol. 59, no. 1-2, pp. 73-84, 2003.
25. T. R. Gowrishankar and J. C. Weaver, "An approach to electrical modeling of single and multiple cells," Proc. Nat. Acad. Sci. USA, vol. 100, no. 6, pp. 3203-3208, 2003.
26. D. A. Stewart, T. R. Gowrishankar, and J. C.Weaver, "Transport lattice approach to describing cell electroporation: use of a local asymptotic model," IEEE Trans. Plasma Sci., vol. 32, no. 4, pp. 1696-1708, Aug. 2004.
27. _, "Three dimensional transport lattice model for describing action potentials in axons stimulated by external electrodes," Bioelectrochemistry, 2006, (Jan 26, Epub ahead of print).
28. R. A. Adams, Ed., Sobolev Spaces. New York: Academic, 1975.
29. I. Babuska, "The finite element method with lagrangian multipliers," Numer. Math., vol. 20, pp. 179-192, 1973.
30. F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods. New York: Springer, 1991.
31. J. Huang and J. Zhou, "A mortar element method for elliptic problems with discontinuous coefficients," IMA J. Numer. Anal., vol. 22, pp. 549-576, 2002.
32. B. I.Wohlmuth, Discretization Methods and Iterative Solvers Based on Domain Decomposition, ser. Lecture Notes in Computational Science and Engineering. Berlin, Germany: Springer-Verlag, 2001, vol. 17.
33. B. P. Lamichhane and B. I. Wohlmuth, "Mortar finite elements for interface problems," Computing, vol. 72, pp. 333-348, 2004.
34. M. Benzi, G. H. Golub, and J. Liesen, "Numerical solution of saddle point problems," Acta Numerica, pp. 1-137, 2005.
35. W. Krassowska and J. C. Neu, "Response of a single cell to an external electric field," Biophys. J., vol. 66, pp. 1768-1776, 1994.
36. 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.
37. S. Weidmann, "Electrical constants of trabecular muscle from mammalian heart," J. Physiol., vol. 210, no. 4, pp. 1041-1054, 1970.
38. J. Clark and R. Plonsey, "A mathematical evaluation of the core conductor model," Biophys. J., vol. 6, no. 1, pp. 95-112, 1966.
39. R. C. Barr, R. Plonsey, and C. R. Johnson, "Membrane current from transmembrane potentials in complex core-conductor models," IEEE Trans. Biomed. Eng., vol. 50, no. 4, pp. 405-411, Apr. 2003.
40. R. Plonsey and R. C. Barr, Bioeleciricity: a Quantitative Approach. New York: Kluwer Academic/Plenum, 2000.
41. E. Neumann, A. E. Sowers, and C. A, Jordan, Electroporation and Electrofusion in Cell Biology. Norwell, MA: Kluwer Academic., 1989.
42. J. C. Weaver, "Electroporation; a general phenomenon for manipulating cells and tissues," Cell. Biochem., vol. 51, no. 4, pp. 426-435, 1993.
43. K. A. DeBruin and W. Krassowska, "Electroporation and shock-induced transmembrane potential in a cardiac fiber during defibrillation strength shocks," Ann. Biomed. Eng., vol. 26, no. 4, pp. 584-596, 1998.
44. _, "Modeling electroporation in a single cell: I. effects of field strength and rest potential," Biophys. J., vol. 77, no. 3, pp. 1213-1224, 1999.
45. _, "Modeling electroporation in a single cell: II. Effects of ionic concentration," Biophys. J., vol. 77, pp. 1225-1233, 1999.
46. J. C. Weaver, "Electroporation of cells and tissues," IEEE Trans. Plasma Sci., vol. 28, no. 1, pp. 24-33, Feb. 2000.
47. K. C. Smith, J. C. Neu, and W. Krassowska, "Model of creation and evolution of stable electropores for dna delivery," Biophys. J., vol. 86, no. 5, pp. 2813-2826, 2004.
48. T. R. Gowrishankar, A. T. Esser, Z. Vasilkoski, K. C. Smith, and J. C. Weaver, "Microdosimetry for conventional and supra-electroporation in cells with organelles," Biochem. Biophys. Res. Commun., vol. 341, pp. 1266-1276, 2006.