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Improved numerical approach for electrical modeling of biological cell clusters

Medical & Biological Engineering & Computing volume 48, pages 311–319 (2010)Cite this article

Abstract

This article presents an efficient numerical approach to simulate the process of polarization and ion conduction in membranes of biological cells subjected to intense electric fields. The proposed method uses Coulomb’s law to calculate the electric field on the surface of the cell membrane and the continuity equation for calculating the difference in electric potential between the faces of the membrane. The behavior of the membrane conductance is described by a model of electroporation proposed in literature. This method provides results that agree well with the analytical model of polarization of an isolated cell suspended in electrolytic solution and also provides results for the conductance of the membrane during electroporation of cells in concentrated suspensions that agree with experimental results already published.

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References

  1. Barnet A, Weaver JC (1991) Electroporation: a unified, quantitative theory of reversible electrical breakdown and mechanical rupture in artificial planar bilayer membranes. Bioelectrochemistry 25:163–182

    Article  Google Scholar 

  2. Chen C, Smye SW, Robinson MP, Evans JA (2006) Membrane electroporation theories: a review. Med Biol Eng Comput 44:5–14

    Article  Google Scholar 

  3. DeBruin KA, Krassowska W (1998) Electroporation and shock-induced transmembrane potential in cardiac fiber during defibrillation strength shocks. Ann Biomed Eng 26:584–596

    Article  Google Scholar 

  4. DeBruin KA, Krassowska W (1999) Modeling electroporation in a single cell. I. Effects of field strength and rest potential. Biophys J 77:1213–1224

    Article  Google Scholar 

  5. DeBruin KA, Krassowska W (1999) Modeling electroporation in a single cell. II. Effects of ionic concentration. Biophys J 77:1225–1233

    Article  Google Scholar 

  6. Fricked H (1953) The electric permittivity of a dilute suspension of membrane covered ellipsoids. J Appl Phys 24:644–646

    Article  Google Scholar 

  7. Gehl J (2003) Electroporation, theory and methods, perspectives for drug delivery, gene therapy and research. Acta Physiol Scand 177:437–447

    Article  Google Scholar 

  8. Glaser RW, Leikin SL, Chernomordik LV, Pastushenko VF, Sokirko AI (1988) Reversible electrical breakdown of lipid bilayers: formation and evolution of pores. Biochim Biophys Acta 940:275–287

    Article  Google Scholar 

  9. Gowrishankar TR, Weaver JC (2003) An approach to electric modeling of single and multiple cells. PNAS 100(6):3203–3208

    Article  Google Scholar 

  10. Hibino M, Masaya S, Itoh H, Nagayama K, Kinosita K (1991) Membrane conductance of an electroporated cell analyzed by sub-microsecond imaging of transmembrane potential. Biophys J 58:209–220

    Article  Google Scholar 

  11. Kinosita K, Tsong TY (1979) Voltage-induced conductance in human erythrocyte. Biochim Biophys Acta 554:479–497

    Article  Google Scholar 

  12. Mali B, Jarm T, Corovic S, Paulin-Kosir MS, Cemazar M, Sersa G, Miklavcic D (2008) The effect of electroporation pulses on functioning of the heart. Med Biol Eng Comput 46:745–757

    Article  Google Scholar 

  13. Miklavčič D, Puc M (2006) Electroporation. In: Akay M (ed) Wiley encyclopedia of biomedical engineering. Wiley, New York, pp 1–10

    Google Scholar 

  14. Mir LM (2001) Therapeutic perspectives of in vivo electropermeabilization. Bioelectrochemistry 53:1–10

    Article  Google Scholar 

  15. Miklavcic D, Kotnik T (2004) Electroporation for electrochemotherapy and gene therapy. In: Rosch PJ, Markov MS (eds) Bioelectromagnetic medicine. Marcel Dekker, New York, pp 637–656

    Google Scholar 

  16. Nickoloff JA (1995) Animal cell electroporation and electrofusion protocols, 1st edn. Humana Press Inc., New Jersey

    Google Scholar 

  17. Nikolski VP, Efimov IR (2005) Electroporation of the heart. Europeace 7:46–154

    Google Scholar 

  18. Pavlin M, Slivnik T, Miklavčič D (2002) Effective conductivity of cell suspensions. IEEE Trans Biomed Eng 49:77–80

    Article  Google Scholar 

  19. Pavlin M, Pavselj N, Miklavčič D (2002) Dependence of induced transmembrane potential on cell density, arrangement, and cell position inside a cell system. IEEE Trans Biomed Eng 49:605–612

    Article  Google Scholar 

  20. Pavlin M, Kandušer M, Reberšek M, Pucihar G, Hart FX, Magjarević R, Miklavčič D (2005) Effect of cell electroporation on the conductivity of a cell suspension. Biophys J 88:4378–4390

    Article  Google Scholar 

  21. Ramos A, Suzuki DOH, Marques JLB (2006) Numerical study of the electrical conductivity and polarization in a suspension of spherical cells. Bioelectrochemistry 68:213–217

    Article  Google Scholar 

  22. Sersa G, Miklavčič D, Cemazar M, Rudolf Z, Puchihar G, Snoj M (2008) Electrochemotherapy in treatment of tumours. Eur J Surg Oncol 34:232–240

    Google Scholar 

  23. Weaver JC, Chizmadzhev YA (1996) Theory of electroporation: a review. Bioelectrochemistry 41:135–160

    Article  Google Scholar 

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Affiliations

  1. Department of Electrical Engineering, Centre of Technological Science, University of Santa Catarina State (UDESC), Joinville, Santa Catarina, 89223-100, Brazil

    Airton Ramos

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  1. Airton Ramos
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Correspondence to Airton Ramos.

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Ramos, A. Improved numerical approach for electrical modeling of biological cell clusters. Med Biol Eng Comput 48, 311–319 (2010). https://doi.org/10.1007/s11517-010-0591-4

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  • DOI: https://doi.org/10.1007/s11517-010-0591-4

Keywords

  • Numerical simulation
  • Biological cell polarization
  • Membrane conductance
  • Electroporation
  • Membrane potential