European Biophysics Journal

, Volume 32, Issue 6, pp 519–528 | Cite as

Effect of electric field induced transmembrane potential on spheroidal cells: theory and experiment

  • Blaž Valič
  • Muriel Golzio
  • Mojca Pavlin
  • Anne Schatz
  • Cecile Faurie
  • Bruno Gabriel
  • Justin Teissié
  • Marie-Pierre Rols
  • Damijan Miklavčič


The transmembrane potential on a cell exposed to an electric field is a critical parameter for successful cell permeabilization. In this study, the effect of cell shape and orientation on the induced transmembrane potential was analyzed. The transmembrane potential was calculated on prolate and oblate spheroidal cells for various orientations with respect to the electric field direction, both numerically and analytically. Changing the orientation of the cells decreases the induced transmembrane potential from its maximum value when the longest axis of the cell is parallel to the electric field, to its minimum value when the longest axis of the cell is perpendicular to the electric field. The dependency on orientation is more pronounced for elongated cells while it is negligible for spherical cells. The part of the cell membrane where a threshold transmembrane potential is exceeded represents the area of electropermeabilization, i.e. the membrane area through which the transport of molecules is established. Therefore the surface exposed to the transmembrane potential above the threshold value was calculated. The biological relevance of these theoretical results was confirmed with experimental results of the electropermeabilization of plated Chinese hamster ovary cells, which are elongated. Theoretical and experimental results show that permeabilization is not only a function of electric field intensity and cell size but also of cell shape and orientation.


Chinese hamster ovary cells Electroporation Finite-element modelling Spheroidal cells Transmembrane potential 




length of box side


membrane thickness

gϕϕ and gττ

elements of metric tensor in spheroidal coordinates


arc length on an ellipse


vector of the point T(x,y,z) lying at the surface of the spheroid


cell radius in the case of a sphere

R1, R2=R3

axes of cell in the case of a spheroid (prolate spheroid: R 1>R 2=R 3; oblate spheroid R 1<R 2=R 3)


area (surface)


point at the surface of the spheroid


ratio between R 1 and R 2

ϑ, ϕ, r

spherical coordinates

τ, ϕ, σ

spheroidal coordinates



applied electric field


normal component of electric current at the surface of the spheroid


depolarizing factor in the i=x, y and z directions


azimuth angle in the spherical coordinate system; the angle between the symmetry axis of the spheroid and the external electric field


polar angle in the spherical coordinate system


electric potential


conductivity of cytoplasm


external medium conductivity


conductivity of cell membrane


transmembrane potential


threshold or critical transmembrane potential


induced transmembrane potential


resting transmembrane potential



The authors thank C. Millot for providing CHO cells. M.G. was supported by a grant from the Association Française contre les Myopathies (AFM). This work was partly supported by the Ministry of Education, Science and Sport of the Republic of Slovenia through various grants and partly by the Cliniporator project (grant QLK3-1999-00484) under the framework of the 5th PRCD of the European Commission.


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Copyright information

© EBSA 2003

Authors and Affiliations

  • Blaž Valič
    • 1
  • Muriel Golzio
    • 2
  • Mojca Pavlin
    • 1
  • Anne Schatz
    • 2
  • Cecile Faurie
    • 2
  • Bruno Gabriel
    • 2
  • Justin Teissié
    • 2
  • Marie-Pierre Rols
    • 2
  • Damijan Miklavčič
    • 1
  1. 1.Faculty of Electrical EngineeringUniversity of LjubljanaLjubljanaSlovenia
  2. 2.Institut de Pharmacologie et de Biologie Structurale du CNRS, UMR 5089ToulouseFrance

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