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MODELING OF ELECTRIC CURRENTS AND ELECTROMAGNETIC FIELDS
Modeling of electric current and electromagnetic field distribution
gives valuable insight into the process of electroporation.
Experimenting on models is easier and much more flexible than on
real biological systems, and sometimes it is also the only way to
evaluate the role of certain stimulation conditions. Still, one
should keep in mind that a model is a rather simplified version of
real conditions. As such, it provides additional information and
help in planning of experiments, but it can not substitute studies
on biological systems.
distinct approaches are used in modeling – the analytical
and the numerical one. The analytical methods are physically more
revealing, yielding solutions is form of expressions, but their
range of applicability is limited to simple geometries and linear phenomena. In contrast, the
numerical approach can be applied to very intricate
conditions, but fails to give explicit relations. The heterogeneous
composition of tissues makes the analytical approach practically
impossible, but numerical methods are suitable,
especially the finite elements method. The essence of this method is
the division of the model into small units (finite elements), inside
which the electrical properties follow a defined function, and then
solving the equations for each of these units. The program packages
we are using for this purpose are Maxwell and EMAS (both by
Ansoft Corp.) and FEMLAB
(by Comsol Inc.).
Valic B, Pavlin M, Miklavcic D. The effect of resting
transmembrane voltage on cell electropermeabilization: a numerical
analysis. Bioelectrochemistry 63: 311-315, 2004. [PDF]
- Pavlin M, Miklavcic D. Effective conductivity of a suspension
of permeabilized cells: a theoretical analysis. Biophys. J.
85: 719-729, 2003. [PDF]
- Sel D, Mazeres S, Teissié J, Miklavcic D. Finite-element
modeling of needle electrodes in tissue from the perspective of
frequent model computation. IEEE Trans. Biomed. Eng.
50: 1221-1232, 2003. [PDF]
- Valic B, Golzio M, Pavlin M, Schatz A, Faurie C, Gabriel B,
Teissié J, Rols MP, Miklavcic D. Effect of electric field induced
transmembrane potential on spheroidal cells: theory and
experiment. Eur. Biophys. J. 32: 519-528, 2003. [PDF]
- Pavlin M, Pavselj N, Miklavcic D. Dependence of induced
transmembrane potential on cell density, arrangement, and cell
position inside a cell system. IEEE Trans. Biomed. Eng.
49: 605-612, 2002. [PDF]
- Semrov D, Miklavcic D. Calculation of the electrical
parameters in electrochemotherapy of solid tumours in mice.
Comput. Biol. Med. 28: 439-448, 1998. [PDF]
- Susil R, Semrov D, Miklavcic D. Electric field induced
transmembrane potential depends on cell density and organization.
Electro. Magnetobiol. 17: 391-399, 1998. [PDF]