![](bg6.png)
5 CONCLUSIONS
A systematic approach based on the combined use of
Design of Experiments and Response Surface
Methodology has been applied for evaluating the
effects induced on the dynamics of the Trans-
Membrane Voltage of a biological cell by the
characteristics of the applied electric pulses. The
proposed methodology is applied to a lumped
parameter circuit, subjected to a trapezoidal pulse.
The combined use of DoE and RSM allows to
reliably identify the parameters set leading to the
highest peak value of the TMV. The parameters
which show the greatest influence are the max value
of the applied pulse and the slew rate whereas the
response is almost insensitive to the pulse duration.
The proposed approach can be easily extended in
order to study the effects of the pulse characteristics
on the response of more complex circuit models
taking into account also the internal cell structures
(nucleus, organelles, etc), such as those describing
the cell behaviour to ultrashort, high-intensity pulses
for intracellular manipulation.
ACKNOWLEDGEMENTS
This work has been carried out with the financial
support of ex MURST 60% funds of the University
of Salerno.
REFERENCES
Beebe S.J.,. Buescher E.S, Schoenbach K.H.,
“Intracellular effect of ultrashort electrical pulses,”
Bioelectromagnetics, vol. 22, pp.440–448, 2001.
Bilska, A.O., DeBruin, K.A., Krassowska W. 2000,
Theoretical modelling of the effects of shock duration,
frequency and strength on the degree of
electroporation, Bioelectrochemistry, 51, 2000, 133-143.
Citro, N., Tucci, V. 2006. A detailed analysis of the
electrical dynamics of the Hogkin-Huxley cellular
model including electroporation. Proc. of the 4th Int.
Workshop on Biological Effects of Electromagnetic
Fields. ISBN/ISSN: 960-233-173-9, Vol. 2: 853-860.
Citro, N., De Vivo, B., Spagnuolo, G., Tucci, V. (2005),
“Range Analysis of Biological Cells Subjected to
Pulsed Electric Fields”, Conf. on Electrical Insulation
and Dielectric Phenomena, 10.1109/
CEIDP.2005.1560732, pp. 511-514.
DeBruin, K.A., Krassowska W., 1999. Modelling
Electroporation in a Single Cell. I. Effects of Field
Strength and Rest Potential. Biophysical Journal. 77:
1213-1224.
Heida, T., Wagenaar, J. B. M., Rutten, W. L. C., Marani,
E. 2002. Investigating Membrane Breakdown of
Neuronal Cells Exposed to Nonuniform Electric Fields
by Finite-Element. Modeling and Experiments. IEEE
Trans. On Biomedical Engineering. 49-10:1195-1203.
Hodgkin, A.L., Huxley, A.F. 1952. A quantitative
description of membrane current and its application to
conduction and excitation in nerve. Journal of.
Physiology. 117: 500-544.
Hofmann, G. A., Dev, S. B. Dimmer, S., Nanda G. S.
1999. Electroporation therapy: a new approach for the
treatment of head and neck cancer, IEEE Trans. On
Biomedical Engineering. Volume: 46, Issue: 6, 752-
759.
Joshi, R.P., Hu, Q., Schoenbach, K.H. 2004. Modeling
studies of cell response to ultrashort, high-intensity
electric fields-implications for intracellular
manipulation. IEEE Transactions on Plasma Science.
Vol. 32, issue 4, part II: 1677- 1686.
Joshi, R.P., Hu, Q., Schoenbach, K.H. 2004. Energy-
landscape-model analysis for irreversibility and ist
pulse-width dependence in cells subjected to a high-
intensity ultrashort electric pulse. Physical Review E
69, 051901.
Koyamada, K., Sakai, K., Itoh, T. 2004. Parameter
Optimization Technique Using The Response Surface
Methodology. Proc. of the 26th Annual Int. Conf. of
the IEEE EMBS San Francisco, CA, USA Sept. 1-5.
Kotnik, T., Miklavcic, D. 2006. Theoretical Evaluation of
Voltage Inducement on Internal Membranes of
Biological Cells Exposed to Electric Fields.
Biophysical Journal. 90:480-491.
Miller, C. E., Henriquez, C.S. 1988. Three Dimensional
Finite Element Solution for Biopotential: Erythrocyte
in an Applied Field. IEEE Transaction on Biomedical
Engineering. Vol. 35, No. 9: 712-718.
Neumann, E., Sowers E., and Jordan C. A.,
Electroporation and Electrofusion in Cell Biology
.
New York: Plenum, 1989.
NIST/SEMATECH e-Handbook of Statistical Methods,
http://www.itl.nist.gov/div898/handbook/
Sukharev, S. I., et al. 1992,. Electroporation and
electrophoretic DNA transfer into cells. The effect of
DNA interaction with electropores. Biophys. J. 1992,
63(5): 1320–1327.
Vasilkoski, Z., Esser, A. T., Gowrishankar, T. R., Weaver,
J.C. 2006. Membrane electroporation: The absolute
rate equation and nanosecond time scale pore creation.
2006. Physical Review E 74. 021904.
Weaver, J.C. 2000, Electroporation of cells and tissues,
IEEE Transactions on Plasma Science, 2000, Vol. 28,
Issue: 1, 24-33.
EFFICIENT EVALUATION OF THE INFLUENCE OF ELECTRIC PULSE CHARACTERISTICS ON THE
DYNAMICS OF CELL TRANS-MEMBRANE VOLTAGE
145