Numerical modeling in electroporation-based biomedical applications
Background. Numerous experiments have to be performed before a biomedical application is put to practical use in clinical environment. As a complementary work to in vitro, in vivo and medical experiments, we can use analytical and numerical models to represent, as realistically as possible, real biological phenomena of, in our case, electroporation. In this way we can evaluate different electrical parameters in advance, such as pulse amplitude, duration, number of pulses, or different electrode geometries. Such numerical models can contribute significantly to the understanding of an experiment and treatment planning as well as to the design of new electroporation devices and electrodes.
Methods. We used commercially available modeling software, based on finite element method. We constructed a model of a subcutaneous tumor during electrochemotherapy (EMAS) and a model of skin during gene electrotransfer (COMSOL Multiphysics). Tissue-electrode geometries, pulse parameters and currentvoltage measurements from in vivo experiments were used to develop and validate the models.
Results. To describe adequately our in vivo observations, a tissue conductivity increase during electroporation was included in our numerical models. The output currents of the models were compared to the currents and the voltages measured during in vivo experiments and a good agreement was obtained. Also, when comparing the voltages needed for a successful electropermeabilization as suggested by the models, to voltages applied in experiments and achieving a successful electrochemotherapy or in vivo gene electrotransfer, good agreement can be observed.
Conclusions. Modeling of electric current and electric field distribution during cell and tissue electroporation proves to be helpful in describing different aspects of the process and allowing us to design electrodes and electroporation protocols as a part of treatment planning.
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Prausnitz MR Corbett JD Gimm JA Golan DE Langer R Weaver JC. Millisecond measurement of transport during and after an electroporation pulse. Biophys J 1995; 68: 1864-70.
Teissié J Eynard B Gabriel B Rols MP. Electropermeabilization of cell membranes. Adv Drug Deliver Rev 1999; 35: 3-19.
Sersa G Cemazar M Miklavcic D. Antitumor effectiveness of electrochemotherapy with cis-diamminedichloroplatinium (II) in mice. Cancer Res 1995; 55: 3450-5.
Heller R Gilbert R Jaroszeski MJ. Clinical application of electrochemotherapy. Adv Drug Deliver Rev 1999; 35: 119-29.
Sersa G Cemazar M Miklavcic D Rudolf Z. Electrochemotherapy of tumours. Radiol Oncol 2006; 40: 163-74.
Hojman P Gissel H Gehl J. Sensitive and precise regulation of haemoglobin after gene transfer of erythropoietin to muscle tissue using electroporation. Gene Therapy 2007; 14: 950-9.
Zhang L Nolan E Kreitschitz S Rabussay DP. Enhanced delivery of naked DNA to the skin by non-invasive in vivo electroporation. Biochim Biophys Acta 2002; 1572: 1-9.
Pavselj N Préat V. DNA electrotransfer into the skin using a combination of one high- and one low-voltage pulse. J Control Release 2005; 106: 407-15.
Mir LM Bureau MF Gehl J Rangara R Rouy D Caillaud J-M et al. High-efficiency gene transfer into skeletal muscle mediated by electric pulses. PNAS 1999; 96: 4262-7.
Prausnitz MR. The effects of electric current applied to skin: A review for transdermal drug delivery. Adv Drug Deliver Rev 1996; 18: 395-425.
Prausnitz MR. A practical assessment of transdermal drug delivery by skin electroporation. Adv Drug Deliver Rev 1999; 35: 61-76.
Denet A-R Vanbever R Préat V. Skin electroporation for transdermal and topical delivery. Adv Drug Deliver Rev 2004; 56: 659-74.
Dev SB Dhar D Krassowska W. Electric field of a six-needle array electrode used in drug and DNA delivery in vivo: Analytical versus numerical solution. IEEE T Bio-Med-Eng 2003; 50:1296-300.
Zupanic A Corovic S Miklavcic D. Optimization of electrode position and electric pulse amplitude in electrochemotherapy. Radiol Oncol 2008; 42: 93-101.
Pavselj N Préat V Miklavcic D. A numerical model of skin electropermeabilization based on in vivo experiments. Ann Biomed Eng 2007; 35: 2138-44.
Sel D Macek-Lebar A Miklavcic D. Feasibility of employing model-based optimization of pulse amplitude and electrode distance for effective tumor electropermeabilization. IEEE T Bio-Med-Eng 2007; 54: 773-81.
Pavselj N Bregar Z Cukjati D Batiuskaite D Mir LM Miklavcic D. The course of tissue permeabilization studied on a mathematical model of a subcutaneous tumor in small animals. IEEE T Bio-Med-Eng 2005; 52: 1373-81.
Miklavcic D Pavselj N Hart FX. Electric properties of tissues. In: Wiley encyclopedia of biomedical engineering. New York: John Wiley & Sons; 2006. p. 3578-89.
Pliquett U Langer R Weaver JC. Changes in the passive electrical properties of human stratum corneum due to electroporation. Biochim Biophys Acta 1995; 1239: 111-21.
Schmeer M Seipp T Pliquett U Kakorin S Neumann E. Mechanism for the conductivity changes caused by membrane electroporation of CHO cell-pellets. Phys Chem Chem Phys 2004; 6: 5564-74.
Geddes LA Baker LE. The specific resistance of biological material-a compendium of data for the biomedical engineer and physiologist. Med Biol Eng 1967; 5: 271-93.
Schwan HP Kay CF. Specific resistance of body tissues. Circ Res 1956; 4: 664-70.
Epstein BR Foster KR. Anisotropy in the dielectric properties of skeletal muscle. Med Biol Eng Comput 1983; 21: 51-5.
Burger HC Van Dongen R. Specific resistance of body tissues. Phys Med Biol 1960; 5: 431-447.
Rush S Abildskov JA McFee R. Resistivity of body tissues at low frequencies. Circ Res 1963; 12: 40-50.
Gabriel C Gabriel S Corthout E. The dielectric properties of biological tissue: I. Literature survey. Phys Med Biol 1996; 41: 2231-49.
Gabriel S Lau RW Gabriel C. The dielectric properties of biological tissue: II. Measurements in the frequency range 10 Hz to 20 GHz. Phys Med Biol 1996; 41: 2251-69.
Yamamoto T Yamamoto Y. Dielectric constant and resistivity of epidermal stratum corneum. Med Biol Eng 1976; 14: 494-500.
Chizmadzhev YA Indenbom AV Kuzmin PI Galichenko SV Weaver JC Potts RO. Electrical properties of skin at moderate voltages: Contribution of appendageal macropores. Biophys J 1998; 74: 843-56.
Gallo SA Oseroff AR Johnson PG Hui SW. Characterization of electric-pulse-induced permeabilization of porcine skin using surface electrodes. Biophys J 1997; 72: 2805-11.