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Analytical and numerical quantification and comparison of the local electric field in the tissue for different electrode configurations.

Corović S, Pavlin M, Miklavcic D - Biomed Eng Online (2007)

Bottom Line: By comparing the local electric field distribution calculated for different electrode configurations to the ratio U/d, we show that the parameter U/d can differ significantly from the actual calculated values of the local electric field inside the treated tissue.Using numerical models we further calculate the needed voltage for a specific electrode configuration to achieve adequate E inside the target tissue while minimizing damages of the surrounding tissue.We present also analytical solutions, which provide a convenient, rapid, but approximate method for a pre-analysis of electric field distribution in treated tissue.

View Article: PubMed Central - HTML - PubMed

Affiliation: University of Ljubljana, Faculty of Electrical Engineering, Ljubljana, Slovenia. selma.corovic@fe.uni-lj.si

ABSTRACT

Background: Electrochemotherapy and gene electrotransfer are novel promising treatments employing locally applied high electric pulses to introduce chemotherapeutic drugs into tumor cells or genes into target cells based on the cell membrane electroporation. The main focus of this paper was to calculate analytically and numerically local electric field distribution inside the treated tissue in two dimensional (2D) models for different plate and needle electrode configurations and to compare the local electric field distribution to parameter U/d, which is widely used in electrochemotherapy and gene electrotransfer studies. We demonstrate the importance of evaluating the local electric field distribution in electrochemotherapy and gene electrotransfer.

Methods: We analytically and numerically analyze electric field distribution based on 2D models for electrodes and electrode configurations which are most widely used in electrochemotherapy and gene electrotransfer. Analytical calculations were performed by solving the Laplace equation and numerical calculations by means of finite element method in two dimensions.

Results: We determine the minimal and maximal E inside the target tissue as well as the maximal E over the entire treated tissue for the given electrode configurations. By comparing the local electric field distribution calculated for different electrode configurations to the ratio U/d, we show that the parameter U/d can differ significantly from the actual calculated values of the local electric field inside the treated tissue. By calculating the needed voltage to obtain E > U/d inside the target tissue, we showed that better electric field distribution can be obtained by increasing the number and changing the arrangement of the electrodes.

Conclusion: Based on our analytical and numerical models of the local electric field distribution we show that the applied voltage, configuration of the electrodes and electrode position need to be chosen specifically for each individual case, and that numerical modeling can be used to optimize the appropriate electrode configuration and adequate voltage. Using numerical models we further calculate the needed voltage for a specific electrode configuration to achieve adequate E inside the target tissue while minimizing damages of the surrounding tissue. We present also analytical solutions, which provide a convenient, rapid, but approximate method for a pre-analysis of electric field distribution in treated tissue.

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Related in: MedlinePlus

Calculated electric field distribution for the geometries with parallel plate electrodes. Numerical results of the electric field distribution for geometries defined in Fig. 1: a) the infinite plate electrodes case, b) the target tissue symmetrically placed between the finite plate electrodes and c) the non-symmetrical example when the target tissue is not entirely in-between the finite plate electrodes. The circle represents the target tissue e.g. tumor tissue and the white region represents part of tissue where E ≥ U/d.
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Figure 3: Calculated electric field distribution for the geometries with parallel plate electrodes. Numerical results of the electric field distribution for geometries defined in Fig. 1: a) the infinite plate electrodes case, b) the target tissue symmetrically placed between the finite plate electrodes and c) the non-symmetrical example when the target tissue is not entirely in-between the finite plate electrodes. The circle represents the target tissue e.g. tumor tissue and the white region represents part of tissue where E ≥ U/d.

Mentions: In order to compare and quantify the influence of geometry, number and position of different electrode configurations on the electric field distribution we used the same parameter U/d = 1.15 V/cm in all models. We present the calculated electric field with equal scale of E from 0 to 1.15 V/cm. The values of electric field strength are shown by colour scale legend (see Figs. 3 and 4) with the maximal value representing the ratio U/d = 1.15 V/cm in order to demonstrate the region below (color scale) and above the value U/d (white region). The encircled region in Figs. 3a–3c and Figs. 4a–4e represent one of the possible geometries and positions of the target tissues. It is within this target tissue that the electric field needs to be sufficiently high (E > Erev).


Analytical and numerical quantification and comparison of the local electric field in the tissue for different electrode configurations.

Corović S, Pavlin M, Miklavcic D - Biomed Eng Online (2007)

Calculated electric field distribution for the geometries with parallel plate electrodes. Numerical results of the electric field distribution for geometries defined in Fig. 1: a) the infinite plate electrodes case, b) the target tissue symmetrically placed between the finite plate electrodes and c) the non-symmetrical example when the target tissue is not entirely in-between the finite plate electrodes. The circle represents the target tissue e.g. tumor tissue and the white region represents part of tissue where E ≥ U/d.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2100058&req=5

Figure 3: Calculated electric field distribution for the geometries with parallel plate electrodes. Numerical results of the electric field distribution for geometries defined in Fig. 1: a) the infinite plate electrodes case, b) the target tissue symmetrically placed between the finite plate electrodes and c) the non-symmetrical example when the target tissue is not entirely in-between the finite plate electrodes. The circle represents the target tissue e.g. tumor tissue and the white region represents part of tissue where E ≥ U/d.
Mentions: In order to compare and quantify the influence of geometry, number and position of different electrode configurations on the electric field distribution we used the same parameter U/d = 1.15 V/cm in all models. We present the calculated electric field with equal scale of E from 0 to 1.15 V/cm. The values of electric field strength are shown by colour scale legend (see Figs. 3 and 4) with the maximal value representing the ratio U/d = 1.15 V/cm in order to demonstrate the region below (color scale) and above the value U/d (white region). The encircled region in Figs. 3a–3c and Figs. 4a–4e represent one of the possible geometries and positions of the target tissues. It is within this target tissue that the electric field needs to be sufficiently high (E > Erev).

Bottom Line: By comparing the local electric field distribution calculated for different electrode configurations to the ratio U/d, we show that the parameter U/d can differ significantly from the actual calculated values of the local electric field inside the treated tissue.Using numerical models we further calculate the needed voltage for a specific electrode configuration to achieve adequate E inside the target tissue while minimizing damages of the surrounding tissue.We present also analytical solutions, which provide a convenient, rapid, but approximate method for a pre-analysis of electric field distribution in treated tissue.

View Article: PubMed Central - HTML - PubMed

Affiliation: University of Ljubljana, Faculty of Electrical Engineering, Ljubljana, Slovenia. selma.corovic@fe.uni-lj.si

ABSTRACT

Background: Electrochemotherapy and gene electrotransfer are novel promising treatments employing locally applied high electric pulses to introduce chemotherapeutic drugs into tumor cells or genes into target cells based on the cell membrane electroporation. The main focus of this paper was to calculate analytically and numerically local electric field distribution inside the treated tissue in two dimensional (2D) models for different plate and needle electrode configurations and to compare the local electric field distribution to parameter U/d, which is widely used in electrochemotherapy and gene electrotransfer studies. We demonstrate the importance of evaluating the local electric field distribution in electrochemotherapy and gene electrotransfer.

Methods: We analytically and numerically analyze electric field distribution based on 2D models for electrodes and electrode configurations which are most widely used in electrochemotherapy and gene electrotransfer. Analytical calculations were performed by solving the Laplace equation and numerical calculations by means of finite element method in two dimensions.

Results: We determine the minimal and maximal E inside the target tissue as well as the maximal E over the entire treated tissue for the given electrode configurations. By comparing the local electric field distribution calculated for different electrode configurations to the ratio U/d, we show that the parameter U/d can differ significantly from the actual calculated values of the local electric field inside the treated tissue. By calculating the needed voltage to obtain E > U/d inside the target tissue, we showed that better electric field distribution can be obtained by increasing the number and changing the arrangement of the electrodes.

Conclusion: Based on our analytical and numerical models of the local electric field distribution we show that the applied voltage, configuration of the electrodes and electrode position need to be chosen specifically for each individual case, and that numerical modeling can be used to optimize the appropriate electrode configuration and adequate voltage. Using numerical models we further calculate the needed voltage for a specific electrode configuration to achieve adequate E inside the target tissue while minimizing damages of the surrounding tissue. We present also analytical solutions, which provide a convenient, rapid, but approximate method for a pre-analysis of electric field distribution in treated tissue.

Show MeSH
Related in: MedlinePlus