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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 in-homogeneous models. Numerical results of the electric field distribution for needle electrode configurations defined in Figs. 2a-2c: a) two needle electrodes, b) four needle electrodes, c) six needle electrodes in two rows taking into account two-times higher conductivity of the target tissue compared to surrounding tissue (conductivity of the target tissue is σtt = 0.4 S/m and conductivity of the surrounding tissue σst = 0.2 S/m). In all cases the applied voltage was set in such a way that U/d = 1.15 V/cm.
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Figure 6: Calculated electric field distribution for in-homogeneous models. Numerical results of the electric field distribution for needle electrode configurations defined in Figs. 2a-2c: a) two needle electrodes, b) four needle electrodes, c) six needle electrodes in two rows taking into account two-times higher conductivity of the target tissue compared to surrounding tissue (conductivity of the target tissue is σtt = 0.4 S/m and conductivity of the surrounding tissue σst = 0.2 S/m). In all cases the applied voltage was set in such a way that U/d = 1.15 V/cm.

Mentions: In order to analyze possible effects of tissue inhomogeneities we made additional models where target tissue had increased conductivity which is based on the fact that the tumor tissue has in general higher conductivity than its surrounding tissue. Namely, from the literature [19,45] we determined that reasonable approximation for conductivity of the target (tumor) tissue is σtt = 0.4 S/m and conductivity of the surrounding tissue σst = 0.2 S/m. In Fig. 6 we compare electric field distributions calculated numerically using FEM method for two, four needle electrodes and six needle electrodes taking into account higher conductivity of the target tissue compared to the surrounding tissue.


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 in-homogeneous models. Numerical results of the electric field distribution for needle electrode configurations defined in Figs. 2a-2c: a) two needle electrodes, b) four needle electrodes, c) six needle electrodes in two rows taking into account two-times higher conductivity of the target tissue compared to surrounding tissue (conductivity of the target tissue is σtt = 0.4 S/m and conductivity of the surrounding tissue σst = 0.2 S/m). In all cases the applied voltage was set in such a way that U/d = 1.15 V/cm.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 6: Calculated electric field distribution for in-homogeneous models. Numerical results of the electric field distribution for needle electrode configurations defined in Figs. 2a-2c: a) two needle electrodes, b) four needle electrodes, c) six needle electrodes in two rows taking into account two-times higher conductivity of the target tissue compared to surrounding tissue (conductivity of the target tissue is σtt = 0.4 S/m and conductivity of the surrounding tissue σst = 0.2 S/m). In all cases the applied voltage was set in such a way that U/d = 1.15 V/cm.
Mentions: In order to analyze possible effects of tissue inhomogeneities we made additional models where target tissue had increased conductivity which is based on the fact that the tumor tissue has in general higher conductivity than its surrounding tissue. Namely, from the literature [19,45] we determined that reasonable approximation for conductivity of the target (tumor) tissue is σtt = 0.4 S/m and conductivity of the surrounding tissue σst = 0.2 S/m. In Fig. 6 we compare electric field distributions calculated numerically using FEM method for two, four needle electrodes and six needle electrodes taking into account higher conductivity of the target tissue compared to the surrounding tissue.

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