Differences in the Electric Field Distribution Predicted with a Mathematical Model of Cylindrical Electrodes of Finite Length vs. Infinite Length: A Comparison Based on Analytical Solution
Cylindrical-shaped metal electrodes are used in numerous medical specialties to force an electric field into the surrounding tissue (e.g., in electrical stimulation and electroporation). Although these electrodes have a limited length in reality, previous mathematical modeling studies have simplifie...
| Main Authors: | , |
|---|---|
| 格式: | Article |
| 語言: | English |
| 出版: |
MDPI AG
2023-10-01
|
| 叢編: | Mathematics |
| 主題: | |
| 在線閱讀: | https://www.mdpi.com/2227-7390/11/21/4447 |
| _version_ | 1827765628801384448 |
|---|---|
| author | Ricardo Romero-Mendez Enrique Berjano |
| author_facet | Ricardo Romero-Mendez Enrique Berjano |
| author_sort | Ricardo Romero-Mendez |
| collection | DOAJ |
| description | Cylindrical-shaped metal electrodes are used in numerous medical specialties to force an electric field into the surrounding tissue (e.g., in electrical stimulation and electroporation). Although these electrodes have a limited length in reality, previous mathematical modeling studies have simplified the physical situation and have built a model geometry based on a cylindrical electrode of infinite length, which allows for reducing the model from 2D to 1D. Our objective was to quantify the differences in the electric field values between the finite and infinite electrode cases and assess the adequacy of the mentioned simplification for different values of electrode diameter and length. We used analytical solutions for the electric field distribution. We found that the electric field distribution is substantially different for both cases, not only near the edges of the electrode (when finite length is assumed) and in close locations (<1 mm), but even in the central area and at distances greater than 2 mm. Our work presents analytical solutions for both cases (finite and infinite length), which, despite the oscillations derived from computational limitations, could be used by researchers involved in electric field modeling in biological tissues, in order to quantify the possible error generated with simple models in geometric terms that assume infinite length. |
| first_indexed | 2024-03-11T11:25:16Z |
| format | Article |
| id | doaj.art-54fb6bbcb15e46c3a3221d4c0f2b68e1 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T11:25:16Z |
| publishDate | 2023-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-54fb6bbcb15e46c3a3221d4c0f2b68e12023-11-10T15:07:54ZengMDPI AGMathematics2227-73902023-10-011121444710.3390/math11214447Differences in the Electric Field Distribution Predicted with a Mathematical Model of Cylindrical Electrodes of Finite Length vs. Infinite Length: A Comparison Based on Analytical SolutionRicardo Romero-Mendez0Enrique Berjano1Facultad de Ingeniería, Universidad Autónoma de San Luis Potosí, Zona Univeristaria, San Luis Potosi 78290, MexicoBioMIT, Department of Electronic Engineering, Universitat Politècnica de València, Camino de Vera, 46022 Valencia, SpainCylindrical-shaped metal electrodes are used in numerous medical specialties to force an electric field into the surrounding tissue (e.g., in electrical stimulation and electroporation). Although these electrodes have a limited length in reality, previous mathematical modeling studies have simplified the physical situation and have built a model geometry based on a cylindrical electrode of infinite length, which allows for reducing the model from 2D to 1D. Our objective was to quantify the differences in the electric field values between the finite and infinite electrode cases and assess the adequacy of the mentioned simplification for different values of electrode diameter and length. We used analytical solutions for the electric field distribution. We found that the electric field distribution is substantially different for both cases, not only near the edges of the electrode (when finite length is assumed) and in close locations (<1 mm), but even in the central area and at distances greater than 2 mm. Our work presents analytical solutions for both cases (finite and infinite length), which, despite the oscillations derived from computational limitations, could be used by researchers involved in electric field modeling in biological tissues, in order to quantify the possible error generated with simple models in geometric terms that assume infinite length.https://www.mdpi.com/2227-7390/11/21/4447analytical solutioncylindrical electrodeelectrical problemelectroporationelectrical stimulation |
| spellingShingle | Ricardo Romero-Mendez Enrique Berjano Differences in the Electric Field Distribution Predicted with a Mathematical Model of Cylindrical Electrodes of Finite Length vs. Infinite Length: A Comparison Based on Analytical Solution Mathematics analytical solution cylindrical electrode electrical problem electroporation electrical stimulation |
| title | Differences in the Electric Field Distribution Predicted with a Mathematical Model of Cylindrical Electrodes of Finite Length vs. Infinite Length: A Comparison Based on Analytical Solution |
| title_full | Differences in the Electric Field Distribution Predicted with a Mathematical Model of Cylindrical Electrodes of Finite Length vs. Infinite Length: A Comparison Based on Analytical Solution |
| title_fullStr | Differences in the Electric Field Distribution Predicted with a Mathematical Model of Cylindrical Electrodes of Finite Length vs. Infinite Length: A Comparison Based on Analytical Solution |
| title_full_unstemmed | Differences in the Electric Field Distribution Predicted with a Mathematical Model of Cylindrical Electrodes of Finite Length vs. Infinite Length: A Comparison Based on Analytical Solution |
| title_short | Differences in the Electric Field Distribution Predicted with a Mathematical Model of Cylindrical Electrodes of Finite Length vs. Infinite Length: A Comparison Based on Analytical Solution |
| title_sort | differences in the electric field distribution predicted with a mathematical model of cylindrical electrodes of finite length vs infinite length a comparison based on analytical solution |
| topic | analytical solution cylindrical electrode electrical problem electroporation electrical stimulation |
| url | https://www.mdpi.com/2227-7390/11/21/4447 |
| work_keys_str_mv | AT ricardoromeromendez differencesintheelectricfielddistributionpredictedwithamathematicalmodelofcylindricalelectrodesoffinitelengthvsinfinitelengthacomparisonbasedonanalyticalsolution AT enriqueberjano differencesintheelectricfielddistributionpredictedwithamathematicalmodelofcylindricalelectrodesoffinitelengthvsinfinitelengthacomparisonbasedonanalyticalsolution |