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Electric current density distribution in planar solid tumor and its surrounding healthy tissue generated by an electrode elliptic array used in electrotherapy

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  • Aguilera, Andrés Ramírez
  • Cabrales, Luis Enrique Bergues
  • Ciria, Héctor Manuel Camué
  • Pérez, Yudelmis Soler
  • González, Fidel Gilart
  • González, Maraelys Morales
  • Zamora, Lisset Ortíz
  • Palencia, Fabiola Suárez
  • Salas, Miriam Fariñas
  • Bestard, Nailet Real
  • González, Gustavo Sierra
  • Cabrales, Idelisa Bergues

Abstract

The knowledge of the electric current density distribution generated by an electrode array is very useful in electrotherapy for tumor treatment. We propose an innovative mathematical approach that takes into account planar solid tumor elliptic geometry, electrical differences between it and its surrounding healthy tissue, and positioning of the electrodes with respect to tumor-surrounding healthy tissue interface. We show the distributions of the electric current density in leading order and first correction terms in a heterogeneous planar medium formed by two regions (tumor and its surrounding healthy tissue) in function of these parameters. The results show that when electrodes are completely inserted in tumor and/or its conductivity is higher than that of its surrounding healthy tissue, the electric current density lines concentrate more in tumor and its tumor-surrounding healthy tissue interface. No significant differences are reported between the electric current density distributions in leading-order and first-order correction for each parameter investigated. However, norm of this physical magnitude reveals that these distributions are different when the ratio between radius of the electrodes and radius of the tumor is less than 0.8. We conclude that the analytical modeling presented in this study is of practical interest because it provides a convenient way to visualize the electric current density distributions generated by an electrode elliptic array in order to efficiently destroy the localized planar tumors with the minimum damage to organism, through an increase of the potential applied to the electrodes, the tumor conductivity with respect to its surrounding healthy tissue and insertion of all electrodes into tumor.

Suggested Citation

  • Aguilera, Andrés Ramírez & Cabrales, Luis Enrique Bergues & Ciria, Héctor Manuel Camué & Pérez, Yudelmis Soler & González, Fidel Gilart & González, Maraelys Morales & Zamora, Lisset Ortíz & Palencia, , 2010. "Electric current density distribution in planar solid tumor and its surrounding healthy tissue generated by an electrode elliptic array used in electrotherapy," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(9), pages 1886-1902.
    • Handle: RePEc:eee:matcom:v:80:y:2010:i:9:p:1886-1902
    DOI: 10.1016/j.matcom.2010.02.004
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    References listed on IDEAS

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    1. Cabrales, Luis Enrique Bergues & Aguilera, Andrés Ramírez & Jiménez, Rolando Placeres & Jarque, Manuel Verdecia & Ciria, Héctor Manuel Camué & Reyes, Juan Bory & Mateus, Miguel Angel O’Farril & Palenc, 2008. "Mathematical modeling of tumor growth in mice following low-level direct electric current," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 78(1), pages 112-120.
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    Cited by:

    1. Soba, Alejandro & Suárez, Cecilia & González, Maraelys Morales & Cabrales, Luis Enrique Bergues & Pupo, Ana Elisa Bergues & Reyes, Juan Bory & Martínez Tassé, José Pablo, 2018. "Integrated analysis of the potential, electric field, temperature, pH and tissue damage generated by different electrode arrays in a tumor under electrochemical treatment," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 146(C), pages 160-176.
    2. Pupo, Ana Elisa Bergues & González, Maraelys Morales & Cabrales, Luis Enrique Bergues & Reyes, Juan Bory & Oria, Eduardo José Roca & Nava, Juan José Godina & Jiménez, Rolando Placeres & Sánchez, Franc, 2017. "3d current density in tumors and surrounding healthy tissues generated by a system of straight electrode arrays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 138(C), pages 49-64.
    3. Ciria, Héctor Manuel Camué & Cabrales, Luis Enrique Bergues & Aguilera, Andrés Ramírez & Nava, Juan José Godina & Joa, Javier Antonio González & García, Raudel Peña & González, Gustavo Sierra & Gonzál, 2012. "Influence of electrode array parameters used in electrotherapy on tumor growth kinetics: A mathematical simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(8), pages 1396-1406.
    4. Hamdy M. Youssef & Alaa A. El-Bary, 2020. "Voltage and Time Required for Irreversible Thermal Damage of Tumor Tissues during Electrochemotherapy under Thomson Effect," Mathematics, MDPI, vol. 8(9), pages 1-21, September.

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