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3d current density in tumors and surrounding healthy tissues generated by a system of straight electrode arrays

Author

Listed:
  • 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, Francisco Martínez
  • Ciria, Héctor Manuel Camué
  • Cabrales, Jesús Manuel Bergues

Abstract

The knowledge of the adequate current density distribution to apply when using different electrode arrays in tumor tissue and the healthy surrounding tissue is one of the most significant challenges to improve the effectiveness of electrochemical treatment. This paper proposes a mathematical approach to obtain a three-dimensional analytical expression for the current density generated by multi-needle electrodes. Such array of electrodes can be allocated in an arbitrary shape and inserted anywhere in the tumor. Calculations of the electrical potential and electric current density distributions based on a three-dimensional model for different straight multi-needle electrode configurations are carried out by solving the Laplace equation. The results show that appropriate positioning, insertion depth and electrodes polarity are essential for tumor treatment with direct current and multiple needle electrodes, arranged in concentric circumferences, concentrate a higher electric current density in the tumor. This configuration of multiple straight needle electrodes inserted along the tumor improves the effectiveness of electrochemical treatment because the current density covers the entire volume of the tumor, unlike those configurations that are inserted in the tumor base and only partially cover its volume.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:138:y:2017:i:c:p:49-64
    DOI: 10.1016/j.matcom.2017.01.004
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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. Castañeda, Antonio Rafael Selva & Pozo, Josue Mariño del & Ramirez-Torres, Erick Eduardo & Oria, Eduardo José Roca & Vaillant, Sorangel Bolaños & Montijano, Juan I. & Cabrales, Luis Enrique Bergues, 2023. "Spatio temporal dynamics of direct current in treated anisotropic tumors," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 609-632.
    2. 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.

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