title: Analytical and numerical solutions of the potential and electric field generated by different electrode arrays in a tumor tissue under electrotherapy.
abstract: BACKGROUND
  Electrotherapy is a relatively well established and efficient method of tumor treatment. In this paper we focus on analytical and numerical calculations of the potential and electric field distributions inside a tumor tissue in a two-dimensional model (2D-model) generated by means of electrode arrays with shapes of different conic sections (ellipse, parabola and hyperbola).
  
  
  METHODS
  Analytical calculations of the potential and electric field distributions based on 2D-models for different electrode arrays are performed by solving the Laplace equation, meanwhile the numerical solution is solved by means of finite element method in two dimensions.
  
  
  RESULTS
  Both analytical and numerical solutions reveal significant differences between the electric field distributions generated by electrode arrays with shapes of circle and different conic sections (elliptic, parabolic and hyperbolic). Electrode arrays with circular, elliptical and hyperbolic shapes have the advantage of concentrating the electric field lines in the tumor.
  
  
  CONCLUSIONS
  The mathematical approach presented in this study provides a useful tool for the design of electrode arrays with different shapes of conic sections by means of the use of the unifying principle. At the same time, we verify the good correspondence between the analytical and numerical solutions for the potential and electric field distributions generated by the electrode array with different conic sections.
authors.affiliation: Departamento de Investigaciones, Centro Nacional de Electromagnetismo Aplicado, Universidad de Oriente, Santiago de Cuba 90400, Cuba. berguesc@yahoo.com
authors.forename: Ana E
authors.initials: AE
authors.lastname: Bergues Pupo
authors.forename: Juan Bory
authors.initials: JB
authors.lastname: Reyes
authors.forename: Luis E
authors.initials: LE
authors.lastname: Bergues Cabrales
authors.forename: Jesús M
authors.initials: JM
authors.lastname: Bergues Cabrales
mesh_terms: D004599:Electric Stimulation Therapy / Q000379:methods*; D004566:Electrodes; D004574:Electromagnetic Fields; D006801:Humans; D008962:Models, Theoretical; D009369:Neoplasms / Q000532:radiotherapy; D012996:Solutions
chemical_list: D012996:Solutions