TY - JOUR
T1 - Analytical and numerical solutions of the potential and electric field generated by different electrode arrays in a tumor tissue under electrotherapy
AU - Bergues Pupo, Ana E.
AU - Reyes, Juan B.
AU - Bergues Cabrales, Luis E.
AU - Bergues Cabrales, Jesús M.
N1 - Funding Information:
This work was partially supported by Ministry of Superior Education of the Republic of Cuba under the grant #6.176. The authors acknowledge the San Jorge University for economical support of this research. The authors wish to thank Mario Hechavarría Sánchez, Emilio Suárez and Leonardo Mesa Torres for their technical assistance, and the anonymous reviewer # 2 of Mathematics and Computer in Simulation magazine (reference [15]), who suggested the realization of this work. Also, we wish to thank in a special way the reviewers for their invaluable recommendations and suggestions.
PY - 2011/9/24
Y1 - 2011/9/24
N2 - 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.Conclusion: 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.
AB - 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.Conclusion: 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.
KW - Electric field
KW - Electrotherapy
KW - Tumor
UR - http://www.scopus.com/inward/record.url?scp=80053172450&partnerID=8YFLogxK
U2 - 10.1186/1475-925X-10-85
DO - 10.1186/1475-925X-10-85
M3 - Artículo
C2 - 21943385
AN - SCOPUS:80053172450
SN - 1475-925X
VL - 10
JO - BioMedical Engineering Online
JF - BioMedical Engineering Online
M1 - 85
ER -