Analytical Solution for Electrical Problem Forced by a Finite-Length Needle Electrode: Implications in Electrostimulation
Joint Authors
Berjano, Enrique
Romero-Méndez, Ricardo
Pérez-Gutiérrez, Francisco G.
Oviedo-Tolentino, Francisco
Source
Mathematical Problems in Engineering
Issue
Vol. 2019, Issue 2019 (31 Dec. 2019), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2019-05-19
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
Needle electrodes, widely used in clinical procedures, are responsible for creating an electric field in the treated biological tissue.
This is achieved by setting a constant voltage along the length of their metallic section.
In accordance with Laplace’s equation, the electric field is spatially non-uniform around the electrode surface.
Mathematical modelling can provide useful information on the spatial distribution of electrical fields.
Indeed, exact solutions for the electrical problem are indispensable for validating numerical codes.
All the analytical models developed to date to solve the needle electrode electrical problem have been one-dimensional models, which assumed an electrode of infinite length.
We here propose the first analytical solution based on a two-dimensional model that considers the real length of the electrode in which the Laplace equation is solved through the method of separation of variables, dealing with the nonhomogeneous source term and boundary conditions by Green’s functions.
On assuming a needle electrode of given length, the problem combines boundary conditions on the electrode boundary (of the first and second kind).
Since this rules out using the Sturm-Liouville Theorem, the problem is decomposed into two different problems and the principle of superposition is used.
The solution obtained can reproduce a reasonable electric field around the electrode, especially the edge effect characterized by an extremely high gradient around the electrode tip.
American Psychological Association (APA)
Romero-Méndez, Ricardo& Pérez-Gutiérrez, Francisco G.& Oviedo-Tolentino, Francisco& Berjano, Enrique. 2019. Analytical Solution for Electrical Problem Forced by a Finite-Length Needle Electrode: Implications in Electrostimulation. Mathematical Problems in Engineering،Vol. 2019, no. 2019, pp.1-10.
https://search.emarefa.net/detail/BIM-1194747
Modern Language Association (MLA)
Romero-Méndez, Ricardo…[et al.]. Analytical Solution for Electrical Problem Forced by a Finite-Length Needle Electrode: Implications in Electrostimulation. Mathematical Problems in Engineering No. 2019 (2019), pp.1-10.
https://search.emarefa.net/detail/BIM-1194747
American Medical Association (AMA)
Romero-Méndez, Ricardo& Pérez-Gutiérrez, Francisco G.& Oviedo-Tolentino, Francisco& Berjano, Enrique. Analytical Solution for Electrical Problem Forced by a Finite-Length Needle Electrode: Implications in Electrostimulation. Mathematical Problems in Engineering. 2019. Vol. 2019, no. 2019, pp.1-10.
https://search.emarefa.net/detail/BIM-1194747
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1194747