3D Stationary electric current density in a spherical tumor treated with low direct current: An analytical solution

Electrotherapy with direct current delivered through implanted electrodes is used for local control of solid tumors in both preclinical and clinical studies. The aim of this research is to develop a solution method for obtaining a three-dimensional analytical expression for potential and electric current density as functions of direct electric current intensity, differences in conductivities between the tumor and the surrounding healthy tissue, and length, number and polarity of electrodes. The influence of these parameters on electric current density in both media is analyzed. The results show that the electric current density in the tumor is higher than that in the surrounding healthy tissue for any value of these parameters. The conclusion is that the solution method presented in this study is of practical interest because it provides, in a few minutes, a convenient way to visualize in 3D the electric current densities generated by a radial electrode array by means of the adequate selection of direct current intensity, length, number, and polarity of electrodes, and the difference in conductivity between the solid tumor and its surrounding healthy tissue.

[1]  E. M. Lifshitz,et al.  Electrodynamics of continuous media , 1961 .

[2]  D. Miklavčič,et al.  Electrode commutation sequence for honeycomb arrangement of electrodes in electrochemotherapy and corresponding electric field distribution. , 2008, Bioelectrochemistry.

[3]  D. Miklavčič,et al.  ELECTRIC PROPERTIES OF TISSUES , 2006 .

[4]  Marcelo M. Morales,et al.  Exposure of human leukemic cells to direct electric current , 2007, Cell Biochemistry and Biophysics.

[5]  Dieter Haemmerich,et al.  In vivo electrical conductivity of hepatic tumours. , 2003, Physiological measurement.

[6]  Hoi Young Lee,et al.  Introduction of Electrochemical Therapy (EChT) and Application of EChT to The Breast Tumor , 2007 .

[7]  Luis Enrique Bergues Cabrales,et al.  Distributions of the potential and electric field of an electrode elliptic array used in tumor electrotherapy: Analytical and numerical solutions , 2009, Math. Comput. Simul..

[8]  HC Ciria,et al.  Antitumor effectiveness of different amounts of electrical charge in Ehrlich and fibrosarcoma Sa-37 tumors , 2004, BMC Cancer.

[9]  K. Foster,et al.  Dielectric Properties of VX-2 Carcinoma Versus Normal Liver Tissue , 1986, IEEE Transactions on Biomedical Engineering.

[10]  Luis Enrique Bergues Cabrales,et al.  Mathematical modeling of tumor growth in mice following low-level direct electric current , 2008, Math. Comput. Simul..

[11]  J. Moore,et al.  Low-level direct electrical current therapy for hepatic metastases. I. Preclinical studies on normal liver. , 1995, British Journal of Cancer.

[12]  Kenneth R. Foster,et al.  Dielectric Properties of Tissues , 2008 .

[13]  L. Vodovnik,et al.  Tumor treatment by direct electric current-tumor temperature and pH, electrode material and configuration , 1993 .

[14]  S. Ueno,et al.  Low‐frequency conductivity tensor of rat brain tissues inferred from diffusion MRI , 2009, Bioelectromagnetics.

[15]  Miriam Fariñas Salas,et al.  Electrochemical treatment of mouse Ehrlich tumor with direct electric current , 2001, Bioelectromagnetics.

[16]  Damijan Miklavcic,et al.  Finite-element modeling of needle electrodes in tissue from the perspective of frequent model computation , 2003, IEEE Transactions on Biomedical Engineering.

[17]  Vasilii S Vladimirov.  Equations of mathematical physics , 1971 .

[18]  K. Hultenby,et al.  Animal models for treatment of unresectable liver tumours: a histopathologic and ultra-structural study of cellular toxic changes after electrochemical treatment in rat and dog liver. , 2003, Bioelectrochemistry.

[19]  Jürgen Hescheler,et al.  Direct current electrical fields induce apoptosis in oral mucosa cancer cells by NADPH oxidase‐derived reactive oxygen species , 2008, Bioelectromagnetics.

[20]  Damijan Miklavčič,et al.  Importance of tumour coverage by sufficiently high local electric field for effective electrochemotherapy , 2006 .

[21]  B. R. Pullan,et al.  The effects of low-level direct current therapy on a preclinical mammary carcinoma: tumour regression and systemic biochemical sequelae. , 1994, British Journal of Cancer.

[22]  D Miklavcic,et al.  Electric current density imaging of mice tumors , 1997, Magnetic resonance in medicine.

[23]  V. S. Vladimirov.  Equations of mathematical physics /3rd edition/ , 1976 .

[24]  Jacqueline K. Telford,et al.  In vivo measurement of tumor conductiveness with the magnetic bioimpedance method , 2000, IEEE Transactions on Biomedical Engineering.

[25]  J. Herbertz.  Comment on the ICNIRP guidelines for limiting exposure to time-varying electric, magnetic, and electromagnetic fields (up to 300 GHz) , 1998, Health physics.

[26]  Reilly Jp.  Comments concerning "Guidelines for limiting exposure to time-varying electric, magnetic, and electromagnetic fields (up to 300 GHz)". , 1999 .

[27]  Mojca Pavlin,et al.  Analytical and numerical quantification and comparison of the local electric field in the tissue for different electrode configurations , 2007, Biomedical engineering online.

[28]  J. McDougall,et al.  Variations of dose and electrode spacing for rat breast cancer electrochemical treatment , 2001, Bioelectromagnetics.

[29]  E. Kirson,et al.  A Pilot Study with Very Low-Intensity, Intermediate-Frequency Electric Fields in Patients with Locally Advanced and/or Metastatic Solid Tumors , 2008, Oncology Research and Treatment.

[30]  J. McDougall,et al.  Electrochemical treatment of mouse and rat fibrosarcomas with direct current. , 1997, Bioelectromagnetics.

[31]  Siegfried Piepenbrock,et al.  In vivo myograph measurement of muscle contraction at optimal length , 2007, Biomedical engineering online.

[32]  S Vinitha Sree,et al.  The Use of Tissue Electrical Characteristics for Breast Cancer Detection: A Perspective Review , 2008, Technology in cancer research & treatment.

[33]  J. Olsson,et al.  Electrochemical treatment (EChT) effects in rat mammary and liver tissue. In vivo optimizing of a dose-planning model for EChT of tumours. , 2001, Bioelectrochemistry.

[34]  Deepak Dhar,et al.  Electric field of a six-needle array electrode used in drug and DNA delivery in vivo: analytical versus numerical solution , 2003, IEEE Transactions on Biomedical Engineering.