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

Bioelectromagnetics

Volumn 32, Issue 2, 2011, Pages 120-130

  Jiménez, Rolando Placeres ^a,b   Pupo, Ana Elisa Bergues ^b   Cabrales, Jesús Manuel Bergues ^c   Joa, Javier Antonio González ^b   Cabrales, Luis Enrique Bergues ^b,d   Nava, Juan José Godina ^d   Aguilera, Andrés Ramírez ^b   Mateus, Miguel Angel O'Farril ^e   Jarque, Manuel Verdecia ^f   Brooks, Soraida Candida Acosta ^g  

^a FEDERAL UNIVERSITY OF SÃO CARLOS   (Brazil)

^b UNIVERSIDAD DE ORIENTE   (Cuba)

^c UNIVERSIDAD SAN JORGE   (Spain)

^d INSTITUTO POLITÉCNICO NACIONAL   (Mexico)

^e Hospital Oncologico Docente Provincial Conrado Benitez   (Cuba)

^f Hospital Infantil Sur   (Cuba)

^g Hospital Provincial Saturnino Lora   (Cuba)

Author keywords

Electric current density; Electrotherapy; Mathematical modeling; Tumor

Indexed keywords

CURRENT DENSITY; ELECTRODES; ELECTROTHERAPEUTICS;

CURRENT INTENSITY; DIRECT-CURRENT; ELECTRIC CURRENT DENSITY; ELECTROTHERAPY; HEALTHY TISSUES; IMPLANTED ELECTRODES; LOCAL CONTROL; MATHEMATICAL MODELING; SOLID TUMORS; SOLUTION METHODS;

TUMORS;

ARTICLE; BIOLOGICAL MODEL; ELECTRIC CONDUCTIVITY; ELECTRODE; ELECTROSTIMULATION THERAPY; METHODOLOGY; NEOPLASM;

ELECTRIC CONDUCTIVITY; ELECTRIC STIMULATION THERAPY; ELECTRODES; MODELS, BIOLOGICAL; NEOPLASMS;

EID: 78651311314     PISSN: 01978462     EISSN: 1521186X     Source Type: Journal    
DOI: 10.1002/bem.20611     Document Type: Article

References (37)

1. Aguilera AR, Cabrales LEB, Ciria HMC, Pérez YS. 2008. ONCOMAPET® software. Cuban National Bureau of Standards (No. 399-2008).
2. Aguilera AR, Cabrales LEB, Ciria HMC, Pérez YS, Oria ER, Brooks SA. 2009. Distributions of the potential and electric field of an electrode elliptic array used in electrotherapy: Analytical and numerical solutions. Math Comput Simul 79: 2091-2105.
3. Cabrales LB, Ciria HC, Bruzón RP, Quevedo MS, Aldana RH, De Oca LM, Salas MF, Peña OG. 2001. Electrochemical treatment of mouse Ehrlich tumor with direct electric current. Bioelectromagnetics 22: 316-322.
4. Cabrales LEB, Aguilera AR, Placeres RJ, Jarque MV, Mateus MAO, Ciria HMC, Reyes JB, Ávila MG. 2008. Mathematical modeling of tumor growth in mice following low-level direct electric current. Math Comp Simul 78: 112-120.
5. Chou CK, McDougall JA, Ahn C, Vora N. 1997. Electrochemical treatment of mouse and rat fibrosarcomas with direct current. Bioelectromagnetics 18: 14-24.
6. Ciria HMC, Quevedo MS, Cabrales LEB, Bruzón RNP, Salas MF, Peña OG, González TR, López DS, Flores M. 2004. Antitumor effectiveness of different amounts of electrical charge in Ehrlich and fibrosarcoma Sa-37 tumors. BMC Cancer 4: 87-91.
7. ČoroviČ S, Pavlin M, MiklavČiČ D. 2007. Analytical and numerical quantification and comparison of the local electric field in the tissue for different electrode configurations. Biomed Eng Online 6: 1-14.
8. Dev BS, Dhar D, Krassowska W. 2003. Electric field of a six-needle array electrode used in drug and DNA delivery in vivo: Analytical versus numerical solution. IEEE Trans Biomed Eng 50: 1296-1300.
9. Dodd NJF, Moore JV, Taylor TV, Zhoo S. 1993. Preliminary evaluation of low level direct current therapy using magnetic resonance imaging and spectroscopy. Phys Med 4: 2-8.
10. Foster KR, Schwan HP. 1996. Dielectric properties of tissues. Chapter 1. Polk C, Postow E, editors. Handbook of biological effects of electromagnetic fields. 2nd edition. Boca Raton, FL: CRC Press. pp. 68-70.
11. Griffin DT, Dodd NFJ, Moore JV, Pullan BR, Taylor TV. 1994. The effects of low level direct current therapy on a preclinical mammary carcinoma: Tumor regression and systemic biochemical sequelae. Br J Cancer 69: 875-878.
12. Griffin DT, Dodd NJF, Zhao S, Pullan BR, Moore JV. 1995. Low level direct electrical current therapy for hepatic metastases. I. Preclinical studies on normal liver. Br J Cancer 72: 31-34.
13. Haemmerich D, Staelin ST, Tsai JZ, Tungjitkusolmun S, Mahvi1 DM, Webster JG. 2003. In vivo electrical conductivity of hepatic tumours. Physiol Meas 24: 251-260.
14. Haltiwanger S. 2008. The Electrical Properties of Cancer Cells. (Last accessed 2 April 2008).
15. ICNIRP. 1998. Guidelines for limiting exposure to time-varying electric, magnetic, and electromagnetic fields up to 300 GHz. International commission on non-ionizing radiation protection. Health Phys 74(4): 494-522.
16. Jarque MV, Mateus MAF, Palencia FS, Cabrales LEB, Jing-Hong L, Ciria HMC, Brooks SCA, Salas MF, Quevedo MCS, Bestard NR, Fernández SG, González TR, Hernández MR, Bordelois KC. 2007. First clinical experiences in Cuba over the use of electrotherapy in four patients with superficial malignant solid tumors. Rev MEDISAM 11: 1-8.
17. Landau LD, Lifshitz EM. 1984. Electrodynamics of continuous media. Vol. 8, 3rd edition. Course of theoretical physics. New York: Pergamon Press.
18. Lin XZ, Jen CM, Chou CK, Chou CS, Sung MJ, Chou TC. 2000. Saturated saline enhances the effect of electrochemical therapy. Dig Dis Sci 45: 509-514.
19. MiklavČiČ D, Serša G, Kryžanowski M, NovakoviČ S, BobanoviČ F, Golouh R. 1993. Tumor treatment by direct electric current tumor temperature and pH, electrode material and configuration. Bioelectrochem Bioenerg 30: 209-220.
20. MiklavČiČ D, Corovic S, Pucihar G, Pavselj N. 2006a. Importance of tumour coverage by sufficiently high local electric field for effective electrochemotherapy. Eur J Cancer Suppl 4: 45-51.
21. MiklavČiČ D, Pavšelj N, Hart FX. 2006b. Electric properties of tissues. In: Akay M, editor. Wiley encyclopedia of biomedical engineering. Vol. 6. New York: John Wiley and Sons. pp. 3578-3589.
22. Ng E, Sree S, Ng K, Kaw G. 2008. The use of tissue electrical characteristics for breast cancer detection: A perspective review. Tech Cancer Res Treat 7: 295-308.
23. Reberšek M, ČoroviĆ S, Serša G, MiklavČiČ D. 2008. Electrode commutation sequence for honeycomb arrangement of electrodes in electrochemotherapy and corresponding electric field distribution. Bioelectrochemistry 74: 26-31.
24. Ren RL, Vora N, Yang F, Longmate J, Wang W, Sun H, Li JR, Weiss L, Staud C, McDougall JA, Chou CK. 2001. Variations of dose and electrode spacing for rat breast cancer electrochemical treatment. Bioelectromagnetics 22: 205-211.
25. Salzberg M, Kirson E, Palti Y, Rochlitza C. 2008. A pilot study with very low-intensity, intermediate-frequency electric fields in patients with locally advanced and/or metastatic solid tumors. Onkologie 31: 362-365.
26. Sekino M, Ohsaki H, Yamaguchi-Sekino S, Iriguchi N, Ueno S. 2009. Low-frequency conductivity tensor of rat brain tissues inferred from diffusion MRI. Bioelectromagnetics 30: 489-499.
27. Šel D, Mazeres S, Teissié J, MiklavČiČ D. 2003. Finite-element modeling of needle electrodes in tissue from the perspective of frequent model computation. IEEE Trans Biomed Eng 50: 1221-1232.
28. Serša I, Beravs K, Dodd NJF, Zhao S, MiklavČiČ D, Demsar F. 1997. Electric current density imaging of mice tumors. Magn Reson Med 37: 404-409.
29. Smith SR, Foster KR, Wolf GL. 1986. Dielectric properties of VX-2 carcinoma versus normal liver tissue. IEEE Trans Biomed Eng 33: 522-524.
30. Smith DG, Potter SR, Lee BR, Ko WW, Drummond WR, Telford JK, Partin AW. 2000. In vivo measurement of tumor conductiveness with the magnetic bioimpedance method. IEEE Trans Biomed Eng 47: 1403-1405.
31. Tijonov AN, Samarsky AA. 1983. Equations of mathematical physics. 3rd edition. Moscow: Mir Publishers.
32. Veiga VF, Nimrichter L, Teixeira CA, Morales MM, Alviano CS, Rodrigues ML, Holandino C. 2005. Exposure of human leukemic cells to direct electric current: Generation of toxic compounds inducing cell death by different mechanisms. Cell Biochem Biophys 42: 61-74.
33. von Euler H, Nilsson E, Olsson JM, Lagersted AS. 2001. Electrochemical treatment (EchT) effects in rat mammary and liver tissue. In vivo optimizing of a dose-planning model for EchT of tumours. Bioelectrochemistry 54: 117-124.
34. von Euler H, Olsson JM, Hultenby K, Thorne A, Lagerstedt AS. 2003. 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. Bioelectrochemistry 59: 89-98.
35. Wartenberg M, Wirtz N, Grob A, Niedermeier W, Hescheler J, Peters SC, Sauer H. 2008. Direct current electrical fields induce apoptosis in oral mucosa cancer cells by NADPH oxidase-derived reactive oxygen species. Bioelectromagnetics 29: 47-54.
36. Yoon DS, Ra YM, Ko DG, Kim YM, Kim KW, Lee HY, Xin YL, Zhang W, Li ZH, Kwon HU. 2007. Introduction of electrochemical therapy (EChT) and application of EChT to the breast tumor. J Breast Cancer 10: 162-168.
37. Yuling X. 2004. The development of electrochemical therapy in China. In: Proceedings of the 8th Congress on Tumors of International Association of Biological Closed Electric Circuits. pp. 4-8. Nanning, China, September 21-23.