Diffusion-Drift Modeling of a Growing Breast Cancerous Cell

IEEE Transactions on Biomedical Engineering

Volumn 56, Issue 10, 2009, Pages 2370-2379

  Hassan, Ahmed M ^a   El Shenawee, Magda ^a  

^a University of Arkansas   (United States)

Author keywords

Bioelectric phenomena; biological cells; biophysics; cancer; MCF 7 cells

Indexed keywords

ALGORITHM; ARTICLE; BIOLOGICAL MODEL; BREAST TUMOR; CELL CYCLE G1 PHASE; CELL CYCLE S PHASE; CELL GROWTH; COMPUTER SIMULATION; ELECTROMAGNETIC FIELD; ELECTROPHYSIOLOGY; FEMALE; HUMAN; PATHOLOGY; PHYSIOLOGY; TUMOR CELL LINE;

ALGORITHMS; BREAST NEOPLASMS; CELL GROWTH PROCESSES; CELL LINE, TUMOR; COMPUTER SIMULATION; ELECTROMAGNETIC FIELDS; ELECTROPHYSIOLOGICAL PHENOMENA; FEMALE; G1 PHASE; HUMANS; MODELS, BIOLOGICAL; S PHASE;

EID: 74049145269     PISSN: 00189294     EISSN: 15582531     Source Type: Journal    
DOI: 10.1109/TBME.2009.2024539     Document Type: Article

References (31)

1. Ph. A. Anninos, A. Kotini, N. Koutlaki, A. Adamopouos, G. Galazios, and P. Anastasiadis, “Differential diagnosis of breast lesions by use of biomagnetic activity and non-linear analysis,” Eur. J. Gynaecol. Oncol., vol. 21, no. 6, pp. 591–595, 2000.
2. A. Kotini, A. Anastasiadis, N. Koutlaki, D. Tamiolakis, P. Anninos, and P. Anastiadis, “Biomagnetism in gynecologic oncology. Our experience in Greece,” Eur. J. Gynaecol. Oncol., vol. 27, no. 6, pp. 594–596, 2006.
3. A. Hassan, M. El-Shenawee, and H. Eswaran, “A feasibility study for passive detection of breast tumors using naturally generated magnetic fields,” presented at the IEEE AP-S Symp. USNC/URSI Nat. Radio Sci. Meeting, San Diego, CA, Jul. 2008, pp. 5–12.
4. A. Marino, D. Morris, M. Schwalke, I. Iliev, and S. Rogers “Electrical potential measurements in human breast cancer and benign lesions,” Tumor Biol., vol. 15, pp. 147–152, 1994.
5. M. Faupel, D. Vanel, V. Barth, R. Davies, I. S. Fentiman, R. Holland, J. L. Lamarque, V. Sacchini, and I. Schreer “Electropotential evaluation as a new technique for diagnosing breast lesions,” Eur. J. Radiol., vol. 24, no. 1, pp. 33–38, Jan. 1997.
6. V. Sacchini “Report of the European school of oncology task force on electropotentials in the clinical assessment of neoplasia,” Breast, vol. 5, pp. 282–286, 1996.
7. J. Cuzick, R. Holland, V. Barth, R. Davies, M. Faupel, I. Fentiman, H. Frischbier, J. LaMarque, M. Merson, V. Sacchini, D. Vanel, and U. Veronesi “Electropotential measurements as a new diagnostic modality for breast cancer,” Lancet, vol. 352, pp. 359–363, Aug. 1998.
8. S. Baillet, J. Mosher, and R. Leahy, “Electromagnetic brain mapping,” IEEE Signal Process. Mag., vol. 18, no. 6, pp. 14–30, Nov. 2001.
9. J. Vrba, S. E. Robinson, J. McCubbin, C. L. Lowery, H. Eswaran, P. Murphy, and H. Preissl, “Searching for the best model: Ambiguity of inverse solutions and application to fetal magnetoencephalography,” J. Phys. Med. Biol., vol. 52, pp. 757–776, Jan. 2007.
10. J. Sarvas “Basic mathematical and electromagnetic concepts of the biomagnetic inverse problem,” Phys. Med. Biol., vol. 32, pp. 11–22, 1987.
11. M. Levin, “Bioelectromagnetics in morphogenesis,” Bioelectromagnetics, vol. 24, pp. 295–315, 2003.
12. R. Bingelli and R. Weinstein “Membrane potentials and sodium channels: Hypothesis for growth regulation and cancer formation based on changes in sodium channels and gap junctions,” J. Theor. Biol., vol. 123, pp. 377–401, 1986.
13. C. Mummery, J. Boonstra, L. Tertoolen, P. Van Der Saag, and S. De Laat “Modulation of functional and optimal (Na+–K+)ATPase activity during the cell cycle of neuroblastoma cells,” J. Cell. Physiol., vol. 107, no. 1, pp. 1–9, 1981.
14. J. Boonstra, C. Mummery, L. Tertoolen, P. Van Der Saag, and S. De Laat “Cation transport and growth regulation in neuroblastoma cells. Modulations of K+ transport and electrical membrane properties during the cell cycle,” J. Cell. Physiol., vol. 107, no. 1, pp. 75–83, 1981.
15. J. Strobl, W. Wonderlin, and D. Flynn “Mitogenic signal transduction in human breast cancer cells,” Gen. Pharmacol., vol. 26, no. 8, pp. 1643–1649, 1995.
16. W. Wonderlin, K. Woodfork, and J. Strobl “Changes in membrane potential during the progression of MCF-7 human mammary tumor cells through the cell cycle,” J. Cell. Physiol., vol. 165, pp. 177–185, 1995.
17. H. Ahidouch and A. Ahidouch, “K+ channel expression in human breast cancer cells: Involvement in cell cycle regulation and carcinogenesis,” J. Membr. Biol., vol. 221, pp. 1–6, 2008.
18. J. Enderle, S. Blanchard, and J. Bronzino, Introduction to Biomedical Engineering, 2nd ed. New York: Elsevier/Academic, 2005.
19. S. Yoganathan and S. Banerjee “A new decoupled algorithm for non-staionary, transient simulations of GaAs MOSFET's,” IEEE Trans. Electron Devices, vol. 39, no. 7, pp. 1578–1587, Jul. 1992.
20. D. L. Scharfetter and H. K. Gummel “Large-signal analysis of a silicon read diode oscillator,” IEEE Trans. Electron Devices, vol. ED-16, no. 1, pp. 64–77, Jan. 1969.
21. J. Kreskovsky “A hybrid central difference scheme for solid-state device simulation,” IEEE Trans. Electron Devices, vol. 34, no. 5, pp. 1128–1133, May 1987.
22. G. Marshall and P. Mocskos “Growth model for ramified electrochemical deposition in the presence of diffusion, migration, and electroconvection,” Phys. Rev. E, vol. 55, no. 1, pp. 549–563, 1997.
23. S. Ferreira, Jr., M. Martins, and M. Vilela, “Reaction-diffusion model for the growth of avascular tumor,” Phys. Rev. E, vol. 65, no. 2, pp. 021907–1–021907-8, 2002.
24. M. Chaplain and H. Byrne “Mathematical models for tumour angiogenesis: Numerical simulations and nonlinear wave solutions,” Bull. Math. Biol., vol. 57, pp. 461–486, 1995.
25. H. Lodish, A. Berk, P. Matsudaira, C. Kaiser, M. Krieger, M. Scott, S. Zipursky, and J. Darnell, Molecular Cell Biology, 5th ed. San Francisco, CA: Freeman, 2003.
26. B. Hille, Ion Channels of Excitable Membranes, 3rd ed. Sunderland, MA: Sinauer Associates, 2001.
27. P. Czapski, C. Ramon, L. Huntsman, G. Bardy, and Y. Kim “Effects of tissue conductivity variations on the cardiac magnetic fields simulated with a realistic heart-torso model,” Phys. Med. Biol., vol. 41, pp. 1247–1263, 1996.
28. A. Deutsch, S. Dormann, and P. Maini, Cellular Automaton Modeling of Biological Pattern Formation, 1st ed. Cambridge, MA: Birkhauser Boston, 2004, ch. 4.
29. A. Patel, E. Gawlinskia, S. Lemiexue, and R. Gatenbyb, “Cellular automaton model of early tumor growth and invasion: The effects of native tissue vascularity and increased anaerobic tumor metabolism,” J. Theor. Biol., vol. 213, pp. 315–331, 2001.
30. F. Dorr “The direct solution of the discrete Poisson equation on a rectangle,” SIAM Rev., vol. 12, no. 2, pp. 248–263, Apr. 1970.
31. V. Lew and R. Bookchin, “Volume, pH, and ion-content regulation in human red cells: Analysis of transient behavior with an integrated model,” J. Membr. Biol., vol. 92, pp. 57–74, 1986.