A Study on Cancer-Cell Invasion Based On the Diffuse Interface Model
In this study, a three-dimensional haptotaxis model to simulate the migration of a population of cancer cells has been proposed. The invasion of cancer cells is related with the hapto-attractant and the effect of the interface energies between the cells and the ECM. The diffuse interface model, which incorporates the haptotaxis mechanism and interface energies, is employed. The semi-implicit Fourier spectral scheme is adopted for efficient evaluation of the simulation. The simulation results thoroughly reveal the dynamics of cancer-cell migration.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1082061Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1104
 D. Vignjevic, and G. Montagnac, "Reorganisation of the dendritic actin network during cancer cell migration and invasion" Semin. Cancer. Biol., vol. 18, 12, 2008.
 D. G. Mallet, and G. J. Pettet, "A mathematical model of integrin-mediated haptotactic cell migration" B. Math. Biol., vol. 68, 231, 2006.
 X. L. Shen, L. H. Qian, and M. Falzon, "PTH-related protein enhances MCF-7 breast cancer cell adhesion, migration, and invasion via an intracrine pathway" Exp. Cell. Res., vol. 294, 420, 2004.
 F. Wang, R. Zhang, T. Xia, E. Hsu, Y. Cal, Z. Gu, and O. Hankinson, "Inhibitory effects of nitric oxide on invasion of human cancer cells" Cancer. Lett., vol. 257, 274, 2007.
 I. S. Zagon, K. A. Rahn, and P. J. McLaughlin, "Opioids and migration, chemotaxis, invasion, and adhesion of human cancer cells" Neuropeptides, vol. 41, 441, 2007.
 H. Yamaguchi, J. Wyckoff, and J. Condeelis, "Cell migration in tumors" Curr. Opin. Cell. Biol., vol. 17, 559, 2005.
 T. Frisk, S. Rydholm, T. Liebmann, H. A. Svahn, G. Stemme, and H. Brismar, "A microfluidic device for parallel 3-D cell cultures in asymmetric environments" Electrophoresis, vol. 28, 4705, 2007.
 A. Gerisch, and M. Chaplain, "Mathematical modelling of cancer cell invasion of tissue: Local and non-local models and the effect of adhesion" J. Theor. Biol., vol. 250, 684, 2008.
 Ramis-Conde, I., Chaplain, M. A. J., and Anderson, A. R. A., "Mathematical modelling of cancer cell invasion of tissue" Math. Comput. Model., vol. 47, 533, 2008.
 N. Armstrong, K. Painter, and J. Sherratt, "A continuum approach to modeling cell-cell adhesion." J. Theor. Biol. , vol. 243, 98, 2006.
 D. Kim, and W. Lu, "Self-organized nanostructures in multi-phase epilayers" Nanotechnology, vol. 15, 667, 2004.
 W. Lu, and D. Kim, "Engineering nanophase self-assembly with elastic field" Acta. Mater., vol. 53, 3689, 2005.
 Lu, W., and Kim, D. C., "Patterning nanoscale structures by surface chemistry" Nano. Lett., vol. 4, 313, 2004.
 Keller, E. F., "Model for Chemotaxis" J. Theor. Biol. , vol. 30, 225, 1971.
 D. Kim, and W. Lu, "Creep flow, diffusion, and electromigration in small scale interconnects" J. Mech. Phys. Solids. , vol. 54, 2554, 2006.
 D. Kim, and W. Lu, "Three-dimensional model of electrostatically induced pattern formation in thin polymer films" Phys. Rev. B., vol. 73, 035206, 2006.
 Song, J. H., and Kim, D., "Three-Dimensional Chemotaxis Model for a Single Bacterium" J. Comput. Theor. Nanos., vol. 6, 1687, 2009.
 A. Karma, and W. J. Rappel, "Quantitative phase-field modeling of dendritic growth in two and three dimensions" Phys. Rev. E., vol. 57, 4323, 1998.
 D. Kim, "Computational analysis of the interfacial effect on electromigration in flip chip solder joints" Microelectron. Eng., vol. 86, 2132, 2009.
 M. Alber, N. Chen, T. Glimm, and P. M. Lushnikov, "Multiscale dynamics of biological cells with chemotactic interactions: From a discrete stochastic model to a continuous description" Phys. Rev. E., vol. 73, 051901, 2006.
 J. W. Cahn, " Free energy of a nonuniform system.1. Interfacial free energy" J. Chem. Phys., vol. 28, 258, 1958.
 T. J. Mitchison, "Cell Movements - Bray, D" Nature, vol. 357, 32, 1992.
 A. Aman, and T. Piotrowski, "Cell migration during morphogenesis" Dev. Biol., vol. In Press, Corrected proof 2009.
 K. Yamauchi, M. Yang, P. Jiang, M. X. Xu, N. Yamamoto, H. Tsuchiya, K. Tomita, A. R. Moossa, M. Bouvet, and R. M. Hoffman, "Development of real-time subcellular dynamic multicolor imaging of cancer-cell trafficking in live mice with a variable-magnification whole-mouse imaging system" Cancer. Res., vol. 66, 4208, 2006.