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.
[1] D. Vignjevic, and G. Montagnac, "Reorganisation of the dendritic
actin network during cancer cell migration and invasion" Semin.
Cancer. Biol., vol. 18, 12, 2008.
[2] D. G. Mallet, and G. J. Pettet, "A mathematical model of
integrin-mediated haptotactic cell migration" B. Math. Biol., vol. 68,
231, 2006.
[3] 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.
[4] 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.
[5] 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.
[6] H. Yamaguchi, J. Wyckoff, and J. Condeelis, "Cell migration in
tumors" Curr. Opin. Cell. Biol., vol. 17, 559, 2005.
[7] 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.
[8] 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.
[9] 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.
[10] N. Armstrong, K. Painter, and J. Sherratt, "A continuum approach to
modeling cell-cell adhesion." J. Theor. Biol. , vol. 243, 98, 2006.
[11] D. Kim, and W. Lu, "Self-organized nanostructures in multi-phase
epilayers" Nanotechnology, vol. 15, 667, 2004.
[12] W. Lu, and D. Kim, "Engineering nanophase self-assembly with
elastic field" Acta. Mater., vol. 53, 3689, 2005.
[13] Lu, W., and Kim, D. C., "Patterning nanoscale structures by surface
chemistry" Nano. Lett., vol. 4, 313, 2004.
[14] Keller, E. F., "Model for Chemotaxis" J. Theor. Biol. , vol. 30, 225,
1971.
[15] D. Kim, and W. Lu, "Creep flow, diffusion, and electromigration in
small scale interconnects" J. Mech. Phys. Solids. , vol. 54, 2554, 2006.
[16] D. Kim, and W. Lu, "Three-dimensional model of electrostatically
induced pattern formation in thin polymer films" Phys. Rev. B., vol. 73,
035206, 2006.
[17] Song, J. H., and Kim, D., "Three-Dimensional Chemotaxis Model for a
Single Bacterium" J. Comput. Theor. Nanos., vol. 6, 1687, 2009.
[18] 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.
[19] D. Kim, "Computational analysis of the interfacial effect on
electromigration in flip chip solder joints" Microelectron. Eng., vol. 86,
2132, 2009.
[20] 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.
[21] J. W. Cahn, " Free energy of a nonuniform system.1. Interfacial free
energy" J. Chem. Phys., vol. 28, 258, 1958.
[22] T. J. Mitchison, "Cell Movements - Bray, D" Nature, vol. 357, 32,
1992.
[23] A. Aman, and T. Piotrowski, "Cell migration during morphogenesis"
Dev. Biol., vol. In Press, Corrected proof 2009.
[24] 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.
[1] D. Vignjevic, and G. Montagnac, "Reorganisation of the dendritic
actin network during cancer cell migration and invasion" Semin.
Cancer. Biol., vol. 18, 12, 2008.
[2] D. G. Mallet, and G. J. Pettet, "A mathematical model of
integrin-mediated haptotactic cell migration" B. Math. Biol., vol. 68,
231, 2006.
[3] 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.
[4] 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.
[5] 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.
[6] H. Yamaguchi, J. Wyckoff, and J. Condeelis, "Cell migration in
tumors" Curr. Opin. Cell. Biol., vol. 17, 559, 2005.
[7] 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.
[8] 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.
[9] 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.
[10] N. Armstrong, K. Painter, and J. Sherratt, "A continuum approach to
modeling cell-cell adhesion." J. Theor. Biol. , vol. 243, 98, 2006.
[11] D. Kim, and W. Lu, "Self-organized nanostructures in multi-phase
epilayers" Nanotechnology, vol. 15, 667, 2004.
[12] W. Lu, and D. Kim, "Engineering nanophase self-assembly with
elastic field" Acta. Mater., vol. 53, 3689, 2005.
[13] Lu, W., and Kim, D. C., "Patterning nanoscale structures by surface
chemistry" Nano. Lett., vol. 4, 313, 2004.
[14] Keller, E. F., "Model for Chemotaxis" J. Theor. Biol. , vol. 30, 225,
1971.
[15] D. Kim, and W. Lu, "Creep flow, diffusion, and electromigration in
small scale interconnects" J. Mech. Phys. Solids. , vol. 54, 2554, 2006.
[16] D. Kim, and W. Lu, "Three-dimensional model of electrostatically
induced pattern formation in thin polymer films" Phys. Rev. B., vol. 73,
035206, 2006.
[17] Song, J. H., and Kim, D., "Three-Dimensional Chemotaxis Model for a
Single Bacterium" J. Comput. Theor. Nanos., vol. 6, 1687, 2009.
[18] 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.
[19] D. Kim, "Computational analysis of the interfacial effect on
electromigration in flip chip solder joints" Microelectron. Eng., vol. 86,
2132, 2009.
[20] 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.
[21] J. W. Cahn, " Free energy of a nonuniform system.1. Interfacial free
energy" J. Chem. Phys., vol. 28, 258, 1958.
[22] T. J. Mitchison, "Cell Movements - Bray, D" Nature, vol. 357, 32,
1992.
[23] A. Aman, and T. Piotrowski, "Cell migration during morphogenesis"
Dev. Biol., vol. In Press, Corrected proof 2009.
[24] 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.
@article{"International Journal of Medical, Medicine and Health Sciences:62946", author = "Zhang Linan and Jihwan Song and Dongchoul Kim", title = "A Study on Cancer-Cell Invasion Based On the Diffuse Interface Model", abstract = "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.
", keywords = "Haptotaxis, Cancer Cells, Cell Migration, Interface Energy, Diffuse Interface Model", volume = "4", number = "8", pages = "390-4", }
