2011, 8(2): 371-383. doi: 10.3934/mbe.2011.8.371

Tumor cells proliferation and migration under the influence of their microenvironment

1. 

Department of Mathematics, Ohio State University, Columbus, OH 43210, United States

2. 

Department of Mathematics & Statistics, University of Michigan, Dearborn, MI 48128

Received  February 2010 Revised  October 2010 Published  April 2011

It is well known that tumor microenvironment affects tumor growth and metastasis: Tumor cells may proliferate at different rates and migrate in different patterns depending on the microenvironment in which they are embedded. There is a huge literature that deals with mathematical models of tumor growth and proliferation, in both the avascular and vascular phases. In particular, a review of the literature of avascular tumor growth (up to 2006) can be found in Lolas [8] (G. Lolas, Lecture Notes in Mathematics, Springer Berlin / Heidelberg, 1872, 77 (2006)). In this article we report on some of our recent work. We consider two aspects, proliferation and of migration, and describe mathematical models based on in vitro experiments. Simulations of the models are in agreement with experimental results. The models can be used to generate hypotheses regarding the development of drugs which will confine tumor growth.
Citation: Avner Friedman, Yangjin Kim. Tumor cells proliferation and migration under the influence of their microenvironment. Mathematical Biosciences & Engineering, 2011, 8 (2) : 371-383. doi: 10.3934/mbe.2011.8.371
References:
[1]

K. Asano, C. D. Duntsch, Q. Zhou, J. D. Weimar, D. Bordelon, J. H. Robertson and T. Pourmotabbed, Correlation of n-cadherin expression in high grade gliomas with tissue invasion,, J Neurooncol, 70 (2004), 3.  doi: 10.1023/B:NEON.0000040811.14908.f2.  Google Scholar

[2]

S. Aznavoorian, M. L. Stracke, H. Krutzsch, E. Schiffmann and L. A. Liotta, Signal transduction for chemotaxis and haptotaxis by matrix molecules in tumor cells,, J Cell Biol, 110 (1990), 1427.  doi: 10.1083/jcb.110.4.1427.  Google Scholar

[3]

N. A. Bhowmick, E. G. Neilson and H. L. Moses, Stromal fibroblasts in cancer initiation and progression,, Nature, 432 (2004), 332.  doi: 10.1038/nature03096.  Google Scholar

[4]

E. Khain and L. M. Sander, Dynamics and pattern formation in invasive tumor growth,, Phys. Rev. Lett., 96 (2006).  doi: 10.1103/PhysRevLett.96.188103.  Google Scholar

[5]

Y. Kim and A. Friedman, Interaction of tumor with its microenvironment: A mathematical model,, Bull. Math. Biol., 72 (2010), 1029.  doi: 10.1007/s11538-009-9481-z.  Google Scholar

[6]

Y. Kim, J. Wallace, F. Li, M. Ostrowski and A. Friedman, Transformed epithelial cells and fibroblasts/myofibroblasts interaction in breast tumor: A mathematical model and experiments,, J. Math. Biol., 61 (2010), 401.  doi: 10.1007/s00285-009-0307-2.  Google Scholar

[7]

Y. Kim, S. Lawler, M. O. Nowicki, E. A Chiocca and A. Friedman, A mathematical model of brain tumor : Pattern formation of glioma cells outside the tumor spheroid core,, Journal of Theoretical Biology, 260 (2009), 359.  doi: 10.1016/j.jtbi.2009.06.025.  Google Scholar

[8]

G. Lolas, Mathematical modelling of proteolysis and cancer cell invasion of tissue,, in, (2006), 77.   Google Scholar

[9]

M. M. Mueller and N. E. Fusenig, Friends or foes - bipolar effects of the tumour stroma in cancer,, Nat Rev Cancer, 4 (2004), 839.  doi: 10.1038/nrc1477.  Google Scholar

[10]

A. J. Perumpanani and H. M. Byrne, Extracellular matrix concentration exerts selection pressure on invasive cells,, Eur. J. Cancer, 35 (1999), 1274.  doi: 10.1016/S0959-8049(99)00125-2.  Google Scholar

[11]

M. Samoszuk, J. Tan and G. Chorn, Clonogenic growth of human breast cancer cells co-cultured in direct contact with serum-activated fibroblasts,, Breast Cancer Res, 7 (2005).  doi: 10.1186/bcr995.  Google Scholar

[12]

L. M. Sander and T. S. Deisboeck, Growth patterns of microscopic brain tumors,, Phys. Rev. E, 66 (2002).  doi: 10.1103/PhysRevE.66.051901.  Google Scholar

[13]

J. A. Sherratt and J. D. Murray, Models of epidermal wound healing,, Proc. R. Soc. Lond., B241 (1990), 29.  doi: 10.1098/rspb.1990.0061.  Google Scholar

[14]

A. M. Stein, T. Demuth, D. Mobley, M. Berens and L. M. Sander, A mathematical model of glioblastoma tumor spheroid invasion in a three-dimensional in vitro experiment,, Biophys. J., 92 (2007), 356.  doi: 10.1529/biophysj.106.093468.  Google Scholar

[15]

K. R. Swanson, E. C. Alvord and J. D. Murray, A quantitative model for differential motility of gliomas in grey and white matter,, Cell Prolif., 33 (2000), 317.  doi: 10.1046/j.1365-2184.2000.00177.x.  Google Scholar

[16]

K. R. Swanson, E. C. Alvord and J. D. Murray, Virtual resection of gliomas: Effect of extent of resection on recurrence,, Math. Comp. Modelling, 37 (2003), 1177.  doi: 10.1016/S0895-7177(03)00129-8.  Google Scholar

[17]

M. Yashiro, K. Ikeda, M. Tendo, T. Ishikawa and K. Hirakawa, Effect of organ-specific fibroblasts on proliferation and differentiation of breast cancer cells,, Breast Cancer Res Treat, 90 (2005), 307.  doi: 10.1007/s10549-004-5364-z.  Google Scholar

[18]

K. Yuan, R. K. Singh, G. Rezonzew and G. P. Siegal, Cell motility in cancer invasion and metastasis,, in, (2006), 25.   Google Scholar

show all references

References:
[1]

K. Asano, C. D. Duntsch, Q. Zhou, J. D. Weimar, D. Bordelon, J. H. Robertson and T. Pourmotabbed, Correlation of n-cadherin expression in high grade gliomas with tissue invasion,, J Neurooncol, 70 (2004), 3.  doi: 10.1023/B:NEON.0000040811.14908.f2.  Google Scholar

[2]

S. Aznavoorian, M. L. Stracke, H. Krutzsch, E. Schiffmann and L. A. Liotta, Signal transduction for chemotaxis and haptotaxis by matrix molecules in tumor cells,, J Cell Biol, 110 (1990), 1427.  doi: 10.1083/jcb.110.4.1427.  Google Scholar

[3]

N. A. Bhowmick, E. G. Neilson and H. L. Moses, Stromal fibroblasts in cancer initiation and progression,, Nature, 432 (2004), 332.  doi: 10.1038/nature03096.  Google Scholar

[4]

E. Khain and L. M. Sander, Dynamics and pattern formation in invasive tumor growth,, Phys. Rev. Lett., 96 (2006).  doi: 10.1103/PhysRevLett.96.188103.  Google Scholar

[5]

Y. Kim and A. Friedman, Interaction of tumor with its microenvironment: A mathematical model,, Bull. Math. Biol., 72 (2010), 1029.  doi: 10.1007/s11538-009-9481-z.  Google Scholar

[6]

Y. Kim, J. Wallace, F. Li, M. Ostrowski and A. Friedman, Transformed epithelial cells and fibroblasts/myofibroblasts interaction in breast tumor: A mathematical model and experiments,, J. Math. Biol., 61 (2010), 401.  doi: 10.1007/s00285-009-0307-2.  Google Scholar

[7]

Y. Kim, S. Lawler, M. O. Nowicki, E. A Chiocca and A. Friedman, A mathematical model of brain tumor : Pattern formation of glioma cells outside the tumor spheroid core,, Journal of Theoretical Biology, 260 (2009), 359.  doi: 10.1016/j.jtbi.2009.06.025.  Google Scholar

[8]

G. Lolas, Mathematical modelling of proteolysis and cancer cell invasion of tissue,, in, (2006), 77.   Google Scholar

[9]

M. M. Mueller and N. E. Fusenig, Friends or foes - bipolar effects of the tumour stroma in cancer,, Nat Rev Cancer, 4 (2004), 839.  doi: 10.1038/nrc1477.  Google Scholar

[10]

A. J. Perumpanani and H. M. Byrne, Extracellular matrix concentration exerts selection pressure on invasive cells,, Eur. J. Cancer, 35 (1999), 1274.  doi: 10.1016/S0959-8049(99)00125-2.  Google Scholar

[11]

M. Samoszuk, J. Tan and G. Chorn, Clonogenic growth of human breast cancer cells co-cultured in direct contact with serum-activated fibroblasts,, Breast Cancer Res, 7 (2005).  doi: 10.1186/bcr995.  Google Scholar

[12]

L. M. Sander and T. S. Deisboeck, Growth patterns of microscopic brain tumors,, Phys. Rev. E, 66 (2002).  doi: 10.1103/PhysRevE.66.051901.  Google Scholar

[13]

J. A. Sherratt and J. D. Murray, Models of epidermal wound healing,, Proc. R. Soc. Lond., B241 (1990), 29.  doi: 10.1098/rspb.1990.0061.  Google Scholar

[14]

A. M. Stein, T. Demuth, D. Mobley, M. Berens and L. M. Sander, A mathematical model of glioblastoma tumor spheroid invasion in a three-dimensional in vitro experiment,, Biophys. J., 92 (2007), 356.  doi: 10.1529/biophysj.106.093468.  Google Scholar

[15]

K. R. Swanson, E. C. Alvord and J. D. Murray, A quantitative model for differential motility of gliomas in grey and white matter,, Cell Prolif., 33 (2000), 317.  doi: 10.1046/j.1365-2184.2000.00177.x.  Google Scholar

[16]

K. R. Swanson, E. C. Alvord and J. D. Murray, Virtual resection of gliomas: Effect of extent of resection on recurrence,, Math. Comp. Modelling, 37 (2003), 1177.  doi: 10.1016/S0895-7177(03)00129-8.  Google Scholar

[17]

M. Yashiro, K. Ikeda, M. Tendo, T. Ishikawa and K. Hirakawa, Effect of organ-specific fibroblasts on proliferation and differentiation of breast cancer cells,, Breast Cancer Res Treat, 90 (2005), 307.  doi: 10.1007/s10549-004-5364-z.  Google Scholar

[18]

K. Yuan, R. K. Singh, G. Rezonzew and G. P. Siegal, Cell motility in cancer invasion and metastasis,, in, (2006), 25.   Google Scholar

[1]

J. Ignacio Tello. On a mathematical model of tumor growth based on cancer stem cells. Mathematical Biosciences & Engineering, 2013, 10 (1) : 263-278. doi: 10.3934/mbe.2013.10.263

[2]

Tiffany A. Jones, Lou Caccetta, Volker Rehbock. Optimisation modelling of cancer growth. Discrete & Continuous Dynamical Systems - B, 2017, 22 (1) : 115-123. doi: 10.3934/dcdsb.2017006

[3]

Elena Izquierdo-Kulich, José Manuel Nieto-Villar. Mesoscopic model for tumor growth. Mathematical Biosciences & Engineering, 2007, 4 (4) : 687-698. doi: 10.3934/mbe.2007.4.687

[4]

Urszula Ledzewicz, Heinz Schättler, Shuo Wang. On the role of tumor heterogeneity for optimal cancer chemotherapy. Networks & Heterogeneous Media, 2019, 14 (1) : 131-147. doi: 10.3934/nhm.2019007

[5]

Didier Bresch, Thierry Colin, Emmanuel Grenier, Benjamin Ribba, Olivier Saut. A viscoelastic model for avascular tumor growth. Conference Publications, 2009, 2009 (Special) : 101-108. doi: 10.3934/proc.2009.2009.101

[6]

Shuo Wang, Heinz Schättler. Optimal control of a mathematical model for cancer chemotherapy under tumor heterogeneity. Mathematical Biosciences & Engineering, 2016, 13 (6) : 1223-1240. doi: 10.3934/mbe.2016040

[7]

Elena Izquierdo-Kulich, Margarita Amigó de Quesada, Carlos Manuel Pérez-Amor, Magda Lopes Texeira, José Manuel Nieto-Villar. The dynamics of tumor growth and cells pattern morphology. Mathematical Biosciences & Engineering, 2009, 6 (3) : 547-559. doi: 10.3934/mbe.2009.6.547

[8]

Ebraheem O. Alzahrani, Yang Kuang. Nutrient limitations as an explanation of Gompertzian tumor growth. Discrete & Continuous Dynamical Systems - B, 2016, 21 (2) : 357-372. doi: 10.3934/dcdsb.2016.21.357

[9]

Andrea Tosin. Multiphase modeling and qualitative analysis of the growth of tumor cords. Networks & Heterogeneous Media, 2008, 3 (1) : 43-83. doi: 10.3934/nhm.2008.3.43

[10]

Shihe Xu. Analysis of a delayed free boundary problem for tumor growth. Discrete & Continuous Dynamical Systems - B, 2011, 15 (1) : 293-308. doi: 10.3934/dcdsb.2011.15.293

[11]

Yangjin Kim, Hans G. Othmer. Hybrid models of cell and tissue dynamics in tumor growth. Mathematical Biosciences & Engineering, 2015, 12 (6) : 1141-1156. doi: 10.3934/mbe.2015.12.1141

[12]

Manuel Delgado, Ítalo Bruno Mendes Duarte, Antonio Suárez Fernández. Nonlocal elliptic system arising from the growth of cancer stem cells. Discrete & Continuous Dynamical Systems - B, 2018, 23 (4) : 1767-1795. doi: 10.3934/dcdsb.2018083

[13]

Evans K. Afenya, Calixto P. Calderón. Growth kinetics of cancer cells prior to detection and treatment: An alternative view. Discrete & Continuous Dynamical Systems - B, 2004, 4 (1) : 25-28. doi: 10.3934/dcdsb.2004.4.25

[14]

Alexander P. Krishchenko, Konstantin E. Starkov. The four-dimensional Kirschner-Panetta type cancer model: How to obtain tumor eradication?. Mathematical Biosciences & Engineering, 2018, 15 (5) : 1243-1254. doi: 10.3934/mbe.2018057

[15]

K. E. Starkov, Svetlana Bunimovich-Mendrazitsky. Dynamical properties and tumor clearance conditions for a nine-dimensional model of bladder cancer immunotherapy. Mathematical Biosciences & Engineering, 2016, 13 (5) : 1059-1075. doi: 10.3934/mbe.2016030

[16]

John D. Nagy. The Ecology and Evolutionary Biology of Cancer: A Review of Mathematical Models of Necrosis and Tumor Cell Diversity. Mathematical Biosciences & Engineering, 2005, 2 (2) : 381-418. doi: 10.3934/mbe.2005.2.381

[17]

Dan Liu, Shigui Ruan, Deming Zhu. Stable periodic oscillations in a two-stage cancer model of tumor and immune system interactions. Mathematical Biosciences & Engineering, 2012, 9 (2) : 347-368. doi: 10.3934/mbe.2012.9.347

[18]

Shuo Wang, Heinz Schättler. Optimal control for cancer chemotherapy under tumor heterogeneity with Michealis-Menten pharmacodynamics. Discrete & Continuous Dynamical Systems - B, 2019, 24 (5) : 2383-2405. doi: 10.3934/dcdsb.2019100

[19]

Ahuod Alsheri, Ebraheem O. Alzahrani, Asim Asiri, Mohamed M. El-Dessoky, Yang Kuang. Tumor growth dynamics with nutrient limitation and cell proliferation time delay. Discrete & Continuous Dynamical Systems - B, 2017, 22 (10) : 3771-3782. doi: 10.3934/dcdsb.2017189

[20]

Mengli Hao, Ting Gao, Jinqiao Duan, Wei Xu. Non-Gaussian dynamics of a tumor growth system with immunization. Inverse Problems & Imaging, 2013, 7 (3) : 697-716. doi: 10.3934/ipi.2013.7.697

2018 Impact Factor: 1.313

Metrics

  • PDF downloads (10)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]