M for Invasion Morphology Mutation and the Microenvironment

  • Alexander R. A. Anderson
Part of the Modeling and Simulation in Science, Engineering and Technology book series (MSSET)


Oxygen Consumption Rate Cellular Automaton Model Tumour Morphology Movement Probability Tumour Population 
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  1. 1.
    Alarcon, T., Byrne, H. M., and Maini, P. K.: A multiple scale model for tumor growth.Multiscale Model Simul.3, 440–475 (2005).MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Albini, A., and Sporn, M. B.: The tumour microenvironment as a target for chemoprevention.Nature Rev. Cancer,7, (2007), doi:10.1038.Google Scholar
  3. 3.
    Anderson, A. R. A., Sleeman, B. D., Young, I. M., and Griffiths, B. S.: Nematode movement along a chemical gradient in a structurally heterogeneous environment: II. Theory.Fundam. appl. Nematol.,20, 165–172 (1997).Google Scholar
  4. 4.
    Anderson, A. R. A. and Chaplain, M. A. J.: Continuous and discrete mathematical models of tumour-induced angiogenesis.Bull. Math. Biol.,60, 857–899 (1998).MATHCrossRefGoogle Scholar
  5. 5.
    Anderson, A. R. A., Chaplain, M. A. J., Newman, E. L., Steele, R. J. C., and Thompson, A. M.: Mathematical modelling of tumour invasion and metastasis.J. Theoret. Med.,2, 129–154 (2000).MATHGoogle Scholar
  6. 6.
    Anderson, A. R. A.: A hybrid discrete-continuum technique for individual based migration models, inPolymer and Cell Dynamics, eds. W. Alt, M. Chaplain, M. Griebel, J. Lenz, Birkhauser, Boston, MA, 2003.Google Scholar
  7. 7.
    Anderson, A. R. A., and Pitcairn, A.: Application of the hybrid discretecontinuum technique, inPolymer and Cell Dynamics, eds. W. Alt, M. Chaplain, M. Griebel, J. Lenz, Birkhauser, Boston, MA, 2003.Google Scholar
  8. 8.
    Anderson, A. R. A.: A hybrid mathematical model of solid tumour invasion: The importance of cell adhesion.IMA J. Math. Med. and Biol.,22, 163–186 (2005).MATHCrossRefGoogle Scholar
  9. 9.
    Anderson, A. R. A, Weaver, A. M., Cummings, P. T., and Quaranta, V.: Tumor morphology and phenotypic evolution driven by selective pressure from the microenvironment.Cell,127, 905–915 (2006).CrossRefGoogle Scholar
  10. 10.
    Anderson, A. R. A., Chaplain, M. A. J., and Rejniak, K. A.:Single-Cell-Based Models in Biology and Medicine. Birkhauser, Boston, MA, (2007).CrossRefGoogle Scholar
  11. 11.
    Araujo, R. P., and McElwain, D. L. S.: A history of the study of solid tumour growth: The contribution of mathematical modeling.Bull. Math. Biol.66, 1039– 1091 (2004).CrossRefMathSciNetGoogle Scholar
  12. 12.
    Ben-Jacob, E., and Garik, P.: The formation of patterns in non-equilibrium growth.Nature,343, 523–530 (1990).CrossRefGoogle Scholar
  13. 13.
    Ben-Jacob, E., Cohen, I., and Levine, H.: Cooperative self-organization of microorganisms.Advances in Physics,49, 395–554 (2000).CrossRefGoogle Scholar
  14. 14.
    Bierie, B., and Moses, H. L.: Tumour microenvironment: TGF: the molecular Jekyll and Hyde of cancer.Nature Rev. Cancer,6, 506–520 (2006).CrossRefGoogle Scholar
  15. 15.
    Chaplain, M. A. J., Graziano, L., and Preziosi, L.: Mathematical modelling of the loss of tissue compression responsiveness and its role in solid tumour development,Mathematical Medicine and Biology,23:197–229 (2006).MATHCrossRefGoogle Scholar
  16. 16.
    Cristini, V., Frieboes, H. B., Gatenby, R., Caserta, S., Ferrari, M., and Sinek, J.: Morphologic instability and cancer invasion.Clin Cancer Res,127, 6772–6779 (2005).CrossRefGoogle Scholar
  17. 17.
    Daccord, G., Nittmann, J., and Stanley, H. E.: Radial viscous fingers and diffusion-limited aggregation: Fractal dimension and growth sites.Phys. Rev. Lett., 56(4), 336–339 (1986).CrossRefGoogle Scholar
  18. 18.
    Dormann, S., and Deutsch, A.: Modeling of self-organzied avascular tumor growth with a hybrid cellular automaton.In Silico Biology,2, 0035 (2002).Google Scholar
  19. 19.
    Drasdo, D., and Höhme, S.: Individual-based approaches to birth and death in avascular tumors,Mathematical and Computer Modelling,37, 1163–1175 (2003).MATHCrossRefGoogle Scholar
  20. 20.
    Düuchting, W.: Tumor growth simulation.Comput. – Graphics, 14, 505–508 (1990a).CrossRefGoogle Scholar
  21. 21.
    Ferreira, S. C., Martins, M. L., and Vilela, M. J.: Reaction-diffusion model for the growth of avascular tumor.Physical Review E,65, 021907 (2002).CrossRefMathSciNetGoogle Scholar
  22. 22.
    Freyer, J. P., and Sutherland, R. M.: A reduction in the in situ rates of oxygen and glucose consumption of cells on EMT6/Ro spheroids during growth.J. Cell Physiol. 124, 516–524 (1985).CrossRefGoogle Scholar
  23. 23.
    Frieboes, H. B., Zheng, X., Sun, C., Tromberg, B., Gatenby, R., and Cristini, V.: An integrated computational/experimental model of tumor invasion.Cancer Res,66, 1597–1604 (2006).CrossRefGoogle Scholar
  24. 24.
    Gatenby, R. A., and Gawlinski, E. T.: A reaction-diffusion model of cancer invasion.Cancer Research, 56, 5745–5753 (1996).Google Scholar
  25. 25.
    Gerlee, P., and Anderson, A. R. A.: An evolutionary hybrid cellular automaton model of solid tumour growth.Journal of Theoretical Biology,246(4), 583–603 (2007)a.CrossRefMathSciNetGoogle Scholar
  26. 26.
    Gerlee, P., and Anderson, A. R. A.: Stability analysis of a hybrid cellular automaton model of cell colony growth.Physical Review E,75, 051911 (2007)b.CrossRefGoogle Scholar
  27. 27.
    Hanahan, D., and Weinberg, R. A.: The hallmarks of cancer.Cell, 100, 57–70 (2000).CrossRefGoogle Scholar
  28. 28.
    Hynes, R. O.: Integrins: versatility, modulation, and signalling in cell adhesion.Cell, 69, 11–25 (1992).CrossRefGoogle Scholar
  29. 29.
    Jiang, Y., Pjesivac-Grbovic, J. A., Cantrell, C., and Freyer, J. P.: A multiscale model for avascular tumour growth.Biophys. J.,89, 3884–3894 (2005).CrossRefGoogle Scholar
  30. 30.
    Kansal, A. R., Torquato, S., Harsh, G. R., Chiocca, E. A., and Deisboeck, T. S.: Simulated brain tumor growth using a three-dimensional cellular automaton, J.Theor. Biol. 203, 367–382 (2000).CrossRefGoogle Scholar
  31. 31.
    Kessler, D. A., Koplik, J., and Levine, H.: Pattern selection in fingered growth phenomena.Advances in Physics,37, 255–339 (1988).CrossRefGoogle Scholar
  32. 32.
    Lane, D. P.: The regulation of p53 function. Steiner Award Lecture.Int. J. Cancer 57, 623–627 (1994).CrossRefGoogle Scholar
  33. 33.
    Lopez, J. M. and Jensen, H. J.: Generic model of morphological changes in growing colonies of fungi.Physical Review E,65(2), 021903 (2002).CrossRefGoogle Scholar
  34. 34.
    McDougall, S., Anderson, A. R. A., and Chaplain, M. A. J.: Mathematical modelling of dynamic adaptive tumour-induced angiogenesis: Clinical implications and therapeutic targeting strategies.J. Theo. Biol.,241, 564–589 (2006).CrossRefMathSciNetGoogle Scholar
  35. 35.
    Macklin, P., and Lowengrub, J. S.: Evolving interfaces via gradients of geometrydependent interior Poisson problems: Application to tumor growth, J. Comput. Phys.,203(1), 191–220 (2005).MATHCrossRefMathSciNetGoogle Scholar
  36. 36.
    Matrisian, L. M.: The matrix-degrading metalloproteinases.Bioessays,14, 455– 463 (1992).CrossRefGoogle Scholar
  37. 37.
    Matsushita, M., Sano, M., Hayakawa, Y., Honjo, H., and Sawada, Y.: Fractal structures of zinc metal leaves grown by electrodeposition.Phys. Rev. Lett.,53(3), 286–289 (1984).CrossRefGoogle Scholar
  38. 38.
    Matsushita, M., Wakita, J., Itoh, H., Watanabe, K., Arai, T., Matsuyama, T., Sakaguchi, H., and Mimura, M.: Formation of colony patterns by a bacterial cell population.Physica A,274, 190–199 (1999).CrossRefGoogle Scholar
  39. 39.
    Orme, M. E., and Chaplain, M. A. J.: A mathematical model of vascular tumour growth and invasion.Mathl. Comp. Modelling,23, 43–60 (1996).MATHCrossRefGoogle Scholar
  40. 40.
    Othmer, H., and Stevens, A.: Aggregation, blowup and collapse: The ABCs of taxis and reinforced random walks.SIAM J. Appl. Math.,57, 1044–1081 (1997).MATHCrossRefMathSciNetGoogle Scholar
  41. 41.
    Overall, C. M., and Kleifeld, O.: Tumour microenvironment opinion: Validating matrix metalloproteinases as drug targets and anti-targets for cancer therapy.Nature Rev. Cancer,6, 227–239 (2006).CrossRefGoogle Scholar
  42. 42.
    Paszek, M. J., Zahir, N., Johnson, K. R., Lakins, J. N., Rozenberg, G. I., Gefen, A., Reinhart-King, C. A., Margulies, S. S., Dembo, M., Boettiger, D., Hammer, D. A., and Weaver, V. M.: Tensional homeostasis and the malignant phenotype.Cancer Cell,8, 241–254 (2005).Google Scholar
  43. 43.
    Patel, A. A., Gawlinski, E. E., Lemieux, S. K., and Gatenby, R. A.: A cellular automaton model of early tumor growth and invasion: The effects of native tissue vascularity and increased anaerobic tumor metabolism,J. Theoret. Biol.,213, 315–331 (2001).CrossRefMathSciNetGoogle Scholar
  44. 44.
    Pennacchietti, S., Michieli, P., Galluzzo, M., Mazzone, M., Giordano, S., and Comoglio, P. M.: Hypoxia promotes invasive growth by transcriptional activation of the met protooncogene.Cancer Cell,3, 347–361 (2003).CrossRefGoogle Scholar
  45. 45.
    Perumpanani, A. J., Sherratt, J. A., Norbury, J., and Byrne, H. M.: Biological inferences from a mathematical model of malignant invasion.Invasion and Metastases,16, 209–221 (1996).Google Scholar
  46. 46.
    Qi, A., Zheng, X., Du, C., and An, B.: A cellular automaton model of cancerous growth.J. Theor. Biol.,161, 1–12 (1993).CrossRefGoogle Scholar
  47. 47.
    Rejniak, K. A.: A single-cell approach in modeling the dynamics of tumor microregions.Math. Biosci. Eng., 2, 643–655 (2005).MATHMathSciNetGoogle Scholar
  48. 48.
    Rejniak, K. A.: An immersed boundary framework for modelling the growth of individual cells: An application to the early tumour development.J. Theor. Biol., 247, 186–204 (2007).CrossRefMathSciNetGoogle Scholar
  49. 49.
    Sherratt, J. A., and Nowak, M. A.: Oncogenes, anti-oncogenes and the immune response to cancer: A mathematical model.Proc. R. Soc. Lond. B,248, 261–271 (1992).CrossRefGoogle Scholar
  50. 50.
    Smolle, J., and Stettner, H.: Computer simulation of tumour cell invasion by a stochastic growth model.J. Theor. Biol.,160, 63–72 (1993).CrossRefGoogle Scholar
  51. 51.
    Stetler-Stevenson, W. G., Aznavoorian, S., and Liotta, L. A.: Tumor cell interactions with the extracellular matrix during invasion and metastasis.Ann. Rev. Cell Biol.,9, 541–573 (1993).Google Scholar
  52. 52.
    Swanson, K. R., Bridge, C., Murray, J. D., and Alvord Jr., E. C.: Virtual and real brain tumors: Using mathematical modeling to quantify glioma growth and invasion.J. Neuro. Sci.,216, 1–10 (2003).CrossRefGoogle Scholar
  53. 53.
    Ward, J. P., and King, J. R.: Mathematical modelling of avascular-tumour growth II: Modelling growth saturation.IMA J. Math. Appl. Med. Biol.,16, 171–211 (1999).MATHCrossRefGoogle Scholar
  54. 54.
    Zhang, L., Athale, C. A., and Deisboeck, T. S.: Development of a threedimensional multiscale agent-based tumor model: Simulating gene-protein interaction profiles, cell phenotypes and multicellular patterns in brain cancer. J.Theo. Biol. 244, 96–107 (2007).CrossRefMathSciNetGoogle Scholar
  55. 55.
    Zheng, X., Wise, S. M, and Cristini, V.: Nonlinear simulation of tumour necrosis, neo-vascularization and tissue invasion via an adaptive finite-element/level-set method.Bull. Math. Biol., 67, 211–256 (2005).CrossRefMathSciNetGoogle Scholar

Copyright information

© Birkhäuser Boston 2008

Authors and Affiliations

  1. 1.Division of MathematicsUniversity of DundeeDundeeUK

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