Skip to main content
SpringerLink
Log in

Mathematical Modelling of Solid Tumour Growth: Applications of Pre-pattern Formation

  • Chapter
Morphogenesis and Pattern Formation in Biological Systems

  • 636 Accesses

Abstract

The year 2002 saw both the 50th anniversary of Turing’s seminal paper on morphogenesis [33], and the 30th anniversary of Gierer and Meinhardt’s equally important paper concerning activator-inhibitor theory [9]. These two papers have had a huge influence on the application of reaction-diffusion pre-pattern theory as a mechanism to describe spatio-temporal pattern formation in many biological systems. Specific applications of the theory (to name but a few) can be found in processes in developmental biology, population biology, ecology and interacting chemical systems. It is not our intention in this chapter to discuss the range of applications — for a comprehensive account of the theory and references to the many other applications, the interested reader is referred to the books [17, 22]. Instead, here we apply reaction-diffusion pre-pattern theory to a specific problem on a spherical domain, that of a growing avascular solid tumour We also suggest actual chemicals known to be produced by tumours (autocrine growth factors) which could give rise to the pre-patterns and examine their relevance in the light of clinical and experimental observations.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Albo, D., Berger, D.H., Wang, T.N., Xu, X.L., Rothman, V. and Tuszynski, G.P. (1997). Thrombospondin-1 and transforming-growth-factor-betal promote breast tumor cell invasion through up-regulation of the plasminogen/plasmin system. Surgery, 122, 493 - 499

    Article  Google Scholar 

  2. Becciolini, A., Balzi, M., Barbarisi, M., Faraoni, P., Biggeri, A. and Potten, C.S. (1997). 3H-thymidine labelling index (TLI) as a marker of tumour growth heterogeneity: evaluation in human solid carcinomas. Cell Prolif. 30, 117 - 126

    Google Scholar 

  3. Chaplain, M.A.J. (1995). Reaction-diffusion prepatterning and its potential role in tumor invasion. J. Biol. Sys., 3, 929 - 936

    Article  Google Scholar 

  4. Chaplain, M.A.J., Ganesh, M. and Graham, LG. (2001). Spatio-temporal pattern formation on spherical surfaces: numerical simulation and application to solid tumour growth. J. Math. Biol., 42, 387 - 423

    Article  MathSciNet  MATH  Google Scholar 

  5. Crampin, E.J., Gaffney, E.A. and Maini, P.K. (1999). Reaction and diffusion on growing domains: Scenarios for robust pattern formation. Bull. Math. Biol., 61, 1093 - 1120

    Article  Google Scholar 

  6. Crampin, E.J., Hackborn, W.W. and Maini, P.K. (2002). Pattern formation in reaction-diffusion models with nonuniform domain growth. Bull. Math. Biol., 64, 747 - 769

    Article  Google Scholar 

  7. Ethier, S.P. (1995). Growth factor synthesis and human breast cancer progression. J. Natl. Cancer Inst., 87, 964 - 973

    Article  Google Scholar 

  8. Freyer, J.P. and Sutherland, R.M. (1986). Proliferative and clonogenic heterogeneity of cells from EMT6/Ro multicellular spheroids induced by the glucose and oxygen supply. Cancer Res., 46, 3513 - 3520

    Google Scholar 

  9. Gierer, A. and Meinhardt, H. (1972). A theory of biological pattern formation. Kybernetik, 12, 30 - 39

    Article  Google Scholar 

  10. Hata, A., Shi, Y.G. and Massagué, J. (1998). TGF-0 signaling and cancer: structural and functional consequences of mutations in Smads. Molecular Medicine Today, 4, 257 - 262

    Article  Google Scholar 

  11. Ito, R., Kitadai, Y., Kyo, E., Yokozaki, H., Yasui, W., Yamashita, U., Nikai, H. and Tahara, E. (1993). Interleukin la acts as an autocrine growth stimulator for human gastric carcinoma cells. Cancer Res., 53, 4102 - 4106

    Google Scholar 

  12. Iversen, O.H. (1991). The hunt for endogenous growth-inhibitory and or tumor suppression factors - their role in physiological and pathological growth-regulation. Adv. Cancer Res., 57, 413 - 453

    Article  Google Scholar 

  13. Jannink, I., Risberg, B., Vandiest, P.J., and Baak, J.P.A. (1996). Heterogeneity of mitotic-activity in breast-cancer. Histopathol., 29, 421 - 428

    Article  Google Scholar 

  14. Keski-Oja, J., Postlethwaite, A.E. and Moses, H.L. (1988). Transforming growth factors and the regulation of malignant cell growth and invasion. Cancer Invest.,6, 705-724

    Google Scholar 

  15. Lolas, G. (1999). Spatio-temporel Pattern Formation and Reaction Diffusion Equations. MSc Thesis, University of Dundee, Dundee

    Google Scholar 

  16. Massagué, J. (1998). TGF,O signal transduction. Annu. Rev. Biochem., 67, 753 - 791

    Article  Google Scholar 

  17. Meinhardt, H. (1982). Models of Biological Pattern Formation. Academic Press, London

    Google Scholar 

  18. Moses, M.L., Yang, E.Y. and Pietenpol, J.A. (1990). TGF-0 stimulation and inhibition of cell proliferation: new mechanistic insights. Cell, 63, 245 - 247

    Article  Google Scholar 

  19. Mueller, M.M., Herold-Mende, C.C., Riede, D., Lange, M., Steiner, H.-H. and Fusenig, N.E. (1999). Autocrine growth regulation by granulocyte colony-stimulating factor and granulocyte macrophage colony-stimulating factor in human gliomas with tumor progression. Am. J. Pathol., 155, 1557-1567 292 M. Chaplain et al.

    Google Scholar 

  20. Mueller-Klieser, W. (1987). Multicellular spheroids: A review on cellular aggregates in cancer research. J. Cancer Res. Clin. Oncol., 113, 101 - 122

    Article  Google Scholar 

  21. Murray, J.D. (1982). Parameter space for Turing instability in reaction diffusion mechanisms: a comparison of models. J. theor. Biol.. 98, 143 - 163

    Article  Google Scholar 

  22. Murray, J.D. (1993). Mathematical Biology ( Second Edition ). Springer-Verlag, London

    Book  MATH  Google Scholar 

  23. Palmqvist, R., Oberg, A., Bergstrom, C., Rutegard, J.N., Zackrisson, B. and Stanling, R. (1998). Systematic heterogeneity and prognostic significance of cell proliferation in colorectal cancer. Br. J. Cancer, 77, 917 - 925

    Article  Google Scholar 

  24. Pusztai, L., Lewis, C.E. and Yap, E. (eds.). (1996). Cell Proliferation in Cancer: Regulatory Mechanisms of Neoplastic Cell Growth. Oxford University Press, Oxford

    Google Scholar 

  25. Quinn, K.A., Treston, A.M., Unsworth, E.J., Miller. M.-J., Vos, M., Grimley, C., Battey, J., Mulshine, J.L. and Cuttitta, F. (1996). Insulin-like growth factor expression in human cancer cell lines. J. Biol. Chem., 271, 11477 - 11483

    Google Scholar 

  26. Rahimi, N., Tremblay, E., McAdam, L., Roberts, A. and Elliott, B. (1998). Autocrine secretion of TOE-beta 1 and TGF-beta 2 by pre-adipocytes and adipocytes: A potent negative regulator of adipocyte differentiation and proliferation of mammary carcinoma cells. In Vitro Cell. Dew Biol. Animal, 34, 412 - 420

    Article  Google Scholar 

  27. Rosfjord, E.C. and Dickson, R.B. (1999). Growth factors, apoptosis and survival of mammary epithelial cells. J. Mammary Gland Biol. Neoplasia, 4, 229 - 237

    Article  Google Scholar 

  28. 28, Rozengurt, E. (1999). Autocrine loops, signal transduction and cell cycle abnormalities in the molecular biology of lung cancer. Curr. Opin. Oncol., 11, 116 - 122

    Google Scholar 

  29. Sessa, F., Bonato, M., Bisoni, D., Bosi, F. and Capella, C. (1997). Evidence of a wide heterogeneity in cancer cell population in gallbladder adenocarcinomas. Lab. Invest., 76, 860

    Google Scholar 

  30. Sutherland, R.M. (1988). Cell and environment interactions in tumor microregions: the multicell spheroid model. Science 240, 177 - 184

    Article  Google Scholar 

  31. Tahara, E., Yasui W. and Yokozaki, H. (1996). Abnormal growth factor networks in neoplasia, chapter 6, pp. 133 - 153, in: L. Pusztai, C.E. Lewis and E. Yap (eds.). Cell Proliferation in Cancer: Regulatory Mechanisms of Neoplastic Cell Growth. Oxford University Press, Oxford

    Google Scholar 

  32. Takahashi, J.A., Mori, H., Fukumoto, M., Igarashi, K., Jaye, M., Oda, Y., Kikuchi, H. and Hatanaka, M. (1990). Gene expression of fibroblast growth factors in human gliomas and meningiomas: demonstration of cellular source of basic fibroblast growth factor mRNA and peptide in tumor tissues. Proc. Natl, Acad. Sci. USA, 87, 5710 - 5714

    Article  Google Scholar 

  33. Turing, A.M. (1952). The chemical basis of morphogenesis. Phil. Trans. Roy. Soc. Loud., B237, 37 - 72

    Article  Google Scholar 

  34. Westermark, B. and Heldin, C.-H. (1991). Platelet-derived growth factor in autocrine transformation. Cancer Res,, 51, 5087 - 5092

    Google Scholar 

  35. Wibe, E., Lindmo, T. and Kaalhus, O. (1981). Cell kinetic characteristics in different parts of multicellular spheroids of human origin. Cell Tissue Kinet., 14, 639 - 651

    Google Scholar 

  36. Yanagihara, K. and Tsumuraya, M. (1992). Transforming growth factor /31 induces apoptotic cell death in cultured human gastric carcinoma cells. Cancer Res., 52, 4042-4045 24 Pre-pattern Formation and Tumour Growth 293

    Google Scholar 

  37. Yoshida, K., Kyo, E., Tsujino. T., Sano, T., Niimoto, M., and Tahara, E. (1990). Expression of epidermal growth factor, transforming growth factor-a and their receptor genes in human carcinomas: implication for autocrine growth. Cancer Res., 81, 43 - 51

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. The SIMBIOS Centre, Division of Mathematics, University of Dundee, Dundee, DD1 4HN, Scotland UK

    Mark A. J. Chaplain & Georgios Lolas

  2. School of Mathematics, University of New South Wales, Sydney, NSW 2052, Australia

    Mahadevan Ganesh

  3. Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, UK

    Ivan G. Graham

Authors
  1. Mark A. J. Chaplain
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mahadevan Ganesh
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ivan G. Graham
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Georgios Lolas
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Biological Chemistry, College of Bioscience and Biotechnology, Chubu University, 1200 Matsumoto-cho, 487-8501, Kasugai, Aichi, Japan

    Toshio Sekimura D.Sc. (Professor) (Professor)

  2. Department of Biological Science and Technology, Faculty of Engineering, University of Tokushima, 2-1 Minami-Josanjima, 780-8506, Tokushima, Japan

    Sumihare Noji D.Sc. (Professor) (Professor)

  3. National Institute for Basics Biology, 38 Nishigonaka, 444-8585, Myodaiji-cho, Okazaki, Aichi, Japan

    Naoto Ueno Ph.D. (Professor) (Professor)

  4. Centre for Mathematical Biology, Mathematical Institute, University of Oxford, 24-29 St. Giles’, OX1 3LB, Oxford, UK

    Philip K. Maini Ph.D. (Professor) (Professor)

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer Japan

About this chapter

Cite this chapter

Chaplain, M.A.J., Ganesh, M., Graham, I.G., Lolas, G. (2003). Mathematical Modelling of Solid Tumour Growth: Applications of Pre-pattern Formation. In: Sekimura, T., Noji, S., Ueno, N., Maini, P.K. (eds) Morphogenesis and Pattern Formation in Biological Systems. Springer, Tokyo. https://doi.org/10.1007/978-4-431-65958-7_24

Download citation

  • DOI: https://doi.org/10.1007/978-4-431-65958-7_24

  • Publisher Name: Springer, Tokyo

  • Print ISBN: 978-4-431-65960-0

  • Online ISBN: 978-4-431-65958-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation