Skip to main content
SpringerLink
Log in

Multiscale Modelling of Cancer: Micro-, Meso- and Macro-scales of Growth and Spread

  • Chapter
  • First Online:
Approaching Complex Diseases

Part of the book series: Human Perspectives in Health Sciences and Technology ((HPHST,volume 2))

Abstract

Cancer is a complex disease, a complicated phenomenon involving many inter-related processes across a wide range of spatial and temporal scales. It is one of the leading causes of morbidity and mortality across the globe, with around 14 million new cases in 2012, and this figure is set to rise over the next 20 years. The latest statistics from the World Health Organisation show that there were 8.8 million deaths from cancer in 2015. While treatment for cancer is continually improving (for some cancers the success rates are excellent), our understanding of the disease is ever increasing thanks to basic scientific research, the best mathematical modelling (viz. mathematical oncology) can provide even greater insight into the complexity of the disease and its treatment. Biomedical scientists and clinicians have recognised the need to integrate data and information across a range of spatial and temporal scales (from genes to tissues) in order to fully understand cancer. In this chapter we present an overview of some recent developments in the multiscale mathematical modelling of cancer at each of the three scales and give discuss how this might be used to provide more targeted and patient-specific treatment of the disease in the years ahead.

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 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
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

References

  1. Alarcon, T., H. Byrne, and P. Maini. 2003. A cellular automaton model for tumour growth in inhomogeneous environment. Journal of Theoretical Biology 225: 257–274.

    Article  CAS  PubMed  Google Scholar 

  2. Alberts, B., D. Bray, K. Hopkin, A. Johnson, J. Lewis, M. Raff, K. Roberts, and P. Walter, eds. 2010. Essential cell biology. New York/London: Garland Publishing, Inc.

    Google Scholar 

  3. Alcaraz, J.L., M. Buscemi, X. Grabulosa, B. Trepat, R. Fabry, D. Farre, and D. Navajas. 2003. Microrheology of human lung epithelial cells measured by atomic force. Biophysical Journal 84: 2071–2079.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  4. Andasari, V., A. Gerisch, G. Lolas, A. South, and M. Chaplain. 2011. Mathematical modeling of cancer cell invasion of tissue: Biological insight from mathematical analysis and computational simulation. Journal of Mathematical Biology 63 (1): 141–171.

    Article  PubMed  Google Scholar 

  5. Andasari, V., R. Roper, M.H. Swat, and M.A.J. Chaplain. 2012. Integrating intracellular dynamics using CompuCell3D and Bionetsolver: Applications to multiscale modelling of cancer cell growth and invasion. PLoS ONE 7 (3): e33726.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  6. Anderson, A.R.A., and M.A.J. Chaplain. 1998. Continuous and discrete mathematical models of tumour-induced angiogenesis. Bulletin of Mathematical Biology 60: 857–899.

    Article  CAS  PubMed  Google Scholar 

  7. Armstrong, N.J., K.J. Painter, and J.A. Sherratt. 2006. A continuum approach to modelling cell–cell adhesion. Journal of Theoretical Biology 243 (1): 98–113.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  8. Busenberg, S., and J.M. Mahaffy. 1985. Interaction of spatial diffusion and delays in models of genetic control by repression. Journal of Mathematical Biology 22: 313–333.

    Article  CAS  PubMed  Google Scholar 

  9. Chaplain, M.A.J., M. Ptashnyk, and M. Sturrock. 2015. Hopf bifurcation in a gene regulatory network model: Molecular movement causes oscillations. Mathematical Models and Methods in Applied Sciences 25 (6): 1179–1215.

    Article  CAS  Google Scholar 

  10. Chu, Y.S., W.A. Thomas, O. Eder, E. Pincet, J.P. Thiery, and S. Dufour. 2004. Force measurements in e-cadherin–mediated cell doublets reveal rapid adhesion strengthened by actin cytoskeleton remodeling through rac and cdc42. The Journal of Cell Biology 167: 1183–1194.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  11. Cytowski, M., and Z. Szymańska. 2014. Large scale parallel simulations of 3-d cell colony dynamics. IEEE Computational Science and Engineering 16 (5): 86–95.

    Article  Google Scholar 

  12. ———. 2015. Enabling large scale individual-based modelling through high performance computing. ITM Web of Conferences 5: 00014.

    Article  Google Scholar 

  13. ———. 2015. Large scale parallel simulations of 3-d cell colony dynamics. ii. coupling with continuous description of cellular environment. IEEE Computational Science and Engineering 17 (5): 44–48.

    Article  Google Scholar 

  14. D’Antonio, G., P. Macklin, and L. Preziosi. 2013. An agent-based model for elasto-plastic mechanical interactions between cells, basement membrane and extracellular matrix. Mathematical Biosciences and Engineering 10: 75–101.

    Article  PubMed  Google Scholar 

  15. Domschke, P., D. Trucu, A. Gerisch, and M.A.J. Chaplain. 2014. Mathematical modelling of cancer invasion: Implications of cell adhesion variability for tumour infiltrative growth patterns. Journal of Theoretical Biology 361: 41–60.

    Article  PubMed  Google Scholar 

  16. Drasdo, D., and S. Höhme. 2005. A single-cell-based model of tumor growth in vitro: Monolayers and spheroids. Physical Biology 2: 133–147.

    Article  CAS  PubMed  Google Scholar 

  17. Franssen, L.C., T. Lorenzi, A.E.F. Burgess, and M.A.J. Chaplain. 2019. A mathematical framework for modelling the metastatic spread of cancer. Bulletin of Mathematical Biology 81: 1965–2010.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  18. Galle, J., M. Loeffler, and D. Drasdo. 2005. Modelling the effect of deregulated proliferation and apoptosis on the growth dynamics of epithelial cell populations in vitro. Biophysical Journal 88: 62–75.

    Article  CAS  PubMed  Google Scholar 

  19. Gerisch, A., and M. Chaplain. 2008. Mathematical modelling of cancer cell invasion of tissue: Local and non-local models and the effect of adhesion. Journal of Theoretical Biology 250 (4): 684–704.

    Article  CAS  PubMed  Google Scholar 

  20. Glass, L., and S.A. Kauffman. 1970. Co-operative components, spatial localization and oscillatory cellular dynamics. Journal of Theoretical Biology 34: 219–237.

    Article  Google Scholar 

  21. Goodwin, B.C. 1965. Oscillatory behaviour in enzymatic control processes. Advances in Enzyme Regulation 3: 425–428.

    Article  CAS  PubMed  Google Scholar 

  22. GP, G.P.G., and J. Massagué. 2006. Cancer metastasis: Building a framework. Cell 127 (4): 679–695.

    Article  CAS  Google Scholar 

  23. Griffith, J.S. 1968. Mathematics of cellular control processes. i. negative feedback to one gene. Journal of Theoretical Biology 20: 202–208.

    Article  CAS  PubMed  Google Scholar 

  24. Gumbiner, B.M. 2005. Regulation of cadherin-mediated adhesion in morphogenesis. Nature Reviews. Molecular Cell Biology 6: 622–634.

    Article  CAS  PubMed  Google Scholar 

  25. Hamis, S., G.G. Powathil, and M.A.J. Chaplain. 2019. Blackboard to bedside: A mathematical modeling bottom-up approach toward personalized cancer treatments. JCO Clinical Cancer Informatics (3): 1–11. https://doi.org/10.1200/CCI.18.00068.

  26. Hanahan, D., and R.A. Weinberg. 2000. The hallmarks of cancer. Cell 100: 57–70.

    Article  CAS  PubMed  Google Scholar 

  27. ———. 2011. Hallmarks of cancer: The next generation. Cell 144: 646–674.

    Article  CAS  PubMed  Google Scholar 

  28. Hillen, T., and K. Painter. 2001. Global existence for a parabolic chemotaxis model with prevention of overcrowding. Advances in Applied Mathematics 26 (4): 280–301.

    Article  Google Scholar 

  29. Hirata, H., S. Yoshiura, T. Ohtsuka, Y. Bessho, T. Harada, K. Yoshikawa, and R. Kageyama. 2002. Oscillatory expression of the bHLH factor Hes1 regulated by a negative feedback loop. Science 298: 840–843.

    Article  CAS  PubMed  Google Scholar 

  30. Jagiella, N., B. Müller, M. Müller, I.E. Vignon-Clementel, and D. Drasdo. 2016. Inferring growth control mechanisms in growing multi-cellular spheroids of nsclc cells from spatial-temporal image data. PLoS Computational Biology 12 (2): e1004412.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  31. Lachowicz, M., M. Parisot, and Z. Szymańska. 2016. Intracellular protein dynamics as a mathematical problem. Discrete and Continuous Dynamical Systems. Series B 21: 2551–2566.

    Article  Google Scholar 

  32. Lahav, G., N. Rosenfeld, A. Sigal, N. Geva-Zatorsky, A.J. Levine, M.B. Elowitz, and U. Alon. 2004. Dynamics of the p53-Mdm2 feedback loop in individual cells. Nature Genetics 36: 147–150.

    Article  CAS  PubMed  Google Scholar 

  33. Macnamara, C.K., and M.A.J. Chaplain. 2016. Diffusion driven oscillations in gene regulatory networks. Journal of Theoretical Biology 407: 51–70.

    Article  PubMed  Google Scholar 

  34. ———. 2017. Spatio-temporal models of synthetic genetic oscillators. Mathematical Biosciences and Engineering 14: 249–262.

    Article  PubMed  Google Scholar 

  35. Macnamara, C.K., E.I. Mitchell, and M.A.J. Chaplain. 2019. Spatial-stochastic modelling of synthetic gene regulatory networks. Journal of Theoretical Biology 468: 27–44.

    Article  CAS  PubMed  Google Scholar 

  36. Mahaffy, J.M. 1988. Genetic control models with diffusion and delays. Mathematical Biosciences 90: 519–533.

    Article  Google Scholar 

  37. Mahaffy, J.M., and C.V. Pao. 1984. Models of genetic control by repression with time delays and spatial effects. Journal of Mathematical Biology 20: 39–57.

    Article  CAS  PubMed  Google Scholar 

  38. Mahaffy, R.E., C.K. Shih, F.C. McKintosh, and J. Kaes. 2000. Scanning probe-based frequency-dependent microrheology of polymer gels and biological cells. Physical Review Letters 85: 880–883.

    Article  CAS  PubMed  Google Scholar 

  39. Miron-Mendoza, M., V. Koppaka, C. Zhou, and W.M. Petroll. 2013. Techniques for assessing 3-d cell-matrix mechanical interactions in vitro and in vivo. Experimental Cell Research 319: 2470–2480.

    Article  CAS  PubMed  Google Scholar 

  40. Näthke, I.S., L. Hinck, and W.J. Nelson. 1995. The cadherin/catenin complex: Connections to multiple cellular processes involved in cell adhesion, proliferation and morphogenesis. Seminars in Developmental Biology 6: 89–95.

    Article  Google Scholar 

  41. Powathil, G.G., D.J. Adamson, and M.A.J. Chaplain. 2013. Towards predicting the response of a solid tumour to chemotherapy and radiotherapy treatments: Clinical insights from a computational model. PLoS Computational Biology 9 (7): e1003120. https://doi.org/10.1371/journal.pcbi.1003120.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  42. Ramis-Conde, I., D. Drasdo, A.R.A. Anderson, and M.A.J. Chaplain. 2008. Modelling the the influence of the E-cadherin-β-catenin pathway in cancer cell invasion: A multi-scale approach. Biophysical Journal 95: 155–165.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  43. Ritchie, T., W. Zhou, E. McKinstry, M. Hosch, Y. Zhang, I.S. Näthke, and J.F. Engelhardt. 2001. Developmental expression of catenins and associated proteins during submucosal gland morphogenesis in the airway. Experimental Lung Research 27: 121–141.

    Article  CAS  PubMed  Google Scholar 

  44. Schaller, G., Meyer-Hermann, M.: Multicellular tumor spheroid in an off-lattice Voronoi-Delaunay cell model. Physical Review E 71, 051910–1–051910–16 (2005)

    Google Scholar 

  45. Schlüter, D.K., I. Ramis-Conde, and M.A.J. Chaplain. 2012. Computational modeling of single cell migration: The leading role of extracellular matrix fibers. Biophysical Journal 103: 1141–1151.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  46. ———. 2015. Multi-scale modelling of the dynamics of cell colonies: Insights into cell-adhesion forces and cancer invasion from in silico simulations. Journal of the Royal Society, Interface 12: 20141080.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  47. Shymko, R.M., and L. Glass. 1974. Spatial switching in chemical reactions with heterogeneous catalysis. The Journal of Chemical Physics 60: 835–841.

    Article  CAS  Google Scholar 

  48. Sturrock, M., A. Hellander, A. Matzavinos, and M.A.J. Chaplain. 2013. Spatial stochastic modelling of the hes1 gene regulatory network: Intrinsic noise can explain heterogeneity in embryonic stem cell differentiation. Journal of the Royal Society, Interface 10: 20120988.

    Article  PubMed  PubMed Central  Google Scholar 

  49. Sturrock, M., A.J. Terry, D.P. Xirodimas, A.M. Thompson, and M.A.J. Chaplain. 2011. Spatio-temporal modelling of the Hes1 and p53-Mdm2 intracellular signalling pathways. Journal of Theoretical Biology 273: 15–31.

    Article  CAS  PubMed  Google Scholar 

  50. ———. 2012. Influence of the nuclear membrane, active transport, and cell shape on the Hes1 and p53-Mdm2 pathways: Insights from spatio-temporal modelling. Bulletin of Mathematical Biology 74: 1531–1579.

    Article  CAS  PubMed  Google Scholar 

  51. Szymańska, Z., M. Cytowski, E.I. Mitchell, C.K. Macnamara, and M.A.J. Chaplain. 2018. Computational modelling of cancer development and growth: Modelling at multiple scales and multiscale modelling. Bulletin of Mathematical Biology 80: 1366–1403.

    Article  PubMed  Google Scholar 

  52. Szymańska, Z., M. Parisot, and M. Lachowicz. 2014. Mathematical modeling of the intracellular protein dynamics: The importance of active transport along microtubules. Journal of Theoretical Biology 363: 118–128.

    Article  PubMed  CAS  Google Scholar 

  53. Weinberg, R.A. 2007. The biology of cancer. New York: Garland Science.

    Google Scholar 

  54. Zaman, M.H., L.M. Trapani, A.L. Sieminski, D. MacKellar, H. Gong, R.D. Kamm, A. Wells, D.A. Lauffenburger, and P. Matsudaira. 2006. Migration of tumor cells in 3d matrices is governed by matrix stiffness along with cell-matrix adhesion and proteolysis. PNAS 103: 10889–10894.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, University of St Andrews, St Andrews, Scotland

    Mark A. J. Chaplain

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

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mark A. J. Chaplain .

Editor information

Editors and Affiliations

  1. Department of Experimental Medicine, Sapienza University of Rome, Rome, Italy

    Mariano Bizzarri

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Chaplain, M.A.J. (2020). Multiscale Modelling of Cancer: Micro-, Meso- and Macro-scales of Growth and Spread. In: Bizzarri, M. (eds) Approaching Complex Diseases. Human Perspectives in Health Sciences and Technology, vol 2. Springer, Cham. https://doi.org/10.1007/978-3-030-32857-3_7

Download citation

Publish with us

Policies and ethics

Search

Navigation