Bulletin of Mathematical Biology

, Volume 80, Issue 5, pp 1366–1403 | Cite as

Computational Modelling of Cancer Development and Growth: Modelling at Multiple Scales and Multiscale Modelling

  • Zuzanna Szymańska
  • Maciej Cytowski
  • Elaine Mitchell
  • Cicely K. Macnamara
  • Mark A. J. Chaplain
Special Issue : Mathematical Oncology


In this paper, we present two mathematical models related to different aspects and scales of cancer growth. The first model is a stochastic spatiotemporal model of both a synthetic gene regulatory network (the example of a three-gene repressilator is given) and an actual gene regulatory network, the NF-\(\upkappa \)B pathway. The second model is a force-based individual-based model of the development of a solid avascular tumour with specific application to tumour cords, i.e. a mass of cancer cells growing around a central blood vessel. In each case, we compare our computational simulation results with experimental data. In the final discussion section, we outline how to take the work forward through the development of a multiscale model focussed at the cell level. This would incorporate key intracellular signalling pathways associated with cancer within each cell (e.g. p53–Mdm2, NF-\(\upkappa \)B) and through the use of high-performance computing be capable of simulating up to \(10^9\) cells, i.e. the tissue scale. In this way, mathematical models at multiple scales would be combined to formulate a multiscale computational model.


Multiscale cancer modelling Gene regulatory network Spatial stochastic model Individual-based model Computational simulations 

Mathematics Subject Classification

35Q92 92C05 92C40 92C42 92C50 



ZS acknowledges the support of the National Science Centre Poland Grant 2011/01/D/ST1/04133, National Science Centre Poland Grant 2014/15/B/ST6/05082 and The National Centre for Research and Development Grant STRATEGMED1/233224/10/NCBR/2014. MAJC and CKM gratefully acknowledge support of EPSRC Grant No. EP/N014642/1 (EPSRC Centre for Multiscale Soft Tissue Mechanics—With Application to Heart & Cancer). EM was supported by an EASTBIO Ph.D. Fellowship. The authors thank Bartosz Borucki from ICM for his help in with the VisNow medical imaging software.


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Copyright information

© Society for Mathematical Biology 2017

Authors and Affiliations

  1. 1.ICMUniversity of WarsawWarsawPoland
  2. 2.Division of MathematicsUniversity of DundeeDundeeScotland, UK
  3. 3.School of Mathematics and StatisticsUniversity of St AndrewsSt AndrewsScotland, UK

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