Journal of Mathematical Biology

, Volume 47, Issue 5, pp 424–452

Modelling the early growth of ductal carcinoma in situ of the breast

  • S.J. Franks
  • H.M. Byrne
  • J.R. King
  • J.C.E. Underwood
  • C.E. Lewis
Article

DOI: 10.1007/s00285-003-0214-x

Cite this article as:
Franks, S., Byrne, H., King, J. et al. J. Math. Biol. (2003) 47: 424. doi:10.1007/s00285-003-0214-x

Abstract.

The growth of a tumour in a rigid walled cylindrical duct is examined in order to model the initial stages of tumour cell expansion in ductal carcinoma in situ (DCIS) of the breast. A nutrient-limited growth model is formulated, in which cell movement is described by a Stokes flow constitutive relation. The effects on the shape of the tumour boundary of the material properties (i.e. the viscosity) and the extent to which the cells adhere to the duct wall are studied using numerical and asymptotic methods. It is shown how stable, non-planar, interface configurations result and that, during these initial stages, before the duct wall has been breached, few cells die and a nutrient-rich model is usually sufficient to capture the behaviour. Finally, we discuss the relevance of this approach to DCIS and suggest possible avenues for further work.

Key words or phrases:

 DCIS Stokes flow Nutrient-limited growth Slender approximation Stability 

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • S.J. Franks
    • 1
    • 2
  • H.M. Byrne
    • 1
  • J.R. King
    • 1
  • J.C.E. Underwood
    • 2
  • C.E. Lewis
    • 2
  1. 1.Centre for Mathematical Medicine, School of Mathematical SciencesUniversity of NottinghamNottingham NG7 2RDUK
  2. 2.Division of Genomic MedicineUniversity of Sheffield Medical SchoolUK

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