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Quiescence as a mechanism for cyclical hypoxia and acidosis

  • Kieran SmallboneEmail author
  • David J. Gavaghan
  • Philip K. Maini
  • J. Michael Brady
Article

Abstract

Tumour tissue characteristically experiences fluctuations in substrate supply. This unstable microenvironment drives constitutive metabolic changes within cellular populations and, ultimately, leads to a more aggressive phenotype. Previously, variations in substrate levels were assumed to occur through oscillations in the hæmodynamics of nearby and distant blood vessels. In this paper we examine an alternative hypothesis, that cycles of metabolite concentrations are also driven by cycles of cellular quiescence and proliferation. Using a mathematical modelling approach, we show that the interdependence between cell cycle and the microenvironment will induce typical cycles with the period of order hours in tumour acidity and oxygenation. As a corollary, this means that the standard assumption of metabolites entering diffusive equilibrium around the tumour is not valid; instead temporal dynamics must be considered.

Keywords

Acidity Hypoxia Delay differential equations 

Mathematics Subject Classification (2000)

92B99 35K57 

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Kieran Smallbone
    • 1
    Email author
  • David J. Gavaghan
    • 2
  • Philip K. Maini
    • 3
  • J. Michael Brady
    • 4
  1. 1.Manchester Centre for Integrative Systems BiologyManchester Interdisciplinary BiocentreManchesterUK
  2. 2.Oxford University Computing LaboratoryOxfordUK
  3. 3.Centre for Mathematical Biology, Mathematical InstituteUniversity of OxfordOxfordUK
  4. 4.Department of Engineering ScienceUniversity of OxfordOxfordUK

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