Display options
Cite
Grimes DR, Fletcher AG, Partridge M. Oxygen consumption dynamics in steady-state tumour models. R Soc Open Sci. 2014;1(1):140080doi: 10.1098/rsos.140080.
Grimes, D. R., Fletcher, A. G., & Partridge, M. (2014). Oxygen consumption dynamics in steady-state tumour models. Royal Society open science, 1(1), 140080. https://doi.org/10.1098/rsos.140080
Grimes, David Robert, et al. "Oxygen consumption dynamics in steady-state tumour models." Royal Society open science vol. 1,1 (2014): 140080. doi: https://doi.org/10.1098/rsos.140080
Grimes DR, Fletcher AG, Partridge M. Oxygen consumption dynamics in steady-state tumour models. R Soc Open Sci. 2014 Sep 24;1(1):140080. doi: 10.1098/rsos.140080. eCollection 2014 Sep. PMID: 26064525; PMCID: PMC4448765.
Copy Download .nbib Format: NLM
Share it on

R Soc Open Sci. 2014 Sep 24;1(1):140080. doi: 10.1098/rsos.140080. eCollection 2014 Sep.

Oxygen consumption dynamics in steady-state tumour models.

Royal Society open science

David Robert Grimes, Alexander G Fletcher, Mike Partridge

Affiliations

  1. Cancer Research UK/MRC Oxford Institute for Radiation Oncology, Gray Laboratory , University of Oxford , Old Road Campus Research Building, Off Roosevelt Drive, Oxford OX3 7DQ, UK.
  2. Wolfson Centre for Mathematical Biology , Mathematical Institute, University of Oxford , Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK.

PMID: 26064525 PMCID: PMC4448765 DOI: 10.1098/rsos.140080

Abstract

Oxygen levels in cancerous tissue can have a significant effect on treatment response: hypoxic tissue is both more radioresistant and more chemoresistant than well-oxygenated tissue. While recent advances in medical imaging have facilitated real-time observation of macroscopic oxygenation, the underlying physics limits the resolution to the millimetre domain, whereas oxygen tension varies over a micrometre scale. If the distribution of oxygen in the tumour micro-environment can be accurately estimated, then the effect of potential dose escalation to these hypoxic regions could be better modelled, allowing more realistic simulation of biologically adaptive treatments. Reaction-diffusion models are commonly used for modelling oxygen dynamics, with a variety of functional forms assumed for the dependence of oxygen consumption rate (OCR) on cellular status and local oxygen availability. In this work, we examine reaction-diffusion models of oxygen consumption in spherically and cylindrically symmetric geometries. We consider two different descriptions of oxygen consumption: one in which the rate of consumption is constant and one in which it varies with oxygen tension in a hyperbolic manner. In each case, we derive analytic approximations to the steady-state oxygen distribution, which are shown to closely match the numerical solutions of the equations and accurately predict the extent to which oxygen can diffuse. The derived expressions relate the limit to which oxygen can diffuse into a tissue to the OCR of that tissue. We also demonstrate that differences between these functional forms are likely to be negligible within the range of literature estimates of the hyperbolic oxygen constant, suggesting that the constant consumption rate approximation suffices for modelling oxygen dynamics for most values of OCR. These approximations also allow the rapid identification of situations where hyperbolic consumption forms can result in significant differences from constant consumption rate models, and so can reduce the computational workload associated with numerical solutions, by estimating both the oxygen diffusion distances and resultant oxygen profile. Such analysis may be useful for parameter fitting in large imaging datasets and histological sections, and allows easy quantification of projected differences between functional forms of OCR.

Keywords: hypoxia; mathematical modelling; oxygen

References

  1. Ann Biomed Eng. 1997 May-Jun;25(3):565-72 - PubMed
  2. Microvasc Res. 1971 Apr;3(2):125-41 - PubMed
  3. Int J Radiat Oncol Biol Phys. 1993 Feb 15;25(3):481-9 - PubMed
  4. Ann Biomed Eng. 2004 Nov;32(11):1519-29 - PubMed
  5. Semin Radiat Oncol. 2011 Apr;21(2):111-8 - PubMed
  6. Acta Oncol. 1995;34(3):313-6 - PubMed
  7. Cell Metab. 2006 Mar;3(3):187-97 - PubMed
  8. J Biol Chem. 1990 Sep 15;265(26):15392-402 - PubMed
  9. Br J Radiol. 1953 Dec;26(312):638-48 - PubMed
  10. Recent Results Cancer Res. 1984;95:1-23 - PubMed
  11. Biophys J. 1984 Sep;46(3):343-8 - PubMed
  12. Br J Radiol. 1972 Jul;45(535):515-24 - PubMed
  13. Growth. 1966 Jun;30(2):157-76 - PubMed
  14. IMA J Math Appl Med Biol. 1997 Mar;14(1):39-69 - PubMed
  15. J R Soc Interface. 2014 Jan 15;11(92):20131124 - PubMed
  16. Nucl Med Biol. 2012 Oct;39(7):986-92 - PubMed
  17. Br J Cancer. 1955 Dec;9(4):539-49 - PubMed
  18. Br J Cancer. 1995 Oct;72(4):869-74 - PubMed
  19. Microvasc Res. 1978 Nov;16(3):391-405 - PubMed
  20. J Math Biol. 2001 Oct;43(4):291-312 - PubMed
  21. Int J Radiat Oncol Biol Phys. 1992;22(3):397-402 - PubMed
  22. Arch Biochem Biophys. 1979 Jul;195(2):485-93 - PubMed
  23. Semin Radiat Oncol. 2011 Apr;21(2):101-10 - PubMed
  24. J Theor Biol. 2006 Sep 21;242(2):440-53 - PubMed
  25. Int J Radiat Oncol Biol Phys. 1988 Sep;15(3):691-7 - PubMed

Publication Types