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3 - Acid-mediated tumor growth

Published online by Cambridge University Press:  05 December 2012

William E. Schiesser
Affiliation:
Lehigh University, Pennsylvania
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Publisher: Cambridge University Press
Print publication year: 2012

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References

[1] Bianchini, L. and Fasano, A. (2009), A model combining acid-mediated tumour invasion and nutrient dynamics, Nonlinear Anal. Real, 10, 1955–1975CrossRefGoogle Scholar
[2] Fasano, A., Herrero, M. A., and Rodrigo, M. R. (2009), Slow and fast invasion waves in a model of acid-mediated tumour growth, Math. Biosci., 220, 45–56CrossRefGoogle Scholar
[3] Gatenby, R. A. and Gawlinski, E. T. (1996), A reaction-diffusion model of cancer invasion, Cancer Res., 56, 5745–5753Google ScholarPubMed
[4] Martin, G. R. and Jain, R. K. (1994), Noninvasive measurement of interstitial pH profiles in normal and neoplastic tissue using fluorescence ratio imaging spectroscopy, Cancer Res., 54, 5670–5674Google Scholar
[5] Martin, N. K.Gaffney, E. A., Gatenby, R. A., et al. (2011), A mathematical model of tumour and blood pHe regulation: the HCO−3/CO2 buffering system, Math. Biosci., 230, 1–11CrossRefGoogle Scholar
[6] Patel, A. A.Gawlinski, E. T., Lemieux, S. K., and Gatenby, R. A. (2001), A cellular automation model of early tumor growth and invasion: the effects of native tissue vascularity and increased anaerobic tumor metabolism, J. Theor. Biol., 213, 315–331CrossRefGoogle Scholar
[7] Singh, R. K. and Siegal, G. P. (1995), Amino acid transport systems modulate human tumor cell growth and invasion: a working hypothesis, Med. Hypotheses, 44, 195–201CrossRefGoogle ScholarPubMed
[8] Smallbone, K., Gatenby, R. A., and Maini, P. K. (2008), Mathematical modelling of tumour acidity, J. Theor. Biol., 255, 106–112CrossRefGoogle ScholarPubMed

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  • Acid-mediated tumor growth
  • William E. Schiesser, Lehigh University, Pennsylvania
  • Book: Partial Differential Equation Analysis in Biomedical Engineering
  • Online publication: 05 December 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9781139137096.004
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  • Acid-mediated tumor growth
  • William E. Schiesser, Lehigh University, Pennsylvania
  • Book: Partial Differential Equation Analysis in Biomedical Engineering
  • Online publication: 05 December 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9781139137096.004
Available formats
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Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Acid-mediated tumor growth
  • William E. Schiesser, Lehigh University, Pennsylvania
  • Book: Partial Differential Equation Analysis in Biomedical Engineering
  • Online publication: 05 December 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9781139137096.004
Available formats
×