A mathematical model of tumour and blood pHe regulation: The HCO3-/CO2 buffering system

Natasha K Martin, Eamonn A Gaffney, Robert A Gatenby, Robert J Gillies, Ian F Robey, Philip K Maini

Research output: Contribution to journalArticle (Academic Journal)peer-review

31 Citations (Scopus)


Malignant tumours are characterised by a low, acidic extracellular pH (pHe) which facilitates invasion and metastasis. Previous research has proposed the potential benefits of manipulating systemic pHe, and recent experiments have highlighted the potential for buffer therapy to raise tumour pHe, prevent metastases, and prolong survival in laboratory mice. To examine the physiological regulation of tumour buffering and investigate how perturbations of the buffering system (via metabolic/respiratory disorders or changes in parameters) can alter tumour and blood pHe, we develop a simple compartmentalised ordinary differential equation model of pHe regulation by the HCO3-/CO2 buffering system. An approximate analytical solution is constructed and used to carry out a sensitivity analysis, where we identify key parameters that regulate tumour pHe in both humans and mice. From this analysis, we suggest promising alternative and combination therapies, and identify specific patient groups which may show an enhanced response to buffer therapy. In addition, numerical simulations are performed, validating the model against well-known metabolic/respiratory disorders and predicting how these disorders could change tumour pHe.
Original languageEnglish
Pages (from-to)1-11
Number of pages11
JournalMathematical Biosciences
Issue number1
Publication statusPublished - Mar 2011

Bibliographical note

Copyright © 2010 Elsevier Inc. All rights reserved.


  • Animals
  • Extracellular Space
  • Alkalosis, Respiratory
  • Computer Simulation
  • Bicarbonates
  • Hydrogen-Ion Concentration
  • Humans
  • Algorithms
  • Mice
  • Models, Biological
  • Acidosis
  • Acid-Base Equilibrium
  • Blood
  • Neoplasms
  • Kinetics
  • Buffers
  • Acidosis, Respiratory
  • Alkalosis
  • Carbon Dioxide


Dive into the research topics of 'A mathematical model of tumour and blood pHe regulation: The HCO3-/CO2 buffering system'. Together they form a unique fingerprint.

Cite this