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A cellular automaton model examining the effects of oxygen, hydrogen ions and lactate on early tumour growth

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Abstract

Some tumours are known to exhibit an extracellular pH that is more acidic than the intracellular, creating a ‘reversed pH gradient’ across the cell membrane and this has been shown to affect their invasive and metastatic potential. Tumour hypoxia also plays an important role in tumour development and has been directly linked to both tumour morphology and aggressiveness. In this paper, we present a hybrid mathematical model of intracellular pH regulation that examines the effect of oxygen and pH on tumour growth and morphology. In particular, we investigate the impact of pH regulatory mechanisms on the cellular pH gradient and tumour morphology. Analysis of the model shows that: low activity of the Na\(^+\)/H\(^+\) exchanger or a high rate of anaerobic glycolysis can give rise to a “fingering” tumour morphology; and a high activity of the lactate/H\(^+\) symporter can result in a reversed transmembrane pH gradient across a large portion of the tumour mass. Also, the reversed pH gradient is spatially heterogenous within the tumour, with a normal pH gradient observed within an intermediate growth layer within the spheroid. We also include a fractal dimension analysis of the simulated tumour contours, in which we compare the fractal dimensions of the simulated tumour surfaces with those found experimentally via photomicrographs.

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Acknowledgments

M.A. was supported by a studentship from the Engineering and Physical Sciences Research Council.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Strathclyde, Glasgow, UK

    Maymona Al-Husari

  2. Unit of Oral and Maxillofacial Medicine and Surgery, School of Clinical Dentistry, University of Sheffield, Sheffield, UK

    Craig Murdoch

  3. Department of Molecular and Clinical Pharmacology, Institute of Translational Medicine, MRC Centre for Drug Safety Science, The University of Liverpool, Liverpool, UK

    Steven D. Webb

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  1. Maymona Al-Husari
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Al-Husari, M., Murdoch, C. & Webb, S.D. A cellular automaton model examining the effects of oxygen, hydrogen ions and lactate on early tumour growth. J. Math. Biol. 69, 839–873 (2014). https://doi.org/10.1007/s00285-013-0719-x

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