Oxygen-Driven Tumour Growth Model: A Pathology-Relevant Mathematical Approach

Juan A. Delgado-SanMartin*, Jennifer I. Hare, Alessandro P S de Moura, James W T Yates, Edwin Wang (Editor)

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)
7 Downloads (Pure)


Xenografts -as simplified animal models of cancer- differ substantially in vasculature and stromal architecture when compared to clinical tumours. This makes mathematical model-based predictions of clinical outcome challenging. Our objective is to further understand differences in tumour progression and physiology between animal models and the clinic. To achieve that, we propose a mathematical model based upon tumour pathophysiology, where oxygen -as a surrogate for endocrine delivery- is our main focus. The Oxygen-Driven Model (ODM), using oxygen diffusion equations, describes tumour growth, hypoxia and necrosis. The ODM describes two key physiological parameters. Apparent oxygen uptake rate ((Formula presented.)) represents the amount of oxygen cells seem to need to proliferate. The more oxygen they appear to need, the more the oxygen transport. (Formula presented.) gathers variability from the vasculature, stroma and tumour morphology. Proliferating rate (kp) deals with cell line specific factors to promote growth. The KH,KN describe the switch of hypoxia and necrosis. Retrospectively, using archived data, we looked at longitudinal tumour volume datasets for 38 xenografted cell lines and 5 patient-derived xenograft-like models. Exploration of the parameter space allows us to distinguish 2 groups of parameters. Group 1 of cell lines shows a spread in values of (Formula presented.) and lower kp, indicating that tumours are poorly perfused and slow growing. Group 2 share the value of the oxygen uptake rate ((Formula presented.)) and vary greatly in kp, which we interpret as having similar oxygen transport, but more tumour intrinsic variability in growth. However, the ODM has some limitations when tested in explant-like animal models, whose complex tumour-stromal morphology may not be captured in the current version of the model. Incorporation of stroma in the ODM will help explain these discrepancies. We have provided an example. The ODM is a very simple -and versatile- model suitable for the design of preclinical experiments, which can be modified and enhanced whilst maintaining confidence in its predictions.

Original languageEnglish
Article numbere1004550
JournalPLoS Computational Biology
Issue number10
Publication statusPublished - 30 Oct 2015

Bibliographical note

We acknowledge Lucas Dias Fernandes and Dr Nicolas Rubido from the University of Aberdeen and Dr Neil Evans from the University of Warwick for the broad discussions on the mathematics.


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