Cancer modelling
We are interested in modelling the dynamics of cancer progression and treatment from a number of different view points and on various spatial and temporal scales. Below some areas of interest are outlined in more detail. Please contact Professor Philip K. Maini or Dr Eamonn Gaffney for further information.
Chemotherapeutic and anti-angiogenesis treatments
Most of the existing mathematical models for tumour growth and tumour-induced angiogenesis neglect blood flow, yet this is an important factor on which both nutrient and metabolite supply depend. We have developed mathematical models which show how blood flow and red blood cell heterogeneity influence the growth of tissue composed of normal and cancer cells. We first determine the distribution of oxygen in a vascular network, incorporating into our model features of blood flow and vascular dynamics such as structural adaptation, complex rheology and red blood cell circulation. We then study the dynamics of the tissue using a cellular automaton formulation. Our results show that blood flow and red blood cell heterogeneity play a major role in the dynamics of cancer cell growth. At the same time, we have been investigating the effects of chemotherapeutic interventions on tumour cells. We have shown that the standard model for this in the presence of multiple drugs and acquired drug resistance breaks down when the modelling assumptions are made more biologically realistic. In particular, the inclusion of the effects of the cell cycle in the presence of cell cycle phase specific drugs combined with limitations on the frequency with which drugs can be delivered results in a total breakdown of previous scheduling hypotheses. We are now aiming to combine these two models to study the effects of therapies in which both anti-angiogenesis and chemotherapeutic drugs are applied.
Key references in this area
- E. A. Boston and E. A. Gaffney (2011). The influence of toxicity constraints in models of chemotherapeutic protocol escalation. Math. Med. Biol. 28:357-384. (eprints)
- H. Perfahl, H. M. Byrne, T. Chen, V. Estrella, T. Alarcon, A. Lapin, R. A. Gatenby, R. J. Gillies, M. C. Lloyd, P. K. Maini, M. Reuss and M. R. Owen (2011). Multiscale modelling of vascular tumour growth in 3D: the roles of domain size & boundary conditions. PLoS One 6. (eprints)
- H. C. Monro and E. A. Gaffney (2009). Modelling chemotherapy resistance in palliation and failed cure. J. Theor. Biol. 257:292-302. (eprints)
- M. R. Owen, T. Alarcon, P. K. Maini, H. M. Byrne (2009). Angiogenesis and vascular remodelling in normal and cancerous tissues. J. Math. Biol. 58:689-721. (eprints)
Therapeutic implications of the acid-mediated invasion hypothesis
In a collaboration involving Professors Robert A. Gatenby and Robert J. Gillies (Moffitt Cancer Center, Florida) and David J. Gavaghan (Computing Laboratory, University of Oxford) we have developed a mathematical model of reaction-diffusion type to predict the excess extracellular hydrogen ion concentration in a growing tumour. This model predicts that avascular tumours will always be benign, but that vascular tumours may become malignant (that is, grow uncontrollably) if a certain combination of model parameters breaches a threshold. This actually suggests the counter-intuitive treatment of adding excess acid to the tissue as a possible method of controlling tumour growth (as it will poison the tumour). Professor Gatenby is presently pursuing this experimentally. We are currently extending our model to incorporate further aspects of the glycolytic pathway and the relationship between extracellular oxygen concentration and cellular acid production. As the tumour microenvironment becomes more toxic, adaptation becomes essential, and we have developed a hybrid cellular automaton model to investigate the cell-microenvironmental interactions that mediate somatic evolution of cancer cells during the development of ductal carcinoma in situ. We are in the process of experimentally verifying this model and preliminary results show that it does indeed correctly predict key aspects of the spatio-temporal evolution of invasive breast cancer. The model suggests further that the transition to aggressively invasive phenotypes may be delayed through novel strategies directed towards interrupting the hypoxia-glycolysis-acidosis cycle and future work will explore the therapeutic potential of this finding.
Key references in this area
- N. K. Martin, E. A. Gaffney, R. A. Gatenby, R. J. Gillies, I. F. Robey and P. K. Maini (2011). A mathematical model of tumour and blood pHe regulation: The HCO-3/CO2 buffering system. Math. Biosci. 230:1-11. (eprints)
- N. K. Martin, E. A. Gaffney, R. A. Gatenby and P. K. Maini (2010). Tumour-stromal interactions in acid-mediated invasion: a mathematical model. J. Theor. Biol. 267:461-470. (eprints)
- R. A. Gatenby, K. Smallbone, P. K. Maini, F. Rose, J. Averill, R. B. Nagle, L. Worrall, R. J. Gillies (2007). Cellular adaptations to hypoxia and acidosis during somatic evolution of breast cancer. Brit. J. Cancer 97:646-653. (eprints)
Colorectal cancer
One of the main areas of research targeted by our recently completed E-Science pilot project on Integrative Biology is the development of models at a range of spatial scales to investigate colorectal cancer. In collaboration with Sir Walter Bodmer (Weatherall Institute of Molecular Medicine, University of Oxford), and Professor S. Jonathan Chapman (OCIAM) we have been developing mathematical models of cell population dynamics in the colonic crypt and in colorectal cancer. We have highlighted shortcomings in previous models which have been used by experimentalists and have developed a more biologically-realistic model which allows us to study the effects of asynchronous cell division and feedback controls. In particular we have shown how the latter (ignored in previous models) is vital for homeostasis. Moreover, we have shown that abnormal disruption of the feedback mechanism can lead eventually to clonal expansion and neoplasia. An application of this research is to determine how control can be restored to the correct level. At the same time, we have developed a multiscale model for crypt cell dynamics which links key signalling agents to the mechanical properties of cells. This is a joint collaboration with Professors David J. Gavaghan (Computing Laboratory) and Helen M. Byrne (University of Nottingham).
Image showing colon crypts together with an illustration of the model set up.
Taken from van Leeuwen et al. (2009).
Key references in this area
- M. D. Johnston, C. M. Edwards, W. F. Bodmer, P. K. Maini and S. J. Chapman (2007). Mathematical modeling of cell population dynamics in the colonic crypt and in colorectal cancer. Proc. Natl. Acad. Sci. USA. 104:4008-4013. (eprints)
- I. M. M. van Leeuwen, G. R. Mirams, A. Walter, A. Fletcher, P. Murray, J. Osborne, S. Varma, S. J. Young, J. Cooper, B. Doyle, J. Pitt-Francis, L. Momtahan, P. Pathmanathan, J. P. Whiteley, S. J. Chapman, D. J. Gavaghan, O. E. Jensen, J. R. King, P. K. Maini, S. L. Waters, H. M. Byrne (2009). An integrative computational model for intestinal tissue renewal. Cell Prolif. 42:617-636. (eprints)
- M. D. Johnston, P. K. Maini, S. J. Chapman, C. M. Edwards and W. F. Bodmer (2010). On the proportion of cancer stem cells in a tumour. J. Theor. Biol. 266:708-711. (eprints)
- P. J. Murray, J. W. Kang, G. R. Mirams, S. Y. Shin, H. M. Byrne, P. K. Maini and K. H. Cho (2010). Modelling spatially regulated β-catenin dynamics and invasion in intestinal crypts. Biophys. J. 99:716-725. (eprints)
- A. G. Fletcher, G. R. Mirams, P. J. Murray, A. Walter, J.-W. Kang, K.-H. Cho, P. K. Maini and H. M. Byrne (2011). Multiscale modeling of colonic crypts and early colorectal cancer. In Multiscale Cancer Modeling. CRC Press, 111-134.
- P. J. Murray, A. Walter, A. G. Fletcher, C. M. Edwards, M. J. Tindall and P. K. Maini (2011). Comparing a discrete and continuum model of the intestinal crypt. Phys. Biol. 8:026011. (eprints)
- S.-J. Dunn, A. G. Fletcher, S. J. Chapman, D.J. Gavaghan and J.M. Osborne (2012). Modelling the role of the basement membrane in the colonic epithelium. J Theor Biol, 298:82-91.
- A. G. Fletcher, C. J. W. Breward and S. J. Chapman (2012). Mathematical modelling of monoclonal conversion in the colonic crypt. J. Theor. Biol. 300:118-133.