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December  2006, 1(4): 515-535. doi: 10.3934/nhm.2006.1.515

The impact of cell crowding and active cell movement on vascular tumour growth

Russell Betteridge 1, , Markus R. Owen 2, , H.M. Byrne 2, , Tomás Alarcón 3, and  Philip K. Maini 1,

1. 

Centre for Mathematical Biology, Mathematical Institute, University of Oxford, 24-29 St Giles', Oxford OX1 3LB, United Kingdom
2. 

Centre for Mathematical Medicine, School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, United Kingdom
3. 

Bioinformatics Unit, Department of Computer Science, University College London, Gower Street, London WC1E 6BT, United Kingdom

Received  September 2006 Published  October 2006

A multiscale model for vascular tumour growth is presented which includes systems of ordinary differential equations for the cell cycle and regulation of apoptosis in individual cells, coupled to partial differential equations for the spatio-temporal dynamics of nutrient and key signalling chemicals. Furthermore, these subcellular and tissue layers are incorporated into a cellular automaton framework for cancerous and normal tissue with an embedded vascular network. The model is the extension of previous work and includes novel features such as cell movement and contact inhibition. We present a detailed simulation study of the effects of these additions on the invasive behaviour of tumour cells and the tumour's response to chemotherapy. In particular, we find that cell movement alone increases the rate of tumour growth and expansion, but that increasing the tumour cell carrying capacity leads to the formation of less invasive dense hypoxic tumours containing fewer tumour cells. However, when an increased carrying capacity is combined with significant tumour cell movement, the tumour grows and spreads more rapidly, accompanied by large spatio-temporal fluctuations in hypoxia, and hence in the number of quiescent cells. Since, in the model, hypoxic/quiescent cells produce VEGF which stimulates vascular adaptation, such fluctuations can dramatically affect drug delivery and the degree of success of chemotherapy.
Keywords: tumour growth, chemotherapy, Multiscale modelling, cell movement..
Mathematics Subject Classification: Primary: 16P9.
Citation: Russell Betteridge, Markus R. Owen, H.M. Byrne, Tomás Alarcón, Philip K. Maini. The impact of cell crowding and active cell movement on vascular tumour growth. Networks and Heterogeneous Media, 2006, 1 (4) : 515-535. doi: 10.3934/nhm.2006.1.515
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