Modelling the Role of Angiogenesis and Vasculogenesis in Solid Tumour Growth |
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Authors: | I J Stamper H M Byrne M R Owen P K Maini |
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Institution: | (1) Centre for Mathematical Medicine, School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, UK;(2) Centre for Mathematical Biology, Mathematical Institute, University of Oxford, 24-29 St Giles’, Oxford, OX1 3LB, UK;(3) Oxford Centre for Integrative Systems Biology, Dept. of Biochemistry, South Parks Road, Oxford, OX1 3QU, UK |
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Abstract: | Recent experimental evidence suggests that vasculogenesis may play an important role in tumour vascularisation. While angiogenesis
involves the proliferation and migration of endothelial cells (ECs) in pre-existing vessels, vasculogenesis involves the mobilisation
of bone-marrow-derived endothelial progenitor cells (EPCs) into the bloodstream. Once blood-borne, EPCs home in on the tumour
site, where subsequently they may differentiate into ECs and form vascular structures.
In this paper, we develop a mathematical model, formulated as a system of nonlinear ordinary differential equations (ODEs),
which describes vascular tumour growth with both angiogenesis and vasculogenesis contributing to vessel formation. Submodels
describing exclusively angiogenic and exclusively vasculogenic tumours are shown to exhibit similar growth dynamics. In each
case, there are three possible scenarios: the tumour remains in an avascular steady state, the tumour evolves to a vascular
equilibrium, or unbounded vascular growth occurs. Analysis of the full model reveals that these three behaviours persist when
angiogenesis and vasculogenesis act simultaneously. However, when both vascularisation mechanisms are active, the tumour growth
rate may increase, causing the tumour to evolve to a larger equilibrium size or to expand uncontrollably. Alternatively, the
growth rate may be left unaffected, which occurs if either vascularisation process alone is able to keep pace with the demands
of the growing tumour.
To clarify further the effects of vasculogenesis, the full model is also used to compare possible treatment strategies, including
chemotherapy and antiangiogenic therapies aimed at suppressing vascularisation. This investigation highlights how, dependent
on model parameter values, targeting both ECs and EPCs may be necessary in order to effectively reduce tumour vasculature
and inhibit tumour growth. |
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Keywords: | Tumour growth Angiogenesis Vasculogenesis Endothelial progenitor cell Therapy |
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