3D Multiscale Modelling of Angiogenesis and Vascular Tumour Growth - Bioanalysis Advanced Materials Methods and Devices - page 30

attention focusses on changes in the vasculature. This framework has been
extended by St ´ phanou et al. [ 33 ] to produce 3D simulations of angiogenesis
and vascular adaptation. More recently, Macklin et al. [ 17 ] coupled a multiphase
model to a discrete model of angiogenesis that accounts for blood flow, non-
Newtonian effects and vascular remodelling. The models are coupled in two ways:
via hydrostatic pressure which is generated by the growing tumour and acts on the
vessels and via oxygen which is supplied by the vessels and stimulates growth.
Lloyd et al. [ 16 ] have developed a model for neoplastic tissue growth which
accounts for blood and oxygen transport and angiogenic sprouting. The strain
(local deformation) in the tumour tissue is assumed to be an increasing function of
the local oxygen concentration. In separate work, Owen et al. [ 20 ], building on the
work of Alarc´n and co-workers [ 1 , 2 , 3 , 4 ], proposed a 2D multiscale model for
vascular tumour growth which combines blood flow, angiogenesis, vascular
remodelling and tissue scale dynamics of multiple cell populations as well as
the subcellular dynamics (including the cell cycle) of individual cells. More
recently, this framework was extended by Owen et al. [ 21 ] to analyse synergistic
anti-tumour effects of combining a macrophage-based, hypoxia-targeted, gene
therapy with chemotherapy.
While several two-dimensional models of angiogenesis consider tumour
growth, few groups account for vascular tumour growth in three space-
dimensions. In an extension to work by Zheng at al. [ 37 ], Frieboes et al. [ 14 ]
couple a mixture model to a lattice-free continuous-discrete model of angiogene-
sis [ 24 ] to study vascular tumour growth. However, the effects of blood flow and
vascular remodelling are neglected. Lee et al. [ 15 ] studied tumour growth and
angiogenesis, restricting vessel sprouting to the tumour periphery and
surrounding healthy tissue. They incorporated vessel dilation and collapse in
the tumour centre and analysed the micro-vessel density within the tumour.
BuildingonworkbySchallerandMeyer-Hermann[ 30 ], Drasdo et al. [ 11 ]
developed a lattice-free model for 3D tumour growth and angiogenesis that
includes biomechanically induced contact inhibition and nutrient limitation.
However, they do not consider an explicit cell cycle model, they neglect the
effects of flow-induced vascular remodelling and they ignore interactions
between normal and tumour cells. Similarly, Shirinifard et al. [ 32 ]presenta3D
cellular Potts model of tumour growth and angiogenesis in which blood flow and
vascular remodelling are neglected, as are the cell cycle and competition between
normal and tumour cells.
In this chapter, we present a 3D multiscale model of angiogenesis and vascular
tumour growth, based on Owen et al. [ 20 ]. In Sect. 3.2 , the mathematical model
and the associated computational algorithm are introduced. Computational
simulations are presented in Sect. 3.3 . There we start by illustrating the growth
of a tumour, nested in healthy tissue with two straight initial vessels. We also
show how vascular networks derived from experimental data can be integrated
in our model.