3D Multiscale Modelling of Angiogenesis and Vascular Tumour Growth - Bioanalysis Advanced Materials Methods and Devices - page 40

• Calculation of pressures and flows within vasculature (vascular layer)
Poiseuille's flow ( 3.16 ) is considered in each branch of the vascular network,
and the pressure at each node is calculated by applying conservation of mass.
The haematocrit is assumed to split symmetrically at bifurcations.

In 1, the successive cellular automaton model is initialized. Then 2 and 3 are
carried out on each time interval Dt until the final simulation time is reached.

3.3 Simulations

The results from a typical simulation, showing the development of a tumour and its
associated network of blood vessels, are depicted in Fig. 3.2 . Simulations were
performed on a 50

50 50 lattice with spacing 40 m m, which corresponds to a

2mm 2 mm cube of tissue. For the following simulations, each lattice

site can be occupied by at most one cell (either normal or cancerous), which
implies that, for the grid size used (40

2mm

m m), the tissue is not densely packed. A

small tumour was implanted at t 0 h in a population of normal cells perfused by

two parallel parent vessels with countercurrent flow (i.e. the pressure drops and
hence flows are in opposite directions). Initially, insufficient nutrient supply in
regions at distance from the vessels causes widespread death of the normal cells.
The surviving tumour cells reduce the p53 threshold for death of normal cells,
which further increases the death rate of the normal cells and enables the tumour to
spread. Initially, due to inadequate vascularisation, most of the tumour cells are
quiescent and secrete VEGF which stimulates an angiogenic response. After a
certain period of time, the quiescent cells die and only a small vascularised tumour
remains, encircling the upper vessel. The tumour expands preferentially along this
vessel, in the direction of highest nutrient supply. Diffusion of VEGF throughout
the domain stimulates the formation of new capillary sprouts from the lower parent
vessel. When the sprouts anastomose with other sprouts or existing vessels, the
oxygen supply increases, enabling the normal cell population to recover. Because
the tumour cells consume more oxygen than normal cells and they more readily
secrete VEGF under hypoxia, VEGF levels are higher inside the tumour, and the
vascular density there is much higher than in the healthy tissue. The tumour
remains localised around the upper vessel until new vessels connect the upper
and lower vascular networks. Thereafter, the tumour cells can spread to the lower
region of the domain until eventually the domain is wholly occupied by cancer
cells and their associated vasculature.
As a further step, we document preliminary results of a vascular tumour growth
simulation for which the initial vascular geometry was taken from multiphoton
fluorescence microscopy (a detailed description of the experimental setting can be
found in [ 22 ]). The aim here is to integrate the mathematical model with in vivo

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