Biomedical Engineering Reference
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observed in simulations with normal cells only. In contrast, we find a high percent-
age of quiescent cancer cells in all states of tumour growth, leading to further
angiogenesis in our simulations (see Fig. 3.4 ). The dark red vessels in row 3 indicate
new vessels that develop after tumour implantation. In conclusion, our model with
the chosen parameter values predicts an increase in the vascular density following
tumour implantation.
3.4 Conclusions
In this chapter we have presented a multiscale model of vascular tumour growth and
angiogenesis. After the introduction, the mathematical model was presented in
Sect. 3.2 where we gave a detailed description of the mathematical models on the
different length scales. Finally, we introduced the computational algorithm that we
use to simulate the model. In the third section, simulation results were shown. We
started by considering the growth of a tumour nested in healthy tissue initially
perfused by two straight and parallel vessels and then studied the evolution of cells
and the vascular system. As proof of concept, we then used an experimentally
derived vessel network to initialise a simulation of tumour growth and angiogene-
sis. To the best of our knowledge, this is the first time this has been done—Secomb,
Pries and co-workers (e.g. [ 31 , 26 ]) have used such networks to study structural
adaptation alone. Our work paves the way for further research which will be more
closely linked with experimental data. In particular, it would be of great interest to
compare our model simulations with experimental data from two or more time
points. The first time point defining the initial conditions for the simulations and
data from later time points used to test the model's predictive power or to estimate
parameter values. We would not expect to obtain a detailed match at later time
points, since we simulate a stochastic system, but we would expect agreement
between experimental and simulated values for certain characteristics, such as
vessel volume fractions and the distributions of vessel radii and segment lengths.
One problem is the large number of parameters contained in multiscale models
such as ours. This makes it nontrivial to parametrise them. One strategy would be to
start by parametrising small and well-defined submodels independently of each
other. In this way, it should then be possible to determine whether coupling the
submodels together gives physiologically realistic results or if additional effects
have to be incorporated. Another important issue is determining the influence that
each system parameter has on the simulation results. This could be established by
performing a comprehensive parameter sensitivity analysis. Such knowledge would
Fig. 3.4 (continued) microscopy and embedded it in a 32
6 cellular automaton domain. In
the first column , the tumour expands radially, and degrades the healthy tissue ( second column ).
The predicted adaptations of the vascular system are shown in the third column where the
experimentally derived network is shown in light red , while the new vessels are coloured in red
32
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