Tumor-Derived Vasculogenesis - Cellular Potts Models: Multiscale Extensions and Biological Applications - page 128

of L T , i.e.,

pct = L T l T
L T

:

Obviously, all the model parameters can theoretically be changed, but we
will only detail biologically reasonable (and therefore most influential and
predictive) variations. We first test the actual clinically viable biomedical in-
terventions. Most current drugs target the VEGF system, either by directly
attacking VEGF molecules (with antibodies such as Bevacizumab and Rani-
mizumab or aptamers such as Pegaptanib), or by preventing the activation of
its tyrosine kinase receptors (with small inhibitor molecules such as sorafenib,
sunitinib, and vatalanib) [366]. We implement such interferences with VEGF
activity by increasing its degradation rate (doubling v ) and, respectively, by
reducing the eectiveness of its uptake (i.e., imposing B(x;t;v) = 0 in Equa-
tion (6.5)). In the first case we observe a phenomenon of high interest: at
the standard nal time (i.e., 24 h) the tubulogenic process is dramatically
downregulated, as shown in Figure 7.9(A), confirming the effectiveness of the
treatment, as lT T 0.24L T (pct = 0.76). However, at much longer times ( 30
h) a pattern emerges, formed by a number of connected networks character-
ized by small lacunae and short chords; see Figure 7.9(B). This is somewhat in
agreement with theoretical results from both previous continuous [9, 154, 360]
and discrete models [261]: the reduced scale of these structures is in fact dic-
tated by the diffusion of the morphogen, which is affected by the increment
of its degradation rate.
However, the delay in the formation of such a reduced-in-length network
is not present in those published works, and is probably due to the fact that
in our model VEGF uptake has a threshold behavior (see Equation (6.5)).
In fact, a slower diffusion of the morphogen causes a temporal shift in the
full-activation of the calcium-dependent cascades. The overall inhibition of
the activity of cell VEGF receptors results instead in a complete disruption of
vascular progression, as lT T 0.08L T (pct = 0.92); see Figure 7.9(C). Without
sequestrating VEGF molecules, in fact, TECs do not completely activate the
downstream intracellular cascades and therefore almost remain in their resting
conditions, characterized by a typical random movement.
Analogous ecient results are obtained by blocking the overall mitogen-
induced calcium entry (with F AA = F NO = 0 in Equation (6.10)). As already
seen, this is the model counterpart of the function of carboxyamidotriazole
(CAI) compound [133, 279]. In particular, a comparison of experimental ob-
servations and numerical results is given in Figure 7.10(A-B): in both cases
we observe a complete disruption of tubule formation, as the TECs remain
almost scattered (lT T 0.12L T and, consequently, pct = 0:88). This is due to
the fact that a dramatic interference in mitogen-induced calcium machinery
results in a clear inhibition of cell adhesive and migratory properties. More-
over, a modulated reduction of calcium influxes confirms the dose-dependent
eciency of CAI, see right panel of the same figure.
By imposing k a = v c = 0 in Equation (6.7) (respectively, k n = v ca = 0