Biomedical Engineering Reference
In-Depth Information
Fig. 2
The evolution of the vessel network with a tumor localized in the center and 20 initial tips
N
(
t
)
i
=
1
(
δ
X
i
(
t
)
∗
K
N
)(
x
)
−
ν
2
m
(
t
,
x
)
.
∂
∂
)+
ν
1
1
N
t
m
(
t
,
x
)=
ε
1
m
(
t
,
x
(12)
In Eqs. (
10
)-(
12
), we consider, as discussed in Sect.
2
, a mollified version of the
marginal spatial random distribution, by means of the convolution with the kernel
K
N
,givenbyEq.(
4
). Figures
2
and
3
show simulation results in the case the tumor,
source of TAF, is located in the centre of the cornea; we consider 20 initial capillary
sprouts. In such a simulation anastomosis is also taken into account. In particular
Figure
2
shows four steps of the capillary network formation in response to the
tumor mass, and its interaction with the underlying chemotactic field, represented
by the shading contour lines in the background. Figure
3
shows different zooms that
illustrate the network structure at lower scales; anastomosis is highlighted.
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