Biomedical Engineering Reference
In-Depth Information
FIGURE 8.3: Initial condition (i.e., at t = 0) of the tumor mass for all sets of
simulations. The dimensions of cells, as well as all the other model parameters,
are given in Table C.8.
p to indicate a much higher dissolution of ECM proteins due to the activity
cell proteolytic enzymes than to the physiological decay. The local level of
tumor-secreted MMPs is instead governed by:
@m
@t = D m r 2 m
m m(( ( x ) );M)
|
+ m (1 (( ( x ) );M))
|
;
(8.7)
| {z }
diffusion
{z
}
{z
}
decay
production
where m is the decay rate in the ECM and D m the diffusion coecient, whose
low value models the fact that proteolysis is strongly localized in the regions
close to the cell membrane, in agreement with experimental evidence in [286].
m is the constant production rate of degrading enzymes, active at each cell
site.
8.3 Simulations in Standard Conditions
The simulation domain is a square lattice of 500 500 sites. The char-
acteristic length of each site is 2 m, and therefore has a physical size of
1 mm. One MCS is set to correspond to 20 sec: the overall simulations stop
 
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