Biomedical Engineering Reference
In-Depth Information
t=4.00
t=5.00
20
20
0
0
−20
−20
−20
0
20
−20
0
20
x
x
t=6.00
t=7.00
20
20
0
0
−20
−20
−20
0
20
−20
0
20
x
x
Fig. 6 A simulation of repeated encapsulation of host tissue by a growing tumor [
58
]. Legend:
White viable tumor. Black necrotic tumor. Figure adapted with permission from [
58
]
Particularly unstable tumors could experience frequent connection and discon-
nection of invasive fingers or bulbs [
51
,
58
,
60
]. (See Fig.
6
for an example of
repeated encapsulation of host tissue). Connection or reconnection of invasive
fingers or bulbs lead to rapid depletion of nutrient in the newly encapsulated host
and tumor tissue, leading to a jump in necrosis. Subsequent disconnection would
rapidly reperfuse the encapsulated regions, leading to the condition where r [ r
N
in previously necrotic tissue. This necrotic tissue would ''come back to life''—an
impossibility. We solved these problems by introducing an additional level set
function /
N
to separately track the necrotic core boundary [
61
,
62
].
Second, because the continuum model linked together many biophysical effects
into very few parameters (much to the benefit of mathematical analysis!), it was
difficult to directly calibrate the model to experimental measurements. Model
calibration required force-fitting the parameters to match experimental growth rate
measurements, and then tuning the remaining parameters to match the simulated
morphologies (as informed by parameter space investigations) to clinical or other
observations (e.g., as in [
33
]). While this makes data-driven simulations possible,
it can hinder the acceptance of mathematical modeling in the biological and
Search WWH ::
Custom Search