Biomedical Engineering Reference
In-Depth Information
clinical communities, who are concerned that complex models with too many free
parameters can be tuned to any desired behavior without necessarily being bio-
logically correct. Upscaling mechanistic cell-scale models can solve such prob-
lems, as in [
23
].
Lastly, even if the necrotic biomechanical properties can be rigorously esti-
mated, continuum models like this one would need further refinement to incor-
porate both the slow and fast dynamics known to play a role in necrosis. In the next
section, we will next describe a mechanistic, patient-calibrated agent-based model
developed by Macklin and collaborators in [
56
] to examine these and other issues.
4 Recent Agent-Based Modeling Results: Impact of Necrotic
Core Biomechanics on DCIS
Agent-based modeling affords us the opportunity to examine the multiscalarity of
necrosis and calcification by implementing both fast and slow time scale processes
in individual cells and investigating the emergent whole-tumor biomechanics and
clinical progression. We present recent work by Macklin et al. in simulating DCIS
for individual patients [
54
-
57
]. The work discussed below includes the most
detailed model of cell necrosis to date, and the first model of calcification. It also
includes the first patient-specific calibration method to use clinically-accessible
pathology from a single time point, as might be available in a standard biopsy.
4.1 Model Overview
In [
54
-
57
], Macklin et al. developed a patient-calibrated, lattice-free agent-based
cell model and applied it to DCIS. Each virtual cell (an agent) has a position x,
velocity v, and time-dependent physical properties. In particular, each cell has a
volume V
ð
t
Þ
and nuclear volume V
N
ð
t
Þ
, which can readily be expressed as
equivalent spherical cell and nuclear radii R
ð
t
Þ
and R
N
ð
t
Þ
, respectively. The cell
also has a maximum adhesion interaction distance R
A
[ R
ð
t
Þ
, which models both
the cell's deformability and uncertainty in its morphology [
56
]. See Fig.
7
(left).
The cell's velocity (and hence position) is governed by the balance of
forces acting upon it: cell-cell adhesion (F
cca
) and ''repulsion'' (resistance to
deformation: F
ccr
), cell-BM adhesion and repulsion (F
cba
and F
cbr
), fluid drag
(
mv), cell-ECM adhesion (F
cma
¼
c
cma
E, where E is the local ECM density),
and the net locomotive (motile) force F
loc
. These forces are balanced by Newton's
second law (conservation of linear momentum). As in [
22
,
35
,
75
], we use the
''inertialess'' assumption of fast force equilibration to explicitly express the
velocity of cell i:
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