Biomedical Engineering Reference
In-Depth Information
uptake term that resolves each cell's volume, then average it across a lower-
resolution mesh (mesh size
1
=
10 the appropriate diffusion length scale) before
solving the reaction-diffusion equation. We apply Dirichlet conditions on the BM,
and use Neumann conditions wherever the lumen intersects the computational
boundary.
We represent the basement membrane using a signed distance function d sat-
isfying d [ 0 in the lumen, d\0 in the stroma, d
¼
0 on the basement membrane,
and
rj j
1. We introduce an auxiliary data structure to reduce the overall
computational cost from
O
N
ð
t
Þ
2
to
O
N
ð
t
ð Þ
, where N
ð
t
Þ
is the number of
simulation objects at time t [
56
]. We implemented the model in cross-platform,
object-oriented C++; we currently plan to open source the simulation framework
in the next year. Towards that end, we introduced MultiCellXML, a new XML-
based standard for sharing multicell agent simulation data. The supplementary
material for [
56
] include sample DCIS simulation datasets (in MultiCellXML
1.0 format) and open source postprocessing and visualization code. Please see
4.1.3 Calibration to Individual Patients, and Key Necrosis
Parameter Values
In [
56
], we introduced the first calibration method to use individual patient
pathology from a single time point, based upon processing several DCIS-affected
ducts for the patient, as described in [
23
]. The proliferative index (PI: the per-
centage of Ki-67 positive cells in the viable rim) and apoptotic index (AI: the
percentage of cleaved Caspase-3 positive cells in the viable rim) were combined
with estimates of the proliferative time scale (s
P
¼
18 h) and apoptotic time
scale (s
A
¼
8
:
6 h) and a population dynamic argument to calibrate the
A
Q$P
phenotypic transitions in the model. The cell density and experimental
reports on cell mechanical response to deformation (see the references in [
56
])
were used to calibrate the mechanical parameters of the model. We calibrated
oxygen transport by solving steady-state reaction-diffusion equations in a simplified
cylindrical duct geometry and matching to the patient's measured viable rim
thickness. In [
56
], we applied the calibration to a single anonymized DCIS patient
with high-grade solid-type DCIS with comedonecrosis; we show the simulation (in
a 1.5 mm, 2-D longitudinal section of duct) after 45 days of growth in this patient in
Fig.
8
. We recently combined this calibration method with an upscaling/coarse-
graining argument to derive patient-specific predictions of surgical excision vol-
umes in [
23
].
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