Biomedical Engineering Reference
In-Depth Information
4.4 Fast Time Scale Necrotic Cell Lysis and Volume Loss
are Responsible for Mechanical ''Tears''
at Perinecrotic Boundary
One notable feature of nearly every DCIS pathology section is a ''tear'' at the
perinecrotic boundary. See the black arrows in Fig.
11
(bottom). The conventional
wisdom is that these tears are not actually present in vivo, but are instead artifacts
that arise from tissue dehydration during sample preparation.
In [
57
], we implemented a preliminary necrosis sub-model where fluid volume
was lost through the membrane gradually throughout necrosis, at a rate propor-
tional to surface area and the remaining fluid fraction:
4pR
2
;
V
V
S
V
dV
ds
¼
2
s
N
log 100
ð
15
Þ
where 0\s\s
C
¼
s
N
is the elapsed time since entering the necrotic state, V
S
is
the cell's solid fraction, and the coefficient was chosen to make this nonlinear ODE
satisfy V
ð
s
N
Þ
V
S
. Fast cell swelling and lysis were neglected. The simulation,
plotted at 30 days in Fig.
12
, did not predict a tear at the perinecrotic boundary.
We therefore hypothesized that if the perinecrotic tear is not an artifact, it must be
caused by a fast time scale process. In [
56
], based upon a more thorough review of
necrosis biology (see
Sect. 2.2
), we implemented the current model with rapid
necrotic cell swelling followed by rapid volume loss. These simulations did
recapitulate the perinecrotic tear. See the tumor leading edge in Fig.
8
.
The mechanistic model is based upon the balance of actual forces with bio-
physically sound parameter values, is calibrated to actual patient data, and suc-
cessfully makes quantitative, validated predictions on DCIS progression. In light of
this care we put into the biological and clinical accuracy of the model, we conclude
that mechanical separation of the viable rim and necrotic core at the perinecrotic
boundary, although exacerbated by tissue dehydration, is in fact a real phenomenon,
rather than a simple artifact. Based upon this new insight, we now interpret tears and
cracks in pathology sections as indicators of a tissue's local biomechanical strength.
4.5 Evidence of Calcification Degradation
at a Very Long Time Scale
Our simulations (Fig.
8
) predict a linear/casting-type calcification, where the cal-
cification forms a long, solid ''plug'' in the center of the duct. See Fig.
13
for a
mammographic image of casting-type microcalcifications. Other calcification
morphologies (e.g., fine pleomorphic) are not predicted by the biophysical
assumptions of our model. While casting-type calcifications correlate with come-
donecrosis
[
85
],
they
are
only
present
in
approximately
30-50 %
of
DCIS
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