Biomedical Engineering Reference
In-Depth Information
region
T
A
in the atlas is provided by the tumor model parameters obtained
in Step 2.
4.3. Biomechanical Finite-Element Model of Tumor Mass-Effect
The aim of the proposed model is to simulate only the mass-effect component
of the tumor growth process via a mechanical FE model constructed from 3Dmed-
ical images. Since tumor growth is not purely a mechanical process, but involves
a host of interacting biological, biochemical, and mechanical mechanisms at dif-
ferent scales, it is essential to initialize the model simulations with a configuration
for the brain from which the target configuration (that deformed by the tumor at
the desired stage of tumor growth) is reachable by solving a mechanical boundary
value problem (BVP).
The proposed model for tumor-induced deformation may be understood with
the aid of Figure 13. Let
κ
o
be the initial configuration of the brain at a reference
time point
t
=0before tumor emergence. The stresses in
κ
o
are assumed negli-
gible. Let
κ
t
be the configuration of the brain at the target macroscopic stage of
tumor development. The bulk tumor, denoted by
T
t
, is assumed to be composed
of proliferative, quiescent, and necrotic tumor cells [80-82]. A region
D
t
of brain
tissue swollen by edema may also be associated with the tumor in
κ
t
.
If
T
t
is resected, the edema is diffused, and the stresses in
κ
t
are allowed to
relax to zero, the brain tissues will reach a relaxed configuration
κ
r
. There is a
relaxed configuration associated with every
κ
t
, and it is, in general, different from
both
κ
t
and
κ
o
.Given
κ
r
, the stresses caused by the tumor, and the amount of
Figure 13.
A schematic showing the three configurations involved in the model.
κ
o
is the
brain before tumor development,
κ
t
is the brain at the desired stage of tumor growth, and
κ
r
is the corresponding relaxed configuration.
T
t
and
D
t
are the bulk tumor and peri-tumor
edema regions in
κ
t
, respectively, while
T
r
and
D
r
are the corresponding regions in
κ
r
.In
κ
r
, the ventricles are denoted by
B
V
.
∂B
01
denotes the outer surface of the brain except
for
∂B
02
, where the falx meets the skull.
