Biomedical Engineering Reference
In-Depth Information
more directly related to apoptotic signaling than necrosis. Many prominent
mathematical models do not incorporate necrosis (e.g., [
8
]), while others generi-
cally model cell death while failing to differentiate between apoptosis and
necrosis. For example, the recent ductal carcinoma in situ (DCIS) model in [
83
]
provided an excellent model of cell death due to energy depletion, but the work did
not differentiate this death process (necrosis) from death due to detachment from
the basement membrane (anoikis). As we shall see below, apoptosis and necrosis
take widely divergent courses, particularly in cases of DCIS that exhibit com-
edonecrosis (necrosis filling the lumen of a gland).
Those models that do include necrosis have often modeled it as an instanta-
neous or fast time scale process by immediately removing necrotic cells from the
simulations (e.g., [
2
]). Others have modeled necrosis as simple volume loss terms
in continuum models (e.g., [
12
,
89
,
90
]), or as inert, persistent debris in discrete
models (e.g., [
21
,
71
]). While these are more true to the generally longer time scale
of necrosis, they still fail to account for the multiscale processes involved and their
potential biomechanical impact on tumor progression. None of these or other prior
works have examined calcification of necrotic debris.
And yet necrosis plays a prominent, essential role in many carcinomas. A 1 mm
tumor spheroid with a typical 100 lm viable rim is over 50 % necrotic by volume.
Cell death in such a significant fraction drastically alters mass transport throughout
a tumor and can lead to steady size dynamics as proliferative cell flux out of
the viable rim balances with fluid flux released by degrading necrotic cells
[
13
,
50
,
52
]. See Fig.
1
(left). Necrosis has a proven prognostic value in breast
cancer, particularly ductal carcinoma in situ (DCIS) [
72
,
92
]: presence or absence
of comedonecrosis is a prominent part of the Van Nuys Prognostic Index (VNPI) [
84
].
Moreover, DCIS is primarily detected as subtle patterns of calcified necrotic tissue in
mammograms [
27
,
29
,
82
]. See Fig.
1
(right). 90 % of all cases of nonpalpable DCIS
are detected and diagnosed on the basis of microcalcifications alone [
69
]. Prominent
tissue necrosis is also observed in other cancer types and can similarly be an important
prognostic indicator [
76
], such as in glioblastoma multiforme [
1
,
70
] and colorectal
cancer [
77
]. Secretions by necrotic cells may promote inflammation in neighboring
''normal'' tissue (tumor-associated stroma) [
9
,
24
,
31
], thereby promoting progres-
sion from in situ to invasive carcinoma [
26
,
37
,
79
].
In this chapter, we shall explore recent efforts by our modeling groups to shed
light on the impact of necrotic tissue biomechanics on tumor progression through
increasingly sophisticated computational modeling. After a brief introduction in
Sect. 2
to the biological background of apoptosis, necrosis, and calcification, we
examine our earliest continuum-scale modeling of necrotic tumor growth
[
51
,
58
-
62
]in
Sect. 3
. Continuum conservation laws describe the biomechanics,
while smaller scales are integrated as constitutive relations. The work gave early
and extensive insights on the impact of necrotic core biomechanics on tumor
growth, characteristic features, sizes, morphology, and stability.
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