Biomedical Engineering Reference
In-Depth Information
individuals, eventually causing an unstable and dispersed morphology of the
tumor. The scattered cells at the front of the mass in fact deeply penetrate
into the host tissue to reach regions with sucient amounts of ECM proteins.
These observations agree with the correlation experimentally found be-
tween the malignancy and the metastatization ability of most tumors and
the activity of the secreted matrix metalloproteinases, see for example [207].
In this regard, it is useful to underline that the inhibition of MMP produc-
tion alone has been demonstrated to be insucient to decrease the overall
malignancy of the disease, see [327].
8.7 Effect of Cell Proliferation
So far, we have correlated the invasive phenotype of a solid tumor with the
biophysical properties of mutated cells, and with their interactions with the
local microenvironment. However, malignant individuals are seen to have also
a higher proliferation rate than their unmutated counterparts. In particular,
as suggested by a number of experimental works as early as [369], the time
between cell divisions has a stochastic distribution, which depends on both the
internal state of each cell and on the time from its last mitotic process (i.e.,
except for extremely rapidly dividing cells, those who recently divided will be
still growing and the likelihood of their reentering the S phase is extremely
small, see [7]).
For each cell , we therefore dene its present probability P
to undergo
mitosis with the following functional form, which resembles that used in a
similar approach [395]:
8
<
0
if
(tt
) t
0
;
n
(t) N
0
n
(t)
+
P
(t) =
(tt
)
2
(tt
)
2
+ 1
:
if (tt
) > t
0
;
(8.9)
where n
(t) and N
0
are, respectively, the present and initial intracellular
amount of growth factors in cell and [ ]
+
is the positive part of the function.
The last time that cell underwent mitosis is denoted by t
while the dormant
period during which the cells are prohibited to proliferate (i.e., it corresponds
to the G1 phase, during which the cells are metabolically active and grow) is
denoted by t
0
and is set equal to 1300 MCS (i.e., 7 h). Since the mitotic
rate greatly varies from tissue to tissue, and between different types of malig-
nancies, this choice represents a compromise between very slow growing and
very aggressive tumor types. Relation (8.9) takes into account that, once the
time since last division exceeds t
0
, the probability of another mitosis slowly
increases, and approaches 1 as it becomes very long. Moreover, a cell needs
Search WWH ::
Custom Search