Biomedical Engineering Reference
In-Depth Information
ior that was not hard-coded into the algorithm implementation. Nonetheless, it
was never the case that maximum velocity occurs under a 100% search preci-
sion. As
k
prolif
, proliferation becomes virtually impossible, and the entire tu-
mor simply dies out before it is able to reach the second nutrient source.
6.3. Structure-Function Relationship
From previous in-vitro studies, it has been suggested that malignant gliomas
form an invasive branching structure on their surface (3), most likely with
higher fractal dimensions than noncancerous tissues, as has been shown also for
other cancers (51,52). This complex pattern appears to function as a facilitator of
rapid tissue infiltration into the surrounding brain parenchyma. The precise
mechanism underlying this "structure-function" relationship, however, remains
unclear. In vivo, the difficulty is imposed by the limited spatial resolutions of
current imaging techniques that prohibit the monitoring of the structure-function
relationship in brain tumor patients over several time points. The contribution of
(8) is, using an agent-based model, to show that a numerical analysis can satis-
factorily reveal the hypothetical link between the observed structural patterns of
malignant brain tumors and their functional properties within a multicellular
framework. We investigated the relationship between the structure of the tumor
surface, measured by its fracticality
d
f
(see Eq. [10]), and the neoplasm's dy-
namic functional performance, measured by the average expansive velocity. As
expected, the tumor accelerates its spatial expansion when the "rewards" for
tumor cells following their peers along traversed pathways increase. "Rewards"
refer to lesser energy expenditure of the succeeding cells and can be thought of
as being directly related to, for instance, the secretion of tissue-degrading prote-
ases, and hence represent a "molecular" dimension. Yet, surprisingly, such an
increase in average velocity is also accompanied by a concomitant increase in
the tumor's surface fracticality, indicating an
emerging structure-function rela-
tionship
that is not inherently assumed at the cellular level. Interestingly, using
our model we found no correlations between tumor diameter and its surface
fracticality; the former increases in an almost monotonic manner, while the latter
shows a complex nonlinear behavior marked by intermittent peaks and troughs.
6.4. Molecular Level Dynamics
Finally, combining this
micro-macro
platform explicitly with the
molecular
modeling level (9), we perform time series of the gene expression of both
Tenascin and PCNA. At the
macroscopic
level, Figure 4 shows the progression
of the tumor system at various time points
t
. At
t
= 180, the directed invasion at
the NE tip of the tumor rim starts to become prominent. Subsequently,
t
= 308
