Biomedical Engineering Reference
In-Depth Information
More recently, in an attempt to emulate the in-vivo setup in an even more
realistic way, sophisticated agent-based models of brain tumors have introduced
further modifications. Among the novel features of these recent models are:
&
Nonlinear feedback
effects through two types of interactions, namely: (i)
local interactions among cancer cells themselves, and (ii) interactions be-
tween cancer cells and their surrounding environment (6-9) represented
by, for example, an adaptive grid lattice.
&
Heterogeneous
cell population as represented by the emergence of distinct
subpopulations, each with different cell clones (10).
&
Phenotypic dichotomy
between cell proliferation and invasion as sup-
ported by recent experimental findings (11,12).
To put this in perspective, in the following section, we briefly review previous
works on tumor modeling.
2.
PREVIOUS WORKS
Based on the choice of methodology, most of the existing models of brain
tumors derive their results from either solving analytically a set of mathematical
equations or from performing Monte Carlo simulations using a numerical plat-
form. The latter follows the longstanding tradition of
cellular automaton
(CA)
models, albeit with considerably richer specification of tumor behavior. For an
excellent review article of cellular automata approaches to the modeling of bio-
logical systems, see (13). In the modeling of complex systems, CA models have
proved to be a versatile tool. For example, (14) and (15) treat the automata as
abstract dynamical systems. In addition, (16) presents and (17) reviews CA ap-
plications that are biologically motivated. (18) presents an early work in tumor
modeling that employs a three-dimensional cellular automaton model to investi-
gate tumor growth. In their model, automaton rules were designed to capture the
nutritional requirements of tumor growth. Being early in the field, their mini-
malist model did not yet consider the impact of other important environmental
variables such as mechanical confinements and toxic metabolites. More recent
efforts include (19), which utilizes a CA model to study growth progression.
(20) also constructed a CA model to successfully generate a growth profile of
tumor cells that follows the well-known Gompertz law. They examine the dy-
namics of tumor growth in the presence of immune system surveillance and me-
chanical stress generated from within the tumor, but they do not explicitly
consider the influence of growth stimulants and inhibitors. (21) employs the CA
approach to investigate the effects of location-specific autocrine and paracrine
factors on tumor growth and morphology. Neither (20) and (21) explicitly con-
sider the mechanics of how tumor cells evaluate the attractiveness of location.
