Biomedical Engineering Reference
In-Depth Information
numerical simulations is the current state of the art in modeling of the (brain)
tumor as a multicellular complex system. New advances in computer micro-
processors as well as programming tools have significantly improved the speed
with which these simulations can be performed. The "agent-based" approach
(see also this volume, Part II, chapter 1 by Shalizi), in which the smallest unit of
observation is the
individual
cancer cell, offers many advantages not possessed
by, for example, the continuum model that has been proposed for cancer in the
preceding chapter 6.2 by Solé, Gonzales Garcia, and Costa. The principal moti-
vations for using an agent-based model to examine the spatio-dynamic behavior
of a malignant brain tumor can be listed in the following non-exhaustive list.
First, to date, conventional clinical imaging techniques can only detect the
presence of malignant behavior after the tumor has reached a critical size larger
than a few millimeters in diameters. Hence, long before the disease process can
be diagnosed on image, the tumor likely has already started to invade the adja-
cent brain parenchyma, thus seriously undermining the options of cytoreductive
therapy. A computational model can therefore be useful in helping to better un-
derstand these critical
early stages
of tumor growth. During such initial stages,
only a relatively small number of tumor cells have emerged in the system;
hence, a continuum model based on the dynamical behavior of tumor "lumps"
(each lump representing a large population of tumor cells) will fail to capture the
early growth process that is highly path dependent on the discrete history of
each individual cell.
Second, an agent-based model is suitable to examine these aggregate (i.e.,
macroscopic) patterns that result from the microscopic (i.e., local) interactions
among many individual components. This
micro-macro
perspective is indispen-
sable in a model of cancer cell heterogeneity that is driven by molecular dynam-
ics. On one hand, the bottom-up approach is useful due to the ability of cancer
cells to proliferate rapidly during tumorigenesis, which leads to intense competi-
tion for dominance among distinct tumor clones (4). On the other hand, the col-
lective behavior of the network of individual cancer cells may result in emerging
large-scale multicellular patterns, which calls for a system-level outlook. Indeed,
the assumed rapid nonlinear growth of brain tumors during the initial stage and
the subsequent invasion into regions of least resistance, most permission, and
highest attraction would indicate an "emergent" behavior that is the hallmark of
a complex dynamic self-organizing system (3).
Third, such agent-based models can easily handle both space and time
si-
multaneously
. In a realistic model of malignant tumor systems, space must be
taken into account explicitly because there are only limited numbers of locations
exhibiting an abundance of nutrients and low tissue consistency. Thus, there
should be a fierce spatial competition among tumor cells to reside in such favor-
able locations. On the other hand, time serves as a constraining variable since
future prognosis of the host patients are critically dictated by the past history of
events. Small changes during the initial stage of tumorigenesis may induce tu-
