Biomedical Engineering Reference
In-Depth Information
mor cells to experience a genetic switch (5), which in turn can transform a be-
nign growth into an aggressively expanding, malignant tumor.
From the methodological standpoint, the advantage of using a numerical
platform is that it circumvents the need to solve analytically the underlying
mathematical equations. That is, instead of relying on theorems and closed-form
solutions, the statistical properties of the system are estimated by spinning the
model forward a sufficient number of times. Such desirable advantages of an
agent-based model, however, do not come without a "price" for the user.
First, as for any other theoretical approach that is based on a numerical plat-
form, calibration of the model parameters using experimental data is often diffi-
cult due to (i) the lack of the latter in some cases, or (ii) the fact that they have
been collected over a wide range of different experimental setups, thus rendering
combinations of the results nontrivial. Without proper prior experiments, how-
ever, robustness of the model prediction must be verified by exhaustive explora-
tion of the relevant parameter space, which is often of high-dimensional order
and therefore computationally can be very resource intensive. If, in addition, the
model also contains stochastic elements that can potentially have a significant
effect on the outcome, then a Monte Carlo simulation must be performed across
various random seeds to ensure robustness.
Second, even if data are available, translating an in-vivo or in-vitro experi-
mental setup into an operational in-silico model can be a formidable exercise.
The challenge is to confine the number of cellular characteristics and environ-
mental variables into a manageable few, preferably those that are most pertinent
to the question posed by the researcher. This of course is a critical step and has
to be carefully balanced against
over
simplification. Nonetheless, stripping a
complex biological organism to its bare essentials is necessary to render any
model tractable, which in turn allows one to establish cause-effect relationships.
On balance, however, it is clear that, as long as the researcher is aware of
the model limitations, the potential benefits of an agent-based framework far
outweigh its deficiencies. Typically, a realistic tumor model exhibits the follow-
ing features:
&
An agent-based model treats both
space and time explicitly
and in a
dis-
crete
manner. Discretized time allows the assessment of tumor progression
at various time steps.
&
Explicit inclusion of
environmental variables
that have proved critical in
guiding tumor proliferation and invasion—such as nutrient sources, me-
chanical confinements, toxic metabolites, and diffusive biochemical at-
tractants.
&
Variable
grid lattice: allowing more than one cell to share the same loca-
tion, capturing the spatial and resource competition among the tumor cells
themselves. Such cellular clustering arguably guides the overall spatio-
temporal behavior of the tumor system (6).
