Biomedical Engineering Reference
In-Depth Information
Figure 4
. Collisions in the HPP lattice gas rule. Horizontal collisions produce vertically mov-
ing particles (top) and vice versa (middle). Particles moving at right angles pass by each other
unchanged (bottom, omitting the reflections and rotations of this figure).
momentum approximately obey the equations of continuous fluid mechanics.
Numerical experiments show that this rule reproduces many fluid phenomena,
such as diffusion, sound, shockwaves, etc. However, with this rule, the agree-
ment with fluid mechanics is only approximate. In particular, the square lattice
makes the large-scale dynamics anisotropic, which is unphysical. This in turn
can be overcome in several ways—for instance, by using a hexagonal lattice
(123). The principle here—get the key parts of the small-scale "microphysics"
right, and the interesting "macrophysics" will take care of itself—is extensively
applied in studying pattern formation, including such biologically relevant phe-
nomena as phase separation (124), excitable media (125), and the self-assembly
of micelles (126,127).
5.
AGENT
-
BASED MODELS
If there is any
one
technique associated with complex systems science, it is
agent-based modeling. An agent-based model is a computational model that
represents individual agents and their collective behavior. What, exactly, do we
mean by "agent"? Stuart Kauffman has offered
15
the following apt definition:
"An agent is a thing which does things to things." That is, an agent is a persistent
thing that has some
state
we find worth representing, and which interacts with
other agents, mutually modifying each others' states. The components of an
agent-based model are a collection of agents and their states, the rules governing
the interactions of the agents, and the environment within which they live. (The
environment need not be represented in the model if its effects are constant.)
The state of an agent can be arbitrarily simple, say just position, or the color of a
cell in a CA. (At this end, agent-based models blend with traditional stochastic
