Biomedical Engineering Reference
In-Depth Information
bacteria (4), and germinal centers, where the remarkable process of affinity
maturation occurs (5).
This reorganization is mediated by a complex array of signaling molecules.
Long-range communication is accomplished by the secretion and binding of
cytokines, of which there are over 200 distinct types in humans (6). A subset of
the cytokines, the chemokines, is responsible for the regulation of cell migration
and trafficking to bring the appropriate cells to the site of infection or the rele-
vant lymphoid tissues (7,8). Short-range interactions are mediated by mem-
brane-bound receptor-ligand systems that are engaged upon direct contact of
cells bearing the complementary molecules.
I am developing microsimulation models to study this essential characteris-
tic of immune systems. These models represent the cellular components as
agents: computational objects with stochastic internal dynamics that unfold con-
ditioned directly by the state of their "receptors," which states themselves de-
pend on the concentrations of relevant ligands, both soluble and membrane-
bound. These cellular agents migrate stochastically, responding to gradients of
chemotactic and haptotactic molecules. These molecules, and other soluble fac-
tors, are treated as continua, modeled by partial differential equations with ap-
propriate cell types as sources and sinks.
Both the spatial and temporal degrees of freedom are continuous, and the
overall dynamics are given by a Markov process.
This chapter will just begin to address the larger questions of spatial
organization and inducible reorganization of the immune response during its
response to infection. I will consider the earliest stages of the immune response
and focus attention on the phenomenon of microinflammation, by which I mean
to indicate the dramatic increase in density of phagocytic cells and their aggre-
gation in response to local infection, as well as the local increase in concen-
tration of proinflammatory cytokines that accompanies and mediates this cellu-
lar reorganization.
The primary aims of the chapter are twofold. The first is to describe the
modeling technique, field-coupled agent modeling (F-CAM), in general—the
use of an agent-based approach for cellular components, their activities and mo-
tions coordinated through fields of continuous variables, the soluble factors, all
evolving in continuous space and time. The second is to call attention to the po-
tentially pivotal role of spatial organization in a phenomenon as uncomplicated
(relatively speaking) as the phagocytic response to a sharply circumscribed bac-
terial infection. The importance of spatial organization is addressed within this
volume in a strikingly different way in Part III, chapter 4.3 (by Perelson, Bragg,
and Wiegel).
In what follows I will first describe key components of the model in
mathematical detail, then touch briefly upon an illustration of its use to first ana-
lytically, then via simulation.
