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of T
H
cell activation requires the interaction of three immune agents: dendritic
cells (which we shall call APCs from this point forth), foreign antigen and T
H
cells. For these agents to interact, they must be spatially close and able to move
appropriately. From a computational point of view, these immune agents can
be considered as specific agent types within a model, each with its own set of
movement and interaction behaviours. Based on these observations a two-layer
cellular automaton (CA) type approach in which APC, antigen and T
H
cell
agents move and interact was chosen as the modelling tool. This was deemed
suitable as in a CA each element of the system is modelled individually in a
physical space. Having chosen to use this approach, it was possible to reduce
some of the complexity present in the real lymph node by reducing it to 2
spatial dimensions. Whilst reducing the spatial complexity of the system, this
still enables the elements of the system to move in a non-trivial way.
The approach we have taken to model the immune agents and their movement
due to a chemokine, is similar to that of Maree
et al.
[17] who have modelled
the movement of
Dictyostelium disciodeum
amoebae due to a chemical gradi-
ent. They use a hybrid CA/partial differential equation model, where the CA is
used to represent the physical details of the amoebae and the partial differential
equation models the chemical gradient. In our model, two separate layers exist: a
chemical space
and an
agent space
. The chemical space models the action of the
chemokine produced by the paracortex to attract naive T
H
cells and APCs pre-
senting antigen. The agent space provides the environment where the agents of
the model can move and interact. Both layers are implemented as 2 dimensional
grids of cells, with the agent space placed directly on top of the chemical space.
Both grids therefore share the same dimensions and co-ordinate system, so for
example grid reference (2
,
3) in the agent space would relate directly to the same
grid reference in the chemical space. The contents of the cells in the chemical
space are integer values representing a level of chemokine, and the contents of
the cells in the agent space can either be one of the agent types or empty. See
Fig. 1 for pictorial example. Wrap around occurs between the right and left edges
of the cellular spaces, but not at the top and bottom. This produces an effect
whereby the top of the space represents the afferent lymph vessels where lymph
enters the node, and the bottom of the space represents the efferent lymph node
through which the lymph leaves the node. Time is represented in the model by
discrete steps called iterations, and when the model is simulated it runs for a
user defined number of iterations. At each model iteration all the cells in the
chemical space update, followed by agent movements in the agent space, and
lastly agent interactions.
4.2
Chemical Space
Upon initialisation of the model each cell in the chemical space is set to an in-
teger value representing a chemokine concentration. These values are randomly
generated integers between 0 and a user defined maximum value. At each iter-
ation of the model, the chemokine values update according to a diffusion rule,
whereby the value at each cell is shared out equally to all the its neighbours.
