This document explains details underlying the simulation, including assumptions made in the model and techniques used to numerically simulate the processes. We distinguish between User controlled parameters (bold) and programmer controlled variables (italics) where applicable.
The three major components of the simulation include:
The environment consists of spatial and temporal components
of the simulation. The rectangular region holds a
40x40 grid, with each unit grid square of dimensions
DX, DY representing an area
10 microns by 10 microns. The region simulated is thus
400 microns by 400 microns. (This can be changed only by
The simulation proceeds in discrete time steps.
Two distinct time scales occur in the phenomena being
modelled : Chemical
diffusion occurs on a fast timescale relative to movement
and interactions of cells. To capture this, while avoiding
excessive computational load, we use a short
time increment, dt, to compute chemical diffusion, and a longer time
increment, DT, for calculating cell interactions and
updating states and positions of the cells.
Results are displayed once per
macro time step, i.e.,
n=DT/dt is the number of numerical
iterations between display steps. Currently,
dt=0.0125 and DT=0.5, are convenient, so that
In the initial state, when each run is started, a single source of
soluble Beta-amyloid ("the stimulus") is placed in the center
of the region assumed to contain healthy neuronal tissue.
All parameters have default values which can be viewed and reset
interactively before starting a run, or after stopping a run.
For example, the parameter initial fiber occupancy
determines the frequency of occurance of amyloid
fibers in the region,
if any. The
number of microglia
and astrocytes are selected by
initial microglia count and initial astrocyte count
and are also placed randomly within the region. The relative
effects of various chemicals on neuronal health can also
be explored interactively.