Summary of the Simulation Assumptions and Formulation

      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:

  1. Environment
  2. Cells
  3. Chemicals
Changes to the environment can only be made internally by the programmer. However, most parameters that govern cell and chemical properties can be modifed interactively by the user.

The program models interactions of glial cells, which can move, with neurons that are immotile. The motile glial cells, microglia and astrocytes, are represented by so called "agents" (i.e. discrete entities that obey specified rules, including rules for movement, change of state, etc). Neurons form the background "tissue", and their state (healthy, stressed, or dead) is followed during the course of the simulation. Cells of a given type obey identical rules, though their behaviour depends on specific influences over the course of time, and these may differ from cell to cell.

The secretion, diffusion, and uptake of a variety of chemicals such as Beta-amyloid, and several cytokines, are followed with discretised versions of the differential equations that keep track of diffusion, production, and uptake.

The Environment


      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 programmer.)


      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 n=40.


      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.

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