Saturday, September 17, 2011

Build a numerical simulation in medicine and biology. Part Three.

How exactly does this example of a simulation actually work? Looking at the kinetics of plants growth (green dots) one can come to the conclusion that they tend to diffuse. This means that they extend its reach into areas adjacent. Of course there are different ways to use the plant migration vectors (birds, wind etc.), in order to deal with distant sites. In my simulation, we can set three factors responsible for plant growth.

1st Plant growth, is responsible for the speed with which the plant increases the intensity of a given area, which has already been occupied by it. 
2nd Diffusion Plant, specifies the rate at which the plant occupies the areas adjacent to already occupied. 
3rd Generating plants every x cycles, is associated with the random creation of plants on the board, this is reflected in the use of vectors carrying the seeds over long distances. 




The role of herbivores meet the so-called "agents", ie objects performing certain functions and having the ability to communicate with each other. Agents move on the board in the manner defined by several variables. Pheromone, which is the key to communication, diffuse, and at the same time is removed (extinction). Each agent has a finite pool of receptors to saturate, if the maximum concentration is reached, it will not be able to determine the local gradient and make a decision about choosing the direction of movement, which is consistent with the mechanisms reported in nature. It should be noted that the saturation kinetics and regulation of neural receptors, are essential for adequate response to a stimulus.


1st Pheromone diffusion coefficient : Corresponds to the rate of diffusion of signal substances in the domain of spatial simulation. The higher the value, the faster diffuses a pheromone, allowing agents to react in a range of non-zero concentration. The high diffusion coefficient causes a more rapid achievement of equilibrium, thus reducing the time shift between finding a food source, and the following of it. 
2nd Persistence of pheromone associated with disappearance of the old sources and cleaning the spatial domain of residual pheromone. Too high durability makes the receptors fully saturated and the agent will not be able to make decisions about the direction of movement. Too low durability will cause the disappearance of the signal before agent reaches its source. 



It is worth mentioning that the simulation takes place on the board, whose boundaries satisfy the condition of zero flow (no flux boundary). Nothing gets across the border simulation. 
Agents have a random component of mobility (random movement of agents), which is particularly the more important for the movement, the lower the local gradient of pheromone. This means that if no food source, the objects are moving randomly, but also if there is too much of food around.




The simulation consists of a spatial domain X of X field, defined by the variable "simulation size" You can also choose a number of agents, changing the "agents number" selector. Selecting a large value, the action slows down, because this increases a computational cost. Cose is roughly proportional to the sum of second power of array dimension and number of agents.

 At any moment, pressing pause, freezes  the simulation for a moment and allows the user to track the pheromone concentrations, without losing the view of the board with food and agents behavior. 
Feel free to use the simulation in you own purposes.

No comments:

Post a Comment

Related Posts Plugin for WordPress, Blogger...