Tuesday, November 9, 2010: 12:30 PM
250 C Room (Salt Palace Convention Center)
Considering the high level of complexity of angiogenesis and the numerous and correlated factors involved, mathematical and computational representations of these processes are very useful to study the effects of different factors separately and to investigate angiogenesis in an organized manner. This paper proposes a multi-agent framework to model angiogenesis and examines the impact of the changes in different parameters and properties of the synthetic biogel scaffolds on angiogenesis. Our current model is a 2-D model in which we use agents to represent the segments of capillaries and also normal tissue cells. Using the model developed, we can study the emergent behavior of the tissue and vasculature. This behavior is directly affected by the parameters included in the model and as a result, we have the ability to model different kinds of cells by changing the relevant parameters. Our framework is implemented in Java and using the open source agent modeling and simulation environment RePast (Recursive Porous Agent Simulation Toolkit). The RePast toolkit is a Java-based framework for agent simulation and provides features such as an event scheduler and visualization tools. The agents created interact with virtual representation of the physical environment. The design of the simulation environment follows general guidelines of object oriented programming. We have different layers to govern different processes. The agents are tissue cells and segment of capillaries. The choice of the segments is verified in the limiting case when a segment size is approaching the size of one endothelial cell, in which the system approaches the real-life situation. However, due to the size of the problem, such an approximation of the size using segments is necessary. We aim to select a size which will be suitable enough to give a real-life approximation while enabling the use of less number of agents and to save computational resources. Each segment can undertake a number of actions. Every segment is considered as a node and each node has the option of activating itself and generating a sprout in the direction of the highest growth factor gradient. These segments are only able to change their direction by making new sprouts. The tip cell/node at each blood vessel sprout can elongate until some limit (maximum allowable length). Then, another node will be generated and it becomes the leading node. There are different options when sprouting, the leading node in the sprout may choose to attach to other sprouts, elongate again or make another sprout by proliferation. In order to facilitate calculating the gradients, nutrients and other growth factors, a rectangular grid is used. The update on the amounts of the different growth factors and nutrients are based on the magnitude of their diffusion coefficients in the medium. It is assumed that the amount will stay constant at each grid site and is changing from one site to another. The amount is assumed to be concentrated in the center of mass of each grid site to make the distance calculations easier. All the agents are acting on another layer, called space, based on the environmental information they collect and their internal logic. Their network formation and connections are handled by another network layer. This hierarchical structure and the high level of object oriented programming enables us to extend the structure in many ways and provides great flexibility. We are currently working on the 3-D extension of the framework and some preliminary results will be presented as well. The case studies will be demonstrated on a 2-D space using a growth factor concentration profile depending only on y-coordinate. We are investigating the effect of pore size on the rate of angiogenesis to help designing porous biogels with optimum pore size yielding the fastest vessel growth rate. Another case study will show the effect of RGD-peptide concentration on the speed of movement of endothelial cells. Figure 1 shows some preliminary results without the effects of different scaffold properties.