This way, an effective method for studying these effects "in vitro" may be found. A number of models have been proposed to describe fluid effects on the vascular remodelling in the embryo. One point which is often missed in these analogies is the fact that the process occurs within a living system; dead end can break off and reattach elsewhere, branches close and open at junctions or form valves, and vessels are extremely deformable, able to quickly adapt to new conditions and form new pathways. Theoretically, the formation of the vascular tree can be thought of in terms of percolation theory. The network of tubes arises randomly and will eventually establish a path between two separate and unconnected points. Once some critical number of sprouting tubes have migrated into a previously unoccupied area, a path called a fractal can be established between these two points. Fractals are biologically useful constructions, as they rely on an infinite increase in surface area, which in biological terms translates to a vast increase in transport efficiency of nutrients and wastes. The fractal path is flexible; if one connection is broken, another forms to re-establish the path. This is a useful illustration of how the vascular tree forms, although it cannot be used as a model. The diffusion-limited aggregation model has given simulated results which are closest in comparison to vascular trees "in vivo". This model suggests that vascular growth occurs along a gradient of shear stress at the vessel wall, which results in the growth of vessel radii. Diffusion-limited aggregation proposes that an aggregate grows by the fusion of random walkers, which themselves walk along a pressure gradient. Random walk is simply a probability-based version of the diffusion equation. Thus, in applying this model to the vascular tree, small, resistant vessels must be replaced with large, conducting vessels in order to balance the pressure across the entire system. This model yields a structure which is more random at the tips than in the major lines, which is related to the fact that Laplacian formulations are stable when speed is negative with respect to pressure gradient. In major lines, this is always so, but in small sprouts the speed fluctuates around 0, leading to unstable, random behaviour. Another large component of the remodelling process is the disconnection of branched vessels, which then migrate to distal areas in order to supply blood homogeneously. Branching morphogenesis has been found to follow the dielectric breakdown model, in that only the vessels with sufficient flow will enlarge, while others will close off.