Blood Vessel Networks

A new mathematical model is leading to insights about the formation of blood vessel networks. The model, proposed by researchers from several Italian institutions (contact A. de Candia, 011+39-081676805), accurately mimics vascular structures formed by cells randomly spread on a gel matrix. Chemical cues entice cells on a growing medium to migrate and aggregate into groups. Below a certain cell density, the model and related experiments show many disconnected groups are formed. Above a critical density known as the percolation limit, a spanning cluster of cells connected across large distances is formed (see images at www.aip.org/mgr/png). Exactly at the percolation threshold, such a cluster exhibits a fractal structure with a fractal dimension of about 1.9. (The fractal dimension specifies how much of the available space is filled. For a 2-dimensional gel plate, the surface is entirely filled at a fractal dimension of 2.) In addition, both experiment and the new model point out that the fractal dimension is different when the cells are observed at different scales. At scales of about 0.8 millimeters or less, the fractal dimension of the cell networks drops to about 1.5. The researchers speculate that the change in dimension may be indicative of the dynamics that led to the formation of the cellular networks in the first place. The good agreement between the model and in-vitro experiments on gel growing media suggests that we may soon gain a better understanding of the formation of vascular networks in living creatures, as well as the pathological vascular formation that accompanies certain cancers and other ailments. (A. Gamba et al., Physical Review Letters, 21 March 2003)