The appearance, or the phenotype, of a living creature is always the product of its predisposition and its environment. In the wake of the decoding of the human genome, however, the second factor slipped somewhat into obscurity. There were probably many investigations aimed at a deeper understanding of the functioning of life forms by turning off the genes. Attempts by scientists to describe physiological processes in an organism with the help of higher mathematics, however, have been less frequent.

An egg came first

ETH researcher Dominik Szczerba, who works at the Computer Vision Lab in the Department of Information Technology and Electro-Engineering (1), is not put off by these problems. In the pertinent literature he found images that an experimental biologist had made of capillary growth in the embryo of a hen's egg. It was also mentioned that microstructures visible in the images, hairlike blood vessels, so-called capillaries, could be the result of the physicall interaction between the blood circulation and the tissue. If that were so, thought Szczerba, then it should also be possible to describe the process mathematically.

For his model of the formation of capillaries, i.e., blood vessels less than 10 micrometers in diameter, Szczerba looked upon the tissue as a regular sponge (2), through which blood flows without turbulences or pulsation. He then measured the average speed flow in film sequences, which had also been shot in hens' embryos. He expected the resulting shear stress between tissue and blood to lead to a rearrangement in the model, as cells would be inserted or extracted depending on the tension. The researcher recorded the situation mathematically by describing the forces of the blood flow by means of modified Navier-Stokes equations and describing the tissue as a network of discrete cellular units.

Support at the spot of lowest resistance

When Szczerba varied the threshold value at which cells were either inserted or extracted he was fairly amazed. For certain values, the shape of the growing vessels was almost identical to that of the real situation in the hens' embryos. The first indication for the validity of the model was therefore given, but the simulation went even further. Because the model of the ETH researcher also provided an explanation for a phenomenon that has puzzled scientists up until now. It had been observed that when blood vessels bifurcate, i.e. branch out in another direction, a sort of tissue pillar is formed before the angle of bifurcation changes. Szczerba's model shows that the supports are always formed there where the shear stress is smallest. It would seem that mechanical interaction is responsible for the strength of change in the angle of bifurcation.

Virtual micro-vascular growth: A numerical simulation shows the influence of shear stress on the development of capillaries. Above left, the situation to start off, based on a real photograph. The three rows show the development of different value levels (Pictures: Reprinted from J Theor Biol. 234 (1), Szczerba D, Szekely G, “Computational model of flow-tissue interactions in intussusceptive angiogenesis“ 87-97, Copyright (2005) with permission of Elsevier). large

Simulating the influence of radioactivity in the future

The ETH scientist emphasises that his simulation still needs to be improved, despite having great similarity with reality. For example, the patterns generated by his model were too symmetrical in comparison with natural structures. Szczerba wants to improve his model by integrating additional, biological factors. Moreover, the equations on which the simulation is based could be improved mathematically.

When asked about the practical use of his research Szczerba cites his main work at the Computer Vision Lab. Together with colleagues, he is working on the development of a virtual macroscopic vascular system. This would help surgeons to practise virtual operations, in the same way as pilots train on flight simulators. Szczerba also expresses the hope that a microscopic vascular model, perhaps after suitable refinement, could serve, for example, to investigate the effects of nuclear radiation on capillaries.

Simulation of a support forming before the bifurcation of a vessel. The structure in a.... resembles a photo of a real structure. The colours codify the strength of the shear stress. large