Supracellular structural principle and geometry of blood vessels.

All the supracellular structures of multicellular organisms are subordinate to a single structural principle. It is a particular space division minimizing the potential energy of the constituent units in a field of mechanical force and is specified as equilibrium space division (ESD). Three-dimensional ESD is characterized by the feature that three faces unite to an edge and four edges converge to a corner, but other geometrical characters are susceptible to variation. Blood vessels are localized predominantly on edges of ESD, so that their geometry depends largely on ESD. ESD is represented approximately by a model of complete space division with uniform beta-tetrakaidecahedra, and some geometrical parameters of blood vessels can be derived theoretically from ESD, partly with the aid of the above-mentioned model. ESD is a statistical process under incomplete restrictions. It is consequently impossible to interpret the morphogenesis of supracellular structures directly from genetic information in a deterministic manner.