3-DIMENSIONAL IMAGE-ANALYSIS AND FRACTAL CHARACTERIZATION OF KIDNEY ARTERIAL VESSELS

Three-dimensional data sets of kidney arterial vessels obtained from resin casts by serial sectioning and by Micro-NMR-CT, have been analyzed by the mass-radius analysis for the scaling of mass and surface. For the mass we find a D(F) almost-equal-to 2.2 in the resolution range between 1 to 10 nm and for the surface about D(F) almost-equal-to 2.0 below 3 mm and scaling exponent up to D(F) almost-equal-to 2.5 at 10 mm resolution. 3D modelling of vessel systems is achieved by recursive application of growth and branching generators. From these models both morphological and dynamical parameters of fractal transport systems can be derived and used for the interpretation of scaling and allometry of metabolic rates in organisms. Examples of fractal organization in biology are also demonstrated in mycelial growth patterns and in porous gel structures in the molecular range.