On the Fractal Nature of Nervous Cell System

NEUROANATOMYbecause they evoked considerations much similar reported as far as thirty years ago by a Swiss Group (Paumgartner et al., 1981) in a pioneer study which clearly demonstrated the influence of resolution scale, i.e., objective magnification, on the estimates of geometric irregular features of liver cell membranes, or in other words the role of resolution scale at which the measurements were performed.The large observed discrepancy was consistently annulled while the variations reported by different investigators could be explained by taking into account the "resolution effect" according to the concepts of the Fractal geometry, such as the irregularity, the statistical self-similarity, the scale invariance of form, the occurrence of repetitive morphologic determinants and the fractal, i.e., non-integer dimension, rather than the trivial methodological factors called upon to explain estimate variations across different studies.Biologic structures with irregular shape and complex morphology should not be approximated to ideal geometric objects, since far from the real pictures, while a single scale of measurements should not be adopted a priori if an objective morphological description of complex objects has to be achieved (Losa and Nonnenmacher, 1996).It should be pointed out that fractal and conventional morphometric approaches, built up on distinct epistemological principles, may set the understanding of the biologic reality at different level.The former describes the morphological complexity within an experimental interval of observation scales that obviously encompasses the Euclidean dimension, while the latter proceeds at a primary level, i.e., by reducing cellular shapes and tissue structures to monotone elements which could be described by means of deterministic rules.Nevertheless, fractal and conventional morphometry may represent complementary analytical/