Physiological Laws of Sensory Visual System in Relation to Scaling Power Laws in Biological Neural Networks Isabel Gonzalo-Fonrodona1 andMiguelA.Porras2 1 Departamento de Optica.´ Facultad de Ciencias F´ısicas. Universidad Complutense de Madrid. Ciudad Universitaria s/n. 28040-Madrid. Spain
[email protected] 2 Departamento de F´ısica Aplicada. ETSIM. Universidad Polit´ecnica de Madrid. Rios Rosas 21. 28003-Madrid. Spain Abstract. Measurements of some visual functions (visual fields, acuity and visual inversion) versus intensity of stimulus, including facilitation, carried out by Justo Gonzalo in patients with central syndrome, are seen to follow Stevens’ power law of perception. The characteristics of this syndrome, which reveals aspects of the cerebral dynamics, allow us to conjecture that Stevens’ law is in these cases a manifestation of the universal allometric scaling power law associated with biological neural networks. An extension of this result is pointed out. 1 Introduction Half a century ago, Stevens [1] formulated his well-known relation between sen- sation or perception P and the physical intensity of a stimulus S, expressed mathematically as a power law of the type P = pSm , (1) where p is a constant and m depends on the nature of the stimulus. This law is regarded as more accurate than the logarithmic Fechner’s law, but is not exempt from criticism. In a different, and somewhat more general context, it was argued that in biological organisms, mass is the determinant factor for the scaling of the phys- iological behavior. If M is the mass of the organism, many observable biological quantities, for instance Y , are statistically seen to scale with M according to a power law of the form Y = kMn , (2) where k is a constant and, in formal similitude with Stevens’ law, the exponent n changes from one observable to another, leading to different (allometric) behavior of observables with respect to mass M.