Dynamic strain similarity in vertebrates; an alternative to allometric limb bone scaling

Galileo (1638) observed that "nature cannot grow a tree nor construct an animal beyond a certain size, while retaining the proportions which suffice in the case of a smaller structure". However, subsequent measurement has shown that limb bone dimensions are scaled geometrically with body size (Alexander et al., 1979a), and that the material properties of their constituent bone tissue are similar in animals over a wide range of body weight (Sedlin & Hirsch, 1966; Yamada, 1970; Burstein et al., 1972; Biewener, 1982). If, as suggested in previous scaling arguments (McMahon, 1973; Biewener, 1982), vigorous locomotion involved the same proportional forces over a wide range of animal size, this would create a paradox since large animals would be in far greater danger of skeletal failure than small ones. However, in vivo strain gauge implantations have shown that, during high speed running, axial force as a proportion of body weight (G) in the limb bones of animals decreases as a function of body size from 6.9 G in a 7 kg turkey to 2.8 G in a small (130 kg) horse. Estimates of axial force in larger animals suggest that this is further reduced to 0.8 G in a 2500 kg elephant. Nevertheless, it appears that, regardless of animal size or locomotory style, the peak stresses in the bones of these animals are remarkably similar. Therefore, throughout the range of animals considered (350 times differences in mass), we suggest that similar safety factors to failure are maintained, not by allometrically scaling bone dimensions, but rather by allometrically scaling the magnitude of the peak forces applied to them during vigorous locomotion.(ABSTRACT TRUNCATED AT 250 WORDS)