Theoretical and empirical scaling patterns and topological homology in bone trabeculae

Trabecular or cancellous bone is a major element in the structural design of the vertebrate skeleton, but has received little attention from the perspective of the biology of scale. In this study, we investigated scaling patterns in the discrete bony elements of cancellous bone. First, we constructed two theoretical models, representative of the two extremes of realistic patterns of trabecular size changes associated with body size changes. In one, constant trabecular size (CTS), increases in cancellous bone volume with size arise through the addition of new elements of constant size. In the other model, constant trabecular geometry (CTG), the size of trabeculae increases isometrically. These models produce fundamentally different patterns of surface area and volume scaling. We then compared the models with empirical observations of scaling of trabecular dimensions in mammals ranging in mass from 4 to 40x10(6)g. Trabecular size showed little dependence on body size, approaching one of our theoretical models (CTS). This result suggests that some elements of trabecular architecture may be driven by the requirements of maintaining adequate surface area for calcium homeostasis. Additionally, we found two key consequences of this strongly negative allometry. First, the connectivity among trabecular elements is qualitatively different for small versus large animals; trabeculae connect primarily to cortical bone in very small animals and primarily to other trabeculae in larger animals. Second, small animals have very few trabeculae and, as a consequence, we were able to identify particular elements with a consistent position across individuals and, for some elements, across species. Finally, in order to infer the possible influence of gross differences in mechanical loading on trabecular size, we sampled trabecular dimensions extensively within Chiroptera and compared their trabecular dimensions with those of non-volant mammals. We found no systematic differences in trabecular size or scaling patterns related to locomotor mode.