Theoretical and Empirical Scaling Patterns and Topological Homology in Bone Trabeculae
Journal of Experimental Biology (1998) 201: 573-590
Sharon M. Swartz, Antigone Parker and Christine Huo

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 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 of scaling patterns related to locomotor mode.