THEORETICAL AND EMPIRICAL SCALING PATTERNS AND TOPOLOGICAL HOMOLOGY IN BONE TRABECULAE

Trabecular or cancellous bone is a major element in the structural des ign of the vertebrate skeleton, but has received little attention from the perspective of the biology of scale, In this study, we investigat ed scaling patterns in the discrete bony elements of cancellous bone, First, we constructed two theoretical models, representative of the tw o extremes of realistic patterns of trabecular size changes associated with body size changes, In one, constant trabecular size (CTS), incre ases in cancellous bone volume with size arise through the addition of new elements of constant size, In the other model, constant trabecula r geometry (CTG), the size of trabeculae increases isometrically, Thes e models produce fundamentally different patterns of surface area and volume scaling, We then compared the models with empirical observation s 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 suggest s that some elements of trabecular architecture may be driven by the r equirements of maintaining adequate surface area for calcium homeostas is. Additionally, we found two key consequences of this strongly negat ive allometry, First, the connectivity among trabecular elements is qu alitatively different for small versus large animals; trabeculae conne ct primarily to cortical bone in very small animals and primarily to o ther 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 infl uence of gross differences in loading on trabecular size, we sampled d imensions extensively within Chiroptera and compared their trabecular dimensions with those of non-volant mammals, We found no systematic di fferences in trabecular size or scaling patterns related to locomotor mode.