Allometric scaling and biomechanical behavior of the bone tissue: an experimental intraspecific investigation

Adaptation of bone to different loads has received much attention. This paper examines the consequences of differences in size on bones from the same animal species.

The study was conducted on 32 canine radii. Their geometry, densitometry and mechanical properties were determined and one-way ANOVA was used to analyze their distribution by sex. Bending failure was observed during the mechanical test. The bones were then likened to thin beams and the mechanical parameters of interest were appraised via beam theory. A multiple linear regression model with stepwise analyses was employed to determine which parameters rule the mechanical characteristics. The relationships between the bone mass and the parameters investigated were analyzed by means of a model II regression in order to state how the scaling of the bone characteristics act on its mechanical behavior.

The linear regression model demonstrated that an animal's mass, its sex and the mineral content and the geometrical properties of its bones almost entirely predict their mechanical behavior. A close fit was found between the experimentally determined and the theoretical slopes of the log regressed allometric equations. The work to failure was found to scale almost linearly with the animal and bone mass and the macroscopical bone material properties were found to be mass invariant. The allometric equations showed that as the animal mass increases, employing proportionally the same amount of tissue, bones get proportionally shorter and proportionally distribute their tissue further from the cross-sectional centroid.

Our results suggest that dimensional analysis on the assumption of geometrical self-similarity and mechanical testing according to classic elastic solutions are reasonable in bones tested in accordance to our set up. The bone geometry is the parameter able to curb the energy effects of an animal mass increase. The allometric scaling of the bone length and the cross-sectional layout, without an increase in the amount of material proportionally employed, preserves linear with the animal mass the amount of energy necessary to fracture a bone and restrain the rise of stresses and strains in the cross-section.