Frontal sinuses and head-butting in goats: a finite element analysis. 2008. Andrew A. Farke. Journal of Experimental Biology 211: 3085-3094.
Abstract: Frontal sinuses in goats and other mammals have been hypothesized to function as shock absorbers, protecting the brain from blows during intraspecific combat. Furthermore, sinuses are thought to form through removal of `structurally unnecessary' bone. These hypotheses were tested using finite element modeling.
Three-dimensional models of domesticated goat (Capra hircus) skulls were constructed, with variable frontal bone and frontal sinus morphology, and loaded to simulate various head-butting behaviors. In general, models with sinuses experienced higher strain energy values (a proxy for shock absorption) than did models with unvaulted frontal bones, and the latter often had higher magnitudes than models with solid vaulted frontal bones. Furthermore, vaulted frontal bones did not reduce magnitudes of principal strain on the surface of the endocranial cavity relative to models with unvaulted frontal bones under most loading conditions.
Thus, these results were only partially consistent with sinuses, or the bone that walls the sinuses, acting as shock absorbers. It is hypothesized that the keratinous horn sheaths and cranial sutures are probably more important for absorbing blows to the head. Models with sinuses did exhibit a more `efficient' distribution of stresses, as visualized by histograms in which models with solid frontal bones had numerous unloaded elements. This is consistent with the hypothesis that sinuses result at least in part from the removal of mechanically unnecessary bone.