Frontal sinuses and head-butting in goats: a finite element analysis

Abstract

SUMMARYFrontal 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 ʻstructurally unnecessaryʼ 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 ʻefficientʼ 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. Supplementary material available online at

The Global Impact of Sutures Assessed in a Finite Element Model of a Macaque Cranium

“…Therefore, bony interdigitations within sutures play a critical role in allowing external compressive loads to be absorbed as tensile forces through sutural fibers running between the inosculated sutural surfaces (Herring, 2008). Thus, sutures are better modeled as homogeneous suture-bone functional units in order to simplify this phenomenon (Farke, 2008;Wang et al, 2008b).…”

“…There is no consensus on the elastic modulus of sutural tissue, as indicated by widely varying published data. For example, 1.2 MPa ), 10 MPa (Moazen et al, 2009), 50 MPa (Odame et al, 2005), 0.4 GPa (Farke, 2008), and 0.5-2.5 GPa (Wang et al, 2008b) (Radhakrishnan and Mao, 2004) while internasal sutures in ewes are 0.9 MPa (Meunier et al, 2009). However, based on strain gage experiments, these values might understate the stiffness of sutural structure.…”

“…In FEA the structure of interest (e.g., a skull) is modeled as a mesh of simple bricks and tetrahedra (finite elements) joined at nodes, the elements are assigned material properties, certain nodes are constrained against motion, forces are applied, and displacements, stresses and strains at each node and within each element are calculated. Recent advances in computer software and imaging technology have made it possible to capture and digitally reconstruct skeletal geometry with great precision, thereby facilitating the generation of detailed finite element models (FEMs) of bony structures, including non-human vertebrate crania (Rayfield et al, 2001;Castañ o et al, 2002;Rayfield, 2004Rayfield, , 2005aRayfield, ,b, 2007Richmond et al, 2005;Strait et al, 2005Strait et al, , 2007Strait et al, , 2008Strait et al, , 2009Dumont et al, 2005;Wroe et al, 2007, Wroe andcoworkers 2008;McHenry et al, 2007;Kupczik et al, 2007;2009;Farke, 2008;Pierce et al, 2008;Rayfield and Milner, 2008;Bourke et al, 2008;Moreno and coworkers, 2008;Moazen et al, 2008Moazen et al, , 2009). However, the incorporation of realistic muscle forces, bone material properties, modeling constraints, and experimental bone strain data are equally important components of FEA that are necessary to ensure biologically meaningful results (e.g., Richmond et al, 2005;Strait et al, 2005;Ross et al, 2005;Rayfield, 2007).…”

“…Recently, the impact of sutures has been more vigorously discussed and investigated using FEA in various living and fossil species (Rayfield, 2004(Rayfield, , 2005Kupczik et al, 2007Kupczik et al, , 2009Wang et al, 2007bWang et al, , 2008aFarke, 2008;Moazen et al, 2009;Fitton et al, 2009;Jasinoski et al, 2010) and various conclusions as to their significance on local and global skull biomechanics have been reached. Some finite element models of vertebrate crania that did not include sutures have obtained reasonable results in relation to in vivo bone strain studies (e.g., Strait et al, 2005), but others have not, as was the case in the less refined alligator models (Metzger et al, 2005).…”

Ontogenetic Change in Temporal Bone Pneumatization in Humans

“…Scientists have begun to revisit the subject of pneumatization in the past few years. Most of these newer studies focus on the paranasal sinuses (Farke, 2008;Rae and Koppe, 2008;Zollikofer and Weissmann, 2008;Smith et al, 2010), but there is an also emerging literature concerning pneumatization within the temporal bone (e.g., Balzeau and Grimaud-Hervé, 2006;Balzeau and Radovcic, 2008;Flohr et al, 2009).…”