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First published online September 19, 2008
Journal of Experimental Biology 211, 3085-3094 (2008)
Published by The Company of Biologists 2008
doi: 10.1242/jeb.019042
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Frontal sinuses and head-butting in goats: a finite element analysis

Andrew A. Farke

Department of Anatomical Sciences, Stony Brook University, NY 11794-8081, USA


Figure 1
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  		Fig. 1. Schematics of models and loading conditions used in this study. (A–E) Schematics of hypothetical goat skulls in parasagittal section. (A) Unvaulted frontal (UF); (B) vaulted cortical bone-filled frontal (SFC); (C) vaulted trabecular bone-filled frontal (SFT); (D) vaulted frontal with unstrutted sinus (US); (E) vaulted frontal with strutted sinus (SS). The endocranial cavity (ec) and sinuses (fs) are indicated in black and trabecular bone is indicated in gray, along with the external cortex (ecx) and internal cortex (icx) of the frontal bone. Schematics of finite element models in (F) dorsal and (G) left lateral views, with arrows indicating the location and direction of modeled loads for various loading cases. DHL, double horn loading case; FL, frontal loading case; SHF, single horn front loading case; SHL, single horn lateral loading case; SHT, single horn tip loading case.

 

Figure 2
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  		Fig. 2. Left lateral views of finite element meshes for (A) the models with vaulted frontals (including the models with strutted and unstrutted sinuses and solid frontals) and (B) the model with unvaulted frontals. Scale bar, 10 cm.

 

Figure 3
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  		Fig. 3. Schematic indicating the location of nodes sampled for further analysis. (A) Schematic in left lateral view, with the location at which nodes were sampled within the frontal bone indicated by `fri'. This view also indicates the location of the plane across which the endocranium was `opened' in order to visualize principal strain patterns on the roof of the endocranial cavity. (B) View of the internal surface of the calvaria, with the dark gray area indicating the region of the endocranium that was sampled for the analyses presented in Tables 2 and 3 and Tables S2 and S3 in the supplementary material, and illustrated in Figs 4 and Fig. S1 in the supplementary material. fps, frontoparietal suture; ifs, interfrontal suture.

 

Figure 4
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  		Fig. 4. View of the internal surface of the rostral region of the endocranial cavity, between the cribriform plate of the ethmoid (at the top of the images) and the frontoparietal sutures (at the bottom of the images), showing patterns of principal strains under the double-horn (A–E,K–O) and frontal (F–J,P–T) loading conditions. The top two rows (A–J) show maximum principal strain; the bottom two rows show minimum principal strain (K–T). From the left, the model geometries illustrated are unvaulted frontal (A,F,K,P), cortical bone-filled vaulted frontal (B,G,L,Q), trabecular bone-filled vaulted frontal (C,H,M,R), vaulted frontal with unstrutted sinus (D,I,N,S) and vaulted frontal with strutted sinus (E,J,O,T). The scale bar indicates principal strain magnitudes in microstrain (µ{epsilon}).

 

Figure 5
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  		Fig. 5. Histograms of distributions of von Mises stress values within the frontal bone, exclusive of the surface of the endocranial cavity, for models under the double-horn loading (A–E) and the frontal loading (F–J) conditions. The vertical axis indicates the number of nodes with that value (all models normalized to 100,000 nodal values). For some parts (C,F,H), the peak has been truncated in order to conserve space. Model geometries illustrated include the unvaulted frontal (A,F), vaulted cortical bone-filled frontal (B,G), vaulted trabecular bone-filled frontal (C,H), vaulted frontal with unstrutted sinus (D,I) and vaulted frontal with strutted sinus (E,J).

 

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© The Company of Biologists Ltd 2008