Mammalian circumorbital features such as the supraorbital rim (browridge), postorbital bar, interorbital pillar, and postorbital septum are purportedly adaptations to resist torsion of the facial skull relative to the neurocranium during unilateral mastication (Greaves, 1985, 1991, 1995; also Rosenberger, 1986; for alternative masticatory explanations for circumorbital structures see Bookstein et al., 1999; Endo, 1966; Hilloowala and Trent, 1988a,b; Lahr and Wright, 1996; Oyen et al., 1979; Rak, 1983; Rangel et al., 1985; Russell, 1985; Tattersall, 1995; Wolpoff, 1996). This torsion of the craniofacial "cylinder" results from molar bite forces, which twist the working-side (WS) toothrow and face about a central anteroposterior axis in one direction, and relatively high balancing-side (BS) condylar reaction forces, which twist the cranial vault in the opposite direction. Jaw-adductor and nuchal forces on the working and balancing sides also produce significant axial torques during mastication and it is unlikely that their moments cancel each other out (Figure 1) (Hylander et al., 1991a,b). In turn, the facial torsion model predicts that twisting stresses are oriented 45° relative to the long axis of the skull, with the BS postorbital bar loaded axially in tension and the WS postorbital bar loaded axially in compression (Greaves, 1985, 1991, 1995).
In testing any hypothesis of craniofacial function, it is logical to inquire what constitutes a sufficiently high level of strain, stress, or load for a cranial element to be considered a "functional adaptation" to a masticatory loading regime. If a structure is optimized for bearing masticatory stresses, it is necessary to demonstrate that the observed safety factor (strain level at yield/observed strain) is no larger than 4 or 5 as this indicates that the structure is arguably optimized for resisting routine masticatory loads (i.e., it exhibits maximum strength with minimum tissue) (cf., Hylander et al., 1991a,b).1
Prior work demonstrates that peak-strain magnitudes from the anthropoid mandible, maxilla, and zygoma during unilateral mastication (Hylander, 1979a,b; Hylander and Ravosa, 1992; Hylander and Johnson, 1992, 1997a,b; Hylander et al., 1991a,b, 1998; Ross and Hylander, 1996) fall within the range of values at midshaft for vertebrate postcranial elements, which experience high stresses during locomotion (cf., Biewener, 1993;
1 Strain is a dimensionless unit that equals the change in length (L) of an object relative to its original length (L). It is measured in microstrain (^£), e.g., 1 X 10-6 cm/cm. The largest tensile strain is the maximum principal strain (e1), whereas the largest compressive strain is the minimum principal strain (£2). Tensile strains are positive and compressive strains negative. Shear strains ("/max = £1-£2) are used as overall descriptors of peak masticatory forces along the facial skull. The angular value of £x is measured versus the long (A) axis of one of the delta-rosette gage elements. Positive values are measured counterclockwise to the A axis and negative values are clockwise to the A axis. The angular value of £2 is determined by adding or subtracting 90° to the value of £r
skull during left-sided unilateral mastication (adapted from Ravosa et al., 2000a). Extrinsic forces causing facial torsion about a central cranial axis are the bite force (FB), working-(FCW) and balancing-side (FCB) condylar reaction forces, and working-(FMW) and balancing-side (FMB) jaw-adductor forces (A). Although not depicted, facial torsion is also likely to be affected by working- and balancing-side nuchal forces. In this case, chewing results in a counterclockwise rotation of the facial skull versus the cranial vault (A). Expected strains during left-sided mastication are depicted for the left postorbital bar (B) and interorbit (C). Both ^ (tension) and e2 (compression) are oriented 45° versus the cranial axis. When chewing changes from the left side of the dental arcade to the right, principal-strain directions (^ and e2) reverse due to a shift in the direction of torsion. Predicted strain directions for the WS postorbital bar are similar in the facial torsion model and NVPH.
Lanyon and Rubin, 1985). In contrast, peak-strain levels during mastication for the anthropoid circumorbital region are much lower than those values recorded at the mandible, maxilla, and zygomatic arches (Bouvier and Hylander, 1996a,b; Hylander and Johnson, 1992, 1997a,b; Hylander and
Ravosa, 1992; Hylander et al., 1991a,b, 1998; Ross and Hylander, 1996). This presence of a significant strain gradient indicates that circumorbital structures are routinely overbuilt for stresses encountered during routine biting and chewing. Thus, the amount of circumorbital bone mass could be decreased significantly without causing it to experience structural failure during normal masticatory behaviors (Hylander et al., 1991a,b).
On the other hand, if circumorbital peak strains were large, then a considerable reduction in the amount of cortical bone at the postorbital bar, interorbital pillar, and browridge would likely result in dangerously high strains (as would occur with the mandibular corpus and symphysis). This in turn would suggest that circumorbital structures are functional adaptations to resist masticatory stresses since they appear designed to maximize strength with a minimum of material.
Until recently all studies of primate circumorbital strains were of anthropoids, taxa which possess the derived condition of a bony postorbital septum along the lateral orbital wall. Compared to anthropoids, greater galagos (Strepsirrhini, Primates) recruit relatively less BS jaw-adductor force during unilateral mastication, which explains why they possess unfused mandibular symphyses (Hylander, 1979a,b; Hylander et al., 1998, 2000, 2004; Ravosa and Hogue, 2004; Ravosa et al., 2000a-c; Vinyard et al., this volume). Moreover, as the first modern primates had unfused symphyses and postorbital bars, galagos likely provide a good extant analog for the masticatory complex of basal euprimates (Ravosa, 1991a, 1996, 1999; Ravosa and Hylander, 1994). As there are no circumorbital strain data for an alert mammal with only a postorbital bar (but no postorbital septum), the galago in vivo analyses are of further importance for interpreting circumorbital form in other mammals with this more common character state (Cartmill, 1970, 1972; Noble et al., 2000; Pettigrew et al., 1989; Ravosa et al., 2000a,b). In evaluating the galago experimental evidence vis-à-vis the facial torsion model, peak-strain magnitude data are considered first and the principal-strain direction data are discussed next (Ravosa et al., 2000a,b).
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