• sheep;
  • skull;
  • bone architecture;
  • bone strain;
  • stereology;
  • optimization


  1. Top of page
  2. Abstract
  7. Acknowledgements

Does the skull of the sheep behave as a tube or as a complex of independent bones linked by sutures? Is the architecture within cranial bones optimized to local strain alignment? We attempted to answer these questions for the sheep by recording from rosette strain gauges on each frontal and maxillary bone and from single-axis gauges on each dentary of five sheep while they fed on hay. Bone structure was assessed at each rosette gauge site by stereological analysis of high-resolution radiographs. Structural and strain orientations were tested for statistical agreement. Ranges of strain magnitudes were ±1200 μϵ on the mandible, ±650 μϵ on the frontals, and ±400 μϵ on the maxillae. Each gauge site experienced one strain signal when on the working (chewing) side and a different one when on the balancing (nonchewing) side. The two signals differed in mode, magnitude, and orientation. For example, on the working side, maxillary gauges were under mean compressive strains of –132 μϵ (S.D., 73.3 μϵ), oriented rostroventrally at 25°–70° to the long axis of the skull. On the balancing side, the same gauges were under mean tensile strains of +319 μϵ (S.D., 193.9 μϵ), at greater than 65° to the cranial axis. Strain patterns on the frontals are consistent with torsion and bending of the whole skull, indicating some degree of tube-like mechanical behavior. Frontal and maxillary strains also showed a degree of individual loading, resulting from modulation of strains across sutures and local effects of muscle activity. The sheep skull seems to behave as a tube made of a complex of independent bones. Structural orientation was in statistically significant agreement with the orientation of working-side compressive principal strain ϵ2, even though principal tensile strains may be as large or larger. Cranial bone architecture in sheep is not optimized to both strain signals it experiences. Anat Rec 264:325–338, 2001. © 2001 Wiley-Liss, Inc.

The cranial skeleton in mammals has proved to be extremely plastic in its ability to adapt to the demands of the numerous functions it performs. Cranial form has been modified, for example, under the demands of dietary specialization (Smith and Savage, 1959), variation in brain size (Radinsky, 1968), and rotation of the orbits for wide-field or stereoscopic vision (Cartmill, 1970). This plasticity suggests that cranial form within a species is optimized for the parameters of each function that is relevant to the species.

There has long been interest from zoologists and physical anthropologists in analyzing the natural design of the skull in individual species and comparatively. Analyses fall into two broad areas, which may be termed functional design and structural design.

Most analyses of functional design have investigated how the skull performs a given function. Many recent efforts derive from the seminal work of Smith and Savage (1959), who compared the lever mechanics of the jaws of generalized carnivores and herbivores. Other pertinent issues are how well the skull performs a function and how it has been adapted for the function. For example, Kiltie (1982) considered the jaws and masticatory muscles of several species of suid as lever systems, calculated the biting forces produced by them, and related the resulting forces to the hardness or consistency of the diet of each species.

Structural design analyses focus on how the skull is constructed to resist the forces acting on it (Thomason, 1991), how the sutures function to transmit force between bones and absorb impact (Jaslow, 1990; Herring and Teng, 2000), and whether the internal architecture of individual cranial bones is aligned with the predominant directions of stress or strain (Buckland-Wright, 1978). Aspects of all three issues are addressed in the present work, which is an analysis of structural design in the cranium of the sheep (Ovis aries).

The work has several aims, the first of which is to add to the number of species for which in vivo cranial strain data are available. Strains are recorded from rosette gauges on the maxillae and frontal bones and from single-axis gauges on the mandibles of adult sheep during unrestrained feeding. Previous workers have reported strains from the cranial bones of miniature pigs (Teng and Herring, 1998; Herring and Teng, 2000), the mandibles of opossums (Crompton and Hylander, 1989; Crompton, 1995), and facial bones and/or mandibles of the galago, macaque, and owl monkey among the primates (Hylander and Johnson, 1997; Hylander et al., 1998; Ravosa et al., 2000b).

The second aim is to use the strain records from the separate bones to address the question of whether the mammalian skull behaves mechanically as a single unit or as a complex of parts linked by sutures. Greaves (1985, 1995) has proposed that artiodactyl and canid skulls behave as short beams and that unilateral biting will load the skull primarily in torsion. Under torsional loading, stress isobars should form helices at 45° to the skull's long axis, and the postorbital bar should form a strut resisting the compression isobars (Greaves, 1985). Interpreting the skull as a solid beam has been challenged by Herring and Teng (2000), who recorded from cranial bones and across sutures in miniature pigs while feeding. Their results suggest that local loading, from whichever of the masseter and temporalis muscles were active, was a stronger determinant of bone and suture strain than global loading of the skull via the teeth. They concluded that skulls with patent sutures did not behave as solid beams but as complexes of independent parts.

The third aim is to address the question of whether the architecture of cranial bones in sheep is aligned with predominant strain directions. Buckland-Wright (1978) recorded strains on dried cat skulls during simulated biting. He then examined the architecture within the bones using high-resolution radiographs taken of the sagittally split skulls. Thickenings and channels within the bones showed a strong tendency to align with surface strains. Denser regions of bone were seen in adjacent bones on either side of sutures. Buckland-Wright called these “continua” and suggested that stresses were preferentially transmitted between and through bones along these denser regions. Continua, therefore, would represent an intermediate interpretation between the beam hypothesis and that of the complex of parts. A difficulty with this interpretation is that strains recorded in vivo from pigs and primates vary widely in orientation direction during the chewing cycle and depend on which side the bolus is being chewed. The work has not been reexamined for the frontal bones and maxillae on species other than cats. To address this issue, radiographs are taken postmortem of the bone underlying the rosette gauge sites. Predominant orientations of channels and cortical thickenings within the facial bones at each gauge site are assessed stereologically and compared with orientations of principal strains.

The final contribution of this work is in comparing the structural design of the cranium and upper jaw with that of the mandible, which is relatively slight. Upper and lower jaws experience equal and opposite forces through the teeth. Are the strains in each of comparable magnitude? An exact answer will not be provided because the uniaxial gauges used on the mandible do not necessarily provide maximal strain magnitudes. But the comparison of strains between upper and lower jaw bones will provide some insight as to the relative strength of each.


  1. Top of page
  2. Abstract
  7. Acknowledgements

Five adult sheep were used for this experiment (four ewes, one wether; Arcott or Suffolk crossbreeds; weight range, 55–71 kg). All had been maintained in a research herd at the University of Guelph and fed daily on hay, postweaning, until the experiment.

Strain Data Collection

Strain gauge implantation.

A rosette strain gauge (N32-FA-2-120-11, Showa Measuring Instruments Co., Tokyo, Japan), with 40-cm lead wires and connector already attached, was glued to the surface of each frontal bone and each maxilla at the approximate sites shown in Figure 1. Three single-element gauges (N11-FA-2-120-11, Showa) were glued to the ventral border of each dentary approximately equally spaced along the length of the premolar-molar grinding battery (Fig. 1). Locations of each mandibular gauge were homologous among sheep, within half a tooth width.

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Figure 1. Approximate locations of rosette strain gauges on the left and right maxillae (LMax and RMax, respectively) and frontal bones (LFront and RFront) and of single-element gauges on the mandibles (only gauge sites for the right mandible are shown: RMand). The LMax gauge is depicted in this and subsequent figures as being visible through the skull. Skull axis (SA) is positioned as described in the text. Insets show the sign convention for angle α (between principal strain ϵ2 and SA) used in Table 1.

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Strain gauges were implanted under general anesthesia using sterile techniques by modifying for this species and body region general procedures that have been previously described (Biewener, 1992). All procedures used here were preapproved by the University of Guelph's Animal Care Committee in accordance with Canadian federal regulations on animal use in research.

The external jugular vein was catheterized and anesthesia was induced with 25 mg of sodium pentobarbital/kg of body weight injected into the vein. A cuffed endotracheal tube was inserted to maintain a patent airway and prevent aspiration of saliva and rumen contents. Anesthesia was maintained by sodium pentobarbital introduced through the catheter via peristaltic pump, at an average dose rate of 16 mg/min. The dose rate was adjusted as necessary, under continuous monitoring of the animal for the duration of the surgery.

Each gauge site was exposed in turn by sharp and blunt dissection. A region of periosteum large enough to accommodate the footprint of the gauge was scraped off the bone, and this area was cleaned with acetone and alcohol and allowed to dry. The gauge was attached with VetBond cyanoacrylate adhesive (3M Animal Care Products, St. Paul, MN). A sigmoid bend was put in the lead wires for strain relief and sutured to the subcutaneous fascia. All lead wires were brought subcutaneously to the top of the head between the horn buds and resutured at that point. The lightweight connectors were tied loosely to the wool at the nape.

Following surgery the animal was administered Banamine (2.2 mg/kg) for analgesia and was allowed to recover in a small, soft-walled enclosure under continuous surveillance. Banamine (1.1 mg/kg) was given again that night and on the next morning. A companion sheep was present in an elevated cage and visible to the experimental animal at all times.

Recording strain data.

Strains were recorded the day of surgery and on the day after. The animals were monitored as they recovered from anesthesia until they regained their feet, at which point they each began to look for food and water. As soon as an animal accepted food by hand, the strain gauges were connected to main leads from the strain conditioning amplifiers (DiCaprio and Thomason, 1989) and the circuits were brought close to balancing. The amplifiers were calibrated using a shunt resistor so that an output of 1 V represented 1000 μϵ (microstrain) with a full-scale deflection of ±10 V (±10,000 μϵ). Noise was minimal compared with signal peaks, so filtering was limited to the low-pass value of 5000 Hz, which is standard for the amplifiers. Digital filtering was applied later merely to improve the appearance of the traces.

A recording trial started when the animal was presented with a sample of food by hand, took a mouthful, and began to chew. The recording equipment was triggered manually and collected strains associated with chewing for 22.5 sec. Strains were recorded digitally at 66.7 Hz/channel—by an A-D converter (Metrabyte DASH-16, Keithley Instruments Inc., Taunton, MA) mounted in a generic PC—and were saved to disk.

The sheep were presented three food types in separate trials: alfalfa, chopped hay, and concentrate in pellet form. For the purposes of the present work, we considered only the strains recorded when feeding on hay, because this was the feed the animals had received for most of their lives. We reasoned that any relationships observed between bone strain and structure would be most relevant for this feed type. The reason for giving three food types was to compare the strains and strain energy per chew in reducing feeds of different consistency and nutrient and roughage content, which will be presented elsewhere. All details of the protocol pertinent to the present work are included here.

Up to 24 trials were recorded for each animal on each of the two recording days. This number was necessary because the three food types were presented separately and because we could record only 15 of the 18 total electrical channels at one time. Trials were repeated after swapping in or out one rosette or three single-strain channels until all gauges had been recorded at least twice for each food type. This swapping of gauges and the loss of some during the experiment produced the variability in number (n) of peaks presented in Table 1 of the Results.

Table 1. The mean (with standard deviation) and absolute maximum (|Max|) strains recorded at each gauge site for each sheep while masticating hay
Frontal, working
Frontal, balancing
Maxilla, working
Maxilla, balancing
  1. For maxillary and frontal rosette gauges, values of the two principal strains ε1 and ε2 are presented with the angle of orientation α of ε2 to the central axis of the skull. For mandibular gauges, strain values are presented for the rostral, middle and caudal gauges on each mandible. All strains are in microstrain (με) and angles are in degrees in a range of ±90°. See Figure 1 for the sign convention for angles from each rosette.

  2. Missing data are indicated by .. .

Mandible, working
Mandible, balancing
Reduction of strain data.

A program custom written in GAUSS (Aptech Systems Inc., Maple Valley, WA) calculated magnitudes of maximum and minimum principal strains (ϵ1 and ϵ2) and the orientation (ϕ) of ϵ2 with respect to the rosette's axis. It extracted peak values of ϵ2 for each chewing cycle and values of ϵ1 and ϕ at peak ϵ2. (As preliminary steps, the program applied a low-pass filter to all channels of raw data at 10 times the primary frequency, i.e., at approximately 25 Hz, and corrected for drift of the baselines from zero.)

The strain output of the mandibular gauges was found to indicate unequivocally the side of chewing: strain was tensile (ϵ1 > ϵ2) on the working side and compressive (ϵ2 > ϵ1) on the balancing side (Fig. 2), as has been previously noted for opossums and primates (Crompton, 1995; Hylander et al., 1998). The program was, therefore, modified to segregate strains from working- and balancing-side chewing cycles.

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Figure 2. A model of mandibular bending (after Crompton (1995)). The working-side dentary is under 4-point bending from the muscular force M, the reaction force from the bolus B, force S transmitted from the balancing side at the symphysis, and a reaction force J at the jaw joint. The net bend on the body of the dentary under the tooth row is upwards, which puts the ventral border into tension. On the working side, there is a 3-point bend between the reaction force at the jaw joint J, the muscular force M, and the reaction at the symphysis –S (equal and opposite to S). The net downward bend on the dentary puts the ventral border into compression.

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Orientation of strains to skull axis.

The sheep were euthanatized (with 340 mg of intravenous sodium pentobarbital/kg) following the second recording day, and the gauge sites were exposed. The central axis of each rosette gauge was marked by drilling 0.5-mm-diameter holes where the axis met the edges of the gauge. The skulls were cleaned in a dermestid colony, degreased, lightly bleached, and dried. The axis of each skull (Fig. 1, SA) was defined as a midsagittal line parallel to the ventral borders of the external auditory meatus and the tip of the premaxilla. Bone was removed from the ventral aspect of the brain case and secondary palate to allow a thin metal rod to be physically placed along this line. The axis of each rosette was determined with respect to reference line SA, from digital images taken perpendicular to the plane of the gauge with a video camera (CCD-72, Dage-MTI, Inc., Michigan City, IN). Image-analysis software (Optimas, Bioscan Inc., Edmunds, WA) was used to determine the gauge angle with respect to the projection of reference line SA onto the plane of the gauge. Angles of orientation of the peak principal strains (ϕ), which were initially calculated with respect to the central axis of the rosette, were now expressed with respect to the skull's axis as angle α. Strain peaks from each chew (with associated orientations for the rosette data) were individually assigned codes for sheep, food type, gauge site, and side of chewing and were saved for statistical analysis.

Structural Analysis


The skulls were split midsagittally with a band saw, and the maxillary and ethmoid conchae were removed. Each skull half was radiographed twice in a cabinet radiography system (Faxitron 8050, Hewlett-Packard, Field Services, McMinnville, OR), with the frontal and maxillary gauge sites in turn pressed against high-resolution film (Industrex AA 400, Kodak, Rochester, NY). The degree of exposure was controlled automatically by a feedback loop in the machine, while the rate was set at low by the operator to enhance resolution.

Stereological principles.

The stereological procedure and analysis that followed was based on one developed over a number of years for use in metallurgy and the study of bone structure (the development is reviewed by Turner (1992)) and is now in use by other workers (e.g., Teng and Herring, 1995). The principle is that if a grid of parallel lines is rotated from 0° to 180° with respect to an axis on the structure (in this case the skull axis), the average length of portions (intercepts) of the grid lines overlying trabecular bone varies with the angle (Fig. 3a and b). If the average length, termed the mean intercept length (MIL), is squared and inverted and is plotted against angle on polar coordinates, the theoretical result is an ellipse (Harrigan and Mann, 1984). The orientation of the ellipse's major axis gives the predominant orientation of trabeculae with respect to the external reference line, and the ratio of the lengths of the two axes of the ellipse gives a measure of the degree to which trabeculae are oriented in the predominant direction (Fig. 3c). The grid also has points in a square pattern, so the number of points overlying bone rather than space can be counted. This number is used in the calculation of MIL and of trabecular spacing and number.

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Figure 3. Stereological analysis of bone architecture. a, b: A grid of points and lines is superimposed over a bone sample at various angles θ. The number of points overlying bone (circled) are counted as hxθ. MILs are the heavy lines. The number of ends of these lines is counted as ixθ. c: Values of (MILθ2)–1 are calculated from hxθ and ixθ, and an ellipse is fitted to these data. H1 and H2 are eigenvalues of the axes of the fitted ellipse.

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Stereological procedure.

A region of each radiograph was enlarged and positioned on the monitor of the video digitizing system so that a circular overlain grid had a diameter equivalent to 1 cm of bone, centered on the middle of a selected gauge site. The grid had lines at a scaled spacing (d) of 0.78 mm and a total number of test points (P) of 135 on a square pattern of the same spacing.

Our application of stereology differs from previous work in using radiographs rather than thin slices of trabecular bone. The rationale for using radiographs is that the gauges were positioned on bone less than 2 mm thick and, therefore, that the orientation of strains would vary little through the thickness of the bone. Features visible on the radiographs were thickenings in the cortical bone, channels within it, and the struts bracing the two tables of the diploë. Buckland-Wright's (1978) work on cats demonstrated the correspondence of strain orientation to structure visible in high-resolution radiographs and was a basis for this rationale. The main caveat about the approach is that the resolution of boundaries between bone tissue and space is definitely worse than in thin sections, even though the spaces that are marrow filled in life are air filled and radiolucent in our postmortem specimens. Identifying boundaries consistently on the radiographs required some care on the part of the operator, and all stereological data were collected by one person (W.W.B.).

The procedure followed the clear description in Teng and Herring (1995). The grid was overlain on the image, and the observer counted the number of times (ixθ) the grid lines crossed the boundaries between radiodense bone and more radiolucent channels (Fig. 3a and b). The number of hits of the grid points on bone (hxθ) were also counted. The angle θ between the grid lines and the skull axis was varied from 0° to 170° in 10° increments, and both counts were made at each position. The MIL was calculated from an equation in Turner (1992) at each value of θ as follows:

  • equation image(1)

where d is the spacing between grid lines and points. Squared values of MILθ were inverted and plotted against θ on polar coordinates (Fig. 3c). The plots approximated ellipses described by:

  • equation image(2)

where M11, M22, and M12 are coefficients that were derived by nonlinear regression using the known values of MILθ and θ. Procedure NLIN in SAS (SAS Institute, Cary, NC) calculated the three coefficients for bone at each gauge site. The coefficients were expressed as a tensor M (in which M21 = M12):

  • equation image(3)

and a fabric tensor H was calculated as M–1/2, as defined by Cowin (1985). The eigenvalues H1 and H2 of H were calculated, where H2 is the eigenvalue of the major axis of the ellipse (Fig. 3c). All matrix computations were done by custom-written programs in GAUSS.

Stereological properties of bone at gauge sites.

The direction of predominant orientation (β) of bony structures in the radiograph of each gauge site and the degree of anisotropy were calculated as:

  • equation image(4)

Comparison of Strains With Structure

Quantitative comparison.

The differences (Δ1 and Δ2) between structural angle (β) and the mean angles of orientation of principal strains ϵ1 and ϵ2 were calculated for each gauge site for each sheep, considering working and balancing sides separately. Angles Δ1 and Δ2 express how closely the strains and intraosseous structures are aligned.

Statistical analysis.

Our first null hypothesis was that the predominant orientation of principal strains at the site of each rosette gauge would not equate to the predominant structural orientation at that site, i.e., that Δ1 and Δ2 would not equal zero. The test performed was for agreement between angles α (orientation of ϵ2) and β (structural alignment). For agreement, a regression of (α – β) on (α + β) produces a nonsignificant slope and intercept (P > 0.05; Bland and Altman, 1986). Agreement was also tested between the orientations of ϵ1 (α + 90) and β. Regressions were performed using Procedure REG in SAS.

The second null hypothesis was that the degree of structural anisotropy (H2/H1) would not be related to principal strain magnitudes ϵ1 and ϵ2. We tested for significance of correlations (at P < 0.05) using Procedure CORR in SAS.


  1. Top of page
  2. Abstract
  7. Acknowledgements

Strain Magnitudes and Directions

A typical trace of one trial is in Figure 4, which clearly shows the change from left- to right-side chewing.

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Figure 4. Typical strain trace, from one trial of sheep 5 masticating hay. Maxillary and frontal bone records are principal strains; mandibular records are the uniaxial strain.

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All strains recorded fell in the range –1200 μϵ compressive strain to +1200 μϵ tensile strain, with the extremes both coming from the mandible (Table 1). Mandibular strains may not represent peak values, because the single-element gauges may not have been aligned with the largest principal strain. Similar patterns of strain were seen at each gauge among the five sheep, with working-side gauges being clearly distinguishable from balancing-side gauges (Table 1, Figs. 4 and 5).

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Figure 5. Peak principal strains ϵ1 and ϵ2 at the four rosette sites and single-axis strains for the middle right mandibular site, pooled and averaged for all chews and for all sheep while feeding on hay. Length of each bar represents strain magnitude. Gauge sites abbreviated as in Figure 1. Shaded ellipse represents the bolus on the working side. B, balancing side; W, working side.

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When right or left mandibular gauges were on the working side, they registered tensile strain (positive values) and compressive strain (negative) while on the balancing side (Table 1, Fig. 4). The only exceptions were the caudal gauge of sheep 3 and the rostral gauge of sheep 5, both on the left dentary, which showed compression during left-side chewing. Mean working-side strains, pooled for the mandibles of all five sheep, were 371, 510, and 348 μϵ, from rostral to caudal. Comparable values on the balancing side were –436, –567, and –567 μϵ. There was a tendency for gradients of strain from rostral to caudal, but in opposite directions in different sheep. For example, when the right mandible was on the balancing side, sheep 2 showed strains increasing rostrally (–674, –780, and –859 μϵ), while values decreased rostrally in sheep 3 (–619, –480, and –15 μϵ).


Working-side gauges on the maxilla registered principal compressive strains ϵ2 as large as –379 μϵ (Table 1). Individual means ranged from –63 to –318 μϵ, and the pooled mean was –131 μϵ (S.D., 73.3 μϵ). Corresponding tensile values of ϵ1 were always smaller, reaching a maximum of 300 μϵ, with individual means from 37–163 μϵ, and a pooled mean of 82 μϵ (S.D., 36.0μϵ). Principal strains were oriented such that ϵ2 was inclined down toward the nose at an angle α, usually between 25° and 70° to the cranial axis (Fig. 5).

On the balancing side, tension predominated in the maxilla, usually making ϵ1 absolutely larger than ϵ2. The maximal value for ϵ1 of 955 μϵ was on the right maxilla of sheep 2. Individual means for ϵ1 were in the range of 100–700 μϵ, with a pooled mean of 319 μϵ (S.D., 193.9 μϵ). The smaller corresponding values of ϵ2 had a maximum of –379 μϵ, individual means in the range of –15 to –170 μϵ, and a pooled mean of –79 μϵ (S.D., 52.7 μϵ). The large tensile strains were inclined steeply with respect to the cranial axis SA, all falling within 30° to either side of a perpendicular to SA (Fig. 5).

Frontal bone.

On the working side, frontal gauges showed strain maxima for ϵ1 and ϵ2 of comparable magnitude: 635 and –575 μϵ, respectively (in sheep 1). Individual means ranged from 155 to 515 μϵ for ϵ1, and –92 to –469 μϵ for ϵ2, and the pooled means were 306 μϵ (S.D., 107.9) for ϵ1, and –277 (S.D., 127.5) for ϵ2 (Table 1). Compressive principal strains ϵ2 were inclined toward the working tooth row (Fig. 5) and were within 2° and 29° of the cranial axis, SA.

On the balancing side, frontal strain peaks were lower: 296 and –309 μϵ for ϵ1 and ϵ2, respectively. Individual mean tensile strains ϵ1 ranged from 12–242 μϵ, with a pooled mean of 79 μϵ (S.D., 85.7 μϵ). Individual means of compression strain ϵ2 varied from –17 to –229 μϵ, with a pooled mean of –127 μϵ (S.D., 69.1 μϵ). Compressive strains ϵ2 were mostly inclined toward the active dentition (Fig. 5), as on the working side, but were at more variable angles: within 13° and 82° of the cranial axis.

Bone Structure

Bone structure visible on the radiographs showed strong individual variability (Fig. 6). The structural results are summarized in Table 2 for individual sheep and in Figure 7 for all of the animals pooled. In all cases the bone under the gauge sites was anisotropic: the measure of anisotropy (H2/H1) varied from 1.32–6.85, with a trend toward higher values for the frontal bone sites than for the maxillae (this trend was not tested statistically). The predominant direction of structural orientation for the maxillae was inclined ventrally and rostrally (Fig. 7, upper panel), at angles α varying among sheep from 29°–70° to the cranial axis SA. In the frontal bones the predominant orientation was close to the structural axis (Fig. 7, lower panel), with all but one value of α being within 12° of SA.

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Figure 6. Radiographs of architecture in the maxillae of all five sheep. Upper panel shows whole facial region of sheep 1 for reference. Area sampled was a 1-cm-diameter circle surrounding the two drilled holes that identified the orientation of maxillary rosette. Middle row shows maxillary sample area for sheep 1, 2, and 3, lower row shows sheep 4 and 5. Scale: centers of drilled holes are 0.5 ± 0.05 cm apart.

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Table 2. Stereological values for the bone at each gauge site for which strain records were available
Gauge siteSheepH1H2H2/H1Angle β
  1. H1 and H2 are the eigenvalues of an ellipse describing the predominant orientation of architectural features. Their ratio is a measure of the degree of orientation. Angle β is between the direction of predominant orientation and the cranial axis SA.

Right frontal20.412.786.85−35.1
Left frontal10.352.286.52−4.8
Right maxilla20.740.971.32−28.9
Left maxilla10.380.661.7564.8
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Figure 7. Mean orientation of the bone architecture (given by angle β) underlying each gauge site for all of the sheep. Line length is arbitrary. Gauge abbreviations as in Figure 1.

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Comparison of Strains With Structure

Angles of strain and structural orientation.

When the mean principal strains were superimposed over the predominant structural orientations at each gauge site for each sheep (Figs. 8 and 9), the maxillary gauges showed a clear trend for the compressive strain ϵ2 on the working side to be quite closely aligned with the structural orientation (Fig. 8). Angle Δ2 (between ϵ2 and the structural orientation) was within 33° for both maxillae when on the working side (Table 1), except for the left maxillary gauge in sheep 1, where tensile strain ϵ1 was closely aligned with the bone structure. Ignoring this outlier, the mean angle Δ2 for the working-side maxillae of all sheep pooled was 13.4° (S.D., 9.81°). For the working-side frontal bones (which had no outliers), the mean Δ2 was similar: 13.3° (S.D., 9.36°), with a maximum of 29° (Table 1, Fig. 9).

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Figure 8. Trabecular alignment compared with that of the principal strains for the left and right maxillary (LMax and RMax, respectively) gauges when on the working or balancing side for all five sheep. Figure is essentially an overlay of maxillary strains as in Figure 5, on architectural orientation as in Figure 7, but for all sheep not just means.

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Figure 9. Trabecular alignment compared with that of the principal strains for the left and right frontal (LFront and RFront, respectively) gauges when on the working or balancing side for all five sheep.

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For the balancing-side maxilla, ϵ1 was more closely aligned with the bony structure than ϵ2, but the alignment was weaker than on the working side (Fig. 8). Angle Δ1 had a mean of 28° (S.D., 20.7°) and a maximum of –66°. For the balancing-side frontal bone, ϵ2 was closer than ϵ1 to the structural orientation, but again the alignment was weak (Fig. 9). Angle Δ2 had a mean of 39° (S.D., 20.7°) and a maximum of 66°.

The statistical tests of agreement indicated that compressive strain ϵ2 on the working side was significantly aligned with the predominant orientation of bone architecture (P > 0.05; Table 3). For agreement, this test requires P > 0.05 for slope and intercept of the regression. Orientations of balancing-side ϵ2 and all orientations of ϵ1 were not in significant agreement with structural alignment (P < 0.05 for slope or intercept or both).

Table 3. Results of the statistical tests of agreement between principal strain and structural orientations
  1. The tests give values of the probability that the slopes and intercepts of regressions of (α − β) on (α + β) are significant (P < 0.05). Only for the working side ε2 are both values greater than 0.05.


When correlating the magnitudes of ϵ1 and ϵ2 with trabecular anisotropy (H2/H1), only one correlation was significant (P < 0.05) when sorting by gauge and side of chew: ϵ1 with H2/H1 for gauge left maxillary on the balancing side.


  1. Top of page
  2. Abstract
  7. Acknowledgements

All gauge sites (rosette or single axis) show two strain signals, depending on the side of chewing (Figs. 4 and 5). For the mandible, peak strains tend to be of higher absolute value on the balancing side, possibly indicating greater force generation by the balancing-side musculature. This is not necessarily true, because we cannot be sure that the single-element gauges recorded peak principal strains. The leverage of the muscles is different on balancing and working sides (Fig. 2), which means that the same force might produce different strains on each half of the mandible. It is certain, however, that significant balancing-side muscular activity occurs during the power stroke in sheep, and this is in accord with work on the few other species that have been studied.

Two patterns emerge from the combined data of this and previous studies. First is that the distribution of strains in cranial bones is dependent on the relative degree of recruitment of balancing- and working-side muscle components. Macaques and owl monkeys appear to have high balancing-side recruitment, as seen in sheep, while galagos have less (Hylander et al., 1998). The difference among the primates has been suggested to correlate with the strengthening or fusion of the mandibular symphysis in anthropoids (Hylander et al., 1998). This is not the case in sheep in which the symphysis is mobile. Perhaps the necessity for maintaining occlusion of shear surfaces in sheep by rotating the mandible during the power stroke takes precedence over bracing the symphysis against force transmission from the balancing side, as has been suggested for goats (Lieberman and Crompton, 2000).

The second pattern to emerge from comparative strain data is that muscle action has strong local influence on bone strain magnitudes and orientations. In miniature pigs, combined electromyographic and strain studies have shown that the force of the power stroke is primarily from the ipsilateral masseter and contralateral temporalis (Herring and Teng, 2000). This puts a torque onto the cranium that strains the frontal and parietal bones in the opposite direction than would be expected from the torque owing to unilateral biting. The high tensile strain on the balancing-side maxilla of sheep is also an example of local muscle influence. Strains in the zygomatic bones of miniature pigs resulting from masseter contraction are independent of the chewing side (Herring et al., 1996). In this case the local muscle activity masks the general asymmetry of loading of the whole skull.

Is the Skull Mechanically a Solid Tube or a Complex of Independent Parts?

The present results indicate that the sheep skull (cranium and face) show elements of solid and composite behaviour. Figure 10 shows the general pattern of forces that may be inferred to cause the strains in Figure 5; no attempt has been made to quantify these forces. On the working side, the action of the temporalis and masseter muscles produce the distributed force vectors T and M, respectively (Fig. 10a), with M also representing activity in the medial pterygoid muscle. The arrows illustrate the approximate directions of vector components of the force from different regions of each muscle and, even more approximately, their relative magnitude. The vectors are not linked with specific anatomical parts of each muscle. These muscular forces pull the mandible toward the cranium, exerting force J at the temporomandibular junction and force B at the point of biting (B will be distributed along the grinding battery). The magnitude of J is likely to be reduced by forces from the balancing side, while B is likely to be similarly increased (Crompton and Hylander, 1989). Force B tends to rock the maxilla on the basicranium, rotating it upwards and backwards toward the frontal bones.

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Figure 10. Reconstruction of the probable forces in the masticatory muscles (M and T) and on the cranium. B, biting force; J, jaw joint reaction forces; M, force components in masseter muscle; T, components in temporalis muscle.

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Strain ϵ2 on the working-side maxilla appears to be largely the result of biting force B, as might be expected. There is possibly some influence of masseteric force M adding to tensile strain ϵ1, because ϵ1 is often larger than would be expected from Poisson's ratio. (A unidirectional compressive force will induce compressive strain in the same direction, and a perpendicular tensile strain because the material tries to retain its volume. The magnitude of the tensile strain is less than the compressive strain parallel to the force, the ratio of the two strains being termed Poisson's ratio. It has a value of 0.2–0.4 for bone (Currey, 1984).

The working-side frontal bone appears to be distorted by a compressive force at an acute angle to the skull's axis, with ϵ1 and ϵ2 being close in magnitude. These strains indicate the effects of combined bending and torsion. Force B pushes the maxilla up and back into the frontal bone, effectively bending the skull. The force also twists the skull, because it is asymmetrically placed, tending to drive the maxilla across the dorsal midline.

On the balancing side, force B is absent, and force J may be increased by the action of the jaw adducting muscles on this side (Fig. 10b). On the maxilla, the large, tensile strains appear (Fig. 5) to result from the tension exerted by the active masseter on that side, pulling the bone ventrally. In several cases the perpendicular compressive strains are less than expected from Poisson's ratio, suggesting that a second, separate tension of unknown cause is also present.

Strains on the balancing-side frontal bone are similarly oriented to those on the working side, but are of lower magnitude (Fig. 5). They are in agreement with the suggestion made above that force B both twists and bends the skull. They also give some indication of the modulating effect of cranial sutures on the transmission of forces between skull bones. If the skull were constructed of homogenous material as a single structural unit, the strains on the two frontal bones would be expected to be almost exactly the same. The reduction in strain magnitudes, of 30%–60% from biting to balancing side, shows the effects of the midline and nasomaxillary sutures in redistributing and absorbing the force of biting.

The discussion above leads to the conclusion that the sheep cranium does show solid behavior to a greater extent than does that of the miniature pig, in which muscle activity dominates local strains (Herring and Teng, 2000). Torque on the whole skull appears to be present in galagos, but low strain values are associated with it in the orbital region, which suggests that it is only one component of the mechanical behavior of the skull (Ravosa et al., 2000a). We reiterate Herring and Teng's caveat that considering the skull solely as a beam does not sufficiently describe its mechanical behavior.

This brings us to the function of the postorbital bar in sheep, which Greaves (1985) suggested is to brace the compressive forces associated with torsion from unilateral biting. Cartmill (1970) proposed that the presence of a postorbital bar in many mammals was associated with the reorientation of the orbits for stereoscopic vision. These and other hypotheses concerning the postorbital bar have been quite widely debated in the anthropological literature (Noble et al., 2000; Ravosa et al., 2000b). The present results showed that frontal bone strain was not aligned along a 45° helix as proposed by Greaves (1985). Indeed there was a significant component of tensile strain aimed toward the postorbital bar in most sheep (Fig. 5). This indicates it may not act as a strut resisting compressive strains due to torsion of the whole skull. Its function is more likely to be as a local brace for the orbit, in which case its stiffness may be more important than its strength, as has been suggested for the primate postorbital bar (Ravosa et al., 2000b).

Stereology of Cranial Bones in the Sheep and the Question of Continua

The major finding from the combined strain and stereological analysis was that the predominant orientation of the bone structure was in statistically significant agreement (P > 0.05) with the working-side compressive principal strain ϵ2. This was despite the fact that the tensile principal strain ϵ1 was larger in magnitude on the maxilla and of equivalent magnitude on the frontal bones.

Facing two strain signals is clearly a challenge for the adaptive remodeling processes of bone, which attempt to optimize bone architecture to best resist local loading (Huiskes et al., 2000). In the sheep facial bones, the processes do not appear to attempt an optimization to both strain signals, but to the compressive one selectively. Even though the architecture does align well with the compressive strain, there is no real correlation of the degree of orientation (H2/H1) with strain magnitudes. This finding suggests that the continua identified by Buckland-Wright (1978) may not reflect the trajectories followed by the larger strains in adjacent bone. It also suggests a direction for further study on the mechanism whereby the bone seems to selectively respond to one mode of loading rather than the other.

Comparing Cranial and Mandibular Strains and Construction in Sheep

The upper part of the skull is a robust hollow tube in sheep, made of many bones, while the mandible is a pair of beams in a V shape with a mobile symphysis. They experience equal and opposite resultant forces and moments through the teeth and jaw muscles. How the skull resists those forces is mechanically quite different than how the mandible does because of the differences in construction. Both structures are of essentially the same material (allowing for variation in properties of bone of varying density and porosity). On this basis we might expect that each would be built to achieve equal safety factors in the material, i.e., the same ratio of peak strain magnitudes with respect to the strain at failure of the material (Biewener, 1993). The strain records indicate that this may not be the case: strains are usually higher on the mandible by at least 50% and up to 100% (Table 1). If the single-axis gauges on the mandible did not record peak principal strains, this difference would be exacerbated. Certainly, the strains on all bones studied in the present work are sufficiently low that none are in great danger from failing during normal use. But the mandible seems to have a lower safety factor than do the two cranial bones studied. This implies that the skull is overbuilt, a suggestion that has been previously raised for the macaques and galagos (Hylander and Johnson, 1997; Ravosa et al., 2000b). Among the possible reasons is that the skull has a number of other functions as well as that of providing a lever system for mastication (Smith, 1993; Thomason, 1991). Enclosing the brain and nasal cavity gives the skull its generally tubular shape and dictates the volume that has to be enclosed within the tube. The tubular form certainly confers strength and stiffness on the whole structure, even if there is some mechanical independence of the bones comprising it. The orbital regions provide support and visual direction for the eyes, and the important property of the bones surrounding the orbit may be their rigidity rather than their strength (Ravosa et al., 2000a and b). The sum total of all the extra functional demands on the skull is probably at the root of the differences in mechanical behavior between it and the mandible. Certainly they are the main impediment to fully understanding the structural design of the skull. Comparative and in vivo studies have enabled rapid progress in analysis of cranial functional and structural design in the past few years. The complexity of the problem ensures that it will be several more before a reasonably complete picture is available.


  1. Top of page
  2. Abstract
  7. Acknowledgements

The main findings from this study are as follows:

  • 1
    Unilateral mastication results in markedly different strain signals on working- and balancing-side cranial bones of sheep, as has been previously shown for primates and for some bones in the miniature pig (but not those in the zygomatic arches).
  • 2
    The mechanical behavior of the ovine skull shows aspects of behaving as a solid tube and of a complex of independent bones.
  • 3
    The alignment of architectural features within the frontal and maxillary bones of sheep statistically agrees with the orientation of principal compressive strains ϵ2 on the working side, despite the fact that balancing-side principal tensile strains ϵ1 were of equal or larger magnitude.
  • 4
    The ovine mandible appears to experience larger strains than do the facial bones, indicating that the skull is overbuilt in comparison to the mandible.


  1. Top of page
  2. Abstract
  7. Acknowledgements

We thank Dr. S. Young and Dr. M. Shoukri for advice on the computer programming and statistical procedures, respectively. We thank the three reviewers for their constructive comments, which have improved the paper. Grants from NSERC (OGP0138214 and OGP0002377) were given to J.J.T. and L.E.G., respectively. A visiting professorship grant from NATO was given to A.G.D.


  1. Top of page
  2. Abstract
  7. Acknowledgements