Functional shape of the skull in vertebrates: Which forces determine skull morphology in lower primates and ancestral synapsids?

Authors

  • Holger Preuschoft,

    Corresponding author
    1. Formerly Subdepartment of Functional Anatomy, Anatomisches Institut, Medizinische Fakultät, Ruhr-Universität Bochum, Bochum, Germany
    • Subdepartment of Functional Anatomy, Anatomisches Institut, Medizinische Fakultät, Ruhr-Universität Bochum, Bochum, Germany
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    • Fax: 49-234-3214059

  • Ulrich Witzel

    1. Forschungsbereich Biomechanik, Fakultät für Maschinenbau, Ruhr-Universität Bochum, Bochum, Germany
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Abstract

In order to determine the extent to which the shape of the synapsid skull is adapted for resisting the mechanical loads to which it is subjected, block- or simple plate-shaped finite-element models were constructed and loaded with external muscle and bite forces in locations estimated to resemble points of application of these forces. These 2D or 3D finite-element models were iteratively loaded and modified by removing elements that experience only low stresses, and the resulting morphologies of the models were compared with fossil skulls of synapsids and the skulls of extant mammals. The results suggest that the stress flows in these unspecific models are very similar to the arrangement of bone material in real skulls. Morphological differences between taxa depend on a few a priori conditions: length and position of the tooth rows in relation to the braincase, arrangement of muscles, position of the orbits, and position of the nasal opening. Given these initial conditions, finite-element analysis consistently reveals the close similarity between stress flows and real skulls. The major difference between mammal-like reptiles and primates is the size of the braincase. This difference accounts for most of the morphological divergence. The postorbital bar seems to be a constructional element of the skull, rather than a means to protect the eyes. The skull shapes of higher primates are determined mainly by masticatory forces and less by external forces acting on the head. This study demonstrates the utility of finite-element modeling for testing hypotheses regarding relationships between form and function in vertebrate skulls. © 2005 Wiley-Liss, Inc.

The research reported here is part of a long-term research program seeking to determine whether and to what extent the shape of the vertebrate skull is adapted for resisting the mechanical loads to which it is subjected by biting, the weight of the head and loads carried between the jaws, and accelerations associated with movements. The ultimate question is: What are the reasons for the development of skull shape in evolution and ontogeny? This research program does not seek to find out how the existing skull of a crocodile, a galago, or a macaque behaves under load (see, e.g., Metzger et al., 2005, this issue; Strait et al., 2005, this issue; and Ross et al., 2005, this issue), but rather why the various skull shapes have evolved. In terms of evolutionary theory, the question is: Which selective pressures may have led to the development of specific skull morphologies? This approach is based on empirical information, but the way in which the conclusions are arrived at is deductive, not inductive. Starting from well-known, generally valid rules such as mechanical laws and rules of bone development and bone remodeling (Wolff's law), and taking into consideration observed and theoretically possible load patterns, taxon-specific behaviors, skeletal morphology, and muscle arrangement, this method attempts to deduce the optimal skeletal shapes for resisting the resulting stresses.

In our previous work on skulls, we sought to explain the morphological diversity seen in humans, fossil precursors of modern humans, and living apes (Witzel and Preuschoft, 1999, 2002; Preuschoft and Witzel, 2002, 2004a, b; Preuschoft et al., 2002; Witzel et al., 2004). The present article examines the functional conditions that have led to the skull shapes of the earliest forerunners of mammals and of primitive primates. Many modern strepsirrhine primates (lemurs, lorises, and galagos), the oldest known definitive catarrhine primate (Aegyptopithecus), and therocephalians from the Triassic have many morphological traits of their skulls in common. These include a narrow snout and dental arcade of medium length, which is positioned anterior to, not below, the small braincase; widely flaring zygomatic arches; an otic capsule with the mandibular joint displaced to the rear, close to the level of the occipital condyle; a postorbital bar; and in side view a rather low skull with the orbits facing upward to some degree, i.e., a low degree of frontation, sensu Cartmill (1972). The research reported here investigates the effect that these similarities and differences might have had on the distribution of stresses in the skulls of early mammals and primitive primates.

Deducing Skull Form Using Finite-Element Analysis (FEA)

As a working hypothesis, skull shape is assumed to be dictated by mechanics, more precisely, by the flow of stresses. This working hypothesis is based on Wolff's law (1892) as formulated by Pauwels (1960) or Kummer (1972). It has been confirmed for the locomotor apparatus by experimental evidence and the countless experiences of orthopedists and surgeons (Pauwels, 1973; Maquet, 1984; Carter and Beaupre, 2001). What remains to be determined is whether there is an essential coincidence between mechanical stress and shape in the skull, as well as in the postcranial skeleton. Ross et al. (2004; Ross and Metzger, 2004) have compared the available strains measured in postcranial and cranial bones of tetrapods and found magnitudes, rates, and frequencies of strains to be similar in skulls and in the postcranial skeleton. This is true in spite of the “fundamental difference in the nature of the external forces” that cause bone strain: “Forces acting on the limb bones are largely determined by oscillations of the animal's body mass, which varies with locomotor speed, whereas forces acting on the skull originate primarily from the feeding muscles and bite force and do not increase with chew frequency” (Ross et al., 2004). Therefore, although the authors expect different scaling relationships of cranial and postcranial bones with body mass, their results suggest that the relationships between stress and bone morphology in the postcranial skeleton should also apply in the skull

This working hypothesis is tested by exposing unspecific solid elements to forces similar to those that act on or in skulls under natural conditions, and investigating the stress flows with the aid of 2D or 3D FEA (see also Carter and Beaupre, 2001). These finite-element models (FEMs) are then modified by removing those elements that experience only low stress magnitudes (Witzel and Preuschoft, 2002; Preuschoft and Witzel, 2004a) and the resulting morphologies of the models are compared with existing shapes observed in nature. If appropriate, the resulting reduced models can again be exposed to the same loads, and again the lowly stressed elements are eliminated. This process of reiteration can be repeated several times in a manner similar to the process of adaptation assumed to take place in evolution.

In order to load FEMs, the loads or forces applied to a skull must be estimated. In technical terms, the load cases applied to the FEMs must be defined. The forces that a skull must be able to withstand are bite forces, the weight of the head plus additional loads carried between the jaws, and the inertial forces associated with accelerations during movements. There seems little doubt that biting and mastication are most relevant. In addition, the influence of weight should be considered, although its importance in comparison to mastication is probably low. Many animals also use their teeth to lift rather heavy objects, to rip off parts from immobile masses, or at least try to do so. The movements of the head are sometimes very rapid and take place in different directions. This means that there are external forces acting on the skull that are independent from those evoked by biting and mastication. Some of these external forces have been analyzed in a study by Preuschoft and Witzel (2004b) in the case of dogs. Another load case was proposed recently by Jenkins et al. (2002) in the case of gorgonopsians: a hammer-like application of the heavy symphyseal region of the lower jaw for inserting the dagger-like anterior teeth in snapping prey (“malleognathic jaw function”). One aim of the research presented here is to evaluate the importance of this hypothesized loading regime for skull function and structure in early mammals.

Thus, the aims of the present article are twofold: to investigate the effect of rapid decelerations of the jaws in snapping on the skull, as was assumed recently by Jenkins et al. (2002), and to use FEA to investigate the mechanical significance of widespread (and possibly primitive) morphological traits common to synapsids and many mammals, especially the primitive primates.

MATERIALS AND METHODS

In Vivo Data

In order to estimate the force magnitudes used to load the synapsid and primate models and to investigate the possible significance of the malleognathic jaw function (Jenkins et al., 2002), data on forces exerted on external objects were obtained from dogs and opossums. Seven dogs trained as Schutzhund, weighing between 30 and 41 kg (mean = 34 kg), were studied over 260 trials in Bochum, Germany, in 1983. The animals were provoked to bite, pull, and shake on a dry wooden branch of about 6 cm diameter and 60 cm length, equipped with strain gauges to measure tensile forces along the instrument. The forces were recorded over time and calibrated on an oscilloscope. To get an estimate of the weight and inertial forces, we sectioned the head of a large mongrel dog (Leonberger/German shepherd) and weighed the segments. The data are set out in Table 1.

Table 1. Mass distribution and dimensions of the mammalian heads under investigation
Measurement OpossumDogCat
Upper jawLower jawTotalTotalTotal
Masses of head segments, kgm10.00530.00260.00790.2200.0097
 m20.00910.00640.01550.3250.0159
 m30.01930.01130.03060.9900.0423
 m40.02920.02490.05411.3000.0800
Preym5   2.000 
Lever arms about occipital condyles, cml1  8.622.47.8
 l2  6.617.46.3
 l3  4.811.04.9
 l4  2.93.72.5
Preyl5   20.5 
Lever arms about mandibular joint, cml67.0Same as upper jaw   
 l75.0    
 l83.2    
 l91.3    
Snapls6.0    
Lever arms of neck muscles, cmlm  1.63.52.1

The experiments on American opossums (Didelphis virginiana) were performed in 1973 in the Museum of Comparative Zoology at Harvard University under the guidance of Dr. K. Hiiemae and Dr. A. Thexton of London, following the procedures described in Hiiemae (1978, 1984), including the recordings on X-ray films. Measurements of bite forces were made with a custom-built bite meter consisting of two brass tongues with a diameter of 3 mm, covered by five layers of filter paper and fitted with strain gauges. With some exceptions (as indicated in the text), the animals were awake and could move freely except for the wires connecting EMG electrodes with an oscilloscope. As with the dogs, the head of one animal that had to be euthanized was sectioned after deep freezing (as shown in Fig. 1) and the segments were weighed. The data are set out in Table 1.

Figure 1.

a: Head of an American opossum in side view, cut into segments with centers of partial masses (m). The head as a whole is kept in balance against weight force at the occipital condyles by the neck muscles Fm. b: Head weight evokes downward concave bending moments along the length (l) of the head, which increase caudally by a second power function. c: Biting and chewing evokes upward concave bending moments between the bite point and the mandibular joint, which reach their maximal values along the insertions of the muscles on the skull. Bending moments reach their peak at the place of the muscle resultant. d: Opossum head seen from on top with inertial forces (F) acting on all segments. As in the cat, the most occipital segments are neglected.

Modeling

General principles of mechanics, found in standard textbooks (for example, Lehmann, 1974–1977), are applied. FEA is described in Zienkiewicz (1975) and the particular methods of application used here are dealt with in detail in Witzel and Preuschoft (2005, this issue).

As in Witzel and Preuschoft (2005, this issue), the modeling procedure begins with a 2D or 3D Bauraum, a solid structure that envelops the volume of the skulls of interest. This Bauraum is created in ANSYS 7.0 using 10-noded tetrahedral finite elements. The model was assigned a Young's modulus of 17 Mpa and a Poisson ratio of 0.3.

For the synapsid models, the geometry of the Bauraum was determined by the approximate lengths and widths of the tooth rows, their approximate position to the mandibular joints and to the occipital condyle. The outlines of the tooth rows, and the location of the teeth, were taken from the animals mentioned in the text. The muscle forces were assumed to be applied at the locations of the muscles present in mammals: mm. temporalis and masseter on the lateral side of the corpus mandibulae and pterygoideus medialis on the medial side. In some models, an additional longitudinal tie was added comparable to the m. pterygoideus lateralis.

In the first step of model creation, ample volume was provided for the stress flows. The FEMs were loaded with forces that were just great enough to produce visible stress flows under the arbitrarily assumed Young's modulus and the shape assumed for the respective model (i.e., the available Bauraum). The relative magnitudes of forces exerted against the individual teeth were varied depending on the leverage, i.e., the distances of the bite points from the joint of the biting side in side view and in anterior view (Wolff, 1984). In a second step, the elements that received no or only very low stresses were eliminated, and the remaining reduced shape was loaded again in the same way as before. This reiteration of the FEA can be repeated a second and a third time. This procedure is explained in more detail by Witzel and Preuschoft, 2005 (this issue).

RESULTS

Estimates of Weight, Acceleration, and External Forces Acting on Mammalian Skulls

A calculation of the weight and inertial forces in dogs has been published recently (Preuschoft and Witzel, 2004b). Here we present a corresponding calculation for the opossum and the domestic cat. The lever arms and segment weights are given in Table 1. As a comparison, although the head of the cat is of about the same length as in the opossum, it clearly shows greater masses of the segments and a larger brain than the marsupial and slightly shorter load arms. The reduction of mass in the most distal segments and the concentration of head mass near the occipital condyles are obvious in all forms.

The weight of the head is acting downward (Fig. 1a), and the weight forces are balanced by the neck muscles inserting on large areas of the occiput. The joint forces resulting from the pull of the muscles and the weight are concentrated on the condyles. Under static conditions, the weight of the head alone evokes a torque of m1 × l1 + m2 × l2 + m3 × l3 + m4 × l4. Data of relevance for calculating torques and mass moments of inertia are listed in Table 2.

Table 2. Torques of weight, mass moments of inertia of the head segments*
 OpossumDogCat
Upper jawLower jawTotalTotalTotal
  • *

    Calculated in kgm, kgm2, respectively, sums transformed into Nm.

Static torque, kgm     
 Segment 1  0.679 × 10−30.04930.757 × 10−3
 Segment 2  1.023 × 10−30.05661.002 × 10−3
 Segment 3  1.469 × 10−30.10892.073 × 10−3
 Segment 4  1.569 × 10−30.04812.000 × 10−3
 Total static torque  4.740 × 10−30.26285.832 × 10−3
 Transformation into Nm  46.499 × 10−32.578357.212 × 10−3
Mass moment of inertia about condyle, kgm2     
 Segment 1  5.84 × 10−50.011045.901 × 10−5
 Segment 2  6.75 × 10−50.009846.311 × 10−5
 Segment 3  7.05 × 10−50.0119810.156 × 10−5
 Segment 4  4.55 × 10−50.001785.000 × 10−5
 Prey   0.08405 
 Total mass moment of inertia  24.20 × 10−50.1186929.155 × 10−5
 Transformation into Nm2  237.408 × 10−51.1643286.012 × 10−5
Mass moment of inertia about mandibular joint     
 Segment 12.597 × 10−51.274 × 10−5  
 Segment 22.275 × 10−51.600 × 10−5   
 Segment 31.975 × 10−51.157 × 10−5   
 Segment 40.494 × 10−50.421 × 10−5   
 Total mass moment of inertia7.342 × 10−54.452 × 10−5  
 Transformed into Nm272.023 × 10−543.674 × 10−5  

In the oppossum, the total torque of head weight is 4.65 Ncm. These torques must be countered by the neck muscles (2.906 N in the opossum and 73.67 N in the dog), resulting in a force acting against the occipital condyles of 3.55 N in the opossum and 90 N in the dog. Lifting of a prey rabbit by the dog increases the torque (by 20.5 cm × 19.62 N = 402.2 Ncm), and the muscle force must be increased accordingly to 190 N.

If the head (or only the jaws) is moved, the mass moment of inertia must be overcome. It is defined by segment mass multiplied by the square of its lever arm (Fig. 1d). In other words, the total torque under kinetic conditions is m1 × l12 + m2 × l22 + m3 × l32 + m4 × l42 (Table 2).

Its numerical value is 24.19 × 10−5 kgm2 in the opossum and 0.0346 kgm2 in the dog without prey. After transformation from kg to N, the values are 237.408 × 10−5 Nm2 and 0.3398 Nm2, respectively. These values must be multiplied by angular acceleration to get the momentum of the head (or jaw) movement.

Due to the lack of information on behavior, the following line of calculation cannot be applied to oppossums. Dogs, if encouraged or aggressive, tend to exert considerable kinetic forces on bigger prey animals or simply on the protected arms of a human. In some 30 experiments (data not shown), a first (tensile) impact of about 6–8 kg was observed, followed within seconds by a second, third, and often further impacts of about full body weight of the dog (in our experiments, between 18 and 35 kg; Fig. 2a). These movements were performed with accelerations of about two times earth gravity.

Figure 2.

a: Example of pulling forces exerted by a dog in agonistic shaking. Forces are calibrated by the weight of the dog. b: Agonistic snapping forces exerted by an opossum, with subsequent head shaking. c: Bite forces exerted by an awake opossum. d: Bite forces in an anesthesized opossum after electrical stimulation of m. temporalis and m. masseter.

As an additional load, a typical prey animal of dog-like carnivores is considered in the calculations, namely, a rabbit of 2 kg. If a rabbit is captured, it is usually shaken to death by sideway-directed movements. The moment of inertia that must be overcome in shaking is defined by J = Σli2 × m, as mentioned above. For our calculation, we have assumed an angular acceleration corresponding to 2 G. The muscle force necessary to overcome the mass moment of inertia and to accelerate the snout is 283.8 N, and the reaction force at the occipital condyles amounts to 295.3 N. This force is to be added to the static force derived above from head weight plus prey, so that the total condylar force may easily be 485 N (Preuschoft and Witzel, 2004b). If the same speeds (about 4 m/sec) and accelerations as in the dog (about 2 G) are assumed, the necessary muscle force is 29.6 N, and the joint resultant is 55.9 N in the opossum.

Significance of Kinetic Energy of Jaw for Bite Force and Skull Construction

One aim of this article is to determine whether in long-snouted animals such as opossums, the rapid closing of the jaws in capturing prey or in defensive biting (Fig. 2b) leads to considerable stresses in the jaws because of the negative acceleration when the teeth are making contact with a bitten object. The influence of deceleration and mass inertia during rapid snapping in oppossums was calculated as follows. The impulse contained in the mandibular movement at jaw closure is P = angular velocity × total mass moment of inertia/lever arm length of biting tooth, and this value was added for the lower and upper jaw. The angular velocity obtained from the X-ray films was 747°/sec. The total impulse of both jaws showed the moderate value of 0.970 kgcm/sec. The greatest impulse exerted by the teeth on a bite-meter in snapping, however, was 1,900 kgcm/sec, and the smallest was 212 kgcm/sec. The maximal bite forces measured in unrestricted awake opposums were between 183.4 and 53.9 N between the canines and anterior premolars. Bite forces between the molars in adult anesthesized oppossums were up to 191.3 N on the stimulated and 174.6 on the contralateral sides (Fig. 2c and d). The bite forces in large dogs are reported to be between 180 and 1,000 N, depending on biting enthusiasm and the bite point (Lindner et al., 1995). The ratio between inertia and muscle activity is between 1/2,000 and 1/220. In addition, the EMG activity of the masticatory muscles continued after the contact between the teeth and the bite-meter in free-moving awake animals. Evidently, the deceleration exerts much less influence than active biting and can be disregarded in the analyses.

Synthesis of Skull Form in Synapsids

To investigate the relationship between the common ground plan of synapsid and mammalian skull form (Figs. 3–5) and mechanical loading, a 2D FEA model was built of the right half of a skull in top view. The model consisted initially of a rectangular plate pulled to the left by a force applied near its upper margin. It is supported in the middle and tied to its support on its lower right corner. The force flows concentrate on a triangle, leaving the left half of the plate and its upper right corner and two spots unstressed (Fig. 6a). If the unstressed elements are removed, and a new model is constructed that includes only the stress-bearing parts, the shape in Figure 6b remains. If this shape is loaded again, further areas do not receive any stress and therefore can be eliminated as well. In contrast, at some places, high stress concentrations come close to the margins of the holes in the models.

Figure 3.

a: Side view of Aegyptopithecus zeuxis, a fossil anthropoid from the Oligocene. b: Side view of the recent strepsirrhine primate Eulemur fulvus (courtesy of Mr. H. Raveloson, Strasbourg), to show the similarity to Aegyptopithecus. c: Top view of Aegyptopithecus zeuxis. d: Top view of Eulemeur fulvus.

Figure 4.

Three views of the Early Triassic therocephalian Theriognathus. Note the narrow braincase and the massive wide occiput, which includes the otic capsule and the joint. a: side view, b: top view, and c: occipital view.

Figure 5.

Four views of Middle Permian gorgonopsians. a: Side view of Regisaurus. b and c: Top and bottom view of Sycosaurus. d: Occipital view of Sycosaurus. Note the smallness of the temporal opening and its variable separation from the orbit. Note also the narrow braincase under the rather complete skull roof.

Figure 6.

Two-dimensional unspecific FEA model to investigate basic characteristics in top view of skull shape in synapsids. a: Force flow (colored) in a rectangular plate (empty outline), loaded like the skull of an animal that is pulled by neck muscles to the right side. This illustration represents the first step of reduction, since only the stressed elements are shown in color. b: Second step of reduction. Same model as in a (stress-bearing elements only), under the same load, after elimination of the least stressed elements. c: Same model as in b, supplemented by a symmetrical left half, loaded alternatively by external forces pulling to the right and to the left. The stress patterns in physiological superposition as described by Witzel and Preuschoft elsewhere in this volume. d: Same model as in c, showing the compressive stresses alone (in contrast to the other illustrations, which show total or Von Mises stresses). Note the jugal arches are under tensile stress only.

In shaping the next model, material was added at those places where the stresses are high, changing the outlines of the holes from step to step (Fig. 6a–c). All models exhibit two openings, comparable to the temporal opening and the orbit, separated by the postorbital bar. If combined to a corresponding model of the left half of the skull, the shape in Figure 6c is produced, which exhibits clear similarities to the skull shapes of lower primates or mammal-like reptiles in top view. The anterior opening (orbit), the postorbital bar, and the temporal opening are as clearly visible as its zygomatic arch and the stress flows along the postorbital bar in front and the otic capsule behind the temporal opening. In addition, the braincase in the median plane is very narrow, and a small asymmetrical stress-free area in front of the orbits corresponds to the nasal aperture. The narrow snout of the model is due to the concentration of the external force on one point at its tip. This trait could be changed by two points of force application placed apart from each other. This simple model contains essential traits of a synapsid skull, for example the Early Triassic therocephalian Theriognathus (Fig. 4). Figure 6a–c illustrate total or Von Mises stresses. Figure 6d illustrates the compressive stresses alone, without the tensile component. It is obvious that the jugal arch does not carry compression in these models; its existence in Figure 6 is due to the tensile component.

The much older gorgonopsian, Sycosaurus from the Lower Permian, possesses the vastly closed, complete skull roof so typical of the oldest tetrapods (Fig. 5). This trait is usually interpreted as a relic of armor that protects the anterior end of the body. To test this assumption, and our working hypothesis that biomechanical stresses dictate the shape of the skull, a simple wedge-shaped model was designed. Aside from its general outline, only the dental arcade, the eye openings, and adductor muscles were given a priori. The muscles take their origins from the inner surface of the skull roof (such as m. temporalis) and from the interior of the skull (m. pterygoideus or m. masseter), not from the lateral lower margin (masseter).

Figure 7a shows the model loaded by bite and corresponding muscle forces. If the deep red parts are eliminated, and the model is reduced to the load-bearing finite elements, the shape shown in Figure 7b is produced. This reduced model is again loaded by the same bite forces as before. As can be seen from Figure 8, the nasal channel opens into a wide nasal aperture, which is connected to a nasopalatal passage. The orbits extend rearward into a temporal opening. The highest stresses occur at the origins of the muscles, on the skull roof above and behind the orbits, at the mandibular joint, and at the condyles. On transverse sections (Fig. 9), a vaulted “oral” cavity becomes visible, which expands into deep excavations on both sides of a central beam between the occipital condyle and the skull roof (basioccipitale). The latter beam contains a center that does not receive high stresses. Clearly, this stress-free cavity provides a case for the brain. The comparison with the skull of the gorgonopsian shows essential similarities.

Figure 7.

a: Simple wedge-shaped model of the skull of a primitive mammal-like reptile, loaded by bite forces. b: Reduced model, consisting of the load-bearing elements only, to show the shape after the first step of reduction. c: Color keys.

Figure 8.

Two views of the reduced FEA mode in Figure 7b after the second reiteration of the modeling, again loaded by bite forces. The deep red, nonstress-bearing finite elements can also be eliminated. a: Side view. b: Top view. c: Color keys.

Figure 9.

Posterior views on cross-sections behind the orbits through the reduced model shown in Figure 8. Note the inverted U-shape of the load-bearing elements with a thickened reinforced medial part. The latter is hollow, its unstressed center offering the space for a braincase. c: Color keys.

DISCUSSION

Significance of Kinetic Energy of Jaw for Bite Force and Skull Construction

The in vivo data presented above call into question hypotheses regarding the significance of the effect on the skull of rapid decelerations of the jaws in snapping (Jenkins et al., 2002). The results presented here suggest that the contacts of the teeth to a bitten object do decelerate the jaws rapidly, within less than 1/10 of a second, but do not lead to high forces. The malleognathic jaw function (Jenkins et al., 2002) in the example of a living marsupial does not evoke forces greater than 1/200 or 1/2,000 of those in biting. It must be concluded that the deceleration of the jaws must not be considered as a factor that has lead to special adaptations in the evolution of skull shapes.

On the other hand, the external forces exerted by pulling the head sideway, upward, or downward against the resistance of mass inertia or gravity must definitely be taken into consideration. A previous study showed the importance of gravity, additional external loads, and accelerations in the case of dogs. The forces acting on the skull have been found to be in the same order of size as bite forces. The same calculations for opossums presented here also suggest that the external forces are of the same magnitude as bite forces.

Synthesis of Synapsid Skull Shapes

Applying these forces to the finite-element models led to the synthesis of skulls resembling early synapsids. The total or Von Mises stresses found in the models are in fair agreement with the naturalistic shapes of skulls. However, in the models examined here, the zygomatic arch carries nearly exclusively tensile stresses, as can be seen from Figure 6d. This is not in full agreement with Pauwels' version of Wolff's law, nor with our own results obtained in other studies, which suggest that the essential stresses that lead to the apposition of bone material are compressive. As a matter of fact, the zygomatic arch seems to be exposed to compressive and bending stresses as well by the action of the jaw muscles, as documented by experimental evidence (Rafferty et al., 2000) and as discussed by Witzel et al. (2004). This sort of stressing occurs in biting and chewing and cannot be made visible in a 2D FEA mode such as the one investigated here.

The lengths and widths of the dental rows are in obvious relationship to the feeding habits of an animal and were a priori conditions imposed on the models before the virtual synthesis was initiated. An elongated and narrow dental arcade offers obvious advantages for longer reach and higher speed of the approaching anterior teeth, as well as a reduction of potentially dangerous torsional moments about the longitudinal axis of the jaws (Preuschoft et al., 1986a, b). Likewise, position and size of the eyes are in direct relationship to the mode of life.

If these factors, dental arcade and eye opening, are given, the stress distribution in a solid block of unspecific form is impressively similar to the shapes of real skulls. One of the outstanding results is the unstressed region along the length of the tooth row, equivalent to the nasal channel, which occurs in skulls of quite different forms (Preuschoft and Witzel, 2002, 2004a). The eye openings also seem to appear at places where stresses are minimal or zero. The postorbital bar or postorbital wall appears to be a constructive element of elongated skulls. In some variants of the model, a small hole appeared at the place where the postorbital bar and the anterior zygomatic root merge. This hole is comparable in position to the infraorbital foramen for the maxillary nerve, or the large foramen for the zyomaticofacial branch of the maxillary nerve seen in some primates (e.g., Aegyptopithecus, Ateles, Lagothrix, Brachyteles).

The insertions of the jaw muscles are very significant for determining the loading regime. Their decussation is inevitable for maintaining equilibrium at the mandibular joint in varying applications of bite forces (as shown by Strait et al., 2005, this issue). In addition, all muscles that are inclined in relation to the tooth row exert tensile force components in a longitudinal direction and so relieve the bony elements from tensile stresses. Tension along the skull axis occurs inevitably behind the tooth rows and is sustained by the active tie formed by the muscles that adduct the mandible and the m. pterygoideus lateralis. The cranial base (basioccipitale) is well suited to sustain the joint forces applied to the cranial condyles. In the investigated cases, its direction fits with the direction of the occipital joint resultant.

The most significant difference between primates and mammal-like reptiles is the size of the braincase in the former and its smallness in the latter. In reptiles, the brain fits into just one of the rod-like elements that constitute the (framework-like) construction of the skull. Because the development of the brain in ontogeny precedes the development of the skull, the bony elements can only develop at places not yet occupied by the brain. As a consequence, the large brain in mammals dictates the development of a thin-walled shell construction. The voluminous braincase of mammals implies the enormous strength of a thin-walled shell, which channels the stresses and reduces stresses in other parts, which therefore can be reduced. Most obvious is the reduction in length and thickness of the zygomatic arch.

The skulls of insectivores and some bats, for example, possess wide interorbital diameters, housing the anterior part of the brain. In a former study, Preuschoft and Witzel (2002) have argued that the wide olfactory lobe in some small mammals requires the development of a thin-walled shell construction that channels the stress flows so that zygomatic arches become unnecessary. This interpretation is perfectly supported by the illustrations contributed by Dumont et al., 2005 (this issue). Their images of the skulls of bats reveal a reinforcing plate in the frontal region between the orbits, and no postorbital bar, while they show the stress flows in the thin-walled shell without a zygomatic arch, as derived from the tube-like skull of another bat.

Comparisons With Primates

Our previous analyses of the human facial skeleton modeled the skull in the form of a semicylinder. Loads were applied to the dental arcade from below and supported on top along the margins of the braincase. Eye openings and nasal channel were assumed a priori, but the shape of the latter had to be changed as the result of the experiments. If the finite-element model was reduced to the load-bearing finite elements, a rather human-like shape was produced (Witzel and Preuschoft, 2002). At the lateral margins of the orbits, in the location of the zygomatic bone, a marked stress concentration occurs and extends rearward. Justified by biologically reasonable assumptions that the zygomatic arch existed before the development of the specific human skull shape and functions as the hypomochlion1 between fascia temporalis and m. masseter, the model was modified by applying a series of low, medially directed forces below and lateral to the orbits. By this means, the lateral stress concentration was moved downward, detached from the lateral skull wall, and positioned roughly in the position of the zygomatic arches (Witzel et al., 2004).

Application of this approach to the more prognathous, smaller-brained shape that exists in fossil australopithecines and modern large apes produced a model with a remarkable similarity to a gorilla skull (Preuschoft and Witzel, 2004a). By moderate changes in the positions of the muscle origins, i.e., a concentration of the whole m. temporalis on the skull vault, the browridges disappear, and the model becomes more similar to the skull of an orangutan (Preuschoft and Witzel, 2004a).

The earliest known forerunners of the apes and hominids are rather similar to modern lemurs (Fig. 3). Even without a detailed analysis of the stress flows, the principal stress distribution in the three basic load cases is evident. The place of maximal compressive stress is just in front of and above the orbits (Jenkins et al., 2002; Preuschoft and Witzel, 2002; Rayfield, 2004), requiring reinforcement in that area. Indeed, the illustration of Dumont et al., 2005 (this issue) shows such a reinforcing plate in a bat skull in the form of the upper part of the (incomplete) orbital surroundings, which is separated rostrally and occipitally from the rest of the orbital margins.

Two characteristics of the Early Triassic therocephalian skull modeled in the present study (Figs. 4,7) resemble those found in an FEA model of a hominoid skull (Preuschoft and Witzel, 2004a: Fig. 3A): the lack of stress at the place where the bony eye opening exists and the narrow skeletal bridge between occipital condyle and facial skeleton are also “incarnated.” The vectors of the stress flows show a tendency to avoid the eye opening, separating the zygomatic region in front of the orbits from the postorbital bar or postorbital septum behind. Second, there is a very narrow force flow from the occipital condyle forward. The first of these traits can be related to the often-observed dorsal inclination of the orbits in the skulls of many lower and most fossil primates (Ross, 1995). The latter flow of stresses is reminiscent of the low and straight cranial base (basioccipitale) in strepsirrhine primates (Abbie, 1963; Biegert, 1963; Hofer, 1965; Ross and Ravosa, 1993).

If the basic ways of loading the skulls of long-snouted animals by weight, mass inertia, and bite forces are accurately represented in this study, then the results presented here very probably apply to other long-snouted animals, such as strepsirrhine primates, and carnivorous reptiles. In the short-snouted higher primates, use of the jaws for carrying loads or ripping objects apart seems to be reduced with these tasks performed exclusively with their hands. At least the forces applied to or exerted by the short jaws lead to rather low torques. This leads to a decrease in importance of weight and inertial forces in determining skull form in higher primates and the increased importance of bite forces.

Skull Fenestration

The highest stresses occur regularly at the teeth and at the insertions of muscles. Therefore, the fenestrations of vertebrate skulls can hardly be caused by an inflation of the muscles. Just the reverse holds true: if the muscles are assumed to take their origins from the lower surface of the skull roof, the latter is reinforced. It seems more logical to look for special behaviors as the cause of fenestrations in the skull roof, such as sideway snapping during prey acquisition. Using FEA, fenestrated skull shapes are produced if the jaw muscles are modeled to take their origins from the median rod, namely, the braincase.

The orbital and temporal openings in the skulls of synapsids and of primitive mammals seem to be areas that simply do not receive mechanical stresses from external loads that act in the plane of the tooth row. The postorbital bars are basically constructive elements of the skull, not means to protect the eyeball (contra Cartmill, 1972; Ravosa et al., 2000). The orientation of the orbits seems to be dictated by the stress flows, not by the direction of vision. This statement, however, raises the question as to why in marsupials and in carnivores the postorbital bar is missing. This question will be addressed in a later study.

CONCLUSIONS

In dogs and opossums, the external forces due to gravity and accelerations of the head are of the same order of magnitude as bite and masticatory forces. In contrast, the deceleration of the jaws, when they hit a resistant object in snapping, is much smaller. The assumption of a hammer-like function of the jaws to insert the fangs deeper does not therefore seem very probable (Jenkins et al., 2002). At least this sort of loading does not lead to relevant stress patterns.

The results of our iterative approach to FEA are in agreement with our working hypothesis, namely, the shape of the skull can be synthesized on the basis of mechanical stresses alone and in so far is in accordance with the postcranial skeleton. The stress flows in unspecific models depend on a few factors: the position and the shape of the dental arcade, determining the length and the shape of the snout; the position and size of the eye openings; the arrangement of the muscles; and the size of the brain. The results of this and previous studies suggest that all of these items are relevant factors driving the selective processes determining skull form in several vertebrae lineages.

Acknowledgements

The authors owe a very helpful survey on the skulls of synapsids to Dr. Michael Maisch, Tübingen, who also provided the illustrations in Figures 4 and 5. This is also a late but welcome occasion to thank Dr. Karen Hiiemae and Dr. Alan Thexton for providing the opportunity to measure bite forces under strictly controlled conditions in opossums, cats, and macaques. The huge number of experimental results obtained was at that time very difficult to interpret, and both distinguished colleagues have shown great patience. In the meantime, the authors have learned to understand skull mechanics better. Finally, they thank Dr. C. Ross for the invitation to take part in the workshop and for transforming their text into fluent English. This article is contribution number 4 of the DFG Research Unit “Biology of Sauropod Dinosaurs.”

  • 1

    A hypomochlion is a structure which forces a tendon or a muscle to change its direction, similar to a pulley. It is of course exposed to a redirectional force (see textbooks of mechanics). Well-known examples are the patella, or the malleolus tibialis.

Ancillary