Tyrannosaurus rex, Osborn, 1905

Cost, I. N., Middleton, K. M., Sellers, K. C., Echols, M. S., Witmer, L. M., Davis, J. L. & Holliday, C. M., 2020, Palatal Biomechanics and its Significance for Cranial Kinesis in Tyrannosaurus rex, The Anatomical Record 303, pp. 999-1017 : 1006-1014

RESULTS

Muscle and Bite Forces in Extant Species

Modeled Psittacus bite force (61.78N [rostral bite position]–96.44N [caudal bite position]) was greater than the 16.74N reported for Monk Parakeets ( Myiopsitta monachus ) estimated using PCSA by Carril et al. (2015) as expected given that the skull of P. erithacus is about twice as large. Bite forces in our Gekko models (11.27N [rostral bite position]–18.53N [caudal bite position]) were near ranges reported by both Anderson et al. (2008; 10.1N– 19.1N) and Herrel et al. (2007; 10.78N–16.97N) using bite force meters.

Sensitivity Analysis of Muscle Forces in Tyrannosaurus

The distribution of PCSA values of our sensitivity analysis of theoretical muscle architecture is represented using a heatmap ( Fig. 4 ). Although pennation angle and fiber length are the two parameters on which PCSA depends, there is a functional relationship between pennation and fiber length in which fiber length has a stronger effect on PCSA than pennation angle. For example, when we hold fiber length constant (any horizontal line on Fig. 4 ), larger values of PCSA are associated with low pennation angle, and the largest value was 64 times the smallest value (approximately equal to cos − 1 (89.1-degrees)). When we hold pennation angle constant (any vertical line on Fig. 4 ), larger values of PCSA are associated with shorter fiber length, and the largest value was 100 times larger than the smallest value (equal to 0.01 − 1). This and the construction of the PCSA equation show that the effect of fiber length is greater than that of pennation angle on PCSA (sensu Gans and De Vree, 1987).

Upon this heatmap ( Fig. 4 ), we project the regression line of Bates and Falkingham (2018), which compiled over 1,000 measured vertebrate muscles, along with plots of Bates and Falkingham’ s (2012), Gignac and Erickson’ s (2017), and our phylogenetically bracketed Tyrannosaurus muscle architecture data. Bates and Falkingham’ s (2012) muscle force estimates used combinations of pennation angles of 0–20-degrees and fiber lengths of 0.1–0.4 times muscle length (i.e., 1/10–2/5 times muscle length), which resulted in forces below the regression line, thus corresponding to higher forces. Gignac and Erickson (2017) modeled muscles with 0-degrees pennation and a fiber length equal to muscle length, the combination of which yields the lowest possible PCSA. The PCSA estimates in Tyrannosaurus from the present study fall close to the regression line of all known vertebrate PCSAs published by Bates and Falkingham (2018), suggesting that the values we used are close to predictions from extant taxa and our bite force estimates are reasonable.

Bite forces in our Tyrannosaurus model (35,365N– 63,492N) extensively overlap with the range reported by Bates and Falkingham (2012; 18,065N–57,158N) and are about twice the magnitude predicted by Gignac and Erickson (2017; 8,526–34,522N). These differences between our results and those of Gignac and Erickson (2017) are likely due to our inclusion of pennate jaw muscles, whereas the latter authors modeled all jaw muscles as parallel fibered.

Analyses of Strain Patterns

Strain differences were found among the Gekko models with respect to the bones, sampling region, and posture. The neutral Gekko model ( Fig. 5A ; Supporting Information Videos 1–6: https://players.brightcove.net/656326989001/ mrOxISgynX_default/index.html?videoId=6058428214001) exhibited higher strains in the pterygoid than those in the quadrate or the palatine. The ventral portion of the epipterygoid was extremely strained around the joint with the pterygoid, which may be an artifact of the modeling process wherein the epipterygoid and pterygoid were fused together. The body of the pterygoid, however, is strained across its length, representing a higher strain concentration than in any of the other elements of the palate ( Fig. 5A ). The FAM Gekko model reveals high strains in the quadrate, and pterygoid suggesting that this is not an optimal posture ( Fig. 5B ). However, the MLM Gekko model ( Fig. 5C ) exhibits low strains in the elements of the palate, suggesting that the MLM model is a more optimal posture, along with the neutral posture. The otic process retains slightly higher strains than the other portions of the quadrate in the MLM model. The pterygoid still possesses localized higher strains ( Fig. 5C ), though these are lower compared to the pterygoid in the FAM model ( Fig. 5B ).

The MLM model of Gekko ( Fig. 6 ) possessed lower median strain values (1,731 με) than those of neutral (2,277 με) or FAM (2,714 με) postures ( Table 3). The lowest strain values of Gekko are found in the palatines. However, strains were lowest in different portions of the palatine in each of the postural models of Gekko . The ventral portion of the quadrate was most strained in the FAM Gekko model (6,322 με) and least strained in the neutral posture (1,767 με). Median strain values of whole elements are shown for all taxa in Table 4. The otic and middle regions of the quadrate possessed identical strain profiles in all three postures, despite differences in rotation at the otic joint. Similarly, the pterygoid exhibited a conserved pattern of caudal to rostral strain decrease across all models. The caudal to rostral pattern is observed in the FAM posture in the palatines; however, this is reversed in the neutral posture. In the MLM posture, the rostral region of the palatine was subjected to more strain than the middle region but the caudal region was subjected to the highest strain.

The Psittacus models also experienced differing strains in the bones, sampling region, and between postures. In the neutral Psittacus model ( Fig. 5D ; Supporting Information Videos 7–12: https://players.brightcove.net/6563269 89001/mrOxISgynX_default/index.html?videoId=6058434 297001), the quadrate and pterygoid experienced high strain relative to other parts of the cranium ( Fig. 5D ). The palatine, postorbital process, and the interorbital septum experienced low strains in this posture despite serving as muscle attachment sites ( Fig. 5D ). The FAM Psittacus model revealed high strains on the rostral aspects of many of the kinetic palatal elements ( Fig. 5E ). In the MLM Psittacus model ( Fig. 5F ), strains are noticeably higher at the otic process of the quadrate, the postorbital process, and the middle of the palatine compared to the FAM model ( Fig. 5D ). Strain in the pterygoid is relatively uniform throughout the bone compared to that seen in the palatine.

In Psittacus ( Fig. 7 ), the MLM model exhibited higher overall median strain of the palate (753 με) than neutral (619 με) or FAM (543 με) models ( Table 3). Strain values of the FAM model were the lowest, as expected by observations of feeding behaviors. The MLM model possessed higher overall strains in the palatine and pterygoid, maintaining the same trend as the other Psittacus postures. Pterygoid strains in the MLM model increased from the middle and caudal regions to the rostral region whereas in the neutral model strain steadily decreased moving rostrally. In the FAM model, peak strains were found in the caudal region of the pterygoid, however, the middle region appeared to possess decreased strain. The strain again increased in the rostral sampling region. In all three postures strain decreased from caudal to rostral in the palatines. The otic process of the quadrate possessed the highest strain values across all postural models of Psittacus .

Strain differences found among the Tyrannosaurus model’ s bones, sampling regions, and between postures were highlighted by areas of structural failure. The neutral Tyrannosaurus model ( Fig. 5 ; Supporting Information Videos 13–18: https://players.brightcove.net/656326989001/mrOxISgynX_ default/index.html?videoId=6058438903001) exhibited low strain throughout the palate with the exception of modeling artifacts at joints of the palate. The caudal portion of the pterygoid was weakly strained whereas the body of the quadrate experienced higher strains in the neutral posture ( Fig. 5G ). The palatine and pterygoid exhibited higher strains across their rostral bodies and the quadrate showed high strain values across pterygoid and otic processes ( Fig. 5G ). The joints of the FAM Tyrannosaurus model ( Fig. 5H ) were increasingly strained, particularly at isthmuses and articulations with the cranium. Lower overall strain was found throughout the FAM model, but areas of failure remained prevalent across the palate ( Fig. 5H ). The palatine of the FAM model exhibited lower overall strain than the other elements in the palate ( Fig. 5H ). The MLM Tyrannosaurus model found the otic joint to be highly strained, and the bodies of the quadrate, pterygoid, and palatine bones to all be highly strained ( Fig. 5I ). High strains also propagated throughout the facial skeleton in the MLM model ( Fig. 5I ). Failures in the MLM model were observed throughout the pterygoid and the dorsal ridge of the quadrate body ( Fig. 5I ). Across the Tyrannosaurus models, the lower temporal bar experiences high strains near the quadratojugal-jugal suture that approach or exceed levels of structural failure ( Fig. 5G–I ).

Tyrannosaurus ( Fig. 8 ) exhibited different quantitative strain profiles across the three postural models. The MLM model exhibited the highest median strain values (1,768 με) of the three postural models (neutral 1,542 με; FAM 1259 με; see Table 3). Across all three postures, the quadrate was similarly strained overall, though the middle region was more variable ( Fig. 8 ). The middle region of interest was subjected to more strain than the ventral or otic regions in all postures, but especially in the MLM posture ( Fig. 8 ). The neutral posture exhibited similar ventral and otic strains (1,540 and 1,459 με, respectively); however, the otic strains were noticeably higher in both the MLM and FAM models (1,980 and 2,029 με, respectively). The pterygoid in the MLM posture of Tyrannosaurus was subjected to greater strain than either the neutral or FAM postures. The rostral region of the pterygoid was subjected to the least strain by large margins in both the neutral and MLM models. The most appreciable difference between models, however, can be seen within the caudal portions of the three models ( Fig. 8 ). A slight increase was observed from middle to rostral in the FAM model. In all three postures, the palatine exhibited the highest median strains in the rostral portion with similar strain patterns in the caudal and middle aspects as well. The caudal portion of the palatine was subjected to low median and overall strains in all three models, but this is especially so in the FAM model ( Fig. 8 ).

DISCUSSION

Tyrannosaurus Was Functionally Akinetic

By incorporating cranial joint articular tissues, distributed muscle loads, and posture analysis to infer cranial performance in T. rex , we have gained a nuanced understanding of the biomechanics of the skull. We accurately estimated the biomechanical environment of Gekko and Psittacus using PKC methods and achieved lifelike results prior to modeling T. rex . Rotation of the quadrate 5-degrees rostrocaudally and mediolaterally was sufficient to affect the rostral elements of the palate and the facial skeleton such that lifelike fore–aft and MLMs were reflected in the models of both extant taxa. Functionally acceptable ranges of strain were observed in models of FAM in Psittacus and MLM in Gekko . Equally important, MLM in Psittacus and FAM in Gekko resulted in failures at joints, within individual bones, and across the palate. Thus, the loading behavior of the Tyrannosaurus model also performs with acceptable accuracy with respect to the anatomical potential of the animal. Using these findings, we conclude that Tyrannosaurus was functionally akinetic. Although hypotheses of fore–aft palatal motion in Tyrannosaurus are more supported compared to those of mediolateral palatal motion, the linkages surrounding the otic joint impede fore–aft excursions of the quadrate, and the loading that the palate and craniofacial skeleton experience during bites suggests powered, fore–aft kinesis is extremely unlikely. Like paleognaths ( Gussekloo, 2005), many iguanians and other lepidosaurs ( Jones et al., 2017), many dinosaurs ( Holliday and Witmer, 2007), stem crocodylomorphs ( Pol et al., 2013), and numerous diapsid species, including Tyrannosaurus , remain akinetic despite possessing unsutured otic and palatobasal joints.

Cranial kinesis in Tyrannosaurus has been debated since shortly after the initial description of the taxon. Osborn (1912) recognized the morphological limitations of kinesis in Tyrannosaurus , initially describing the otic joint as immobilized by the pterygoid, quadratojugal, and squamosal via sutures between the quadrate and surrounding bones. Osborn’ s description of the otic joint was refuted by Molnar (1991) who recognized that, although the otic joint was surrounded by sutured elements, the joint itself was smooth and saddle shaped which in turn led to subsequent functional analyses of otic joint kinesis by Molnar (1991, 1998), Rayfield (2005a), and Larsson (2008). Larsson (2008) supported inferences of propalinal (fore–aft) movement of the Tyrannosaurus palate, stating that movement was possible due to osteological anatomy, kinetically competent joints throughout the palate, and streptostylic movement of the quadrate. Molnar (1991, 1998) described streptostylic movement as well, stating that the otic joint could allow for “swings in several directions” (1991, p. 163) and was capable of resisting forces in multiple directions. Although streptostyly and propalinal palatal movements, as a result, appear reasonable in a disarticulated specimen, the rigidity of the facial skeleton, congruency of the otic joint, and the similarities between the neutral and FAM models suggest that any movement of the palate was incidental and potentially injurious to Tyrannosaurus . Moreover, the craniofacial skeleton of adult tyrannosaurs has numerous bony features that defy translational movements of the palate including the following: rigid, unbendable bones, a secondary palate built by massive, co-sutured maxillae, and heavily interdigitated sutural and scarf joints like the frontonasal, circummaxillary, and temporal joints ( Carr, 1999; Snively et al., 2006). These lines of evidence all suggest Tyrannosaurus was functionally akinetic, despite possessing unsutured otic and palatobasal joints ( Figs. 9 and 10 ).

Challenges to Modeling Kinesis and Cranial Function

Despite advances over previous modeling approaches, our process has several important sources of error and uncertainty, including tissue material properties, joint posture and range of motion, and jaw muscle activation patterns. We also acknowledge that taphonomic issues and reconstruction of fossils lead to potential sources of error in modeling extinct taxa as described by Hedrick et al. (2019). Material properties of non-osseous tissues are not well described outside of mammals and are unknown for large, extinct theropod dinosaurs. Wang et al. (2012; testing of various material properties), Lautenschlager (2013; testing of beaks, teeth, and bone), and Cuff et al. (2015; validation study) all explored the impact of various material properties in mammal, dinosaur, and bird FEMs. We used these studies to inform our assignments of skeletal and articular properties to models, bearing in mind that Strait et al. (2005) noted that elastic properties have small impacts on model performance. We therefore constructed our joints with separate materials for the large cranium of Tyrannosaurus (canine patellar tendon) and the smaller crania of Psittacus and Gekko (rat cranial suture). Although sutural areas and joints were modeled in other studies (e.g., Moazen et al., 2009; Jones et al., 2011, 2017; Porro et al., 2011) as FEM elements assigned the properties of sutural or joint materials, this method retains a tightly packed area of the model which would instead be occupied by more flexible material allowing for more deformation in sutures and joints involved in cranial kinesis; cranial sutures not associated with kinesis are less flexible. We consider our method of creating open spaces within the joint capsules of the model and joining these portions using flexible beams to more accurately simulate malleable soft tissue by permitting more realistic deformation at joints; however, further studies are needed to validate these findings. Node anomalies at joint articulations are a result of this joint construction, but do not change the overall strain patterns of the model with fused joints.

Static postures in our models are merely moments in a coordinated series of motions during feeding bouts. Although we only tested three specific instances of what could be a dynamically changing joint articulation, recent studies of ball and socket joints suggest that despite their seemingly flexible ranges of motion, they do not necessarily perform this way (e.g., Manafzadeh and Padian, 2018). Moazen et al. (2008) suggested that the temporal ligaments in Uromastyx stabilized the quadrate during feeding. Analogously, Manafzadeh and Padian (2018) found that only 10% of possible postures were valid once capsular ligaments were included in the ball and socket-shaped articulation. Indeed, Tyrannosaurus quadrates possess enlarged tuberosities on the medial portion of the otic process that bear the features of attachments for large capsular ligaments and complementary ligamentous scars adorn the lateral portion of the otic joint. Likewise, the palatobasal joint is highly congruent with a labrum of pterygoid bone nearly encompassing the basipterygoid condyle, further suggesting pronounced capsular ligaments. Thus, bony joint morphology ( Holliday and Witmer, 2007), loading, and postural analysis suggest that a miniscule, and likely biologically insignificant, envelope of motion was available for the 6-bar linkage system of the robustly built Tyrannosaurus palate, which spans pairs of highly congruent palatobasal, otic, and craniofacial joints compared to the relatively freely moving bird hip joints. Finally, despite slight vagaries in the articulation of our model and that of the original BHI 3033 mount (e.g., palatobasal articulations, epipterygoidpterygoid joint), these morphologies still likely fall within the possible natural variation of the T. rex population making our results biologically realistic and similar to other studies of posture and range of motion (e.g., Gatesy et al., 2010; Mallison, 2010; Claes et al., 2017; Olsen et al., 2017).

We modeled jaw muscles as contracting synchronously at maximal force even though it was likely that, as has been shown in other diapsids, there is variation in the firing sequence and magnitude of cranial musculature ( Busbey, 1989; Nuijens et al., 1997; Herrel et al., 1999; van der Meij and Bout, 2008; Vinyard et al., 2008; Perry and Prufrock, 2018). Protractor and adductor muscles show variation in activation pattern during the feeding cycle, and the loads these muscles impart appear to help stabilize the cranial joints ( Cundall, 1983; Herrel et al., 1999; Holliday and Witmer, 2007). Moreover, the orientation and osteological correlates of the m. protractor pterygoideus indicate that it was highly tendinous, likely pennate, and oriented dorsoventrally and mediolaterally ( Holliday, 2009). This architecture suggests m. protractor pterygoideus had very limited excursion, and, at best, held the palate against the braincase, restraining its movements and filling a largely postural role.

Finally, to further understand the role of muscle loads and constraints on the model, we conducted post hoc tests with neutral Tyrannosaurus models using occipital constraints as well as differential activation of the protractor muscles. Constraints on the occipital surface of the skull were modeled to mimic cervical muscle loads imparted during inertial feeding mechanisms ( Snively and Russell, 2007; Snively et al., 2014) as well as to free the jaw joint from artificial constraints. Additionally, protractor muscles were toggled on and off in the neutral T. rex model to test for their effect on palatal strains. Protractor muscles were found to not alter the distribution and range of strains in the palate suggesting they may not be functionally important, and even may be potentially vestigial. Conversely, occipital constraints shifted and diminished the strains experienced by the quadrate and pterygoid, but increased strains experienced by the epipterygoid as it was cantilevered by its laterosphenoid attachment. Regardless, the low strains experienced by the braincase in the neutral and FAM models in all tests indicate that although the palate was incapable of movement, it was capable of dissipating high strains away from the braincase, thus insulating the neurosensory capsules of the head ( Holliday and Witmer, 2007).

CONCLUSIONS

This study presents a unique method of exploring Tyrannosaurus cranial kinesis that incorporates anatomically distinct, distributed muscle loadings, reconstructions of joint tissues, varying postures of cranial elements, and ultimately analysis of cranial performance using finite element modeling. Its new approaches differ from previous inferences of muscle architecture ( Gignac and Erickson, 2017), joint function ( Molnar, 1991; Rayfield, 2004, 2005a, b), and joint kinematics ( Larsson, 2008). The findings presented here offer a nuanced, integrative approach to testing biomechanical hypotheses of cranial function in extant as well as extinct vertebrate species. Not only are these methods applicable to testing a priori assumptions about kinematics and function in living animals, but they also offer a detailed approach to testing behavioral and functional hypotheses in animals that are impossible to explore using in vivo approaches. Few modeling studies incorporate multiple lines of evidence, such as multiple postures, joint tissues, and distributed muscle loadings in such diverse species, and here we illustrate how powerful these inferential approaches can be using Tyrannosaurus as a case study. These approaches found inferences of gross cranial mobility in Tyrannosaurus to be unsupported and that Tyrannosaurus was functionally akinetic.

Figures

Fig. 4. The relationship between fiber length, pennation angle, and force in muscle physiology and its application to reconstructing function in fossil taxa using recent case studies. PCSA is a function of pennation angle and fiber length and is mapped as a heatmap with contour lines. We replotted the regression line from Bates and Falkingham, 2018 (labeled “B&F 2018”) showing the classic prediction that increasing pennation in order to accommodate shorter muscle fibers increases PCSA. PCSA values from recent studies, Gignac and Erickson, 2017 (labeled “G&E 2017”) and Bates and Falkingham, 2018, of Tyrannosaurus cranial biomechanics are also plotted to show similarities in approaches.

Fig. 5. Heat maps depicting Von Mises strains in Gekko gecko (A–C), Psittacus erithacus (D–F), and Tyrannosaurus rex (G–I) in Left, Neutral; Middle, FAM; and Right, MLM postures of each taxon. Models are shown in left oblique (top), left lateral (middle), and ventral (bottom) views. Heat maps show strains in postural models with all muscles fired simultaneously. Areas of high strain appear in warmer colors; white areas are beyond the scales presented with the models. Cooler colors depict areas of low strain concentration. Bones of the left lateral dermatocranium (i.e., portions of the maxilla, jugal, lacrimal, postorbital, and quadratojugal bones) have been removed on heat maps of T. rex to show details of the palate, although all bones were in place for the analysis.

Fig. 6. Strains of regions of interest in the palatal elements of Gekko gecko. Regions of interest and scatter plots showing individual sample points as well as median strains (color-coded by sampling region) are represented. Otic, middle, and ventral regions correspond to sampling of the quadrate whereas rostral, middle, and caudal regions correspond to sampling areas of the palatine and pterygoid. Each sampling region consists of 50 tetrahedra sampled randomly from the surface of the skeletal element. Horizontal lines representing the median value of the neutral posture are shown in red in each region of the palatal bones to facilitate comparison across postures.

Fig. 7. Strains of regions of interest in the palatal elements of Psittacus erithacus. Regions of interest and scatter plots showing individual sample points as well as median strains (color-coded by sampling region) are represented. Otic, middle, and ventral regions correspond to sampling of the quadrate whereas Rostral, middle, and caudal regions correspond to sampling areas of the palatine and pterygoid. Each sampling region consists of 50 tetrahedra sampled randomly from the surface of the skeletal element. Horizontal lines representing the median value of the neutral posture are shown in red in each region of the palatal bones to facilitate comparison across postures.

Fig. 8. Strains of regions of interest in the palatal elements of Tyrannosaurus rex. Regions of interest and scatter plots showing individual sample points as well as median strains (color-coded by sampling region) are represented. Otic, middle, and ventral regions correspond to sampling of the quadrate whereas Rostral, middle, and caudal regions correspond to sampling areas of the palatine and pterygoid. Each sampling region consists of 50 tetrahedra sampled randomly from the surface of the skeletal element. Horizontal lines representing the median value of the neutral posture are shown in red in each region of the palatal bones to facilitate comparison across postures.

Fig. 9. Comparison of neutral postures of Tyrannosaurus rex and Psittacus erithacus in left rostrolateral view showing effects of protractor muscle activation, constraints, and sutural materials on the behavior of models. Jaw joint constraints with activated (A) and deactivated (B) protractor muscles reveal few differences in strains in the model. Occipital constraints with activated (C) and deactivated (D) protractor muscles reveal significant differences in strain distribution in the palate. Regions of models with hatching represent areas that have been cut away to allow for better visualizations of internal structures. Psittacus erithacus is presented to show differences between using rodent sutural properties (E) and canine sutural properties (F). Rodent sutural properties were used in Psittacus and Gekko and canine sutural properties were used in Tyrannosaurus. Sutural properties were considered based on taxon size.

Fig. 10. Illustration of Tyrannosaurus skull in left lateral (top) and ventral (bottom) views with key functional characteristics of the feeding apparatus. Numerous features of the skull of Tyrannosaurus suggest it was not capable of substantial cranial kinesis.