Tyrannosaurus rex

Analysis of feeding in predatory birds (Snively 2006) suggests capabilities of biological importance to a feeding Tyrannosaurus rex. These include the ability to lift the head away from the food and look from side to side to assess the surroundings, as after attack or swallowing food. Raptors often tear flesh by rearing back with their hind limbs, and their necks must withstand high, externally imposed loadings. The capability to withstand analogous sagittal loadings, and those imposed by lateral flexion when tearing flesh, are testable for T. rex. After excising flesh or when eating larger prey, raptors engage in inertial feeding similar to that seen in other reptiles. If T. rex analogously tossed large bodies of food back in the throat, it would have had to accelerate its head vertically to overcome the inertia of the food, and of its own head and neck. We therefore use results of musculoskeletal dynamic calculations to estimate four performance magnitudes and test three hypotheses related to T. rex feeding. Magnitude 1: Maximum vertical acceleration of the head with the feeding apparatus passing through a neutral posture. Magnitude 2. Maximum vertical load with the feeding apparatus passing through a neutral posture, as the muscles were being stretched by the load. Magnitude 3: Maximum lateral acceleration of the head with feeding apparatus passing through a neutral posture. Magnitude 4. Maximum lateral load with the feeding apparatus passing through a neutral posture, as the muscles were being stretched by the load. Hypothesis 1: Moment-generating capacity of head dorsiflexors increased as the head was dorsiflexed. Hypothesis 2: Moment-generating capacity of head lateroflexors increased from the point of maximum left lateral flexion to the neutral posture, and decreased as the head continued to be swept to the right. Hypothesis 3: The mouth of the examined specimen of Tyrannosaurus rex appears capable of encompassing approximately 50 liters, and therefore 50 kg, of food with an average specific gravity of 1. We test the hypothesis that the craniocervical muscles could impart sufficient acceleration to the head, neck, and a 50 kg bolus of food (with its center of mass medial to the large anterior maxillary teeth), to conduct inertial feeding. Hypotheses 1 and 2 describe possible scenarios of head motion in T. rex when the animal shifted its gaze, or struck laterally at prey by lateroflexion or anteriorly by dorsiflexion. They derive from the observations that muscle moment arms appear to have been most favorable in the neutral posture, and thus accelerations of the head are predicted to have been greatest when the head moved through this position. Because many parameters of musculoskeletal function in fossil animals must be inferred or estimated, sensitivity analyses are highly instructive about the effects of uncertainty of assigned values (Hutchinson and Garcia 2002; Hutchinson 2004a,b). Origins and insertions of major neck muscles are well characterized for T. rex (Snively 2006), and deviations from the animal’s true morphology entail predictably linear errors, or cosine errors that will be small (Richmond 1998), even with ostensibly gross mischaracterization of muscle attachment topology. Variabilities of other parameters would have nonlinear and complex combinatorial effects, and are potentially greater sources of error. We conducted three sensitivity analyses to test the effects of variability and error in various musculoskeletal parameters on inference of inertial feeding in T. rex (hypothesis 3): 1. Sensitivity of accelerations to the presence or absence of interspinous ligaments. Accelerations are calculated with and without inferred ligamentous support against gravity. 2. Effects of head density and inertial properties on accelerations. Different assigned densities of the antorbital region test the sensitivity of dorsiflexive accelerations to inertial properties of the head. 3. Sensitivity of sagittal accelerations to errors of moment estimation, and to muscle recruitment patterns. Moment-generating capacities of head dorsiflexors, contracting unilaterally and bilaterally, are tested for the ability to accelerate 490 N of food tangentially at 1.5 g (a sufficient value for inertial feeding). Sensitivity analysis 3 yields indices of muscle recruitment latitude for a T. rex to be able to engage in inertial feeding with food of greater weight, and to reorient food in its mouth for swallowing, as seen in crocodilians. If a muscle easily imparts the minimum vertical velocity to the food for inertial feeding, more intense recruitment of this muscle, and additive recruitment of others, will be available for feeding on larger masses of food. High recruitment latitude for sagittal acceleration would impart (nearly literal) modulatory ‘‘wiggle room,’’ enabling the animal to accelerate the food in non-sagittal directions to reorient it in the mouth. Conversely, if a muscle is incapable of accelerating the food at a sufficient rate, its force must be augmented by recruitment of additional muscles. Accelerative capacity below the threshold necessary for inertial feeding compromises a muscle’s autonomous utility for this biological role. Morphological and Physiological Background for Tyrannosaurid Neck Dynamics Neck Muscles of Tyrannosaurids Tyrannosaurid neck muscles are described in greater detail elsewhere (Snively 2006). Table 1 lists origins and insertions of major muscles (spanning more than two vertebrae) in tyrannosaurids, with abbreviations given for all listed muscles. Bracketed (Witmer 1995) and extrapolatory reconstruction (Bryant and Russell 1992) indicates that tyrannosaurids had neck muscles variably similar to those of birds and crocodilians (Table 1, Fig. 1A) (Snively 2006). For example, anteriorly originating head dorsiflexive muscles of the M. transversospinalis group (Tsuihiji 2005), M. complexus and M. splenius capitis (hereafter abbreviated as M. spl. cap.), strongly resembled those of birds. The neck dorsiflexor M. transversospinalis cervicis (M. trans. cerv.) had large, crocodilian-like origins from the neural spines, but remarkably avian-like insertions on the epipophyses (Table 1). Despite the avian-like curvature of the tyrannosaurid neck, the largest head dorsiflexor, M. transversospinalis capitis (M. trans. cap.), had crocodilian-like origins from the tips of the neural spines. Its insertion on the parietals is relatively larger and more rugose than in crocodilians, suggesting a large muscle belly. The large lateroflexor M. longissimus capitis superficialis (M. long. cap. sup.) originated from transverse processes and inserted onto the paroccipital processes, similarly to the attachments in non-avian amniotes (Rosse and Gaddum-Rosse 1997; Cleuren and De Vree 2000; Snively 2006). The work-generating capacity of all of these muscles was contingent on their dimensions, moment arms, and physiological properties. Muscle Performance Variables in Extant Animals A muscle’s ability to produce force, work, and power depends on its contractile capabilities. Vertebrate skeletal muscle has similar physiology and contractile properties across taxa. Variations in fiber type composition, internal geometry of muscle fibers, muscle cross-sectional area, and length govern differences in the contraction of different muscles. The force that a muscle produces varies predictably with its length and velocity of contraction, with force generally increasing with length to a point, and decreasing with velocity. The muscle’s fiber type composition and operating temperature influence contraction velocity, with the highest velocities from glycolytic, fast-twitch but rapidly fatiguing fibers, and relatively high but thermoneutral body temperatures. Dozens of dissected extant archosaurs have a preponderance of ‘‘dark meat’’ in their superficial neck muscles (especially in large birds; Snively 2006), suggesting that the muscles have predominately fast oxidative gycolytic fibers (Syme 2006) that can contract rapidly but recover quickly from fatigue. It is reasonable to assume the same properties in the neck muscles of tyrannosaurids, which fall within the phylogenetic bracket of birds and crocodilians (Witmer 1995). Adult T. rex was likely homeothermic with a body temperature of 35–40°C (Gillooly et al. 2006) favorable for muscle function. We assume that it experienced invariance of temperature influences on muscle force, contraction velocity, and power at given muscle lengths (Guyton and Hall 1996), and that its muscle physiological parameters were comparable to those of extant homeotherms. Although different muscles will have similar force-velocity and force-length relationships (Syme 2006), the inherent force-generating capacity of an individual muscle is proportional to the number of sarcomeres in parallel. Hence, the force depends on the collective cross-sectional area of the muscle fibers (large in human power lifters [Akima et al. 2000; Brechue and Abe 2002]). The contraction force will equal this cross-sectional area times the muscle’s specific tension, or the force it produces per unit area (Kawakami et al. 1995; Fukunaga et al. 2001). Muscle Cross-sectional Area. The summed physiological cross-sectional area (PCSA; Thorpe et al. 1999) of a muscle’s fibers is often greater than the anatomical cross-section of a muscle, if the muscle is pennate with fibers angled relative to the line of muscle pull. In fusiform muscles, such as those involved in plantar flexion in humans (Bamman et al. 2000), PCSA is very close to anatomical crosssectional area (ACSA). However, in highly pennate muscles, PCSA and force generation can be dramatically higher than would be estimated using anatomical cross-sectional area (Cheng and Scott 2000). Physiological cross-sectional area (Richmond 1998; Vasavada et al. 1998) depends on a muscle’s mass, m, volume and density (p, typically 1.06 g · cm ̅3), pennation angle (σ), and average

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