of Tyrannosaurus rex

In ~anke,~. an~ K. Carpenter (eds.), 2001, Mesozoic Vertebrate Life. IndIana UmversIty Press, Bloomington, IN.

9. Forelimb Osteology and Biomechanics of Tyrannosaurus rex KENNETH CARPENTER AND MATT SMITH

Abstract Although proportionately the forelimb is very small, the mechanical advantage reveals an efficiently designed force-based system (vs. a velocity-based system) used for securing its prey during predation. In addition, the M. biceps is shown to be 3.5 times more powerful than the same muscle in the human, the straight, columnar humerus provides maximum strength to mass ratio to counter the exerpign of the M. biceps, and the thick cortical bone indicates bone selected for ultimate strength. Such mechanical adaptations can only indicate that the arms were not useless appendages, but were used to hold struggling prey while the teeth dispatched the animal. Tyrannosaurus rex was therefore an active predator and not a mere scavenger, as has been suggested.

Introduction "[W]hat, if anything, did Tyrannosaurus do with its puny front legs anyway?" is a question that has been asked by many individuals (Gould 1980, 12). The hypotheses range from an aid during mating (Osborn 1906), assisting the animal to get up from a prone position (Newman 1970), a vestigial organ (Paul 1988), or an organ whose function decreased with maturity of the animal (Mattison and Griffin 1989). The discovery in recent years of several specimens of Tyrannosaurus rex preserves the first arms of this animal, allowing a testing of the

90

various hypotheses by biomechanical analysis. Because the entire forelimb of Tyrannosaurus has not been described before, a description is presented before the biomechanical analysis.

TABLE 9.1 Measurements for the Forearm of Tyrannosaurus rex (em) MOR555

humerus length

37.7

humerus distal width ulna length ulna prox. anteropost. length ulna width prox. radius length radius prox. anteropost. length

FMNH PR 2081 37.3

8.4

8.9

>19.5

21.9

6.7 6.4

7.1

4.4

>15.1

17.3

4.2

5.2

radius prox. width

2.9

3.7

radiale height radiale anteropost. length

2.1

1.6 -1.8 -1.5

radiale width ulnare height ulnare anteropost. length

2.1

ulnare width

1.5

6.4

metacarpal I length metacarpal I prox. anteropost. length metacarpal I prox. width metacarpal I distal width metacarpal II length metacarpal II prox. anteropost. length

3.0

1.7 3.0

9.4

10.9 4.1

4.9 3.9

metacarpal II prox. width metacarpal II distal width

>8.4

phalanx 1-1 length

>7.5 3.9

phalanx 1-2 (ungual) length phalanx 1-2 (ungual) prox. length phalanx 1-2 (ungual) prox. width

2.5

phalanx II-1 length

5.7

phalanx II-1 prox. anteropost length phalanx II-1 prox. width

4.0

5.5 4.3 3.9

phalanx II-1 distal width

3.7

3.5

7.8 -3.4

7.9

phalanx II-2 length phalanx II-2 prox. anteropost length

3.5

phalanx II-2 prox. width

3.2

3.4 3.4

phalanx II-2 distal width phalanx II-3

2.5

2.9

Forelimb Osteology and Biomechanics of Tyrannosaurus rex • 91

Materials: Parts of specimens used in this study include: CMNH 9380 (holotype, formerly AMNH 973) scapula and humerus; DMNH 30665 (casts of FMNH PR 2081, formerly BHI 2033) right humerus, ulna, radius, metacarpals I and II, phalanges II-I and 2, unguals 1-2 and II-3; MOR 555 parts or most of the left scapula, coracoid, humerus, ulna, radius, metacarpals I and II, carpals, and phalanges I-I, II-I, and 2. Measurements are given in table 9.1. on page 91. Institutional Abbreviations: AMNH, American Museum of Natural History; BHI, Black Hills Institute of Geological Research; CMNH, Carnegie Museum of Natural History; DMNH, Denver Museum of Natural History; MOR, Museum of the Rockies. Anatomical Abbreviations: Lig. collaterale Lc Lig. interosseum radioulnare Liru M. brachialis Mb M. biceps Mbi M. "biceps" tubercle Mbit Mcd M. coracobrachialis dorsalis (two heads) M. Coracobrachialis ventralis Mcv Mdm M. deltoideus minor Mdmj M. deltoideus major Mdms M. deltoideus major superficialis Mdmv M. deltoideus major ventralis M. extensor carpi radialis Mecr Mecu M. extensor carpi ulnaris Meld-I M. extensor longus digiti I Meld-II M. extensor longus digiti II pars distalis Memu M. extensor metacarpi ulnaris Menu M. entepicondylo-ulnaris Meu M. ectepicondylo-ulnaris Mfer M. flexor carpi radialis Mfcu M. flexor carpi ulnari Mfd-I M. flexor digiti I Mflu M. flexor carpi ulnaris Mfld-II M. flexor longes digiti II Mi M. interosseus M. latissimus dorsi MId Mpp M. pectoralis profundus Mps M. pectoralis superficialis M. pronator superficialis et profundus Mpsp Ms M. spinatus Msh M. scapulohumeralis M. subscapularis Mss M. supinator Msu M. serratus ventralis caudalis Msvc Msvcr M. serratus ventralis cranialis M. triceps Mt 92 • Kenneth Carpenter and Matt Smith

Mth Mts Mumd Mumv nas Ref

M. triceps humeralis . M. triceps scapularis M. ulnometacarpi dorsalis M. ulnometacarpi ventralis nonarticular surface Retinaculum m. extensor et flexor metacarpi ulnaris

Osteology and Myology The osteology and myology of the forelimb are intimately connected and are treated together. Most myological studies of dinosaurs have been done with the hind limbs (e.g., Romer 1923; Galton 1969). Only a few studies have included the forelimbs. These include reconstructions of Anatosaurus (= Edmontosaurus) (Lull and Wright 1942), Apatosaurus (Filla and Redman 1994), Chasmosaurus (Russell 1935), Euoplocephalus (Coombs 1978), Iguanodon (Norman 1986), Plateosaurus (Huene 1907-1908), Syntarsus (Raath 1977), Deinonychus (Ostrom 1974), and numerous dinosaurs by Paul (1986). Muscle terminology used below is that of Berge (1979) for birds because of the close phyletic relationship between theropods and birds (e.g., Gauthier 1986; Holtz 1994). Use of avian muscle terminology is a departure from previous forelimb studies, which rely on crocodilian muscle patterns. Furcula. A fused furcula is widespread among theropods (Chure and Madsen 1996; Makovicky and Currie 1998), including Tyrannosaurus bataar (Sabath pers. comm.), so is expected for T. rex. The furcula is similar in most theropods, being a widely open U- or V-shaped structure. Where found articulated, it connects the anterodorsal edge of

- ------------------------- -----------------~~-~

Msh

Msvcr Mss Ms

the acromion plate scapulae. As in birds, one branch of the M. deltoideus major probably originated there (fig. 9.1). Scapula (fig. 9.2). The scapula closely resembles that of the tyrannosaurids Gorgosaurus and Albertosaurus, although there are important differences. The acromial process of the scapula is proportionally taller and the posterior edge more round than in Gorgosaurus and Albertosaurus. The process is concave above the glenoid for the M. triceps scapularis, although it is not certain how much of the area the muscle occupied. The bone is thin and easily damaged, and is best preserved in CMNH 9380 and FMNH PR 2081. The bone thickens

Figure 9.1. Scapula-coracoid and furcula for Tyrannosaurus rex showing muscle origin sites. The furcula is not yet known for T. rex, but is known for T. bataar. See list of anatomical abbreviations for muscle names.


along the margins, especially along the posterior margin and along the contact with the coracoid. This thickening along the coracoid margin is mostly developed on the medial side, immediately above the glenoid. The anterodorsalmost part of the acromial process overhangs the coracoid (best seen in CMNH 9380 Osborn 1906, fig. 6). The sutural surface of the acromion, where it articulates with the coracoid, is very rugose in individuals where the two bones are not coossified. The glenoid is discussed below. In lateral view, the scapular blade is long and straplike, a condition typical of that of many large theropods (e.g., Allosaurus and Albertosaurus). The blade is bowed dorsally, although the degree of this bow is variably developed; it is more prominent in CMNH 9380, than in MOR 555. Functionally, the bow countered the stresses of the M. scapulohumeralis that occupies most of the lower half of the blade. Distally, the scapular blade flares, especially along its dorsal margin, for the caudal portion of the M. trapezius. This flair is even more extensively developed in Albertosaurus (see Parks 1928, fig. 1). The lateral surface of the flair is flat to slightly convex in T. rex. A keel is developed on the ventral margin of the flair for the M. serratus caudalis. In crosssection, the blade is oval to lanceolate (fig. 9.2E,F). The scapula is lateromedially thickest above the glenoid, where it is expanded into a narrow shelf on the medial side (figs. 9.2C, 9.3A). This shelf expands posteriorly onto the blade, where it forms a broad, roughly triangular surface for the M. subscapularis. Coracoid (fig. 9.2). A complete coracoid is known for FMNH PR 2081 and a partial one for MOR 555. The coracoid is a large, oval, concave plate of bone that is pierced by the coracoid foramen. A large. deep chamber is present in the floor of the foramen (MOR 555). Tht lateral surface is demarcated into four areas, three of these separated by broad, low ridges, and the four by a prominent one. These area~ probably indicate areas for the origin of the M. deltoideus major ane minor and the two branches of the M. coracoideus dorsalis (fig. 9.1) Also on the lateral surface, dorsal and anterior to the glenoid, is a larg, distinct tubercle called by Ostrom (1974) the biceps tubercle (Walke [1990] denies that this is the same feature named by him in Spheno suchus). One head of the biceps may have originated there, althougJ usually this muscle has a more extensive origin (possibly the area for M deltoideus major ventralis (fig. 9.1) is actually for one head of the:tV biceps). The M. coracobrachialis ventralis occupies the lower portio! of the coracoid medially. The anteroventral margin of the coracoid I thickened into a distinct lip laterally and medially, although it is be' developed on the medial side. The glenoid is developed on the scapula-coracoid suture (fig. 9.2 The coracoid portion of the glenoid is considerably larger in Tyrann, saurus than it is in Gorgosaurus. In sagittal section, the glenoid longer and the anterior rim much less developed than in Gorgosaun (fig. 9.3B). In cross-section, the glenoid is broader, slightly concave, al has a better developed medial wall than Gorgosaurus. The scapuJ portion of the glenoid is triangular in Tyrannosaurus, although consi

94 • Kenneth Carpenter and Matt Smith

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erably longer than wide. A thin wall occurs along the medial rim marking the edge of the cartilage cap. The entire glenoid is parallelogram-shaped in Tyrannosaurus and subrectangular in Albertosaurus. This difference is due to the greater width of the scapular and coracoid across the glenoid in Tyrannosaurus. In addition, there is a notch on the lateral margin of the glenoid, along the scapula-coracoid suture in Gorgosaurus, but not Tyranno-

Figure 9.2. Scapula-coracoid of Tyrannosaurus rex: FMNH PR 2081 in (A) medial view (from a photograph); MOR 555 in (B) medial, (C) ventral (arrow denotes medial "shelf"), and (D) lateral views; (E) and (F) crosssections. Scale: 10 em.


medial

lateral

lateral

medial

A medial

medial

lateral

lateral

..

Figure 9.3. Comparative sections of the glenoid in T. rex (A) and Gorgosaurus (B). Lower sections in (A) and (B) are sagittal sections comparing glenoid depth. Upper two sections in (A) and (B) are cross-sections. Note medial shelf (arrow) in (A) (upper left).

B saurus. In sagittal section, the glenoid of Tyrannosaurus is a shallow depression, rather than a deep depression as in Gorgosaurus (fig. 9.3A vs. 9.3B). In cross-section, the glenoid is almost flat in Tyrannosaurus and concave in Gorgosaurus. Humerus. Two different morphs of humeri are known (figs. 9.4, 9.5) that seem to indicate sexual dimorphism, as also noted by Larson (1994). Humeri CMNH 9380 and FMNHPR2081 have a pronounced medial curve proximally and are associated with robust skeletons (femur diameter/length = 0.41). The humerus of MOR 555 is almost a straight cylinder and is associated with a gracile skeleton (femur diameter/length = 0.37). The same two humeri morphs are also seen in Tyrannosaurus bataar (see Maleev 1974, figs. 33, 40B). The robust skeletons have been interpreted as females and the gracile skeletons as 96 • Kenneth Carpenter and Matt Smith

male (Carpenter 1990), a conclusion similar to that reached separately by Raath (1990) for Syntarsus. Cortical bone occupies 75% of the humeral diameter at midshaft. The articulating surface of the humeral head faces dorsally and slightly posteriorly so that the head overhangs the shaft (fig. 9.4B,D). The margins of the articular surface, originally capped by the articular cartilage, are marked by a rim and tiny vertical rugosities. These features delineate the articular capsule and the position of the glenohumeral and coracohumeral ligaments. In addition, scars around the head indicate the insertion points (fig. 9.6) for the M. subscapularis, M. scapulohumeralis, M. spinatus, M. deltoideus minor, and M. coracobrachialis ventralis, and origins for the M. biceps and M. triceps humeralis (posterior head). On the humeral shaft, the deltopectoral crest is well developed and in lateral profile forms a broad-based triangle. The crest extends from just below the head to about one-third

Figure 9.4. Humerus of Tyrannosaurus rex (FMNH PR 2081) in (A) anterior, (B) lateral, (C) posterior, (D) medial, (E) proximal, and (F) distal views. Note paleopathology (arrow) at the site of the medial head of the M. triceps humeralis. (G) compares proximal end (heavy line) with distal end (light line). Scale: 10 em.


F , I

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Figure 9.5. Humerus of Tyrannosaurus rex (MOR 555) in (A) anterior, (B) lateral, (C) posterior, (D) medial, (E) proximal, and (F) distal views. Scale: 10 em.

of the humerus. Two heads of the M. pectoralis insert on the anterior and posterior sides of the crest. Elsewhere on the shaft are the insertions for the M. coracoideus dorsalis (combined heads), M. deltoideus major and M. latissimus dorsi, and the origins for M. triceps humeralis (medial head) and M. brachialis. Distally, the radial condyle is larger than the ulnar condyle and both project anteroventrally. The articular surface of the epicondyles extend onto the anteroventral surface, however, much less so than in other theropods, such as Allosaurus. The small size of the epicondylar surfaces limits the amount of flexion and extension that could occur at the elbow (for further discussion of this implication see below). Proxi-


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mal to the epicondyles, the radial fossa and ulnar fossa are partially separated by a ridge of bone; these fossa housed the synovial capsules of the elbow; on the posterior side, the olecranon fossa is practically nonexistent. The ulnar fossa is pierced by a single nutrient foramina in FMNH PR 2081 and a pair in MaR 555; this difference probably reflects individual variation, not sexual dimorphism. Sexual dimorphism, however, is reflected in the greater width across the epicondyles, with FMNH PR 2081 being about 12% wider, reflecting her greater robustness. The M. supinator, M. ectepicondylo-ulnaris, M. pronator superficilias et profundus, and M. flexor carpi ulnari originate around the distal end of the humerus. The origins for all extensors and flexors could not be found because some of them originate on the fascia covering the elbow. There is a peculiar pathology on the medial side of the humerus of FMNH PR 2081. This pathology consists of an arclike, overhanging rim of exostosis and a spur located dorsally (fig. 9.4C,D). The surface of the humerus in visible within the pathology and is only slightly modified from its normal bone surface appearance. What little difference there is, consists of a small patch of irregular, hyperostosic bone beneath the overhang. The pathology occurs at the origin of the medial head of the M. triceps humeralis suggesting that the exostosis is in

D Figure 9.6. Origin and insertion sites on the humerus of Tyrannosaurus rex: (A) anterior, (B) lateral, (C) posterior, and (D) medial. See list of anatomical abbreviations for muscle and ligament names.


Figure 9.7. Ulna of Tyrannosaurus rex: FMNH PR 2081 in (A) anterior, (B) lateral, (C) posterior, (D) medial, (E) proximal, and (F) distal views; MOR 555 in (G) anterior, (H) lateral, and (I) medial views. Radius of Tyrannosaurus rex: FMNH PR 2081 in (j) anterior, (K) lateral, (L) posterior, (M) medial, (N) proximal, and (0) distal views; MOR 555 in (P) anterior, (Q) lateral, and (R) medial views. Scale: 10 em.

A

B

response to partial avulsion of the muscle due to abnormally high stress at the muscle-bone interface. The implications for this are discussed further below. Ulna. The ulna is a stocky, thick-walled bone (fig. 9.6). In MOR 555 the cortical bone occupies 90% of the cross-sectional area of the ulnar shaft as measured 6 cm below the olecranon notch (comparable measurements are not available for FMNH PR 2081). The olecranon is very prominent, although it is more developed in FMNH PR 2081 than MOR 555. A very large scar is present on the posterior side for the M. triceps and for the fascia sheet (retinaculum) for several extensors and flexors (e.g., M. extensor metacarpi ulnaris) (fig. 9.8C,D). The olecranon notch is subtriangular in shape viewed dorsally and most of it slopes laterally towards the radial facet (fig. 9.7E). The notch is considerably wider in FMNH PR 2081 than in MOR 555, reflecting the difference in distal humeral width (fig. 9.7A vs. G). The radial notch is not very distinct (fig. 9.7E). Its posterior border, which corresponds to the Tuberculum ligamentum collateralis ventralis of birds (Baumel 1979), slopes laterally and does not contribute to the articular surface for the humeral ectocondyle, but lies beneath the intercondylar sulcus between the epi- and ectocondyles of the humerus. Instead, the tubercle supports a collateral ligament that extends to the posterolateral corner of the

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ectocondyle. Furthermore, the lateral overhang of this tubercle provides a gliding surface for the tendon of the M. flexor carpi ulnaris, as in birds. A shallow vertical groove on the lateral surface of the olecranon was occupied by the ulnar nerve. A prominent tubercle beneath the radial notch was probably for the insertion of the biceps. Insertion of the biceps on both the ulna and radius occurs by a divided tendon in birds (Chamberlain 1943). The ulnar shaft is compressed laterally and is longer anteroposteriorly to counter the stresses of the M. biceps (figs. 9.7,9.8). Several extensors and flexors of the manus originate on the shaft (fig. 9.8). Distally, the ulna is wider than long with a low ridge extending obliquely across part of the articular face to a styloid process at the anteromedial corner for the ulnar collateral ligament (fig. 9.7F). The ulnar shaft near the humeral and carpal articular surfaces is rugose for the various ligaments binding the bones together. The ulna of FMNH PR 2081 is more robust than that of MOR 555. Radius. The radius is a slender bone, subtriangular in cross-section (fig. 9.7). The surface of the radial head is D-shaped in dorsal view, with the straighter edge abutting against the ulna (fig. 9.7N). This flat surface prevents rotation of the radius, so that the human type of supination and pronation of the manus cannot occur. The result is that the manus faces medially, not ventrally, as is usually shown in life restorations by artists. A low, oblique ridge is present across the proximal surface of the radial head separating the articular surface for the ectocondyle of the humerus anterolaterally, from the nonarticular surface posteromedially. The small, triangular nonarticular surface lies opposite the Tuberculum ligamentum collateralis and also underlies the intercondylar sulcus between the distal condyles of the humerus. The shaft surface is very rugose just below the articular surface for the annular ligament that binds the bone to the ulna. The cortical bone occupies 82 % of the cross-sectional area as measured 5 em below the humeral articular surface. The radial shaft has a pronate twist along its length. On the medial surface, just below the radial head, is a small rugose area for the insertion of the M. biceps (fig. 9.8). This insertion is opposite that on the ulna for the M. biceps. The shaft of the radius has origins for several flexors and extensors for the manus (fig. 9.8). The distal end is wider than long (fig. 9.70) and somewhat oval. A styloid process is developed at the anterolateral corner for the radial collateral ligament. The radius of FMNH PR 2081 is more robust than that of MOR555. Carpals. Two coossified carpals were found with MOR 555 (fig. 9.9A-C), but this may not represent the total number originally present (see Holtz 1994 for further discussion). Maleev (1974) reports the presence of a large, rectangular disclike intermedium in Tyrannosaurus bataar, whereas Barsbold (1983) reports the presence of four carpal elements in T. bataar; interestingly, the intermedium resembles that of Allosaurus (Gilmore 1920) and Acrocanthosaurus (Currie and Carpenter 2000), but not Gorgosaurus (Lambe 1917). In MOR 555 the two carpals probably represent the ulnare and radiale because a fragment of the distal end of the ulna(?) adheres to one of them, the ulnare(?). The presumed ulnare is slightly smaller than the radiale, a condition also Forelimb Osteology and Biomechanics of Tyrannosaurus rex • 101

Lc

Mfld-IT Mem Mfeu

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Mumd

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A B

D Meld- IT

Msu

Mfd-I-t-.... Figure 9.8. Origin and insertions sites on the lower forelimb bones of Tyrannosaurus rex. Ulna in (A) anterior, (B) lateral, (C) posterior, and (D) medial views. Radius in (E) anterior, (F) lateral, (G) posterior, and (H) medial views. (1) proximal ends of ulna and radius (heavy line), distal end of the humerus (light line), and outline of the humeral epicondyles (dashed line). Note the nonarticular surface (nas) of the ulna and radius. See list of anatomical abbreviations for muscle and ligament names.

Liru

H radius ectocondyle

humerus

I

reported for Gorgosaurus (Lambe 1917). Both carpals are small wedges that taper toward one another. There is a slight rim around the articular surfaces for the synovial membrane and for various ligaments connecting the bones to the ulna, radius, and metacarpals. Metacarpal I. This bone is short, stocky, asymmetrical, and Dshaped in cross-section (fig. 9.9C-H). The proximal end is D-shaped in dorsal view (fig. 9G), is slightly concave for a carpal (part of the intermedium?), and slopes dorsomedially. The surface for articulation with metacarpal II is a depression, or synovial cavity, rimmed with rugosity for the collateral ligaments. The synovial cavity is deeper in FMNH PR 2081 than in MOR 555 and is probably due to individual


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Figure 9.9. (above) Carpals and metacarpals of Tyrannosaurus rex. Carpals (MaR 555) in (A) anterior, (B) lateral, and (C) proxi~al views; r = radiale, u = ulnare. Metacarpal I: FMNH PR 2081 in (D) dorsal, (E) medial, (F) palmar, (G) lateral, (H) proximal, and (I) distal views; MaR 555 in (J) dorsal and (K) medial views (arrows show groove for radial artery to digit I). Metacarpal II: FMNH PR 2081 in (L) dorsal, (M) medial, (N) palmar, (0) lateral, (P) proximal, and (Q) distal views; MaR 555 in (R) dorsal and (S) medial views. Scale: 4 em. Figure 9.10. (left) Origin and insertion sites for the articulated metacarpal I and II of Tyrannosaurus rex in (A) dorsal, (B) palmar, and (C) proximal vIews.


Figure 9.11. (opposite page) Phalanges of Tyrannosaurus rex. Phalanx 1-1 (MOR 555) in outline (upper portion missing) in (A) dorsal, and (B) lateral views. Phalanx 1-2 (ungual) (FMNH PR 2081) in (C) medial, (D) dorsal, (E) lateral, and (F) palmar views. Phalanx II-1: FMNH PR 2081 in (G) dorsal, (H) medial, (I) palmar, (J) lateral, (K) proximal, and (L) distal views; MOR 555 in (M) dorsal and (N) medial views. Phalanx II-2: FMNH PR 2081 in (0) dorsal, (P) medial, (Q) palmar, (R) lateral, (S) proximal, and (T) distal views; MOR 555 in (V) dorsal and (V) medial views. Phalanx II-3 (FMNH PR 2081) in (W) medial view. Scale: 4 em.

variation. Ventral to the synovial cavity, just above the medial distal condyle, is a transverse groove (fig. 9.9C,D,I,]) that was probably for the radial artery. In humans, the radial artery extends along the anterior side of the forearm to the wrist, where it wraps around to the dorsal side of the thumb and passes into the palm between metacarpal I and II (Grant 1943; Gray and Goss 1973). This indirect passage to the palm prevents the M. opponeus pollicis from blocking blood flow when it flexes; an analogous situation must have also occurred in T. rex involving the M. adductor digiti I (M. adductor alulae of birds). The distal condyles of metacarpal I in T. rex are not equal, the external one being larger and extending further. A similar condition occurs in many dinosaurs (e.g., Allosaurus, Plateosaurus; see Gauthier 1986) and causes digit 1 to angle away from the axis of the manus. The biomechanical significance for this is discussed in further detail below. A lesion of secondary gout (due to uric acid buildup) is present on the external condyle of the metacarpal of FMNH PR 2081, as reported elsewhere (Rothschild et al. 1997). The damage is such that it affected the articular cartilage and part of the synovial capsule; leakage of synovial fluid may have occurred. Metacarpal II. This metacarpal is almost twice as long as metacarpal I (fig. 9.9K-R). The proximal end is rectangular (fig. 9.9D) and also slopes dorsomedially. A rim denotes the edges of the articular cartilage and synovial capsule that once covered the joint surface. The external or lateral surface bears two facets at the corners for articulation with metacarpal I. Between these two facets is a shallow depression that is the counterpart to the synovial cavity of metacarpal I. On the medial side, opposite the metacarpal I facets, the corners of the articular surface overhang the shaft (fig. 9.9K,L). These tubercles are probably for insertion of the M. extensor carpi radialis and M. flexor carpi radialis. Between these two tubercles is a notch for metacarpal III, which is presumed to have been present, but is missing. The shaft is almost rectangular in cross-section and has a slight medial twist so that the lateral condyle is more palmar than the medial condyle (fig. 9.9P). The medial condyle is larger than the lateral condyle, and projects slightly lower as well (fig. 9.9K,M,Q). Scars, including a small tubercle for the collateral ligaments, are especially prominent in FMNH PR 2081. A rim around the articular surfaces denote the limits of the articular cartilage and synovial capsule. A gout lesion is present in FMNH PR 2081 as well (Rothschild et al. 1997). Phalanx I-I. Only the ventral half of this phalanx is known (fig. 9.11A,B). It resembles that of Gorgosaurus, although the shaft does not show the degree of twist along its axis (the biomechanics for this are discussed in further detail below). The medial distal condyle is slightly larger than the lateral. Phalanx 1-2. This manal ungual (fig. 9.llC-F) is laterally compressed and the cotyles slightly asymmetrical in size; a rim demarcated the edge of the articular cartilage and synovial capsule of the joint. Ventrally the ungual surface is somewhat flat, and the entire surface slopes laterally. There is no "lip" extending above the articular cotyles for the insertion of the M. extensor digitorum. The lateral and medial


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v Forelimb Osteology and Biomechanics of Tyrannosaurus rex • 105

surfaces around the articular cotyles are rugose for the collateralligaments. Ventrally, the tubercle for the surficial tendon of the M. flexor digitorum is prominent and inset from the articular cotyles, thus forming the characteristic ungual "step" or "heel." The palmardigital artery apparently crossed one side to the other dorsal to the synovial sheath encasing the M. flexor digitorum. On each side of the claw core, ungual arteries extended down each side of the claw core. The dorsal digital arteries apparently joined the ungual arteries at a Y-shaped junction on each side of the ungual, dorsal to the tubercle. Phalanx II-l. This is a very unusual bone and could easily be mistaken for a pedal phalanx (fig. 9.11G-N). Its identification, however, is certain because an identical bone is present in T. bataar (Maleev 1974, fig. 36). The proximal end is triangular (fig. 9.11K) due to a very prominent tubercle for the M. extensor digitorum, which is the distal tendinous portion of the M. extensor metacarpi ulnaris. The M. interosseus dorsalis, which originated on the medial surface of metacarpal II, may also have partially inserted on the tubercle. This extensor tubercle shows variation in size, being more prominent in FMNH PR 2081. Ventrolaterally are scars for the insertion of M. interosseous and the deep tendons of M. flexor digitorum. The articular cotyles for reception of metacarpal II are asymmetrical in size, reflecting the difference in the distal articular condyles of that metacarpal; the cotyles are separated by a low ridge. Ventrally, there is a pair of small bumps below the cotyles for collateral ligaments and a rugose area between them for the tendon of the M. flexor carpi radialis. Distally, the articular condyles are asymmetrical, with the lateral condyle larger than the medial. Furthermore, the condyles face ventrally and not distally indicating that phalanx II-2 rotated palmar. Laterally, there are no collateral fossa for the collateral ligaments. Interestingly, phalanx II-l is larger in MOR 555 than in FMNH PR 2081 (fig. 9.11 G,H vs. M,N), a reversal of the trend seen in the other forelimb bones. Phalanx II-2. The articular cotyles are shallow, asymmetrical, and separated by a low ridge. The proximal end is triangular (fig. 9.115) because of a prominent tubercle on the dorsal side for a tendinous slip of the M. extensor digitorum. Ventrolaterally are two small, raised scars for the collateral ligaments; a scar ventrally between them is for the insertion of the M. flexor digitorum. The shaft is slightly bent medially (Fig. 9.11 O,U). Medially, on the ventral side, is a rugose arc in FMNH PR 2081 and a low tubercle in M 0 R 555; these are the terminal insertion sites for the deep tendons of the M. flexor digitorum. The distal articular condyles face ventrally more than dorsally. Dorsolaterally, this is a fossa for the collateral ligament (fig. 9.11RN); a shallow depression is present medially (fig. 9.11P,V). In FMNH PR 2081 there is a small piece of calcified Vincula brevia, the tendon that attaches to the M. flexor digitorum, ventrally between the distal condyles (fig. 9.11 Q). The medial condyle in FMNH PR 2081 shows the degenerative condition of rheumatoid arthritis, which in this case, is connected to renal failure (Greenfield 1986), as evidenced by the gout lesions on the metacarpals. Phalanx II-3. This ungual (fig. 9.11W) is tentatively identified as 106 • Kenneth Carpenter and Matt Smith

belonging to T. rex because it was found associated with FMNH PR 2081. It differs from the other ungual in being much more laterally compressed and in the more dorsally placed grooves for the ungual arteries.

Biomechanics Having described the osteology and myology of the forelimb of T. rex, we now examine the forelimb biomechanically in order to answer Gould's question quoted at the beginning of the chapter. This analysis is done by first determining which of two mechanical systems the forelimb best represents, and then determining the power of the forelimb based on that system. The analysis compares the short forelimb of T. rex with those of Deinonychus, a long-forelimbed theropod, Allosaurus, an intermediate forelimbed theropod, and a human forelimb as a standard. Materials used include: Deinonychus antirrhopus coracoid (YPM 5236), scapula and humerus (AMNH 3015), ulna and radius (YPM 5220), and manus (YPM 5236); Allosaurus fragilis forelimb (DinoLabs uncatalogued); Tyrannosaurus rex forelimb (MOR 555); and Homo sapiens (MOR uncatalogued, commercially obtained, sex unknown). Preliminary results were previously presented by Smith and Carpenter (1990) and Carpenter and Smith (1995). Mechanical Analysis. The forelimb is a third-class lever whose motive force (MF) is located between the resistive force (RF) and the axis of rotation (motive force as used here is the pull of a muscle on a bone, resistive force is the resistance of that bone to being moved, as when it is under load; see fig. 9.12). The motion of the limb may be viewed as one of two mechanical systems. One is a velocity-based system (VBS), typified by cursorial mammals, in which the insertion of limb muscles is close to the axis (allowing more rapid limb movement). The other is the force-based system (FBS), typified by fossorial mammals, in which the inserting limb muscles are farther from the axis (more power to the limb). Which of these two systems is in operation is determined by the ratio of the resistive force to the motive force. The resultant numerical value, the mechanical advantage (MA), is high in a VBS and is low in an FBS because MA decreases as the resistive force moves away from the axis of rotation. Although this dichotomous division is simplistic and in the real world there is actually a continuum between the two systems, recognition of only two systems makes analysis of the T. rex arm easier. For the purpose of analysis, we follow Kreighbaum and Barthels (1985), who recognize that force (mass times acceleration) has four properties: (1) magnitude of force, (2) direction force is applied, (3) line of action (follows the direction of force), and (4) point of application (the attachment of the force that is being applied to the bone). If the line of action passes off-axis (eccentric force), a torque is produced resulting in a turning effect. The off-axis distance to the line of action is called the force arm. The motive force arm (MFA) and resistive force arm (RFA) is the distance from the axis of rotation to the line of action (MF or RF) and will always be perpendicular to the line of action. The equation


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1---------iIRFA T = F (dL) is used to calculate torque, where T is torque, F is force, and dL is the perpendicular length of the force arm. Force is measured in newtons (N) and torque in newton-meters (Nm) or torque units. To calculate MA, either MF or RF must be known or assumed. For convenience, a MF of lOON was used, with the torque units for MF and RF the same to keep the lever arm static (i.e., the lower arm remains perpendicular to the upper arm). Data used in the analysis is presented in table 9.2, with limb lengths standardized to the shortest humerus (Deinonychus) in order to make comparisons equal. The following formulas were used: MFxMFA=T RFxRFA = T RF/MF= MA Using the data in table 9.2 for Homo, lOON x 0.25m = 2.5Nm RF x 0.197m = 2.5Nm RF = 2.5NrnlO.197m = 12.7 100N/12.7N = 7.9 An idealized force-based system would have an MA of 1, whereby one unit of motive force is needed to stabilize one unit of resistive force and an idealized velocity-based system would have an MA of 100. However, such values are not reached in nature because a multitude of forces are in operation on the system at anyone time. In this study, the MAs range from 5.2 (Tyrannosaurus-FMNH PR 2081) to 21.7 (Deinonychus), with the highest value approaching that of a modern eagle, 108 • Kenneth Carpenter and Matt Smith

TABLE 9.2

Data Used to Determine Mechanical Advantage (see fig. 9.12) and Numerical Results; MFA and RFA standardized (see text). Homo sapiens Deinonychus

Allosaurus

Tyrannosaurus FMNH PR 2081

'F ,FA FA F lA

lOON 0.25m 0.197m 12.7N 7.9

lOON O.OlOm 0.215m 4.6N 21.7

lOON 0.052m 0.30m 17.3N 5.8

lOON 0.042m 0.22m 19.25N 5.2

_quila chrysaetos, with an MA of 25 (Smith unpub!.). Not surprisingly, le overall shape of the humerus in Deinonychus is similar to that of the 19le, suggesting similar stresses on the forelimb. The higher MA value Lthe eagle may be due to the glenoid being positioned more laterally ) that the MF vector is more perpendicular to the scapulocoracoid. '1e high MA value indicates that the forelimb of Deinonychus is a Jocity-based system (VBS), where reaching to grasp prey is more ,lportant than having the strength to hold the prey. The limb motion 80ciated with grasping prey may be a precursor to the flight stroke birds (see Gauthier and Padian 1985). Homo sapiens has an MA of 9. The close attachment of the MF to the axis, the resultant short [FA and long radius is a compromise between an FBS and a VBS. The latively close insertion of the MF to the axis gives the radius a melanical advantage in velocity. The MA for the Allosaurus is 5.8 and therefore considered an FBS, where arm strength is important for aIding prey. For Tyrannosaurus the lowest MA was 5.2. The scapula ld coracoid are proportionately the largest in the study, indicating ore surface area for the origin and insertion of various muscle groups. early then, the forearm of T. rex is a force-based system, in which arm -ength is more important than quickness of grasping. Power Analysis. Having established that the forearm of T. rex is a reed-based system, we now examine the power of the forearm. To Llculate the estimated force of a single muscle in a third-class lever, the ass-sectional area of the inserting tendon can be measured based on ,e size of the scar of insertion on the bone. There is a slight flaring of .e tendon at its insertion, causing a slight increase in the size of the ndon at its insertion (personal observations), therefore the results for ndon diameter may be slightly overestimated. The tensile strength of ndon is known, allowing the maximum working range (MWR) and lrmal working range (NWR) to be calculated. The muscle we have l entified as the major MF in our study is the M. biceps. In humans, the 'sertion is only on the humerus (radial tuberosity), whereas in T. rex, in birds, there is a dual insertion on the radius and ulna (see above). 'e have assumed for the purpose of our study that MF is equally Lvided between these two insertions. Again, the human arm is used as basis for comparison, although measurements are not standardized ~cause absolute comparisons are required. Forelimb Osteology and Biomechanics of Tyrannosaurus rex • 109

The surface area of the radial tuberosity of the human radius examined was 130 mm 2. The tensile strength of an average tendon is 100 N/mm 2 (Vogel, 1988). Tendons also have a built-in safety factor relative to the isometric contraction of -3 (= MWR) and a normal working range is one-third of the safety factor (= NWR) (Biewener, pers. comm. to Smith 1987). Using the formula: tendon tensile strength/area 2 x radial tuberosity area 2 = estimated tendon tensile strength (approximates muscle strength) the result is: 100N/mm 2 x 130mm 2 = 13,OOON With a one-third safety factor: 13,OOON/3 = 4,333N (= MWR), and a normal working range of one-third of the safety factor: 4,333N/3 = 1,444N (= NWR) Thus, the tensile strength of the human arm used in this study is 1,444N for the M. biceps. With MF = tensile strength; MFA = O.04m; and RFA = 0.315m. Solving for RF using the formula: MFxMFA =T RFxRFA= T 4,333N X 0.04m = 173Nm RF x 0.315m = 173Nm RF = 550N (= MWR), and 1,444N x O.04m = 58N RF x 0.315m = 58N RF = 184N (= NWR) Converting Newtons to kilograms (9.81 kglN), the resistive force maximum working range (no safety factor) is 56 kg, and the normal working range (including safety factor) 18.75 kg for the skeleton used in the study (-180 cm tall). An estimation of the size of the M. biceps can now be calculated. The strength per cross-sectional area of a muscle has been calculated to be between 4 kg/cm 2 and 8 kg/cm 2 in humans (Ikai and Fukunaga 1968) and 4 kg/cm 2 to 6 kg/cm 2 regardless of taxon (Schmidt-Nielsen 1975). An average strength of 5 kg/cm 2 was used to determine the crosssectional area. The following formula is used: MF(kg)/strength kg x cm'2 = cross-section cm 2 Using the previously determined MF of 147 kg (=1,444N) for the normal working range: 147kg/5kg x cm'2 = 29.4cm 2 Thus, the estimated cross-section of the human M. biceps in this study is 29 cm 2, or a diameter of 6.1 cm. For T. rex (FMNH PR 2081), the area for the insertion of M. biceps on the radius is 132.7 mm 2and on the ulna is 176.6 mm 2. Treating these as separate insertions and with MFA = 0.055m, and RFA = 0.29m: tendon tensile strength for radius: 100N/mm2 x 132.7mm 2 = 13,270N MWR: 4423N x 0.055m = 243N RF x 0.29m = 243N RF = 838.8N = 85.5kg. 110 • Kenneth Carpenter and Matt Smith

NWR: 1474N x 0.055::: 81N RF x 0.29m::: 81N RF ::: 279.6N ::: 28.5kg. and ulna: 100Nmm 2 x 176.6mm2 ::: 17,660N MWR: 5887N x 0.055m ::: 323.8N RF x 0.29m::: 323.8N RF::: 1116.5N::: 113.8kg. NWR: 1962 x 0.055m::: 107.9N RF x 0.29m ::: 107.9N RF::: 371N::: 37.9kg. For the tendon, hence for the M. biceps of T. rex, MWR ::: 1955.3 (::: 199kg.) and NWR ::: 650.6N (66.3kg). The diameter of M. biceps, based on the normal working range, is 9.2 cm. Finally, the limb bones have unusually thick cortical bone. Curry and Alexander (1985) have examined the significance of this in modern animals and their results are applied here. Using their formulas: ratio of marrow cavity radius/bone radius::: K, which is related to bone radius/cortical thickness (Rlt). Applying their formulas to T. rex (MOR 555), for the humerus K ::: 0.25, Rlt::: 1.34; radius K ::: 0.18, R/t ::: 1.22; ulna K ::: 0.1, Rlt::: 1.11. All these values indicate bone selected for ultimate strength or impact loading, rather than for static strength or stiffness.

Discussion Our analysis of the osteology, myology, and biomechanics of the forelimb of Tyrannosaurus rex show that the arm was stoutly built and well muscled. Compared with a human, the M. biceps in T. rex was 3.5 times stronger per N of force in both the maximum and normal working ranges (other flexors, e.g., M. brachialis, were not considered and would certainly increase the arm strength). Such high strength suggests to us that the arms were not atrophied structures nor useless appendages, but rather had a definite function that we believe was to clutch struggling prey. In support of this hypothesis, we note that the range of motion (ROM) for the forelimb from maximum extension to maximum flexion varies considerably among the taxa used in this study, as shown in table 9.3 (tendinous and muscle tissue restrictions of motion were not taken into account, except for Homo; these restrictions prevent the joints from achieving their maximum angle as determined from joint morphology only). ROM was determined from the rim for the articular cartilage on both surfaces of the joint. The range of maximum flexion and extension must be such that the rim for the articular cartilage did not pass into the joint (hyperflexion or hyperextension) (for further discussion, see Carpenter et al. 1994). The greatest ROM is the long arms of the human. Although, at 7.9, the mechanical advantage was rather low for the long lever arms, this seems to be a compromise between a velocity-based system and a force-based system. The second greatest range of motion is Deinonychus, which has a long forelimb, or


long lever arms, and a very high MA value, typical of a VBS, for rapi, reaching out to grasp. The long cursorial running legs (tibia + metat, sals longer than femur) and long forelimbs indicate pursuit and gras ing of prey. Allosaurus has a more restricted ROM, and proportional shorter arms relative to hind limb length than Deinonychus or Hom In addition, the MA of the moderately short lever arms is very 10indicative of a FBS in which clutching prey is more important th reaching out to grasp prey. TABLE 9.3 Range of Movement for Taxa Used in This Study Taxon

Shoulder-upper arm

Upper arm-lower arm (elbow)

Homo Deinonychus Allosaurus Tyrannosaurus Figure 9.13. Maximum range of motion of the forelimb of Tyrannosaurus rex in (A) lateral and (B) anterior views (see text for further information). Also shown is maximum extension and flexion of manus. Path of motion of the claw tips shown in dashed lines and dots. Angle of maximum movement in (A) is 25°. (C) is manus in maximum extension (light lines) and flexion (dark lines). Note that claws angle toward each other in flexion, ensuring they will not be pulled free.

'.

Finally, the least amount of forearm motion is that of T. rex (fi 9.13), which has short arms and the very low MA of an FBS. Tl limited ROM and short lever arm of the forelimb provided a very stab platform for the very powerful M. biceps. This indicates to us that tr forelimbs were used to hold a struggling prey. In support of this inter pretation, we note the pathology along the medial side of the humeru

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A 112 • Kenneth Carpenter and Matt Smith

c

B

in FMNH PR 2081. The site of damage corresponds to the medial head of the M. triceps humeralis, which serves to adduct and extend the lower arm. As noted above, the pathology is characteristic of partial avulsion caused by abnormally high stress loads. Such loads might occur while clutching a large, struggling animal, such as an adult hadrosaur (see Carpenter in press) Indeed, the straight shaft of the humerus, as compared with that of Allosaurus (see Gilmore 1920), is precisely what is expected for maximum strength per unit mass (Bertram and Biewener, 1988). Such conditions occur where the bone must resist axial compression, as it would do in this case with the powerful M. biceps (see fig. 9.12). Furthermore, the very low K and RJt values for the humerus, ulna, and radius indicate bones selected for ultimate strength or impact loading. Finally, to ensure that the struggling prey not escape while the mouth is attempting to kill it, the two ungual claws point somewhat inward (fig. 9.13C) so that they do not slip out of the prey easily.

Conclusion We conclude from our analysis of the forearms of Tyrannosaurus rex that they were used to hold prey while the head dispatched it. Such an interpretation is at odds with interpretation of T. rex as a scavenger because of the small size of the arms as advocated by Horner (1994), Horner and Lessem (1994), and Horner and Dobb (1997), but does support the fossil evidence presented elsewhere (Carpenter 2000). We envision that T. rex stalked or ambushed prey, mostly sub adult or young adult hadrosaurs (see Carpenter 2000). As with most extant predators, the mouth was used to grasp the prey. Then the short, powerful arms were used to grasp or cl utch the prey against the body to prevent its escape while the teeth were disengaged and repeated bites made to kill the prey. We also believe that, as with most predators, T. rex was opportunistic and would have scavenged when given the opportunity. Acknowledgments: We dedicate this chapter to Philip J. Currie in recognition for his work on theropods and for his many years of friendship. Tom Holtz reviewed an earlier version of this paper and we thank him for his input. We also thank several individuals for providing us with specimens or access to materials: Jack Horner (Museum of the Rockies), Peter Larson (Black Hills Institute), James Madsen (DinoLabs), John Ostrom (Yale Peabody Museum), and Charlie McGovern (Stone Company). A complete cast of the bones ofFMNHPR 2081 and of MOR 555 used in this study are housed at the Denver Museum of Natural History. This study was begun when FMNH PR 2081 was still housed at the Black Hills Institute and we thank Peter Larson for the loan of "Sue's" forelimb material. References Barsbold, R. 1983. [Carnivorous dinosaurs from the Cretaceous of Mongolia.] Joint Soviet-Mongolian Palaeontological Expedition Transactions 19: 1-117. (In Russian.) Forelimb Osteology and Biomechanics of Tyrannosaurus rex • 113

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