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Electronic Supplementary Material

Disparity and convergence in bipedal archosaur locomotion

Bates, K.T. & Schachner, E.R.

Institutional Abbreviations used in main text and supplementary data:

BHI, Black Hills Institute of Geological Research, Hill City, South Dakota, USA; MOR, Museum of the Rockies, Montana State University, Bozeman, Montana, USA; YMP, Yale Peabody Museum of Natural History, New Haven, Connecticut, USA.

  1. Material and Methods

  1. Musculoskeletal model construction

Full description of model construction methods can be found in Bates et al. (in press), but are repeated here for completeness. For comparison to the 3D model of Poposaurus gracilis (YMP 57100), the specimens of Allosaurus fragilis (MOR 693) and Struthiomimus sedens (BHI 1266) were chosen because they represent the most complete and well preserved pelvic and hindlimb osteologies within their respective theropod sub-clades. These taxa were chosen specifically because they belong to theropod sub-groups (‘carnosaurs’ [large bodied tetanurans] and Ornithomimosauria) to which bipedal pseudosuchians have been directly compared by previous researchers (e.g., Bonaparte 1984; Chatterjee 1985; Nesbitt 2007; Nesbitt and Norell 2006). The ostrich specimen (BB.3462) mounted at the Manchester Museum (UK) was chosen because mass data was available from a previous study (Bates et al. 2009a) and limb segment lengths closely matched those of specimens for which muscle architecture and moment arms have been published (Smith et al. 2006, 2007). A Polhemus FastSCAN cobra laser scanner (www. polhemus.com) was used to acquire high resolution scans of bone surface geometry of the femur, tibia, fibula, metatarsals and pes of each of the specimens and these were combined with LiDAR (Light Detection And Range) scans of pelvic bones from previous studies (Bates et al. 2009a&b). The resolution of the Polhemus scan depends on wand-object range, and is typically 0.5mm at 200mm range. The scanner is useable up to a range of 0.75m, with an accuracy of approximately 1mm at 200mm range. The scanner operates in real-time and instantly acquires a three dimensional surface image as the handheld scanning wand is swept over an object. The device works by projecting a fan of laser light onto the object while the camera views the laser to record cross sectional depth profiles. The real-time visual feedback on the laptop screen makes controlling the scan wand straightforward and enables monitoring and a high level of quality control on data capture. In order to scan the full 3D surfaces the casts of each limb bone were placed on flat surfaces scanned and then turned over and scanned again, with effort made to scan as much area as possible to ensure maximum amount of overlap in two different scans. Two separate scans of the each bone were then aligned automatically using PolyWorks (www.innovmetric.com) on basis of overlapping areas (see Bates et al. 2008 for more information). Point clouds were then surfaced using a trial version of Silverlining (www.farfieldtechnology.com) which generates smooth meshes through point-cloud data or incomplete mesh data, producing well-formed ‘water tight’ meshes for computer graphics and rapid prototyping.

The Computer-Aided Design (CAD) package Maya (www.autodesk/maya) was used to digitally rearticulate hindlimb bones and reconstruct 3D muscle-tendon units and joint centre positions. As far as possible the femora were re-orientated so that lateral surfaces of the greater and lesser trochanters faced laterally and the anterior surface of the shaft faced cranially and the axis of the femoral head was orientated at 90 degrees to the vertical. The hip joint centre was then specified as the centre of curved medial articular surface of the femoral head sitting within the acetabulum. The shank segment (tibia and fibula) was then re-orientated beneath the femur so that the medial side of the tibial crest lay in the same longitudinal plane as the medial femoral condyle and so that the femoral condyles were centred craniocaudally on top of the tibia, in accordance with Hutchinson et al. (2005, 2008). Again following Hutchinson et al. (2005, 2008), limb bones were displaced at joints to account for the thickness of unpreserved joint tissues. Specifically an additional 7.5% was added to femoral length, 5% to tibiotarsus length and 10% to metatarsal length (Hutchinson et al. 2005). The rigid pelvic segments (combined ilium, ischium and pubis) remained in the articulated positions of the skeletal mounts, but were rotated together so that the pelvis was pitched horizontally. Hip joints were modelled as 3D ball-and-socket joints and all distal joints (knee, ankle, metartarsopharngeal etc.) were treated as simple hinges with one degree of freedom (i.e. flexion/extension). All joints were considered orthogonal and the flexion and extension axes were defined as planar and perpendicular to the cranial-caudal axis of the body (the x-axis in the global co-ordinate system of the models). Rubenson et al. (2007) demonstrated that ostriches do not have orthogonal or uniformly aligned limb joint axes and it is likely that the same applied to the extinct taxa in this study. However, reconstructing joint axes is in extinct taxa is not possible due to the absence of joint tissues and the redundancy in joint articulations and movements (Gatesy et al. 2009). We therefore used the simpler, standardized approach to defining joint axes in all models, including the ostrich, to maintain comparative value. In the case of the ostrich this also allowed comparison of predicted moment arms with the experimental data of Smith et al. (2007), which also assumed simple planar orthogonal joint axes. For broad comparison with published data on theropods (Gatesy et al. 2009; Smith et al. 2006, 2007) and for subsequent modelling we estimated total Range Of Motion (ROM) at major hindlimb joints in Poposaurus using the computer model and through manual manipulation of the fossil bones. Our intention was not an extensive comparison of articular morphology and joint ROM but rather to broadly delimit the maximum plausible 3D movement given the fossilized osteology available.

Pelvic and femoral musculature in nonavian theropods was reconstructed on the basis of osteological correlates of homologous muscle-tendon origins and insertions in extant archosaurs (Hutchinson 2001a&b, 2002; Carrano and Hutchinson 2002; Bates et al. in press; Fig S1). A total of

Fig. S1. Reconstruction of pelvic and femoral muscle origins and insertion in A, Allosaurus, and B, Tyrannosaurus on the basis of archosaurian muscle homologies and the EPB of extant crocodilians and birds (image modified from Bates et al. in press, with B redrawn from Carrano and Hutchinson (2002) by E.R.S).

31 muscles were placed in each limb of the three nonavian theropod models and these are listed in Table 1 in the main text, along with their abbreviations. Muscle origin and insertions in Poposaurus were based on Schachner et al (in press). This reconstruction is based upon the direct examination of the osteology and myology of phylogenetically relevant extant taxa in conjunction with osteological correlates from the skeleton of Poposaurus. This data set includes a series of inferences (presence/absence of a structure, number of components, and origin/insertion sites) regarding 26 individual muscle or muscle groups, three pelvic ligaments, and two connective tissue structures in the pelvis, hindlimb, and pes of Poposaurus. The origin and insertion sites of muscles are listed in Table S1 and shown in Fig. S2.

A combination of via points and cylindrical wrapping surfaces were used to guide 3D muscle paths from origin to insertion points (see Sellers et al. 2003). In the absence of extensive soft tissue preservation in fossils, the precise choice of locations for via points is inevitably arbitrary but can be appropriately guided by information from homologous muscles in extant taxa and skeletal architecture. As far as possible, the 3D paths reconstructed by Hutchinson et al. (2005) for Tyrannosaurus were qualitatively followed here, as these were inferred on the basis of homologous muscle layering observed in extant archosaurs and conform to observations by the authors in dissections (Bates et al. in press; Schachner et al. press). Care was taken to ensure the relative position of via points in homologous muscles were consistent across the models, except where variation was necessitated by skeletal differences and/or to preserve muscle layering. All models in this study were constructed by the same author to minimize individual variation.



Table S1. Origin and insertion of pelvic and hindlimb muscles inferred in Poposaurus.

MUSCLE

ORIGIN

INSERTION

IT 1, 2+3

Dorsal margin of the ilium (I)

Tibial cnemial crest (I)

AMB

Depression on the lateral surface of the proximal pubis (I)

Tibial cnemial crest (I)

FT

Majority of the femoral shaft (I)

Tibial cnemial crest (I)

ILFB

Crest on the lateral postacetabular ilium (I)

Fibular tubercle (I)

IFM

Supraacetabular crest and lateral preacetabular ilium (I)

Lateral surface of the proximal femur (I)

PIFI 1



Cranial margin of the ilium, dorsal to the pubic process (II)

Proximolateral surface of the femur (I)

PIFI 2

Ventral aspect of the preacetabular process (II)

Proximolateral surface of the femur (I)

PIT

Craniolateral surface of the ischium (II)

Proximal tibia (II)

FTI

Caudolateral surface of the postacetabular ilium (I)

Proximal tibia (I)

FTE

Caudolateral surface of the postacetabular ilium (I)

Proximal tibia (I)

ADD 1

Cranioventral ischial shaft (I)

Flange on the caudal surface of the femoral shaft (I or II?)

ADD 2

Caudodorsal ischial shaft (II)

Caudal surface of the distal femoral shaft (I or II?)

PIFE 1

Ventral surface of the pubic apron (II)

Caudal surface of the proximal femur (I)

PIFE 2

Lateral surface of the pubic boot (II)

Caudal surface of the proximal femur (I)

PIFE 3

Lateral surface of the ischial boot (II)

Caudal surface of the proximal femur (I)

ISTR

Medial surface of the ischium (II)

Lateral surface of the proximal femur (I’)

CFB

Iliac brevis fossa (II)

Medial surface of the femur (I)

CFL

Caudal vertebral centra (I’)

Medial surface of the femur (I)

G (lateral head)

Caudolateral femur just distal to the insertion of ADD2 (I)

Plantar surface of metatarsals I-IV with medial head (II)

G (medial head)

Proximal medial tibia (I)

Plantar surface of metatarsals I-IV with lateral head (II)

TA

Cranial surface of the proximal tibia (I)

Proximodorsal surface of metatarsals I-III (IV?) (I)

POP

Proximal medial fibular shaft (I’)

Distal lateral tibial shaft (I’)

PL

Lateral fibula (I’)

Calcaneal tuber (II)

PB

Lateral fibula (I)

Caudolateral surface of metatarsal V (I)

EDL

Lateral femoral condyle (I)

Distal end of the dorsal shaft of metatarsals I-IV (II)

EDB

Craniomedial surface of the tarsals (II)

Dorsal surface of the phalanges (II)

FDL

Caudal femur, distal to GL (I)

Ventral surface of phalanges and unguals (I)

FDB

Plantar aponeurosis (II’)

Ventral surface of the phalanges (II’)

EHL

Cranial surface of the distal fibula (II)

Dorsal surface of metatarsal I’

FHL

Caudolateral aspect of the femur (I’)

Ventral surface of the distal phalanx and ungula of digit I (I’)

Fig S2. Reconstruction of the origins and insertions of pelvic limb musculature of Popsoaurus in left lateral view (modified from Schachner et al. In press). Abbreviations: Abbreviations: ADD 1-2, M. adductor 1-2; AMB, M. ambiens; CFB, M. caudofemoralis brevis; CFL, M. caudofemoralis longus; FT, M. femorotibialis; FTE, M. flexor tibialis externus; FTI, M. flexor tibialis internus; EDB, M. extensor digitorum brevis; EDL, M. extensor digitorum longus; FDL, M. flexor digitorum longus; G, M. gastrocnemius; GL, M. gastrocnemius lateralis; IFM, M. iliofemoralis; ILFB, M. iliofibularis; ISTR, M. ischiotrochantericus; IT 1-3, M. iliotibialis 1-3; PB, M. peroneus brevis; PIFE 2-3, M. puboischiofemoralis externus 2-3; PIFI 1-2, M. puboischiofemoralis internus 1-2; PIT, M. puboischiotibialis; PL, M. peroneus longus; TA, M. tibialis anterior.



  1. Ostrich model

The origins, insertions and 3D paths of 29 pelvic limb muscles were mapped on to the 3D model of the ostrich, using observations from cadaveric dissections and aided by published myological descriptions (Gangl et al. 2004; Smith et al. 2006). To measure the accuracy of the reconstructed muscle moment arms of the 3D model it’s predictions were compared with those derived experimentally from manipulation of cadaveric specimens using the tendon travel method (Smith et al. 2007). The results are shown in Figure S3. Overall the model predictions show an extremely close match to the experimental data, particularly given the level of intra-specific variation present in muscle moment arms for ostriches (Smith et al. 2007). However, a number of consistent differences are present between the model and experimental data. Notably hip extensor moment arms decrease in magnitude to much a greater extent with increasing hip flexion in the experimental data than in the 3D model. The range of motion used in the tendon travel experiments of was largely defined by the movement permitted by the tissues in the cadaveric limbs (Smith et al. 2007; Smith personal communication 2010), hence extensor moment arms are restricted to angles of 5-35 degrees hip joint flexion (versus 0-85 degrees in the 3D model). Ostriches have been shown to reach 60 degrees hip joint flexion during slow running (Rubenson et al. 2007), which would necessitate activation of muscles with extensor moment arms to support the limb at the hip. Extrapolation of the slopes of the experimental hip extensor muscle moment arms beyond 35 degrees flexion results in the prediction that all measured hip extensors, with the exception of FCM and ILFB, switch to being hip flexors by 45 degrees hip joint flexion, with ILFB switching at roughly 65 degrees. Under such circumstance the animal would be unable to counter the net flexor moment at the hip during stance at limb angle recorded in kinematic studies (Rubenson et al. 2007). By contrast, all hip anti-gravity muscles retain extensor moment arms across the entire range of joint motion (i.e. up to 85 degrees hip flexion) in the 3D model, consistent with the mechanics of ostrich running and walking gaits (Rubenson et al. 2004, 2007) and with the geometric relationship between these muscles and the hip joint in this taxon. Hip extensor muscles in the ostrich originate from the pelvis a considerable distance caudoventrally and caudodorsally to the hip joint. Insertion on the femur from this relative direction means that

Fig S3. Comparison of the flexion-extension moment arms of (a-e) hip, (f-g) knee and (h-i) ankle muscles in the 3D model of the ostrich (BB.3462) to the experimental results of Smith et al. (2007).

hip extensors are only likely to switch to flexor moment arms when the hip is in hyper-extension, not simply greater degrees of flexion. Thus we are unable to explain the pronounced decline in extensor muscle arms with increasing hip flexion in the experimental data of Smith et al. (2007) and conclude that the 3D model provides a more plausible approximation of moment arms for these muscles in the ostrich.

The knee joint moment arms of ILFB and FTM (FMT in Smith et al. 2007) in the 3D model also show relatively poor agreement with the experimental measurements. Smith et al. (2007) found that ILFB retained a relatively large flexor moment arm about the knee joint across their full range of measured angles. Although ILFB has similar flexor moment arm magnitudes at extended knee postures (<45 degrees) in the 3D model (Fig. S3f), this muscle quickly switches to being an extensor at flexed joint angles. This represents a limitation in the 3D model. Currently the 3D path of a muscle can be controlled by either via points or wrapping cylinders in GaitSym, but both features cannot be used in the same muscle. Via points were used to produce a realistic hip extensor moment arm for ILFB, but were not sufficient to provide realistic muscle geometry for this muscle around the back of the knee at highly flexed angles. Addition of a wrapping surface for ILFB behind the knee joint would solve this problem, but such a feature cannot be combined with via points in the current version of GaitSym. In the 3D model FTM is consistent with all other knee extensors in that its magnitude is highest at extended joint angles and decreases linearly with increasing knee flexion (Fig. S3f-g). This pattern was true for all knee extensor muscles in the other models in this study and indeed all other knee extensors in the cadaveric experiments (Fig. S3f-g; Smith et al. 2006). This discrepancy likely results how the muscle path around the craniolateral side of the knee was controlled in the tendon travel experiments of Smith et al. (2007) relative to our model. However, given the skeletal and muscle geometry we would expect the extensor moment of the FTM to decrease with increasing joint flexion, as in all other knee extensors, and thus we are confident in the predictions of our model.



RESULTS

  1. Complete hip muscle moment arm data

Figure S4. Predicted muscle moment arms for hip flexion-extension (left), abduction-adduction (centre) and long axis rotation (right) in Poposaurus, Alligator and ornithodiran bipeds over a range of hip joint flexion-extension angles. (a) ADD1, (b) ADD2, (c) AMB, (d) CFB, (e) CFL, (f) FTE, (g) FTI1, (h) FTI3, (i) IFB, (j) IFMa, (k) IFMp, (l) ISTR, (m) IT1, (n) IT3, (o) PIFE1, (p) PIFE2, (q) PIFE3, (r) PIFI1, (s) PIFI2, and (t) PIT. Abbreviations: ADD, M. adductor; AMB, M. ambiens; CFB, M. caudofemoralis brevis; CFL, M. caudofemoralis longus; FTE, M. flexor tibialis externus; FTI1, M. flexor tibialis 1; FTI3, M. flexor tibialis 3; IFB, M. iliofibularis; IFMa, M. iliofemoralis of Poposaurus against ITC of ornithodirans; IFMp, M. iliofemoralis of Poposaurus against IFE of ornithodirans p; ISTR, M. ischiotrochantericus; IT1 & 3, M. iliotibialis 1 & 3; PIFE 2-3, M. puboischiofemoralis 1-3; PIFI1-2, M. puboischiofemoralis 1-2; PIT, M. puboischiotibialis.

  1. Adductor femoris muscle insertions in Poposaurus

In the main text we state that “a raised process midway down the caudal aspect of the femoral shaft and a vertically oriented ridge that extends distally from this process are reconstructed as the insertion sites of ADD1 and 2 in Poposaurus (Schachner et al. in press). These insertion sites of the adductor complex in Poposaurus are significantly larger than those in any other archosaurs, extinct or extant.” Figure S5 shows the insertion sites of ADD1&2 inferred for Poposaurus gracilis YMP57000 (Schachner et al. In press) compare with those of Tyrannosaurus rex (FMNH PR2081) based on personal observations and the reconstructions of Carrano and Hutchinson (2002; their Fig. 6).

Figure S5. Insertions of the adductor femoris muscles (ADD1&2) on the caudal surface of the left femur in (a-b) Tyrannosaurus rex (FMNH PR2081) and (c-d) Poposaurus gracilis (YMP5700). Abbreviations: ADD 1-2, M. adductor 1-2.



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