Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-26T05:55:31.727Z Has data issue: false hasContentIssue false

Analysis of hindlimb muscle moment arms in Tyrannosaurus rex using a three-dimensional musculoskeletal computer model: implications for stance, gait, and speed

Published online by Cambridge University Press:  08 April 2016

John R. Hutchinson
Affiliation:
Biomechanical Engineering Division, Department of Mechanical Engineering, Stanford University, Stanford, California 94305-4038. E-mail: jrhutch@rvc.ac.uk
Frank C. Anderson
Affiliation:
Biomechanical Engineering Division, Department of Mechanical Engineering, Stanford University, Stanford, California 94305-4038. E-mail: jrhutch@rvc.ac.uk
Silvia S. Blemker
Affiliation:
Biomechanical Engineering Division, Department of Mechanical Engineering, Stanford University, Stanford, California 94305-4038. E-mail: jrhutch@rvc.ac.uk
Scott L. Delp
Affiliation:
Biomechanical Engineering Division, Department of Mechanical Engineering, Stanford University, Stanford, California 94305-4038. E-mail: jrhutch@rvc.ac.uk

Abstract

Muscle moment arms are important determinants of muscle function; however, it is challenging to determine moment arms by inspecting bone specimens alone, as muscles have curvilinear paths that change as joints rotate. The goals of this study were to (1) develop a three-dimensional graphics-based model of the musculoskeletal system of the Cretaceous theropod dinosaur Tyrannosaurus rex that predicts muscle-tendon unit paths, lengths, and moment arms for a range of limb positions; (2) use the model to determine how the T. rex hindlimb muscle moment arms varied between crouched and upright poses; (3) compare the predicted moment arms with previous assessments of muscle function in dinosaurs; (4) evaluate how the magnitudes of these moment arms compare with those in other animals; and (5) integrate these findings with previous biomechanical studies to produce a revised appraisal of stance, gait, and speed in T. rex. The musculoskeletal model includes ten degrees of joint freedom (flexion/extension, ab/adduction, or medial/lateral rotation) and 33 main muscle groups crossing the hip, knee, ankle, and toe joints of each hindlimb. The model was developed by acquiring and processing bone geometric data, defining joint rotation axes, justifying muscle attachment sites, and specifying muscle-tendon geometry and paths. Flexor and extensor muscle moment arms about all of the main limb joints were estimated, and limb orientation was statically varied to characterize how the muscle moment arms changed. We used sensitivity analysis of uncertain parameters, such as muscle origin and insertion centroids, to deterimine how much our conclusions depend on the muscle reconstruction we adopted. This shows that a specific amount of error in the reconstruction (e.g., position of muscle origins) can have a greater, lesser, similar, or no effect on the moment arms, depending on complex interactions between components of the musculoskeletal geometry. We found that more upright poses would have improved mechanical advantage of the muscles considerably. Our analysis shows that previously assumed moment arm values were generally conservatively high. Our results for muscle moment arms are generally lower than the values predicted by scaling data from extant taxa, suggesting that T. rex did not have the allometrically large muscle moment arms that might be expected in a proficient runner. The information provided by the model is important for determining how T. rex stood and walked, and how the muscles of a 4000–7000 kg biped might have worked in comparison with extant bipeds such as birds and humans. Our model thus strengthens the conclusion that T. rex was not an exceptionally fast runner, and supports the inference that more upright (although not completely columnar) poses are more plausible for T. rex. These results confirm general principles about the relationship between size, limb orientation, and locomotor mechanics: exceptionally big animals have a more limited range of locomotor abilities and tend to adopt more upright poses that improve extensor muscle effective mechanical advantage. This model builds on previous phylogenetically based muscle reconstructions and so moves closer to a fully dynamic, three-dimensional model of stance, gait, and speed in T. rex.

Type
Articles
Copyright
Copyright © The Paleontological Society 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Literature Cited

Alexander, R. Mc N. 1977. Allometry of the limbs of antelopes (Bovidae). Journal of Zoology 183:124146.CrossRefGoogle Scholar
Alexander, R. Mc N., Jayes, A. S., Maloiy, G. M. O., and Wathuta, E. M. 1981. Allometry of the leg muscles of mammals. Journal of Zoology 194:539552.Google Scholar
An, K. N., Takahashi, K., Harrigan, T. P., and Chao, E. Y. 1984. Determination of muscle orientations and moment arms. Journal of Biomechanical Engineering 106:280283.Google Scholar
Arnold, A. S., and Delp, S. L. 2001. Rotational moment arms of the medial hamstrings and adductors vary with femoral geometry and limb position: implications for the treatment of internally rotated gait. Journal of Biomechanics 34:437447.Google Scholar
Arnold, A. S., Salinas, S., Asakawa, D. J., and Delp, S. L. 2000. Accuracy of muscle moment arms estimated from MRI-based musculoskeletal models of the lower extremity. Computer Aided Surgery 5:108119.Google Scholar
Bakker, R. T. 1986. Dinosaur heresies. William Morrow, New York.Google Scholar
Bakker, R. T. 2002. Speed in tyrannosaurs. Journal of Vertebrate Paleontology 22(Suppl. to No. 3):34A.Google Scholar
Bennett, M. B., and Taylor, G. C. 1995. Scaling of elastic strain energy in kangaroos and the benefits of being big. Nature 378:5659.CrossRefGoogle ScholarPubMed
Biewener, A. A. 1989. Scaling body support in mammals: limb posture and muscle mechanics. Science 245:4548.CrossRefGoogle ScholarPubMed
Biewener, A. A. 1990. Biomechanics of mammalian terrestrial locomotion. Science 250:10971103.Google Scholar
Blanco, R. E., and Mazetta, G. V. 2001. A new approach to evaluate the cursorial ability of the giant theropod Giganotosaurus carolinii . Acta Palaeontologia Polonica 46:193202.Google Scholar
Blob, R. W. 2001. Evolution of hindlimb posture in nonmammalian therapsids: biomechanical tests of paleontological hypotheses. Paleobiology 27:1438.Google Scholar
Blob, R. W. and Biewener, A. A. 2001. Mechanics of limb bone loading during terrestrial locomotion in the green iguana (Iguana iguana) and American alligator (Alligator mississipiensis). Journal of Experimental Biology 204:10991122.Google Scholar
Brown, N. A. T., Pandy, M. G., Buford, W. L., Kawcak, C. E., and McIlwraith, C. W. 2003a. Moment arms about the carpal and metacarpophalangeal joints for flexor and extensor muscles in equine forelimbs. American Journal of Veterinary Research 64:351357.Google Scholar
Brown, N. A. T., Pandy, M. G., Kawcak, C. E., and McIlwraith, C. W. 2003b. Force- and moment-generating capacities of muscles in the distal forelimb of the horse. Journal of Anatomy 203:101113.CrossRefGoogle ScholarPubMed
Bryant, H. N., and Seymour, K. L. 1990. Observations and comments on the reliability of muscle reconstruction in fossil vertebrates. Journal of Morphology 206:109117.Google Scholar
Buford, W. L. Jr., Ivey, F. M. Jr., Malone, J. D., Patterson, R. M., Peare, G. L., Nguyen, D. K., and Stewart, A. A. 1997. Muscle balance at the knee—moment arms for the normal knee and the ACL-minus knee. IEEE Transactions on Rehabilitation Engineering 5:367379.Google Scholar
Carrano, M. T. 2000. Homoplasy and the evolution of dinosaur locomotion. Paleobiology 26:489512.2.0.CO;2>CrossRefGoogle Scholar
Carrano, M. T., and Hutchinson, J. R. 2002. Pelvic and hindlimb musculature of Tyrannosaurus rex (Dinosauria: Theropoda). Journal of Morphology 252:207228.Google Scholar
Charig, A. J. 1972. The evolution of the archosaur pelvis and hindlimb: an explanation in functional terms. Pp. 121151 in Joysey, K. A. and Kemp, T. S., eds. Studies in vertebrate evolution. Oliver and Boyd, Edinburgh.Google Scholar
Christiansen, P. 1999. Long bone scaling and limb posture in non-avian theropods: evidence for differential allometry. Journal of Vertebrate Paleontology 19:666680.Google Scholar
Colbert, E. H. 1964. Relationships of the saurischian dinosaurs. American Museum Novitates 2181:124.Google Scholar
Delp, S. L., and Loan, J. P. 1995. A graphics-based software system to develop and analyze models of musculoskeletal structures. Computers in Biology and Medicine 25:2134.CrossRefGoogle ScholarPubMed
Delp, S. L., and Loan, J. P. 2000. A computational framework for simulating and analyzing human and animal movement. IEEE Computing in Science and Engineering 2:4655.Google Scholar
Delp, S. L., and Zajac, F. E. 1992. Force- and moment-generating capacity of lower-extremity muscles before and after tendon lengthening. Clinical Orthopaedics 284:247259.Google Scholar
Delp, S. L., Loan, J. P., Hoy, M. G., Zajac, F. E., Topp, E. L., and Rosen, J. M. 1990. An interactive graphics-based model of the lower extremity to study orthopaedic surgical procedures. IEEE Transactions in Biomedical Engineering 37:757767.Google Scholar
Delp, S. L., Hess, W. E., Hungerford, D. S., and Jones, L. C. 1999. Variation of rotation moment arms with hip flexion. Journal of Biomechanics 32:493501.Google Scholar
Eckhoff, D. G., Bach, J. M., Spitzer, V. M., Reinig, K. D., Bagur, M. M., Baldini, T. H., Rubernstein, D., and Humphries, S. 2003. Three-dimensional morphology and kinematics of the distal part of the femur viewed in virtual reality, Part II. Journal of Bone and Joint Surgery 85-A:97104.Google Scholar
Farlow, J. O., Smith, M. B., and Robinson, J. M. 1995. Body mass, bone “strength indicator,” and cursorial potental of Tyrannosaurus rex . Journal of Vertebrate Paleontology 15:713725.Google Scholar
Full, R. J., and Ahn, A. N. 1995. Static forces and moments generated in the insect leg: comparison of a three-dimensional musculo-skeletal computer model with experimental measurements. Journal of Experimental Biology 198:12851298.Google Scholar
Gans, C., and De Vree, F. 1987. Functional bases of fiber length and angulation in muscle. Journal of Morphology 192:6385.Google Scholar
Gatesy, S. M. 1990. Caudofemoral musculature and the evolution of theropod locomotion. Paleobiology 16:170186.Google Scholar
Henderson, D. M. 1999. Estimating the masses and centers of mass of extinct animals by 3-D mathematical slicing. Paleobiology 25:85106.Google Scholar
Hotton, N. H. III. 1980. An alternative to dinosaur endothermy: the happy wanderers. In Thomas, D. K. and Olsen, E. C., eds. A cold look at hot-blooded dinosaurs. AAAS Selected Symposium Series 28:311350.Google Scholar
Hutchinson, J. R. 2001a. The evolution of pelvic osteology and soft tissues on the line to extant birds (Neornithes). Zoological Journal of the Linnean Society 131:123168.CrossRefGoogle Scholar
Hutchinson, J. R. 2001b. The evolution of femoral osteology and soft tissues on the line to extant birds (Neornithes). Zoological Journal of the Linnean Society 131:169197.CrossRefGoogle Scholar
Hutchinson, J. R. 2002. The evolution of hindlimb tendons and muscles on the line to crown-group birds. Comparative Biochemistry and Physiology A 133:10511086.Google Scholar
Hutchinson, J. R. 2004a. Biomechanical modeling and sensitivity analysis of bipedal running ability. I. Extant taxa. Journal of Morphology 262:421440.CrossRefGoogle ScholarPubMed
Hutchinson, J. R. 2004b. Biomechanical modeling and sensitivity analysis of bipedal running ability. II. Extinct taxa. Journal of Morphology 262:441461.Google Scholar
Hutchinson, J. R., and Garcia, M. 2002. Tyrannosaurus was not a fast runner. Nature 415:10181021.CrossRefGoogle Scholar
Hutchinson, J. R., and Gatesy, S. M. 2000. Adductors, abductors, and the evolution of archosaur locomotion. Paleobiology 26:734751.2.0.CO;2>CrossRefGoogle Scholar
Kargo, W. J., and Rome, L. C. 2002. Functional morphology of proximal hindlimb muscles in the frog Rana pipiens . Journal of Experimental Biology 205:19872004.Google Scholar
Kargo, W. J., Nelson, F., and Rome, L. C. 2002. Jumping in frogs: assessing the design of the skeletal system by anatomically realistic modeling and forward dynamic simulation. Journal of Experimental Biology 205:16831702.Google Scholar
Keshner, E. A., Statler, K. D., and Delp, S. L. 1997. Kinematics of the freely moving head and neck in the alert cat. Experimental Brain Research 115:257266.Google Scholar
Krevolin, J. L., Pandy, M. G., and Pearce, J. C. 2004. Moment arm of the patellar tendon in the human knee. Journal of Biomechanics 37:785788.Google Scholar
Lambe, L. M. 1917. The Cretaceous carnivorous dinosaur Gorgosaurus . Memoirs of the Canadian Geological Survey 100:184.Google Scholar
Leahy, G. D. 2002. Speed potential of tyrannosaurs great and small. Journal of Vertebrate Paleontology 22(Suppl. to No. 3):78A.Google Scholar
Lieber, R. L. 1992. Skeletal muscle structure and function: implications for rehabilitation and sports medicine. Williams and Wilkins, Baltimore.Google Scholar
Lieber, R. L. 1997. Muscle fiber length and moment arm coordination during dorsi- and plantarflexion in the mouse hindlimb. Acta Anatomica 159:8489.Google Scholar
Maganaris, C. N. 2004. Imaging-based estimates of moment arm length in intact human muscle-tendons. European Journal of Applied Physiology 91:130139.Google Scholar
Maloiy, G. M. O., Alexander, R. Mc N., Njau, R., and Jayes, A. S. 1979. Allometry of the legs of running birds. Journal of Zoology 187:161167.Google Scholar
Molnar, R. M., and Farlow, J. O. 1990. Carnosaur paleobiology. Pp. 210224 in Weishampel, D. B., Dodson, P., and Osmólska, H., eds. The Dinosauria. University of California Press, Berkeley.Google Scholar
Murray, W. M., Buchanan, T. S., and Delp, S. L. 2002. Scaling of peak moment arms of elbow muscles with upper extremity bone dimensions. Journal of Biomechanics 35:1926.Google Scholar
Newman, B. H. 1970. Stance and gait in the flesh-eating dinosaur Tyrannosaurus . Biological Journal of the Linnean Society 2:119123.Google Scholar
Osborn, H. F. 1913. Tyrannosaurus, restoration and model of the skeleton. Bulletin of the American Museum of Natural History 32:9192.Google Scholar
Osborn, H. F. 1916. Skeletal adaptations of Ornitholestes, Struthiomimus and Tyrannosaurus . Bulletin of the American Museum of Natural History 35:733771.Google Scholar
Pandy, M. G. 1999. Moment arm of a muscle force. Exercise and Sport Science Reviews 27:79118.CrossRefGoogle ScholarPubMed
Paul, G. S. 1988. Predatory dinosaurs of the world. Simon and Schuster, New York.Google Scholar
Paul, G. S. 1998. Limb design, function and running performance in ostrich-mimics and tyrannosaurs. Gaia 15:257270.Google Scholar
Perle, A. 1985. Comparative myology of the pelvic-femoral region in the bipedal dinosaurs. Paleontological Journal 19:105109.Google Scholar
Raikova, R. T., and Prilutsky, B. I. 2001. Sensitivity of predicted muscle forces to parameters of the optimization-based human leg model revealed by analytical and numerical analyses. Journal of Biomechanics 34:12431255.Google Scholar
Rome, L. C. 1998. Some advances in integrative muscle physiology. Comparative Biochemistry and Physiology B 120:5172.Google Scholar
Romer, A. S. 1923. The pelvic musculature of saurischian dinosaurs. Bulletin of the American Museum of Natural History 48:605617.Google Scholar
Russell, D. A. 1972. Ostrich dinosaurs from the Late Cretaceous of Western Canada. Canadian Journal of Earth Sciences 9:375402.Google Scholar
Schroeder, W. J., Zarge, J. A., and Lorensen, W. E. 1992. Decimation of triangle meshes. Computer Graphics 26:6570.Google Scholar
Sellers, W. I., Dennis, L. A., and Crompton, R. H. 2003. Predicting the metabolic energy costs of bipedalism using evolutionary robotics. Journal of Experimental Biology 206:11271136.Google Scholar
Spoor, C. W., and Van Leeuwen, J. L. 1992. Knee muscle moment arms from MRI and from tendon travel. Journal of Biomechanics 25:201206.Google Scholar
Tarsitano, S. 1983. Stance and gait in theropod dinosaurs. Acta Palaeontologia Polonica 28:251264.Google Scholar
Thorpe, S. K. S., Crompton, R. H., Günther, M. M., Ker, R. F., and Alexander, R. McN. 1999. Dimensions and moment arms of the hind- and forelimb muscles of common chimpanzees (Pan troglodytes). American Journal of Physical Anthropology 110:179199.Google Scholar
Thulborn, R. A. 1982. Speeds and gaits of dinosaurs. Palaeogeography Palaeoclimatology Palaeoecology 38:227256.Google Scholar
Thulborn, R. A. 1989. The gaits of dinosaurs. Pp. 3950 in Gillett, D. D. and Lockley, M. G., eds. Dinosaur tracks and traces. Cambridge University Press, Cambridge.Google Scholar
Thulborn, R. A. 1990. Dinosaur tracks. Chapman and Hall, London.Google Scholar
Van der Helm, F. C., Veeger, H. E., Pronk, G. M., Van der Woude, L. H., and Rozendal, R. H. 1992. Geometry parameters for musculoskeletal modelling of the shoulder system. Journal of Biomechanics 25: 129–44.Google Scholar
Van Leeuwen, J. L. 1992. Muscle function in locomotion. Advances in Comparative and Environmental Physiology 11:191250.Google Scholar
Walker, A. D. 1977. Evolution of the pelvis in birds and dinosaurs. Pp. 319358 in Mahala Andrews, S., Miles, R. S., and Walker, A. D., eds. Problems in vertebrate evolution (Linnean Society Symposium Series 4).Google Scholar
Welles, S. P. 1986. Thoughts on the origin of the Theropoda. Pp. 3134 in Padian, K., ed. The beginning of the age of dinosaurs. Cambridge University Press, Cambridge.Google Scholar
Witmer, L. M. 1995. The extant phylogenetic bracket and the importance of reconstructing soft tissues in fossils. Pp. 1933 in Thomason, J. J., ed. Functional morphology in vertebrate paleontology. Cambridge University Press, Cambridge.Google Scholar
Zajac, F. E. 1989. Muscle and tendon: properties, models, scaling, and application to biomechanics and motor control. Critical Reviews in Biomedical Engineering 17:359411.Google Scholar