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

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.