Coelophysis musculoskeletal model

Once benchmarked with an extant theropod, the above framework (including the simplified muscle model) was applied to the extinct, non-avian theropod C. bauri to generate a maximal speed running simulation. This relatively small [10 to 25 kg; (45)], Late Triassic (~220 Ma) taxon is the best-known early theropod dinosaur, known from innumerable complete and partial skeletons. It is a good representative of the general bauplan ancestral for Dinosauria and had many anatomical features common to most bipedal dinosaurs in general, including long hindlimbs, short forelimbs, digitigrade stance, a long tail, a relatively long neck, and a small head (15). Its relatively small mass (in dinosaurian terms) is closer to that of early dinosaurs including theropods (70) and is within the range observed in extant bipeds, thus avoiding the potentially confounding (allometric) effect of much larger body size as would occur with some other well-studied theropods (e.g., Tyrannosaurus). Coelophysis, therefore, is an ideal taxon for investigating locomotor biomechanics and its evolution in early bipedal dinosaurs, as well as the evolution of “cursoriality” in bipeds in general.

We used a previously developed model of Coelophysis (17), with a few changes (Fig. 3, A and B, and the Supplementary Materials). The model has three DOFs at the hip (flexion-extension, abduction-adduction, long-axis rotation) and one each (flexion-extension) at the knee, ankle, and MTP joint, as well as 33 MTUs actuating each hindlimb. The forelimbs, which were free to move in the original model, were programmatically locked in a “tucked” position with respect to the body (shoulder extension angle fixed at 45°; see Fig. 2); their very small size (<0.5% of total body mass, shoulder-fingertip distance about a third of hip-toetip distance) indicates that they did not play an important role in locomotion and thus their movements could be safely ignored. Indeed, the forelimbs could have been used to hold food during locomotion. The neck and head formed a single segment, and its joint with the chest was assigned two DOFs (dorsiflexion and lateroflexion). The tail of the original model was split in two at midlength, and both proximal and distal tail joints were assigned two DOFs (dorsiflexion and lateroflexion). In addition, as Coelophysis and other basal theropods have dorsal vertebrae with pre- and postzygopophyses that are strongly inclined laterally (15, 71–73), this suggests capability for a modest amount of body lateroflexion, which may have been important. Lizards can exhibit marked levels of body lateroflexion during bipedal gait, as judged by published still images in dorsal view (57). Thus, the originally singular body segment was split into a cranial “thorax” and caudal “trunk” segment, with the division parallel to the coronal (Y-Z) plane and positioned at the first intervertebral joint cranial to the pubes. These two segments were joined by a back joint that permitted lateroflexion only; dorsiflexion was probably limited given the vertebral morphology and the dorsoventrally deep extent of the body. Thus, the revised model used here comprised 25 free DOFs and had a mass of 13.1 kg. As with the tinamou, ground contact was computed using a single large contact sphere affixed to the middle of the digits segment. On account of the marked difference in size between Coelophysis and the tinamou, the values of several parameters of the system were scaled up from those of the tinamou, assuming isometry (67): muscle activation and deactivation time constants, contact stiffness and dissipation, and joint damping.

As with the tinamou model, variation in MTU length, velocity, and moment arms with respect to joint angles and velocities was represented with polynomial functions, calculated from 5000 randomly varying postures for the hindlimb (six DOFs) and proximal tail (two DOFs). The bounds on the postures sampled were more restrictive than the “bones-only” ranges of motion reported previously (17) and were set based on what was considered plausible for in vivo running poses given the kinematics of extant bipeds [e.g., (34, 74)], as well as MTU path behavior in more extreme poses. We therefore favored using a more restricted range of limb poses, rather than modifying the MTU paths to behave properly at (likely nonphysiological) extreme poses. For both the ambiens and fibularis longus muscles, the part of the MTU representing the inferred secondary tendon to the digital flexors was excluded for the sake of model simplicity.