ArborSim: Articulated, branching, OpenSim routing for constructing models of multi-jointed appendages with complex muscle-tendon architecture.

Computational models of musculoskeletal systems are essential tools for understanding how muscles, tendons, bones, and actuation signals generate motion. In particular, the OpenSim family of models has facilitated a wide range of studies on diverse human motions, clinical studies of gait, and even non-human locomotion. However, biological structures with many joints, such as fingers, necks, tails, and spines, have been a longstanding challenge to the OpenSim modeling community, especially because these structures comprise numerous bones and are frequently actuated by extrinsic muscles that span multiple joints-often more than three-and act through a complex network of branching tendons. Existing model building software, typically optimized for limb structures, makes it difficult to build OpenSim models that accurately reflect these intricacies. Here, we introduce ArborSim, customized software that efficiently creates musculoskeletal models of highly jointed structures and can build branched muscle-tendon architectures. We used ArborSim to construct toy models of articulated structures to determine which morphological features make a structure most sensitive to branching. By comparing the joint kinematics of models constructed with branched and parallel muscle-tendon units, we found that among various parameters-the number of tendon branches, the number of joints between branches, and the ratio of muscle fiber length to muscle tendon unit length-the number of tendon branches and the number of joints between branches are most sensitive to branching modeling method. Notably, the differences between these models showed no predictable pattern with increased complexity. As the proportion of muscle increased, the kinematic differences between branched and parallel models units also increased. Our findings suggest that stress and strain interactions between distal tendon branches and proximal tendon and muscle greatly affect the overall kinematics of a musculoskeletal system. By incorporating complex muscle-tendon branching into OpenSim models using ArborSim, we can gain deeper insight into the interactions between the axial and appendicular skeleton, model the evolution and function of diverse animal tails, and understand the mechanics of more complex motions and tasks.

Rolling of the jaw is essential for mammalian chewing and tribosphenic molar function.

Over the past two centuries, mammalian chewing and related anatomical features have been among the most discussed of all vertebrate evolutionary innovations1-3. Chief among these features are two characters: the dentary-only mandible, and the tribosphenic molar with its triangulated upper cusps and lower talonid basin3-5. The flexible mandibular joint and the unfused symphysis of ancestral mammals-in combination with transformations of the adductor musculature and palate-are thought to have permitted greater mobility of each lower jaw, or hemimandible6,7. Following the appearance of precise dental occlusion near the origin of the mammalian crown8,9, therians evolved a tribosphenic molar with a craggy topography that is presumed to have been used to catch, cut and crush food. Here we describe the ancestral tribosphenic therian chewing stroke, as conserved in the short-tailed opossum Monodelphis domestica: it is a simple symmetrical sequence of lower tooth-row eversion and inversion during jaw opening and closing, respectively, enacted by hemimandibular long-axis rotation. This sequence is coupled with an eversion-inversion rotational grinding stroke. We infer that the ancestral therian chewing stroke relied heavily on long-axis rotation, including symmetrical eversion and inversion (inherited from the first mammaliaforms) as well as a mortar-and-pestle rotational grinding stroke that was inherited from stem therians along with the tribosphenic molar. The yaw-dominated masticatory cycle of primates, ungulates and other bunodont therians is derived; it is necessitated by a secondarily fused jaw symphysis, and permitted by the reduction of high, interlocking cusps10-12. The development of an efficient masticatory system-culminating in the tribosphenic apparatus-allowed early mammals to begin the process of digestion by shearing and crushing food into small boli instead of swallowing larger pieces in the reptilian manner, which necessitates a long, slow and wholly chemical breakdown. The vast diversity of mammalian teeth has emerged from the basic tribosphenic groundplan13.

Evolution of facial innervation in anomodont therapsids (Synapsida): Insights from X-ray computerized microtomography.

Anomodontia was the most successful herbivorous clade of the mammalian stem lineage (non-mammalian synapsids) during the late Permian and Early Triassic. Among anomodonts, Dicynodontia stands apart because of the presence of an osseous beak that shows evidence of the insertion of a cornified sheath, the ramphotheca. In this study, fourteen anomodont specimens were microCT-scanned and their trigeminal canals reconstructed digitally to understand the origin and evolution of trigeminal nerve innervation of the ramphotheca. We show that the pattern of innervation of the anomodont "beak" is more similar to that in chelonians (the nasopalatine branch is enlarged and innervates the premaxillary part of the ramphotheca) than in birds (where the nasopalatine and maxillary branches play minor roles). The nasopalatine branch is noticeably enlarged in the beak-less basal anomodont Patranomodon, suggesting that this could be an anomodont or chainosaur synapomorphy. Our analyses suggest that the presence or absence of tusks and postcanine teeth are often accompanied by corresponding variations of the rami innervating the caniniform process and the alveolar region, respectively. The degree of ossification of the canal for the nasal ramus of the ophthalmic branch also appears to correlate with the presence of a nasal boss. The nasopalatine canal is absent from the premaxilla in the Bidentalia as they uniquely show a large plexus formed by the internal nasal branch of the maxillary canal instead. The elongated shape of this plexus in Lystrosaurus supports the hypothesis that the rostrum evolved as an elongation of the subnarial region of the snout. Finally, the atrophied and variable aspect of the trigeminal canals in Myosaurus supports the hypothesis that this genus had a reduced upper ramphotheca.