Experimental modification of morphology reveals the effects of the zygosphene-zygantrum joint on the range of motion of snake vertebrae

A study on the vertebral column of the dice snake Natrix tessellata (Serpentes, Natricidae) from Denizli (western Anatolia, Turkey)

The vertebral anatomy of snakes has attracted the attention of researchers for decades and numerous studies have been made for extinct and extant species. The present study investigated the morphological variations in vertebral structure among different vertebral regions in the dice snake Natrix tessellata, and provides a detailed anatomical and microstructural description of the vertebral column. Vertebrae were analyzed and compared using x-ray imaging, scanning electron microscopy, micro-computed tomography, and histological techniques. The vertebral column of N. tessellata is divided into three regions: precloacal, cloacal, and caudal. Unlike in many other tetrapods and snakes, the atlas of N. tessellata does not form a complete ring. It has a flat and roughly trilobate shape with a prominent middle lobe. The axis has two hypapophyses. The anterior precloacal region of the vertebral column has longer and more paddle-shaped hypapophyses, distinguishing it from the posterior and mid-trunk vertebrae. The anterior cloacal vertebrae have a short hypapophysis rather than a hemal keel, and the lymphapophysis extends outward, curving slightly. The cotyle and condyle of the caudal vertebrae exhibited a closer resemblance to a rounded shape, while the pleurapophysis extended ventrolaterally and curved ventrally near its distal end. Paired hemapophyses were present at the posterior-most point of the centrum instead of a hypapophysis. In light of previous fossil findings, our anatomical comparison of the vertebral and transverse processes indicates that the extant Natrix has a more flexible and less rigid spine than its ancestors. Overall, the vertebral differences among snake anatomical regions or taxa are a testament to the remarkable diversity and adaptability of these fascinating reptiles.

Function of revolute zygapophyses in the lumbar vertebrae of early placental mammals

The unique morphology of mammalian lumbar vertebrae allows the spine to flex and extend in the sagittal plane during locomotion. This movement increases stride length and allows mammals to efficiently breathe while running with an asymmetric gait. In extant mammals, the amount of flexion that occurs varies across different locomotor styles, with dorsostable runners relying more on movement of long limbs to run and dorsomobile runners incorporating more flexion of the back. Although long limbs and a stabilized lumbar region are commonly associated with each other in extant mammals, many "archaic" placental mammals with short limbs had lumbar vertebrae with revolute zygapophyses. These articulations with an interlocking S-shape are found only in artiodactyls among extant mammals and have been hypothesized to stabilize against flexion of the back. This would suggest that archaic placental mammals may not have incorporated dorsoventral flexion into locomotion to the same extent as extant mammals with similar proportions. We tested the relative mobility of fossil lumbar vertebrae from two early placental mammals, the creodonts Patriofelis and Limnocyon, to see how these vertebrae may have functioned. We compared range of motion (ROM) between the original vertebrae, with revolute morphology and digitally altered vertebrae with a flat morphology. We found that the revolute morphology had relatively little effect on dorsoventral flexion and instead that it likely prevented disarticulation due to shear forces on the spine. These results show that flexion of the spine has been an important part of mammalian locomotion for at least 50 million years.

Functional diversity of snake locomotor behaviors: A review of the biological literature for bioinspiration

Organismal solutions to natural challenges can spark creative engineering applications. However, most engineers are not experts in organismal biology, creating a potential barrier to maximally effective bioinspired design. In this review, we aim to reduce that barrier with respect to a group of organisms that hold particular promise for a variety of applications: snakes. Representing >10% of tetrapod vertebrates, snakes inhabit nearly every imaginable terrestrial environment, moving with ease under many conditions that would thwart other animals. To do so, they employ over a dozen different types of locomotion (perhaps well over). Lacking limbs, they have evolved axial musculoskeletal features that enable their vast functional diversity, which can vary across species. Different species also have various skin features that provide numerous functional benefits, including frictional anisotropy or isotropy (as their locomotor habits demand), waterproofing, dirt shedding, antimicrobial properties, structural colors, and wear resistance. Snakes clearly have much to offer to the fields of robotics and materials science. We aim for this review to increase knowledge of snake functional diversity by facilitating access to the relevant literature.

Contact feedback helps snake robots propel against uneven terrain using vertical bending

Snakes can bend their elongate bodies in various forms to traverse various environments. We understand well how snakes use lateral body bending to push against asperities on flat ground for propulsion, and snake robots can do so effectively. However, snakes can also use vertical bending to push against uneven terrain of large height variation for propulsion, and they can adjust this bending to adapt to novel terrain presumably using mechano-sensing feedback control. Although some snake robots can traverse uneven terrain, few have used vertical bending for propulsion, and how to control this process in novel environments is poorly understood. Here we systematically studied a snake robot with force sensors pushing against large bumps using vertical bending to understand the role of sensory feedback control. We compared a feedforward controller and four feedback controllers that use different sensory information and generate distinct bending patterns and body-terrain interaction. We challenged the robot with increasing backward load and novel terrain geometry that break its contact with the terrain. We further varied how much the feedback control modulated body bending to conform to or push against the terrain to test their effects. Feedforward propagation of vertical bending generated large propulsion when the bending shape matched terrain geometry. However, when perturbations caused loss of contact, the robot easily lost propulsion or had motor overload. Contact feedback control resolved these issues by helping the robot regain contact. Yet excessive conformation interrupted shape propagation and excessive pushing stalled motors frequently. Unlike that using lateral bending, for propulsion generation using vertical bending, body weight that can help maintain contact with the environment but may also overload motors. Our results will help snake robots better traverse uneven terrain with large height variation and can inform how snakes use sensory feedback to control vertical body bending for propulsion.

The relative contributions of multiarticular snake muscles to movement in different planes

Muscles spanning multiple joints play important functional roles in a wide range of systems across tetrapods; however, their fundamental mechanics are poorly understood, particularly the consequences of anatomical position on mechanical advantage. Snakes provide an excellent study system for advancing this topic. They rely on the axial muscles for many activities, including striking, constriction, defensive displays, and locomotion. Moreover, those muscles span from one or a few vertebrae to over 30, and anatomy varies among muscles and among species. We characterized the anatomy of major epaxial muscles in a size series of corn snakes (Pantherophis guttatus) using diceCT scans, and then took several approaches to calculating contributions of each muscle to force and motion generated during body bending, starting from a highly simplistic model and moving to increasingly complex and realistic models. Only the most realistic model yielded equations that included the consequence of muscle span on torque-displacement trade-offs, as well as resolving ambiguities that arose from simpler models. We also tested whether muscle cross-sectional areas or lever arms (total magnitude or pitch/yaw/roll components) were related to snake mass, longitudinal body region (anterior, middle, posterior), and/or muscle group (semispinalis-spinalis, multifidus, longissimus dorsi, iliocostalis, and levator costae). Muscle cross-sectional areas generally scaled with positive allometry, and most lever arms did not depart significantly from geometric similarity (isometry). The levator costae had lower cross-sectional area than the four epaxial muscles, which did not differ significantly from each other in cross-sectional area. Lever arm total magnitudes and components differed among muscles. We found some evidence for regional variation, indicating that functional regionalization merits further investigation. Our results contribute to knowledge of snake muscles specifically and multiarticular muscle systems generally, providing a foundation for future comparisons across species and bioinspired multiarticular systems.

Joint mobility as a bridge between form and function

Joints enable nearly all vertebrate animal motion, from feeding to locomotion. However, despite well over a century of arthrological research, we still understand very little about how the structure of joints relates to the kinematics they exhibit in life. This Commentary discusses the value of joint mobility as a lens through which to study articular form and function. By independently exploring form-mobility and mobility-function relationships and integrating the insights gained, we can develop a deep understanding of the strength and causality of articular form-function relationships. In turn, we will better illuminate the basics of 'how joints work' and be well positioned to tackle comparative investigations of the diverse repertoire of vertebrate animal motion.

Hybrid Compliant Musculoskeletal System for Fast Actuation in Robots

A nature-inspired musculoskeletal system is designed and developed to examine the principle of nonlinear elastic energy storage-release for robotic applications. The musculoskeletal system architecture consists of elastically rigid segments and hyperelastic soft materials to emulate rigid-soft interactions in limbless vertebrates. The objectives are to (i) improve the energy efficiency of actuation beyond that of current pure soft actuators while (ii) producing a high range of motion similar to that of soft robots but with structural stability. This paper proposes a musculoskeletal design that takes advantage of structural segmentation to increase the system's degrees of freedom, which enhances the range of motion. Our findings show that rigid-soft interactions provide a remarkable increase in energy storage and release and, thus, an increase in the undulation speed. The energy efficiency achieved is approximately 68% for bending the musculoskeletal system from the straight configuration, compared to 2.5-30% efficiency in purely soft actuators. The hybrid compliance of the musculoskeletal system under investigation shows promise for alleviating the need for actuators at each joint in a robot.

Snakes combine vertical and lateral bending to traverse uneven terrain

Terrestrial locomotion requires generating appropriate ground reaction forces which depend on substrate geometry and physical properties. The richness of positions and orientations of terrain features in the 3D world gives limbless animals like snakes that can bend their body versatility to generate forces from different contact areas for propulsion. Despite many previous studies of how snakes use lateral body bending for propulsion on relatively flat surfaces with lateral contact points, little is known about whether and how much snakes use vertical body bending in combination with lateral bending in 3D terrain. This lack had contributed to snake robots being inferior to animals in stability, efficiency, and versatility when traversing complex 3D environments. Here, to begin to elucidate this, we studied how the generalist corn snake traversed an uneven arena of blocks of random height variation five times its body height. The animal traversed the uneven terrain with perfect stability by propagating 3D bending down its body with little transverse motion (11° slip angle). Although the animal preferred moving through valleys with higher neighboring blocks, it did not prefer lateral bending. Among body-terrain contact regions that potentially provide propulsion, 52% were formed by vertical body bending and 48% by lateral bending. The combination of vertical and lateral bending may dramatically expand the sources of propulsive forces available to limbless locomotors by utilizing various asperities available in 3D terrain. Direct measurements of contact forces are necessary to further understand how snakes coordinate 3D bending along the entire body via sensory feedback to propel through 3D terrain. These studies will open a path to new propulsive mechanisms for snake robots, potentially increasing the performance and versatility in 3D terrain.

AutoBend: An Automated Approach for Estimating Intervertebral Joint Function from Bone-Only Digital Models

Deciphering the biological function of rare or extinct species is key to understanding evolutionary patterns across the tree of life. While soft tissues are vital determinants of joint function, they are rarely available for study. Therefore, extracting functional signals from skeletons, which are more widely available via museum collections, has become a priority for the field of comparative biomechanics. While most work has focused on the limb skeleton, the axial skeleton plays a critical role in body support, respiration, and locomotion, and is therefore of central importance for understanding broad-scale functional evolution. Here, we describe and experimentally validate AutoBend, an automated approach to estimating intervertebral joint function from bony vertebral columns. AutoBend calculates osteological range of motion (oROM) by automatically manipulating digitally articulated vertebrae while incorporating multiple constraints on motion, including both bony intersection and the role of soft tissues by restricting excessive strain in both centrum and zygapophyseal articulations. Using AutoBend and biomechanical data from cadaveric experiments on cats and tegus, we validate important modeling parameters required for oROM estimation, including the degree of zygapophyseal disarticulation, and the location of the center of rotation. Based on our validation, we apply a model with the center of rotation located within the vertebral disk, no joint translation, around 50% strain permitted in both zygapophyses and disks, and a small amount of vertebral intersection permitted. Our approach successfully reconstructs magnitudes and craniocaudal patterns of motion obtained from ex vivo experiments, supporting its potential utility. It also performs better than more typical methods that rely solely on bony intersection, emphasizing the importance of accounting for soft tissues. We estimated the sensitivity of the analyses to vertebral model construction by varying joint spacing, degree of overlap, and the impact of landmark placement. The effect of these factors was small relative to biological variation craniocaudally and between bending directions. We also present a new approach for estimating joint stiffness directly from oROM and morphometric measurements that can successfully reconstruct the craniocaudal patterns, but not magnitudes, derived from experimental data. Together, this work represents a significant step forward for understanding vertebral function in difficult-to-study (e.g., rare or extinct) species, paving the way for a broader understanding of patterns of functional evolution in the axial skeleton.

Continuous body 3-D reconstruction of limbless animals

Limbless animals such as snakes, limbless lizards, worms, eels and lampreys move their slender, long bodies in three dimensions to traverse diverse environments. Accurately quantifying their continuous body's 3-D shape and motion is important for understanding body-environment interactions in complex terrain, but this is difficult to achieve (especially for local orientation and rotation). Here, we describe an interpolation method to quantify continuous body 3-D position and orientation. We simplify the body as an elastic rod and apply a backbone optimization method to interpolate continuous body shape between end constraints imposed by tracked markers. Despite over-simplifying the biomechanics, our method achieves a higher interpolation accuracy (∼50% error) in both 3-D position and orientation compared with the widely used cubic B-spline interpolation method. Beyond snakes traversing large obstacles as demonstrated, our method applies to other long, slender, limbless animals and continuum robots. We provide codes and demo files for easy application of our method.

A Practical Guide to Measuring Ex vivo Joint Mobility Using XROMM

X-Ray Reconstruction of Moving Morphology (XROMM), though traditionally used for studies of in vivo skeletal kinematics, can also be used to precisely and accurately measure ex vivo range of motion from cadaveric manipulations. The workflow for these studies is holistically similar to the in vivo XROMM workflow but presents several unique challenges. This paper aims to serve as a practical guide by walking through each step of the ex vivo XROMM process: how to acquire and prepare cadaveric specimens, how to manipulate specimens to collect X-ray data, and how to use these data to compute joint rotational mobility. Along the way, it offers recommendations for best practices and for avoiding common pitfalls to ensure a successful study.