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.

Evolutionary convergence of muscle architecture in relation to locomotor ecology in snakes

The epaxial muscles in snakes are responsible for locomotion and as such can be expected to show adaptations in species living in different environments. Here, we tested whether the structural units that comprise the superficial epaxial muscles (semispinalis-spinalis, SSP; longissimus dorsi, LD; iliocostalis, IC) were different in animals occupying similar habitats. To do so, we analyzed and compared the muscle architecture (mass, fiber length, and physiological cross-sectional area) of the superficial epaxial muscle segments in snakes that differ in their habitat use (e.g., arboreal, terrestrial, and aquatic). Our results showed that arboreal species have on average longer muscles and tendons spanning more segments likely important during gap bridging. Moreover, aquatic snakes show relatively heavier semispinalis-spinalis muscles with a greater cross-sectional area. The longissimus dorsi muscles also showed a greater cross-sectional area compared with terrestrial and especially arboreal snakes. Whereas the more strongly developed muscles in aquatic snakes are likely associated with the dense and viscous environment through which they move, the lighter muscles in arboreal snakes may provide an advantage when climbing. Future studies comparing other ecologies (e.g., burrowing snakes) and additional muscle units (e.g., multifidus; hypaxial muscles) are needed to better understand the structural features driving variation in locomotor performance and efficiency in snakes.

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.

Lateral Oscillation and Body Compliance Help Snakes and Snake Robots Stably Traverse Large, Smooth Obstacles

Snakes can move through almost any terrain. Similarly, snake robots hold the promise as a versatile platform to traverse complex environments such as earthquake rubble. Unlike snake locomotion on flat surfaces which is inherently stable, when snakes traverse complex terrain by deforming their body out of plane, it becomes challenging to maintain stability. Here, we review our recent progress in understanding how snakes and snake robots traverse large, smooth obstacles such as boulders and felled trees that lack "anchor points" for gripping or bracing. First, we discovered that the generalist variable kingsnake combines lateral oscillation and cantilevering. Regardless of step height and surface friction, the overall gait is preserved. Next, to quantify static stability of the snake, we developed a method to interpolate continuous body in three dimensions (3D) (both position and orientation) between discrete tracked markers. By analyzing the base of support using the interpolated continuous body 3-D kinematics, we discovered that the snake maintained perfect stability during traversal, even on the most challenging low friction, high step. Finally, we applied this gait to a snake robot and systematically tested its performance traversing large steps with variable heights to further understand stability principles. The robot rapidly and stably traversed steps nearly as high as a third of its body length. As step height increased, the robot rolled more frequently to the extent of flipping over, reducing traversal probability. The absence of such failure in the snake with a compliant body inspired us to add body compliance to the robot. With better surface contact, the compliant body robot suffered less roll instability and traversed high steps at higher probability, without sacrificing traversal speed. Our robot traversed large step-like obstacles more rapidly than most previous snake robots, approaching that of the animal. The combination of lateral oscillation and body compliance to form a large, reliable base of support may be useful for snakes and snake robots to traverse diverse 3-D environments with large, smooth obstacles.

Robotic modelling of snake traversing large, smooth obstacles reveals stability benefits of body compliance

Snakes can move through almost any terrain. Although their locomotion on flat surfaces using planar gaits is inherently stable, when snakes deform their body out of plane to traverse complex terrain, maintaining stability becomes a challenge. On trees and desert dunes, snakes grip branches or brace against depressed sand for stability. However, how they stably surmount obstacles like boulders too large and smooth to gain such 'anchor points' is less understood. Similarly, snake robots are challenged to stably traverse large, smooth obstacles for search and rescue and building inspection. Our recent study discovered that snakes combine body lateral undulation and cantilevering to stably traverse large steps. Here, we developed a snake robot with this gait and snake-like anisotropic friction and used it as a physical model to understand stability principles. The robot traversed steps as high as a third of its body length rapidly and stably. However, on higher steps, it was more likely to fail due to more frequent rolling and flipping over, which was absent in the snake with a compliant body. Adding body compliance reduced the robot's roll instability by statistically improving surface contact, without reducing speed. Besides advancing understanding of snake locomotion, our robot achieved high traversal speed surpassing most previous snake robots and approaching snakes, while maintaining high traversal probability.

Quantitative axial myology in two constricting snakes: Lampropeltis holbrooki and Pantherophis obsoletus

A snake's body represents an extreme degree of elongation with immense muscle complexity. Snakes have approximately 25 different muscles on each side of the body at each vertebra. These muscles serially repeat, overlap, interconnect, and rarely insert parallel to the vertebral column. The angled muscles mean that simple measurements of anatomical cross-sectional area (ACSA, perpendicular to the long-axis of the body) serve only as proxies for the primary determinant of muscle force, physiological cross-sectional area (PCSA, area perpendicular to the muscle fibers). Here, I describe and quantify the musculature of two intraguild constrictors: kingsnakes (Lampropeltis holbrooki) and ratsnakes (Pantherophis obsoletus) whose predation performance varies considerably. Kingsnakes can produce significantly higher constriction pressures compared with ratsnakes of similar size. In both snakes, I provide qualitative descriptions, detail previously undescribed complexity, identify a new lateral muscle, and provide some of the first quantitative measures of individual muscle and whole-body PCSA. Furthermore, I compare measurements of ACSA with measurements of PCSA. There was no significant difference in PCSA of muscles between kingsnakes and ratsnakes. There is, however, a strong relationship between ACSA and PCSA measurements. I could not identify a significant difference in musculature between kingsnakes and ratsnakes that explains their different levels of constriction performance. Unmeasured components of muscle function, such as endurance and force production, might account for differences in performance between two species with similar muscle structure.