Browsing by Subject "Elastic energy"

Elastic energy plays important roles in biology across scales, from the molecular to organismal level, and across the tree of life. The ubiquity of elastic systems in biology is partly due to the variety of useful functions they permit such as the simplification of motor control in running cockroaches and the efficient recycling of kinetic energy in hopping kangaroos. Elastic energy is also responsible for ultrafast movements; the fastest movements in animals are not powered directly by muscle, but instead by elastic energy stored in a spring. By demonstrating that the power required to generate ultrafast movements exceeds the limits of muscle, many studies conclude that energy storage is necessary; but, what these studies do not explain is how the properties of a biological structure affect its capacity for energy storage. In this dissertation, I test the general principles of energy storage by investigating elastic systems at three hierarchical levels of organization: a single structure, multiple connected structures, and a spring system connected to muscle. By using a multi-level approach, my aim is to demonstrate, at each of the mentioned levels, how properties of the spring system affect where or how much energy is stored in the system as well as how these conclusions can be combined to inform our understanding of the biomechanics of hierarchical elastic systems.

When considering spring systems at the level of a single structure, morphology is one major structural aspect that affects mechanics. Continuous changes in morphology are capable of dividing a structure into regions that are responsible for the two contradicting functions that are essential for spring function: energy storage (via deformation) and structural support (via resistance to deformation). Using high quality micro computed tomography scans, I quantify the morphology of the mantis shrimp (Stomatopoda) merus, a single structure of the raptorial appendage hypothesized to store the elastic energy that drives ultrafast strikes. Comparing the morphology among the species, I find that the merus in smashers, species that depend heavily on elastic energy storage, have relatively thicker ventral regions and more eccentric cross-sections than spearers, species that strike relatively slower. I also conclude that differential thickening of a region can provide structural support for resisting spring compression as well as facilitate structural deformation by inducing bending. This multi-level morphological analysis offers a foundation for understanding the evolution and mechanics of monolithic systems in biology.

When two or more structures are connected, their relative physical properties determine whether the structures store energy, provide structural support, or some combination of both. Although the majority of elastic energy is stored via large deformations of the merus in smashers, some spearer species show relatively little meral deformation, and it is unclear whether elastic energy is stored in these systems. To determine whether the apodeme (arthropod tendon) provides energy storage in species that exhibit low meral deformation, I measure the physical properties of the lateral extensor apodeme and the merus to which it is connected. Comparisons of these properties show that in the spearer species I tested, the merus has a relatively higher spring constant than the apodeme, which results in the merus providing structural support and the apodeme storing the majority of elastic energy. Comparing the material properties of the apodemes with those of other structures reveals that apodemes and other biological spring systems share similar material characteristics. This study demonstrates that in order to understand the biomechanics of spring systems comprised of connected structures, it is necessary to compare their relative mechanical properties.

Finally, because muscles are responsible for loading spring systems with potential energy, muscle dynamics can affect elastic energy storage in a spring system. Although spring systems can circumvent the limits imposed by muscle via power amplification, they are not entirely independent from muscle dynamics. For example, if an organism has relatively low time to prepare and stretch the spring prior to the onset of movement, the limits of muscle power can dominate energy storage. To test the effects of muscle dynamics on spring loading, I implement a mathematical model that connects a Hookean spring model to a Hill-type muscle model, representing the muscle-tendon complex of the hindlimbs of American bullfrogs, in which the muscle dynamics are well understood and the duration of spring loading is low. I find that the measured spring constants of the tendons nearly maximize energy storage within the duration of in vivo spring loading. Additionally, the measured spring constants are lower than those predicted to produce maximal energy storage when infinite time is available for spring loading. Together, these results suggest that the spring constants of the tendons of American bullfrogs are tuned to maximize elastic energy for small durations of spring loading. This study highlights the importance of assessing muscle dynamics and their effect on energy storage when assessing the functional significance of spring constants.

Latch-mediated spring actuation (LaMSA) mechanisms allow a broad diversity of organisms to achieve ultrafast motion. Most research into biological LaMSA mechanisms focuses on a narrow size or age range of the organism when the LaMSA mechanism is fully developed. However, the emergence of LaMSA morphology and behavior during early life history offers novel insights into the scaling and ecology of ultrafast movement. In this thesis, I establish the emergence and kinematics of LaMSA morphology in two systems, the mantis shrimp Gonodactylaceus falcatus (Stomatopoda) and the snapping shrimp Alpheus heterochaelis (Alpheidae). I also examine the plasticity of LaMSA development in the snapping shrimp Alpheus heterochaelis. The mantis shrimp’s spring-actuated strike is one of the best-studied LaMSA mechanisms; however, we do not know when the LaMSA morphology or behavior emerges during development. In Chapter 2, I found that the mantis shrimp G. falcatus develop their LaMSA morphology in their fourth larval stage when they transition into the pelagic zone and begin feeding on plankton. Mathematical and physical models of LaMSA kinematics suggest that smaller mechanisms generate greater accelerations. Therefore, I hypothesized that larval mantis shrimp would accelerate their strikes faster than adult mantis shrimp. Larval kinematics showed that larvae achieve accelerations on par or lower than adult mantis shrimp species. However, the larval strikes are much faster than the swimming speeds of other small pelagic organisms. Snapping shrimp generate cavitation bubbles using a LaMSA mechanism in their major claw. However, we do not know when the snapping shrimp LaMSA morphology or behavior emerges during development, nor whether they can generate cavitation bubbles at that size. In Chapter 3, I establish that the snapping shrimp Alpheus heterochaelis develop LaMSA morphology and behavior between one- and two months after hatching, when their carapace is roughly four to five millimeters long. I again hypothesized that the juvenile snapping shrimp would generate accelerations much faster than adults. My data show that juvenile snapping shrimp can generate accelerations two orders of magnitude faster than adults when the juvenile is more than two orders of magnitude smaller in claw mass. Juvenile snapping shrimp struck so quickly that they generated and directed cavitation bubbles at the millimeter scale. Developmental stressors can affect how morphological traits grow across ontogeny. In some cases, resource allocation to specific body parts during development can mitigate the negative effects of stress. To our knowledge, the developmental plasticity of LaMSA morphology and kinematics has not been explored. In Chapter 4, I test whether the development of the snapping shrimp LaMSA morphology and kinematics is affected by changes in feeding frequency. Juvenile snapping shrimp fed less frequently during development grew more slowly than better-fed individuals. However, the snapping shrimp raised in the least frequently fed group developed slightly larger snapping claws relative to their body size than individuals in other food treatments. Feeding treatments did not appear to affect the scaling of LaMSA kinematics. This thesis shows that the emergence of LaMSA morphology and behavior inform ecological transitions across ontogeny. The findings from this work can provide novel insights into how size may constrain ultrafast motion. The methods and systems I developed offer new systems and approaches for learning about the scaling and plasticity of spring-actuated movement.