Mechanosensory Feedback in Lamprey Swimming Models and Applications in the Field of Spinal Cord Regeneration.

The central pattern generator (CPG) in anguilliform swimming has served as a model for examining the neural basis of locomotion. This system has been particularly valuable for the development of mathematical models. As our biological understanding of the neural basis of locomotion has expanded, so too have these models. Recently, there have been significant advancements in our understanding of the critical role that mechanosensory feedback plays in robust locomotion. This work has led to a push in the field of mathematical modeling to incorporate mechanosensory feedback into CPG models. In this perspective piece, we review advances in the development of these models and discuss how newer complex models can support biological investigation. We highlight lamprey spinal cord regeneration as an area that can both inform these models and benefit from them.

Multiscale flow between the branches and polyps of gorgonians.

Gorgonians, including sea fans, are soft corals well known for their elaborate branching structure and how they sway in the ocean. This branching structure can modify environmental flows to be beneficial for feeding in a particular range of velocities and, presumably, for a particular size of prey. As water moves through the elaborate branches, it is slowed, and recirculation zones can form downstream of the colony. At the smaller scale, individual polyps that emerge from the branches expand their tentacles, further slowing the flow. At the smallest scale, the tentacles are covered in tiny pinnules where exchange occurs. In this paper, we quantified the gap to diameter ratios for various gorgonians at the scale of the branches, the polyp tentacles and the pinnules. We then used computational fluid dynamics to determine the flow patterns at all three levels of branching. We quantified the leakiness between the branches, tentacles and pinnules over the biologically relevant range of Reynolds numbers and gap-to-diameter ratios, and found that the branches and tentacles can act as either leaky rakes or solid plates depending upon these dimensionless parameters. The pinnules, in contrast, mostly impede the flow. Using an agent-based modeling framework, we quantified plankton capture as a function of the gap-to-diameter ratio of the branches and the Reynolds number. We found that the capture rate depends critically on both morphology and Reynolds number. The results of the study have implications for how gorgonians modify ambient flows for efficient feeding and exchange.

The role of curvature feedback in the energetics and dynamics of lamprey swimming: A closed-loop model.

Like other animals, lampreys have a central pattern generator (CPG) circuit that activates muscles for locomotion and also adjusts the activity to respond to sensory inputs from the environment. Such a feedback system is crucial for responding appropriately to unexpected perturbations, but it is also active during normal unperturbed steady swimming and influences the baseline swimming pattern. In this study, we investigate different functional forms of body curvature-based sensory feedback and evaluate their effects on steady swimming energetics and kinematics, since little is known experimentally about the functional form of curvature feedback. The distributed CPG is modeled as chains of coupled oscillators. Pairs of phase oscillators represent the left and right sides of segments along the lamprey body. These activate muscles that flex the body and move the lamprey through a fluid environment, which is simulated using a full Navier-Stokes model. The emergent curvature of the body then serves as an input to the CPG oscillators, closing the loop. We consider two forms of feedback, each consistent with experimental results on lamprey proprioceptive sensory receptors. The first, referred to as directional feedback, excites or inhibits the oscillators on the same side, depending on the sign of a chosen gain parameter, and has the opposite effect on oscillators on the opposite side. We find that directional feedback does not affect beat frequency, but does change the duration of muscle activity. The second feedback model, referred to as magnitude feedback, provides a symmetric excitatory or inhibitory effect to oscillators on both sides. This model tends to increase beat frequency and reduces the energetic cost to the lamprey when the gain is high and positive. With both types of feedback, the body curvature has a similar magnitude. Thus, these results indicate that the same magnitude of curvature-based feedback on the CPG with different functional forms can cause distinct differences in swimming performance.

Feeding currents of the upside down jellyfish in the presence of background flow.

The upside-down jellyfish (Cassiopea spp.) is an ideal organism for examining feeding and exchange currents generated by bell pulsations due to its relatively sessile nature. Previous experiments and numerical simulations have shown that the oral arms play an important role in directing new fluid into the bell from along the substrate. All of this work, however, has considered the jellyfish in the absence of background flow, but the natural environments of Cassiopea and other cnidarians are dynamic. Flow velocities and directions fluctuate on multiple time scales, and mechanisms of particle capture may be fundamentally different in moving fluids. In this paper, the immersed boundary method is used to simulate a simplified jellyfish in flow. The elaborate oral arm structure is modeled as a homogenous porous layer. The results show that the oral arms trap vortices as they form during contraction and expansion of the bell. For constant flow conditions, the vortices are directed gently across the oral arms where particle capture occurs. For variable direction flows, the secondary structures change the overall pattern of the flow around the bell and appear to stabilize regions of mixing around the secondary mouths.

Flow structure and transport characteristics of feeding and exchange currents generated by upside-down Cassiopea jellyfish.

Quantifying the flows generated by the pulsations of jellyfish bells is crucial for understanding the mechanics and efficiency of their swimming and feeding. Recent experimental and theoretical work has focused on the dynamics of vortices in the wakes of swimming jellyfish with relatively simple oral arms and tentacles. The significance of bell pulsations for generating feeding currents through elaborate oral arms and the consequences for particle capture are not as well understood. To isolate the generation of feeding currents from swimming, the pulsing kinematics and fluid flow around the benthic jellyfish Cassiopea spp. were investigated using a combination of videography, digital particle image velocimetry and direct numerical simulation. During the rapid contraction phase of the bell, fluid is pulled into a starting vortex ring that translates through the oral arms with peak velocities that can be of the order of 10 cm s(-1). Strong shear flows are also generated across the top of the oral arms throughout the entire pulse cycle. A coherent train of vortex rings is not observed, unlike in the case of swimming oblate medusae such as Aurelia aurita. The phase-averaged flow generated by bell pulsations is similar to a vertical jet, with induced flow velocities averaged over the cycle of the order of 1-10 mm s(-1). This introduces a strong near-horizontal entrainment of the fluid along the substrate and towards the oral arms. Continual flow along the substrate towards the jellyfish is reproduced by numerical simulations that model the oral arms as a porous Brinkman layer of finite thickness. This two-dimensional numerical model does not, however, capture the far-field flow above the medusa, suggesting that either the three-dimensionality or the complex structure of the oral arms helps to direct flow towards the central axis and up and away from the animal.