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.

Proprioceptive feedback amplification restores effective locomotion in a neuromechanical model of lampreys with spinal injuries.

Spinal injuries in many vertebrates can result in partial or complete loss of locomotor ability. While mammals often experience permanent loss, some nonmammals, such as lampreys, can regain swimming function, though the exact mechanism is not well understood. One hypothesis is that amplified proprioceptive (body-sensing) feedback can allow an injured lamprey to regain functional swimming even if the descending signal is lost. This study employs a multiscale, integrative, computational model of an anguilliform swimmer fully coupled to a viscous, incompressible fluid and examines the effects of amplified feedback on swimming behavior. This represents a model that analyzes spinal injury recovery by combining a closed-loop neuromechanical model with sensory feedback coupled to a full Navier-Stokes model. Our results show that in some cases, feedback amplification below a spinal lesion is sufficient to partially or entirely restore effective swimming behavior.

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.

The effect of intrinsic muscular nonlinearities on the energetics of locomotion in a computational model of an anguilliform swimmer.

Animals move through their environments using muscles to produce force. When an animal׳s nervous system activates a muscle, the muscle produces different amounts of force depending on its length, its shortening velocity, and its time history of force production. These muscle forces interact with forces from passive tissue properties and forces from the external environment. Using an integrative computational model that couples an elastic, actuated model of an anguilliform, lamprey-like swimmer with a surrounding Navier-Stokes fluid, we study the effects of this coupling between the muscle force and the body motion. Swimmers with different forms of this coupling can achieve similar motions, but use different amounts of energy. The velocity dependence is the most important property of the ones we considered for reducing energy costs and helping us to stabilize oscillations. These effects are strongly influenced by how rapidly the muscle deactivates; if force decays too slowly, muscles on opposite sides of the body end up fighting each other, increasing energy cost. Work-dependent deactivation, an effect that causes a muscle to deactivate more rapidly if it has recently produced mechanical work, works together with the velocity dependence to reduce the energy cost of swimming.

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.

Reconfiguration and the reduction of vortex-induced vibrations in broad leaves.

Flexible plants, fungi and sessile animals reconfigure in wind and water to reduce the drag acting upon them. In strong winds and flood waters, for example, leaves roll up into cone shapes that reduce drag compared with rigid objects of similar surface area. Less understood is how a leaf attached to a flexible leaf stalk will roll up stably in an unsteady flow. Previous mathematical and physical models have only considered the case of a flexible sheet attached to a rigid tether in steady flow. In this paper, the dynamics of the flow around the leaf of the wild ginger Hexastylis arifolia and the wild violet Viola papilionacea are described using particle image velocimetry. The flows around the leaves are compared with those of simplified physical and numerical models of flexible sheets attached to both rigid and flexible beams. In the actual leaf, a stable recirculation zone is formed within the wake of the reconfigured cone. In the physical model, a similar recirculation zone is observed within sheets constructed to roll up into cones with both rigid and flexible tethers. Numerical simulations and experiments show that flexible rectangular sheets that reconfigure into U-shapes, however, are less stable when attached to flexible tethers. In these cases, larger forces and oscillations due to strong vortex shedding are measured. These results suggest that the three-dimensional cone structure in addition to flexibility is significant to both the reduction of vortex-induced vibrations and the forces experienced by the leaf.

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.

A numerical study of the effects of bell pulsation dynamics and oral arms on the exchange currents generated by the upside-down jellyfish Cassiopea xamachana.

Mathematical and experimental studies of the flows generated by jellyfish have focused primarily on mechanisms of swimming. More recent work has also considered the fluid dynamics of feeding from currents generated during swimming. Here we capitalize on the benthic lifestyle of the upside-down jellyfish (Cassiopea xamachana) to explore the fluid dynamics of feeding uncoupled from swimming. A two-dimensional mathematical model is developed to capture the fundamental characteristics of the motion of the unique concave bell shape. Given the prominence of the oral arms, this structure is included and modeled as a porous layer that perturbs the flow generated by bell contractions. The immersed boundary method is used to solve the fluid-structure interaction problem. Velocity fields obtained from live organisms using digital particle image velocimetry were used to validate the numerical simulations. Parameter sweeps were used to numerically explore the effects of changes in pulse dynamics and the properties of the oral arms independently. Numerical experiments allow the opportunity to examine physical effects and limits within and beyond the biologically relevant range to develop a better understanding of the system. The presence of the prominent oral arm structures in the field of flow increased the flux of new fluid from along the substrate to the bell. The numerical simulations also showed that the presence of pauses between bell expansion and the next contraction alters the flow of the fluid over the bell and through the oral arms.

Parts per quadrillion level ultra-trace determination of polar and nonpolar compounds via solvent-free capillary microextraction on surface-bonded sol-gel polytetrahydrofuran coating and gas chromatography-flame ionization detection.

Sol-gel polytetrahydrofuran (poly-THF) coating was developed for high-sensitivity sample preconcentration by capillary microextraction (CME). Parts per quadrillion (ppq) level detection limits were achieved for both polar and nonpolar analytes through sample preconcentration on sol-gel poly-THF coated microextraction capillaries followed by gas chromatography (GC) analysis of the extracted compounds using a flame ionization detector (FID). The sol-gel coating was in situ created on the inner walls of a fused silica capillary using a sol solution containing poly-THF as an organic component, methyltrimethoxysilane (MTMOS) as a sol-gel precursor, trifluoroacetic acid (TFA, 5% water) as a sol-gel catalyst, and hexamethyldisilazane (HMDS) as a deactivating reagent. The sol solution was introduced into a hydrothermally-treated fused silica capillary and the sol-gel reactions were allowed to take place inside the capillary for 60 min. A wall-bonded coating was formed due to the condensation of silanol groups residing on the capillary inner surface with those on the sol-gel network fragments evolving in close vicinity of the capillary walls. Poly-THF is a medium polarity polymer, and was found to be effective in carrying out simultaneous extraction of both polar and nonpolar analytes. Efficient extraction of a wide range of trace analytes from aqueous samples was accomplished using sol-gel poly-THF coated fused silica capillaries for further analysis by GC. The test analytes included polycyclic aromatic hydrocarbons (PAHs), aldehydes, ketones, chlorophenols, and alcohols. To our knowledge, this is the first report on the use of a poly-THF based sol-gel material in analytical microextraction. Sol-gel poly-THF coated CME capillaries showed excellent solvent and thermal stability (>320 degrees C).

Capillary microextraction on sol-gel dendrimer coatings.

Sol-gel capillary microextraction (CME) is a new direction in the solventless sample preparation for the preconcentration of trace analytes, and presents significant interest in environmental, pharmaceutical, petrochemical, biomedical, agricultural, food, flavor, and a host of other important areas. It utilizes advanced material properties of organic-inorganic hybrid sol-gel polymers to perform efficient extraction and preconcentration of target compounds from a wide variety of matrices. In the present work, a novel benzyl-terminated dendron-based sol-gel coating was developed for CME. A detailed investigation was conducted to evaluate the performance of the newly developed sol-gel dendrimer coatings to perform solventless extraction of a wide range of polar and nonpolar analytes. The characteristic branched architecture of dendrons makes them structurally superior extraction media compared with their traditional linear polymeric counterparts. Sol-gel chemistry was used to chemically immobilize dendritic macromolecules on fused silica capillary inner surface. Due to the strong chemical bonding with the capillary inner walls, sol-gel dendron coatings showed excellent thermal and solvent stability in capillary microextraction in hyphenation with chromatographic analysis. Efficient extraction of a wide range of analytes from their aqueous solutions was accomplished using sol-gel dendron coated fused silica capillaries. Low parts per trillion level detection limits were achieved in CME-GC for both polar and nonpolar analytes including polyaromatic hydrocarbons (PAHs), aldehydes, ketones, phenols, and alcohols.