Neuromechanical wave resonance in jellyfish swimming

By A.P. Hoover, N.W. Xu, B.J. Gemmell, S.P. Colin, J.H. Costello, J.O, Dabiri, and L.A. Miller

Proceedings of the National Academy of Sciences (to appear)

For organisms to have robust locomotion, their neuromuscular organization must adapt to constantly changing environments. In jellyfish, swimming robustness emerges when marginal pacemakers fire action potentials throughout the bell's motor nerve net, which signals the musculature to contract. The speed of the muscle activation wave is dictated by the passage times of the action potentials. However, passive elastic material properties also influence the emergent kinematics, with time scales independent of neuromuscular organization. In this multi-modal study, we examine the interplay between these two timescales during turning. A 3-D computational fluid-structure interaction model of a jellyfish was developed to determine the resulting emergent kinematics, using bidirectional muscular activation waves to actuate the bell rim. Activation wave speeds near the material wave speed yielded successful turns, with a 76-fold difference in turning rate between the best and worst performers. Hyperextension of the margin occurred only at activation wave speeds near the material wave speed, suggesting resonance. This hyperextension resulted in a 34-fold asymmetry in the circulation of the vortex ring between the inside and outside of the turn. Experimental recording of the activation speed confirmed that jellyfish actuate within this range, and flow visualization using particle image velocimetry validated the corresponding fluid dynamics of the numerical model. This suggests that neuromechanical wave resonance plays an important role in the robustness of an organism's locomotory system, and presents an undiscovered constraint on the evolution of flexible organisms. Understanding these dynamics is essential for developing actuators in soft body robotics and bioengineered pumps.

By A.P. Hoover, J. Daniels, J. Nawroth, and K. Katija

Fluids 6 (2), 88, 2021.

Flexible propulsors are ubiquitous in aquatic and flying organisms and are of great interest for bioinspired engineering. However, many animal models, especially those found in the deep sea, remain inaccessible to direct observation in the laboratory. We address this challenge by conducting an integrative study of the giant larvacean, an invertebrate swimmer and "fluid pump" of the mesopelagic zone. We demonstrate a workflow involving deep sea robots, advanced imaging tools, and numerical modeling to assess the kinematics and resulting fluid transport of the larvacean's beating tail. A computational model of the tail was developed to simulate the local fluid environment and the tail kinematics using embedded passive (elastic) and active (muscular) material properties. The model examines how varying the extent of muscular activation affects the resulting kinematics and fluid transport rates. We find that muscle activation in two-thirds of the tail's length, which corresponds to the observed kinematics in giant larvaceans, generates a greater average downstream flow speed than other designs with the same power input. Our results suggest that the active and passive material properties of the larvacean tail are tuned to produce efficient fluid transport for swimming and feeding, and provide new insight into the role of flexibility in biological propulsors.

As fish swim through a fluid environment, they must actively use their fins in concert to stabilize their motion and have a robust form of locomotion. However, there is little knowledge of how these forces act on the fish body. In this study, we employ a 3D immersed boundary model to decode the relationship between roll, pitch, and yaw of the fish body and the driving forces acting on flexible fish bodies. Using bluegill sunfish as our representative geometry, we first examine the role of an actuating torque on the stability of the fish model, with a torque applied at the head of the unconstrained fish body. The resulting kinematics is a product of the passive elasticity, fluid forces, and driving torque. We then examine a constrained model to understand the role that fin geometry, body elasticity, and frequency play on the range of corrective forces acting on the fish. We find non-monotonic behavior with respect to frequency, suggesting that the effective flexibility of the fins play an important role in the swimming performance.

By D. Calvetti, A.P. Hoover, J. Rose, and E. Somersalo

Frontiers in Physics: Social Physics, 2020.

Mathematical models of SARS-CoV-2 (the virus which causes COVID-19) spread are used for guiding the design of mitigation steps and helping identify impending breaches of health care system surge capacity. The challenges of having only lacunary information about daily new infections and mortality counts are compounded by geographic heterogeneity of the population. This complicates prediction, particularly when using models assuming well-mixed populations. To address this problem, we account for the differences between rural and urban settings using network-based, distributed models where the spread of the pandemic is described in distinct local cohorts with nested SE(A)IR models, i.e., modified SEIR models that include infectious asymptomatic individuals. The model parameters account for the SARS-CoV-2 transmission mostly via human-to-human contact, and the fact that contact frequency among individuals differs between urban and rural areas, and may change over time. The probability that the virus spreads into an uninfected community is associated with influx of individuals from communities where the infection is already present, thus each node is characterized by its internal contact and by its connectivity with other nodes. Census data are used to set up the adjacency matrix of the network, which can be modified to simulate changes in mitigation measures. Our network SE(A)IR model depends on easily interpretable parameters estimated from available community level data. The parameters estimated with Bayesian techniques include transmission rate and the ratio asymptomatic to symptomatic infectious individuals. The methodology predicts that the latter quantity approaches 0.5 as the epidemic reaches an equilibrium, in full agreement with the May 22, 2020 CDC modeling. The network model gives rise to a spatially distributed computational model that explains the geographic dynamics of the contagion, e.g., in larger cities surrounded by suburban and rural areas. The time courses of the infected cohorts in the different counties predicted by the network model are remarkably similar to the reported observations. Moreover, the model shows that monitoring the infection prevalence in each county, and adopting local mitigation measures as infections climb beyond a certain threshold, is almost as effective as blanket measures, and more effective than reducing inter-county mobility.

By J.T. Vorhies, A.P. Hoover, and A Madanayake

IEEE Transactions on Circuits and Systems II: Express Briefs, 2020.

A novel method is described for adaptive filtering of light fields to enhance objects at a given depth. Using the frequency domain of an epipolar-plane image (EPI) to select the minimum and maximum depths of an object of interest (OOI) allows greater selectivity over traditional methods and the ability to re-focus a light field as the scene changes. This method is executed on real light fields, where depth information is extracted and used for depth filtering. A light field video is used to show that as an OOI moves to varying depths in a scene, the performance of a fixed-depth filter decreases when compared to an adaptive-depth filter. This method is shown to be robust in an environment where an OOI is moving to different depths in relation to the camera, and has implications in tasks where objects must be identified by their depth, such as in robotics or autonomous vehicles.

By A.L. Davis, A.P. Hoover, and L.A. Miller

Bulletin of mathematical biology 81 (10), 3803-3822, 2019.

The intertidal zone is a turbulent landscape where organisms face numerous mechanical challenges from powerful waves. A model for understanding the solutions to these physical problems, the American horseshoe crab (Limulus polyphemus), is a marine arthropod that mates in the intertidal zone, where it must contend with strong ambient flows to maintain its orientation during locomotion and reproduction. Possible strategies to maintain position include either negative lift generation or the minimization of positive lift in flow. To quantify flow over the shell and the forces generated, we laser-scanned the 3D shape of a horseshoe crab, and the resulting digital reconstruction was used to 3D-print a physical model. We then recorded the movement of tracking particles around the shell model with high-speed video and analyzed the time-lapse series using particle image velocimetry (PIV). The velocity vector fields from PIV were used to validate numerical simulations performed with the immersed boundary (IB) method. IB simulations allowed us to resolve the forces acting on the shell, as well as the local three-dimensional flow velocities and pressures. Both IB simulations and PIV analysis of vorticity and velocity at a flow speed of 13 cm/s show negative lift for negative and zero angles of attack, and positive lift for positive angles of attack in a free-stream environment. In shear flow simulations, we found near-zero lift for all orientations tested. Because horseshoe crabs are likely to be found primarily at near-zero angles of attack, we suggest that this negative lift helps maintain the orientation of the crab during locomotion and mating. This study provides a preliminary foundation for assessing the relationship between documented morphological variation and potential environmental variation for distinct populations of horseshoe crabs along the Atlantic Coast. It also motivates future studies which could consider the stability of the horseshoe crab in unsteady, oscillating flows.

By A.P. Hoover, A.J. Porras, and L.A. Miller

Journal of Fluid Mechanics 863, 1031-1061, 2019.

Diverse organisms that swim and fly in the inertial regime use the flapping or pumping of flexible appendages and cavities to propel themselves through a fluid. It has long been postulated that the speed and efficiency of locomotion are optimized by oscillating these appendages at their frequency of free vibration. In jellyfish swimming, a significant contribution to locomotory efficiency has been attributed to the effects passive energy recapture, whereby the bell is passively propelled through the fluid through its interaction with stopping vortex rings formed during each expansion of the bell. In this paper, we investigate the interplay between resonance and passive energy recapture using a three-dimensional implementation of the immersed boundary method to solve the fluid–structure interaction of an elastic oblate jellyfish bell propelling itself through a viscous fluid. The motion is generated through a fixed duration application of active tension to the bell margin, which mimics the action of the coronal swimming muscles. The pulsing frequency is then varied by altering the length of time between the application of applied tension. We find that the swimming speed is maximized when the bell is driven at its resonant frequency. However, the cost of transport is maximized by driving the bell at lower frequencies whereby the jellyfish passively coasts between active contractions through its interaction with the stopping vortex ring. Furthermore, the thrust generated by passive energy recapture was found to be dependent on the elastic properties of the jellyfish bell.

By A.P. Hoover, R. Cortez, E. Tytell, and L. Fauci

Journal of Fluid Mechanics 847, 386-416, 2018.

Many animals that swim or fly use their body to accelerate the fluid around them, transferring momentum from their flexible bodies and appendages to the surrounding fluid. The kinematics that emerge from this transfer result from the coupling between the fluid and the active and passive material properties of the flexible body or appendages. To elucidate the fundamental features of the elastohydrodynamics of flexible appendages, recent physical experiments have quantified the propulsive performance of flexible panels that are actuated on their leading edge. Here we present a complementary computational study of a three-dimensional flexible panel that is heaved sinusoidally at its leading edge in an incompressible, viscous fluid. These high-fidelity numerical simulations enable us to examine how propulsive performance depends on mechanical resonance, fluid forces, and the emergent panel deformations. Moreover, the computational model does not require the tethering of the panel. We therefore compare the thrust production of tethered panels to the forward swimming speed of the same panels that can move forward freely. Varying both the passive material properties and the heaving frequency of the panel, we find that local peaks in trailing edge amplitude and forward swimming speed coincide and that they are determined by a non-dimensional quantity, the effective flexibility, that arises naturally in the Euler-Bernoulli beam equation. Modal decompositions of panel deflections reveal that the amplitude of each mode is related to the effective flexibility. Panels of different material properties that are actuated so that their effective flexibilities are closely matched have modal contributions that evolve similarly over the phase of the heaving cycle, leading to similar vortex structures in their wakes and comparable thrust forces and swimming speeds. Moreover, local peaks in the swimming speed and trailing edge amplitude correspond to peaks in the contributions of the different modes.This computational study of freely-swimming flexible panels gives further insight into the role of resonance in swimming performance that is important in the engineering and design of robotic propulsors. Moreover, we view this reduced model and its comparison to laboratory experiments as a building-block and validation for a more comprehensive three-dimensional computational model of an undulatory swimmer that will couple neural activation, muscle mechanics and body elasticity with the surrounding viscous, incompressible fluid.

By A.P. Hoover, B.E. Griffith, and L.A. Miller

Journal of Fluid Mechanics, 813:1112-1155, 2017

In many swimming and flying animals, propulsion emerges from the interplay of active muscle contraction, passive body elasticity and fluid–body interaction. Changes in the active and passive body properties can influence performance and cost of transport across a broad range of scales; they specifically affect the vortex generation that is crucial for effective swimming at higher Reynolds numbers. Theoretical models that account for both active contraction and passive elasticity are needed to understand how animals tune both their active and passive properties to move efficiently through fluids. This is particularly significant when one considers the phylogenetic constraints on the jellyfish mechanospace, such as the presence of relatively weak muscles that are only one cell layer thick. In this work, we develop an actively deforming model of a jellyfish immersed in a viscous fluid and use numerical simulations to study the role of active muscle contraction, passive body elasticity and fluid forces in the medusan mechanospace. By varying the strength of contraction and the flexibility of the bell margin, we quantify how these active and passive properties affect swimming speed and cost of transport. We find that for fixed bell elasticity, swimming speed increases with the strength of contraction. For fixed force of contractility, swimming speed increases as margin elasticity decreases. Varying the strength of activation in proportion to the elasticity of the bell margin yields similar swimming speeds, with a cost of transport is substantially reduced for more flexible margins. A scaling study reveals that performance declines as the Reynolds number decreases. Circulation analysis of the starting and stopping vortex rings showed that their strengths were dependent on the relative strength of activation with respect to the bell margin flexibility. This work yields a computational framework for developing a quantitative understanding of the roles of active and passive body properties in swimming.

By A.P. Hoover and L.A. Miller

Journal of Theoretical Biology, 374:13-25, 2015.

A current question in swimming and flight is whether or not driving flexible appendages at their resonant frequency results in faster or more efficient locomotion. It has been suggested that jellyfish swim faster when the bell is driven at its resonant frequency. The goal of this study was to determine whether or not driving a jellyfish bell at its resonant frequency results in a significant increase in swimming velocity. To address this question, the immersed boundary method was used to solve the fully coupled fluid structure interaction problem of a flexible bell in a viscous fluid. Free vibration numerical experiments were used to determine the resonant frequency of the jellyfish bell. The jellyfish bells were then driven at frequencies ranging from above and below the resonant frequency. We found that jellyfish do swim fastest for a given amount of applied force when the bells are driven near their resonant frequency. Nonlinear effects were observed for larger deformations, shifting the optimal frequency to higher than the resonant frequency. We also found that the benefit of resonant forcing decreases for lower Reynolds numbers.

By L. Homa, D. Calvetti, A.P. Hoover, and E. Somersalo

SIAM J. Sci. Comput., 35(3), B778–B798, 2013.

We consider the computational problem arising in magnetoencephalography (MEG), where the goal is to estimate the electric activity within the brain noninvasively from extracranial measurements of the magnetic field components. The problem is severely ill-posed due to the intrinsic nonuniqueness of the solution, and suffers further from the challenges of a weak data signal, its high dimensionality, and complexity of the noise, part of which is due to the brain itself. In this work, we suggest a new algorithm that is based on a truncated conjugate gradient algorithm for least squares with statistically inspired left and right preconditioners. We demonstrate that by carefully accounting for the spatiotemporal statistical structure of the brain noise and by adopting a suitable prior within the Bayesian framework, we can design a robust and efficient method for the numerical solution of the MEG inverse problem which can improve the spatial and temporal resolution of events of short duration. The effectiveness of the proposed method is demonstrated on a synthetic example of localization of spiking simulating the focal onset of epileptic seizures.