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1. The Role of Appendage Spacing in the Hydrodynamics of Metachronal Propulsion

   https://doi.org/10.1115/FEDSM2025-160892  

   Zharfa, Mohammadreza; Peterman, David J; Herrera-Amaya, Adrian; Byron, Margaret L (September 2025, American Society of Mechanical Engineers)

   Abstract Biological systems have often been sources of inspiration for engineering design. Over the past decade, advances in soft robotics have enabled the development of bioinspired technology across a wide range of sizes and applications. When paired with recent advances in miniaturization and manufacturing techniques, soft robotics can be used to investigate the locomotion and bio-hydrodynamics of millimeter-scale swimmers that operate at intermediate Reynolds numbers (100–103). However, it is important to understand the kinematics and dynamics of biological model systems in order to leverage the true potential of bioinspired robots/devices. Ctenophores (comb jellies) are gelatinous marine invertebrates with soft bodies and flexible appendages composed of bundles of millimeter-long cilia; they are the largest animals in the world to locomote using cilia, with each appendage operating at a Reynolds number of approximately 102. Their efficiency, maneuverability, and ubiquity in the global ocean make them a potentially attractive candidate for bioinspired design applications. Each ctenophore has eight rows of paddle-like ciliary bundles (ctenes) that beat metachronally, with a phase lag between neighboring appendages, producing a “metachronal wave” that propagates along the row. This strategy, known as metachronal coordination, is also used by many other organisms (including crustaceans, annelids, and insects) to facilitate feeding, respiration, and locomotion. In general, the performance of a metachronal system depends on a large number of geometrical and dynamical parameters (e.g. beat frequency, phase lag, appendage length, appendage spacing, et al). However, it is unclear how these parameters interact to affect the hydrodynamics of the system overall. We take advantage of natural variation between different species of ctenophores to explore the role of beating frequency, body size, and propulsor spacing in metachronal systems. Using Particle Shadow Velocimetry (PSV), we compare velocity and vorticity fields generated by actively beating ctene rows in three distinct ctenophore species, across a range of beating frequencies and body shapes. Our findings show that ctenophores with more densely packed ctenes (i.e., closer propulsor spacing) generate more coherent flow fields compared to those with higher propulsor spacing at similar Reynolds numbers. Our results highlight the importance of subtle geometric/kinematic differences in driving fluid flow by flexible appendages, and provide a foundation for further investigation of the role of appendage spacing in metachronal coordination for both biological and bioinspired systems. 

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2. Hybrid Metachronal Rowing Augments Swimming Speed and Acceleration via Increased Stroke Amplitude

   https://doi.org/10.1093/icb/icab141  

   Ford, Mitchell P; Ray, William J; DiLuca, Erika M; Patek, S N; Santhanakrishnan, Arvind (June 2021, Integrative and Comparative Biology)

   null (Ed.)

   Synopsis Numerous aquatic invertebrates use drag-based metachronal rowing for swimming, in which closely spaced appendages are oscillated starting from the posterior, with each appendage phase-shifted in time relative to its neighbor. Continuously swimming species such as Antarctic krill generally use “pure metachronal rowing” consisting of a metachronal power stroke and a metachronal recovery stroke, while burst swimming species such as many copepods and mantis shrimp typically use “hybrid metachronal rowing” consisting of a metachronal power stroke followed by a synchronous or nearly synchronous recovery stroke. Burst swimming organisms need to rapidly accelerate in order to capture prey and/or escape predation, and it is unknown whether hybrid metachronal rowing can augment acceleration and swimming speed compared to pure metachronal rowing. Simulations of rigid paddles undergoing simple harmonic motion showed that collisions between adjacent paddles restrict the maximum stroke amplitude for pure metachronal rowing. Hybrid metachronal rowing similar to that observed in mantis shrimp (Neogonodactylus bredini) permits oscillation at larger stroke amplitude while avoiding these collisions. We comparatively examined swimming speed, acceleration, and wake structure of pure and hybrid metachronal rowing strategies by using a self-propelling robot. Both swimming speed and peak acceleration of the robot increased with increasing stroke amplitude. Hybrid metachronal rowing permitted operation at larger stroke amplitude without collision of adjacent paddles on the robot, augmenting swimming speed and peak acceleration. Hybrid metachronal rowing generated a dispersed wake unlike narrower, downward-angled jets generated by pure metachronal rowing. Our findings suggest that burst swimming animals with small appendage spacing, such as copepods and mantis shrimp, can use hybrid metachronal rowing to generate large accelerations via increasing stroke amplitude without concern of appendage collision. 

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3. Omnidirectional propulsion in a metachronal swimmer

   https://doi.org/10.1371/journal.pcbi.1010891  

   Herrera-Amaya, Adrian; Byron, Margaret L (November 2023, PLOS Computational Biology)

   Marsden, Alison (Ed.)

   Aquatic organisms often employ maneuverable and agile swimming behavior to escape from predators, find prey, or navigate through complex environments. Many of these organisms use metachronally coordinated appendages to execute complex maneuvers. However, though metachrony is used across body sizes ranging from microns to tens of centimeters, it is understudied compared to the swimming of fish, cetaceans, and other groups. In particular, metachronal coordination and control of multiple appendages for three-dimensional maneuvering is not fully understood. To explore the maneuvering capabilities of metachronal swimming, we combine 3D high-speed videography of freely swimming ctenophores (Bolinopsis vitrea) with reduced-order mathematical modeling. Experimental results show that ctenophores can quickly reorient, and perform tight turns while maintaining forward swimming speeds close to 70% of their observed maximum—performance comparable to or exceeding that of many vertebrates with more complex locomotor systems. We use a reduced-order model to investigate turning performance across a range of beat frequencies and appendage control strategies, and reveal that ctenophores are capable of near-omnidirectional turning. Based on both recorded and modeled swimming trajectories, we conclude that the ctenophore body plan enables a high degree of maneuverability and agility, and may be a useful starting point for future bioinspired aquatic vehicles. 

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4. Numerical Study of Metachronal Wave‐Modulated Locomotion in Magnetic Cilia Carpets

   https://doi.org/10.1002/aisy.202300212  

   Jiang, Hao; Gu, Hongri; Nelson, Bradley J.; Zhang, Teng (July 2023, Advanced Intelligent Systems)

   Metachronal motions are ubiquitous in terrestrial and aquatic organisms and have attracted substantial attention in engineering for their potential applications. Hard‐magnetic soft materials are shown to provide new opportunities for metachronal wave‐modulated robotic locomotion by multi‐agent active morphing in response to external magnetic fields. However, the design and optimization of such magnetic soft robots can be complex, and the fabrication and magnetization processes are often delicate and time‐consuming. Herein, a computational model is developed that integrates granular models into a magnetic–lattice model, both of which are implemented in the highly efficient parallel computing platform large‐scale atomic/molecular massively parallel simulator (LAMMPS). The simulations accurately reproduce the deformation of single cilium, the metachronal wave motion of multiple cilia, and the crawling and rolling locomotion of magnetic cilia soft robots. Furthermore, the simulations provide insight into the spatial and temporal variation of friction forces and trajectories of cilia tips. The results contribute to the understanding of metachronal wave‐modulated locomotion and potential applications in the field of soft robotics and biomimetic engineering. The developed model also provides a versatile computational framework for simulating the movement of magnetic soft robots in realistic environments and has the potential to guide the design, optimization, and customization of these systems. 

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5. Closer Appendage Spacing Augments Metachronal Swimming Speed by Promoting Tip Vortex Interactions

   https://doi.org/10.1093/icb/icab112  

   Ford, Mitchell P; Santhanakrishnan, Arvind (May 2021, Integrative and Comparative Biology)

   null (Ed.)

   Abstract Numerous species of aquatic invertebrates, including crustaceans, swim by oscillating multiple closely spaced appendages. The coordinated, out-of-phase motion of these appendages, known as “metachronal paddling,” has been well-established to improve swimming performance relative to synchronous paddling. Invertebrates employing this propulsion strategy cover a wide range of body sizes and shapes, but the ratio of appendage spacing (G) to the appendage length (L) has been reported to lie in a comparatively narrow range of 0.2 < G/L ≤ 0.65. The functional role of G/L on metachronal swimming performance is unknown. We hypothesized that for a given Reynolds number and stroke amplitude, hydrodynamic interactions promoted by metachronal stroke kinematics with small G/L can increase forward swimming speed. We used a dynamically scaled self-propelling robot to comparatively examine swimming performance and wake development of metachronal and synchronous paddling under varying G/L, phase lag, and stroke amplitude. G/L was varied from 0.4 to 1.5, with the expectation that when G/L is large, there should be no performance difference between metachronal and synchronous paddling due to a lack of interaction between vortices that form on the appendages. Metachronal stroking at nonzero phase lag with G/L in the biological range produced faster swimming speeds than synchronous stroking. As G/L increased and as stroke amplitude decreased, the influence of phase lag on the swimming speed of the robot was reduced. For smaller G/L, vortex interactions between adjacent appendages generated a horizontally oriented wake and increased momentum fluxes relative to larger G/L, which contributed to increasing swimming speed. We find that while metachronal motion augments swimming performance for closely spaced appendages (G/L <1), moderately spaced appendages (1.0 ≤ G/L ≤ 1.5) can benefit from the metachronal motion only when the stroke amplitude is large. 

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