Magnetic cilia carpets with programmable metachronal waves

Metachronal waves, the coordinated rhythmic beating of cilia, are crucial for various biological processes like fluid transport, locomotion, and feeding. These emergent phenomena arise from phase differences between neighboring cilia. While numerical simulations have explored metachronal waves, experimental studies, particularly using customizable systems, are limited. This research addresses this gap by introducing a novel approach to fabricate and control artificial cilia carpets using magnetic actuation. The goal is to create a highly customizable platform to investigate the fundamental principles of natural cilia carpets and to pave the way for the development of bio-inspired soft robots for biomedical applications. Understanding the dynamics of metachronal waves is essential for advancing our knowledge of biological systems and for designing new micro-robotic devices. Natural cilia exhibit a variety of beating patterns, achieving complex functions. For instance, the Hawaiian bobtail squid utilizes different cilia beating patterns to attract symbiotic bacteria, while starfish larvae dynamically adjust their patterns for swimming and feeding. Current artificial cilia systems are either limited in the number of cilia, customizable parameters, or lack the ability to produce programmable metachronal waves. This study aims to overcome these limitations by developing a soft robotic system that enables the fabrication and control of large arrays of artificial cilia with customizable properties and programmable beating patterns. This allows for a deeper understanding of the emergent phenomena observed in natural cilia carpets and provides a foundation for developing advanced micro-robotic devices.

Previous research on metachronal waves primarily focused on numerical simulations and observations of natural organisms. Studies have investigated the efficiency of different cilia beating patterns, revealing the advantage of metachronal coordination for fluid pumping. Artificial cilia systems have been developed using various actuation methods, such as pneumatic, light, acoustic, electric, and magnetic fields. However, most of these systems either involve a large number of synchronously beating cilia or are limited to a small number of cilia with few customizable parameters. The lack of large-scale, programmable artificial cilia carpets has hindered experimental studies on complex emergent phenomena, particularly metachronal waves. Some efforts have been made to create artificial cilia that exhibit metachronal motion using different lengths or pre-fabricated assemblies, but these systems typically have limited scalability and customization options. This study aims to overcome these limitations by introducing a new fabrication technique that allows for creating large arrays of artificial cilia with programmable magnetization patterns, enabling the generation of various metachronal wave patterns.

The researchers developed a scalable and repeatable method to fabricate stretchable magnetic cilia carpets. The fabrication process involved two steps: First, a 3D-printed mold was created and coated with a thin layer of resin to ensure a smooth surface. Second, a magnetic composite material (NdFeB particles and Ecoflex) was filled into the mold to form the cilia structures. A non-magnetic stretchable substrate (pure Ecoflex) was then added on top, creating a flexible and stretchable cilia carpet. After curing, the carpet was carefully removed from the mold. The key innovation is the use of a stretching and folding technique to encode magnetization patterns into the cilia carpets. The highly stretchable substrate allowed the carpet to conform to various three-dimensional (3D) geometries. By placing the stretched carpet into a magnetizer, complex magnetization patterns were imprinted onto the cilia. This programmable magnetization is the core element for controlling the metachronal waves. The motion of single cilia and the entire carpet was analyzed both experimentally and through simulations. A magneto-elastic model based on Cosserat rod theory was used to simulate the behavior of single cilia under a rotating magnetic field. This model enabled prediction of cilia trajectories under various magnetization directions and magnetic field strengths. Experiments employed a slowly rotating magnetic field to actuate the artificial cilia. The motion was recorded using high-speed imaging, and the trajectories of individual cilia and particles within a fluid were tracked. Fluid transport experiments involved a cilia carpet submerged in 99% glycerol with fluorescent particles. The displacement of these particles was tracked to evaluate the effectiveness of metachronal waves in promoting fluid transport. Experiments were conducted to explore the relationship between metachronal wavelength, cilia density, and fluid transport efficiency. Finally, locomotion experiments were performed on a solid surface, mimicking the movement of a millipede. The influence of metachronal wave type (symplectic, antiplectic) and wavelength on locomotion speed was investigated. The experiments used a rotating magnetic field and tracked the robot's movement to determine locomotion speeds.

The researchers successfully fabricated large-scale (>200 cilia) stretchable magnetic cilia carpets using a two-step molding process with 3D-printed molds. The highly stretchable substrate allowed for encoding various complex magnetization patterns using curved templates in a magnetizer. A magneto-elastic model accurately predicted the motion of individual cilia under a rotating magnetic field, demonstrating the non-reciprocal trajectories crucial for efficient fluid pumping. Experiments showed that the artificial cilia exhibit two phases of motion (synchronized and asynchronous) similar to natural cilia. The different magnetization directions in individual cilia led to diverse trajectories, allowing for precise control over their movement. The system successfully generated programmable metachronal waves, including symplectic and antiplectic patterns with various wavelengths, as well as standing diaplectic waves. Fluid transport experiments confirmed the importance of metachronal waves in enhancing liquid transport. The results showed a threefold increase in propulsion velocity with metachronal waves compared to uniformly beating cilia, consistent with previous numerical findings. The study also revealed a density dependency in propulsion velocity, aligning with numerical simulations. Locomotion experiments on a solid surface demonstrated two modes of movement: crawling and rolling. The transition between these modes was found to depend on the magnetic field strength. A millipede-inspired soft robot exhibited efficient locomotion, with antiplectic waves resulting in significantly higher speeds than symplectic waves. This difference was attributed to the substrate's curvature during the recovery stroke, suggesting an underlying mechanical mechanism.

This study provides a significant advancement in the field of artificial cilia research by offering a highly customizable and experimentally accessible platform. The ability to fabricate large arrays of cilia with programmable magnetization patterns opens new possibilities for investigating the complex dynamics of metachronal waves. The experimental findings validate previous numerical simulations and provide crucial experimental data on the relationship between metachronal wave characteristics and transport efficiency. The successful demonstration of cilia-driven locomotion in both fluid and solid environments showcases the potential of this technology for developing micro-robots for biomedical applications. The findings related to the impact of metachronal wave type and wavelength on locomotion efficiency open new avenues for designing more effective bio-inspired robots. The correlation between the experimental observations and the theoretical model provides a robust basis for future research and design.

This research presents a significant advance in the field of artificial cilia and soft robotics. The developed magnetic cilia carpets offer a highly customizable experimental platform for studying the fundamental principles of metachronal waves and their role in fluid transport and locomotion. The findings validate prior computational models and offer new insights into the design of cilia-inspired soft robots. Future work could focus on miniaturizing the system to the microscale, investigating the influence of different substrates, and exploring more complex cilia arrangements to simulate diverse biological scenarios. Applications in targeted drug delivery, microfluidics, and microrobotics are promising avenues for future development.

The current system's cilia size is limited by the resolution of the 3D printer used to create the molds. The magnetic actuation system (CardioMag) is relatively bulky and slow in dynamic responses. While the experiments were performed in a low Reynolds number environment, further research could explore the behavior of the system at higher Reynolds numbers. The experiments primarily focused on two-dimensional arrays; future research could explore three-dimensional cilia arrangements.