Publisher Correction: Nanomagnetic encoding of shape-morphing micromachines.

An Amendment to this paper has been published and can be accessed via a link at the top of the paper.

Nanomagnetic encoding of shape-morphing micromachines.

Shape-morphing systems, which can perform complex tasks through morphological transformations, are of great interest for future applications in minimally invasive medicine1,2, soft robotics3-6, active metamaterials7 and smart surfaces8. With current fabrication methods, shape-morphing configurations have been embedded into structural design by, for example, spatial distribution of heterogeneous materials9-14, which cannot be altered once fabricated. The systems are therefore restricted to a single type of transformation that is predetermined by their geometry. Here we develop a strategy to encode multiple shape-morphing instructions into a micromachine by programming the magnetic configurations of arrays of single-domain nanomagnets on connected panels. This programming is achieved by applying a specific sequence of magnetic fields to nanomagnets with suitably tailored switching fields, and results in specific shape transformations of the customized micromachines under an applied magnetic field. Using this concept, we have built an assembly of modular units that can be programmed to morph into letters of the alphabet, and we have constructed a microscale 'bird' capable of complex behaviours, including 'flapping', 'hovering', 'turning' and 'side-slipping'. This establishes a route for the creation of future intelligent microsystems that are reconfigurable and reprogrammable in situ, and that can therefore adapt to complex situations.

Scalable high-throughput microfluidic separation of magnetic microparticles.

Surface-engineered magnetic microparticles are used in chemical and biomedical engineering due to their ease of synthesis, high surface-to-volume ratio, selective binding, and magnetic separation. To separate them from fluid suspensions, existing methods rely on the magnetic force introduced by the local magnetic field gradient. However, this strategy has poor scalability because the magnetic field gradient decreases rapidly as one moves away from the magnets. Here, we present a scalable high-throughput magnetic separation strategy using a rotating permanent magnet and two-dimensional arrays of micromagnets. Under a dynamic magnetic field, nickel micromagnets allow the surrounding magnetic microparticles to self-assemble into large clusters and effectively propel themselves through the flow. The collective speed of the microparticle swarm reaches about two orders of magnitude higher than the gradient-based separation method over a wide range of operating frequencies and distances from a rotating magnet.

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

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.

Self-folding soft-robotic chains with reconfigurable shapes and functionalities.

Magnetic continuum soft robots can actively steer their tip under an external magnetic field, enabling them to effectively navigate in complex in vivo environments and perform minimally invasive interventions. However, the geometries and functionalities of these robotic tools are limited by the inner diameter of the supporting catheter as well as the natural orifices and access ports of the human body. Here, we present a class of magnetic soft-robotic chains (MaSoChains) that can self-fold into large assemblies with stable configurations using a combination of elastic and magnetic energies. By pushing and pulling the MaSoChain relative to its catheter sheath, repeated assembly and disassembly with programmable shapes and functions are achieved. MaSoChains are compatible with state-of-the-art magnetic navigation technologies and provide many desirable features and functions that are difficult to realize through existing surgical tools. This strategy can be further customized and implemented for a wide spectrum of tools for minimally invasive interventions.

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Magnetically Active Cardiac Patches as an Untethered, Non-Blood Contacting Ventricular Assist Device.

Patients suffering from heart failure often require circulatory support using ventricular assist devices (VADs). However, most existing VADs provide nonpulsatile flow, involve direct contact between the blood flow and the device's lumen and moving components, and require a driveline to connect to an external power source. These design features often lead to complications such as gastrointestinal bleeding, device thrombosis, and driveline infections. Here, a concept of magnetically active cardiac patches (MACPs) that can potentially function as non-blood contacting, untethered pulsatile VADs inside a magnetic actuationsystem is reported. The MACPs, which are composed of permanent magnets and 3D-printed patches, are attached to the epicardial surfaces, thus avoiding direct contact with the blood flow. They provide powerful actuation assisting native heart pumping inside a magnetic actuation system. In ex vivo experiments on a healthy pig's heart, it is shown that the ventricular ejection fractions are as high as 37% in the left ventricle and 63% in the right ventricle. Non-blood contacting, untethered VADs can eliminate the risk of serious complications associated with existing devices, and provide an alternative solution for myocardial training and therapy for patients with heart failure.

Magnetic cilia carpets with programmable metachronal waves.

Metachronal waves commonly exist in natural cilia carpets. These emergent phenomena, which originate from phase differences between neighbouring self-beating cilia, are essential for biological transport processes including locomotion, liquid pumping, feeding, and cell delivery. However, studies of such complex active systems are limited, particularly from the experimental side. Here we report magnetically actuated, soft, artificial cilia carpets. By stretching and folding onto curved templates, programmable magnetization patterns can be encoded into artificial cilia carpets, which exhibit metachronal waves in dynamic magnetic fields. We have tested both the transport capabilities in a fluid environment and the locomotion capabilities on a solid surface. This robotic system provides a highly customizable experimental platform that not only assists in understanding fundamental rules of natural cilia carpets, but also paves a path to cilia-inspired soft robots for future biomedical applications.

Magnetic quadrupole assemblies with arbitrary shapes and magnetizations.

Magnetic dipole-dipole interactions govern the behavior of magnetic matter across scales from micrometer colloidal particles to centimeter magnetic soft robots. This pairwise long-range interaction creates rich emergent phenomena under both static and dynamic magnetic fields. However, magnetic dipole particles, from either ferromagnetic or paramagnetic materials, tend to form chain-like structures as low-energy configurations due to dipole symmetry. The repulsion force between two magnetic dipoles raises challenges for creating stable magnetic assemblies with complex two-dimensional (2D) shapes. In this work, we propose a magnetic quadrupole module that is able to form stable and frustration-free magnetic assemblies with arbitrary 2D shapes. The quadrupole structure changes the magnetic particle-particle interaction in terms of both symmetry and strength. Each module has a tunable dipole moment that allows the magnetization of overall assemblies to be programmed at the single module level. We provide a simple combinatorial design method to reach both arbitrary shapes and arbitrary magnetizations concurrently. Last, by combining modules with soft segments, we demonstrate programmable actuation of magnetic metamaterials that could be used in applications for soft robots and electromagnetic metasurfaces.