Selective Actuation and Tomographic Imaging of Swarming Magnetite Nanoparticles

Microand nanomotors have seen substantial progress in recent years for biomedical applications. However, three grand challenges remain: (i) high velocities to overcome the blood flow, (ii) spatially selective control to enable complex navigation, and (iii) integration of a medical, tomographic realtime imaging method to acquire feedback information. Here, we report the combination of active magnetic matter and a medical imaging technique, namely magnetic particle imaging (MPI), which addresses these needs. We synthesize ∼200 nm magnetic nanoparticles and observe a macroscopic, collective effect in a homogeneous magnetic field with a rotating field vector. The nanoparticles form a millimeter-sized cloud and reach speeds of 8 mm s−1. This cloud is imaged and selectively steered with an MPI scanner. Our experimental results are supported by a model that highlights the role of the Mason number, the particle’s volume fraction, and the height of the cloud. The successful introduction of a fast swarm of microscopic units and the spatial selectivity of the technique suggest an effective approach to translate the use of microand nanobots into a clinical application.


■ INTRODUCTION
In the emerging field of nano-and microrobotics, most applications aim toward untethered microscopic devices operating inside the human body. 1−4 The goal of such operations range from targeted drug delivery 5,6 to microsurgery, 7 with most recent progress focusing toward biocompatibility and degradability. 8 However, the size of the individual units, currently ranging from 1 to 200 μm, are likely to cause occlusions in small (3−10 μm) capillaries. 9 At the same time, movement speeds in the range of several mm s −1 are necessary to navigate against the blood flow of vascular systems (0.25−1.5 mm s −1 ). 10 These demands work against each other for most of the magnetic microbot locomotion approaches investigated so far since these devices couple their geometrical shape to their movement speed, leading to a speed-size constraint. 11,12 Another fundamental challenge is the medical imaging of such devices. While imaging is clearly mandatory for actively guided devices, feedback information for autonomously acting devices will be necessary to monitor their actions. Recently, first in vitro trials were performed for swarms of swimmers in a positron emission tomography scanner 13 and for individual swimmers using optical imaging with a millimeter-deep penetration depth. 14 However, these approaches either work with ionizing radiation, which is especially disadvantageous for long-term tracking of a moving device, or are severely limited in imaging penetration depth, making a full-body approach impossible to achieve. Additional approaches include fluorescent imaging, ultrasound imaging, computed tomography, magnetic resonance imaging, and single-photon computed tomography (summed up in refs 15 and 16). The advantage of these imaging techniques is that they are established in clinical routines. However, limitations in penetration depth, low temporal or spatial resolution, or the utilized ionizing radiation will constitute difficulties for a successful implementation in the clinic for each of those techniques. As an additional drawback, all of these approaches significantly increase the complexity of the whole procedure. Namely, the imaging units and the steering mechanisms are based on different physical concepts and therefore require multiple detectors, emitters, and control units in the vicinity of the samples. Magnetic particle imaging (MPI), however, is an emerging, tracer-based, tomographic, three-dimensional imaging technique, capable of visualizing the concentration distribution of superparamagnetic nanoparticles. 17 To date, MPI is a preclinical method. One of its strengths lies in vascular imaging as it is free of ionizing radiation and provides real-time visualization. 18,19 Recent studies demonstrated that the magnetic fields of MPI scanners can not only be used for imaging but also for steering magnetic devices of centimeter 20,21 and millimeter 22 size by rotating magnetic fields. However, control of microscopic devices and swarms as well as their spatial selective control has remained unexplored.
In general, spatial selective control of microbots is an open challenge for most investigated micro-and nanobot actuation techniques. Some advances were made for example by chemical or light-based activation of microswimmers. 23 However, feedback-based selective control has not been reported so far but is required for controlling several entities or swarms during application scenarios. Here, we propose a strategy based on MPI and magnetite nanoparticles that simultaneously addresses the three mentioned challenges: sizespeed constraint, spatial selective control, and medical imaging. A high-speed collective rolling effect of nanometer-sized magnetite nanoparticles is achieved in a tubular structure by applying a rotating magnetic field with an MPI scanner. Spatial selectivity is obtained by using superimposed gradient fields. Finally, tomographic imaging is performed using MPI, which relies on the nonlinear magnetization behavior of the swarm's constituents. 17 Overall, we demonstrate how an MPI scanner is Figure 1. Nanoparticle cloud actuation and imaging. Magnetite nanoparticles with an average diameter of 200 nm were synthesized in a solvothermal reduction method. These particles showed a swarming behavior that led to high movement speeds of the resulting nanoparticle cloud in a homogeneous magnetic field with a rotating field vector. The magnetic fields of an MPI scanner were used to control multiples of these clouds simultaneously and spatially selectively. The same scanner was used to image the spatial distribution of the particles, achieving imaging and control in one device. capable of propelling, selecting, and imaging swarms of nanoparticles (see Figure 1).

■ EXPERIMENTAL SECTION AND RESULTS
Active Magnetic Matter. Magnetite nanoparticles were produced with a solvothermal reduction method 24 (see Supporting Information). Scanning electron microscopy (SEM) images are shown in Figure 2a,b. The mean diameter of AMM particles was measured to be 194 nm with a standard deviation of 59 nm (distribution in Figure  2c) from such SEM images. A vibrating sample magnetometer was used to determine the magnetization behavior of the AMM ( Figure  2d). The saturation magnetization of AMM is reached at a magnetic flux density of about 150 mT. The dynamic magnetization curve, which is magnetization dependent on the excitation field, was acquired with a magnetic particle spectrometer with one-dimensional excitation. 25,26 The magnetization curve shows a dynamic hysteresis and an almost linear magnetization behavior (see Figure 2e). The dynamic magnetization behavior is compared to the behavior of Perimag, a commercially available superparamagnetic iron oxide nanoparticle dispersion, which is optimized for and one current standard in MPI. 27 This sample shows a strong nonlinearity in its magnetization curve, which explains numerous harmonics in the amplitude spectrum (see Figure 2f). For AMM, harmonics up to the 11th are distinguishable from the background, indicating that MPI is feasible but with lower sensitivity and spatial resolution compared to Perimag.
We dispersed the nanoparticles in water at a molar iron concentration of 125 mM. The dispersion was then transferred into polyvinyl alcohol tubes for all following experiments. The particles sedimented and were collected and concentrated at one end of the tube with a permanent magnet. In the presence of a homogeneous and rotating magnetic field of a Helmholtz coil setup (see Figure 3a), the particles self-assembled to form a dynamic cloud, which moved inside the plane of rotation on the bottom surface of the tube, as depicted in Figure 3b (Movie S1). The shape of the cloud is a result of sedimentation, the shape of the tube, and magnetic interactions, as described in our theoretical model. This cloud was an out-ofequilibrium state of the assembly of magnetic nanoparticles, which we call AMM. 28 Remarkably, this AMM moved with a velocity of up to 8 mm s −1 at a rotating field frequency of 40 Hz (Figure 3c). For comparison with other micro-and nanobot approaches, the speed can also be described as 40,000 body length s −1 (body length meaning the diameter of a single particle) or as a dimensionless speed (body lengths per turn) of 1000 (calculated via vf −1 d −1 , where v is the velocity, f the frequency, and d the particle diameter). Due to the collective effect, the cloud travels more than 300 times faster than a single particle would. A theoretical model was developed and describes the two most crucial behaviors of the system: the high speed and the independence of speed from the magnetic field's rotation frequency after a critical frequency (see Figure 3c).
Calculation of Cloud Height. Attractive forces between the magnetic nanoparticles in a rotating field make the behavior of their suspension similar to the behavior of liquid droplets, such as oil in water. Its shape is due to the action of gravity and may be found using the methods of capillary hydrodynamics. Since the radius of the cloud is much larger than its thickness, it can be found by the solution of the 2D problem.
The pressure in the cloud (p 2 ) and around (p 1 ) is given by where ρ 2 is the density of the cloud, ρ 1 is the density of the surrounding liquid, h is the thickness of the cloud in the central region, and p 0 is the atmospheric pressure. Introducing the tangent angle of the cloud's interface ϑ(l) (l is the natural parameter), the condition of the capillary equilibrium reads with the surface tension σ = μ 0 M 2 a/24 estimated as the magnetic interaction, where M is the magnetization, μ 0 is the vacuum permeability, and a is the particle radius. By differentiation and with = ϑ sin follows. It is solved at boundary conditions ϑ(0) = 0 (we assume complete nonwetting) and ϑ(∞) = π (interface of the cloud). The solution reads The shape of the cloud can be found by numerically integrating the set of equations cos and d d sin The cloud has a finite thickness in the applied rotating field. This can be represented as surface tension which may be estimated as originating from magnetic interactions. The equilibrium thickness of the cloud coming from the balance of capillary and gravity forces in the 2D case may be estimated as 29 The concentration and density of magnetite in water give Δρ = 1.35 g/ cm 3 . From the surface tension estimation follows σ = 1.2 mJ/m 2 , when considering the saturation magnetization M = 480 kA/m of magnetite and a = 100 nm. With these values, a cloud thickness of h ≈ 0.6 mm results. This is in the same order of magnitude as in the observations, where roughly half the tube radius is occupied (resulting in h ≈ 1.5 mm). We should mention that our calculated value may be overestimated since the particles are polydomain and their remanent magnetization is smaller than the saturation magnetization. Nevertheless, it allows rationalizing the observations according to which the thickness of the cloud is larger with the rotating magnetic field activated.
Calculation of Cloud Velocity. The behavior of the cloud in the rotating field is reduced to the problem of the flow of the cloud induced by the rotation of magnetic particles. This is a typical problem of flow caused by antisymmetric stress σ ik a acting on a free interface. 30 In our case, we have an infinite layer, the angular velocity of the field ω⃗ = (−ω, 0, 0), a synchronous rotation of the particles, and the field σ = K e Next, the rotational drag coefficient α = nα 0 (n is the number of particles per unit volume) must be estimated. In the limit of elongated chainlike structures formed under the action of a rotating field, α 0 may be estimated as α 0 = 2ηV(L/2a) 2 , where V is the particle volume, L is the chain length, and 2a is the particle diameter, hence L/2a is the number of particles in the chain. In ref 31, it is shown that the number of particles in the chain is established such that the chain stays in the synchronous regime. An increase in the frequency of the rotating field causes the viscous forces to break the chain after a certain critical frequency. Numerical and physical experiments 31 showed that the number of particles in the chain to keep the synchronous regime can be estimated according to = This is a reasonable value for a rotating field with 4 mT amplitude as shown in the magnetization curve in Figure 2d, where about 7% is reached. The velocity of the cloud at the transition to the chain-breaking regime for the suspension with the volume fraction of the particles φ = nV = 0.07 (calculated from the particle concentration with an estimated cloud volume) can be calculated using The particles form rotating chains under the influence of the external magnetic field. Higher frequencies lead to a higher rotation speed of these chains but also to shorter chain lengths. The model predicts the key ingredients of the observed high speeds as the Mason number, the particle's volume fraction, and the height of the cloud. The first and last parameters are influenced by the particle's magnetization, making it the core parameter of the technique.
Spatially Selective Control of AMM. The spatially selective control of the AMM was performed inside a preclinical MPI scanner with a method previously proposed for centimeter-sized screws 20 1). A 360°view of the volume representations can be found in Supporting Information. A fraction of the nanoparticles did not move as it was stuck to the petroleum jelly that sealed the tube. The movement has been achieved using rotating fields of the same scanner with 10 Hz and 6 mT.
field-free point (FFP) and spatially encodes the particle signal. The drive field is a three-dimensional homogeneous field and excites the particles for imaging purposes. Frequencies around 25 kHz are used. Third, focus fields, which are homogeneous offset fields, are used to shift the field of view in space. To selectively steer AMM, sinusoidal currents (10Hz) with different phases were applied to the focus field coils, which generated a homogeneous rotating magnetic field inside the scanner. By superimposing the rotating field with the gradient field of the scanner, a FFP that traveled on an ellipsoidal trajectory was created. A more detailed description of how the magnetic fields of an MPI scanner can be used for actuation and of the applied field configuration can be found in Supporting Information. When the FFP was driven around a tube of choice, with the rotation axis perpendicular to the tube, only the AMM inside this tube experienced a fully rotating magnetic field vector, leading to a forward movement. Nanoparticles outside the FFP trajectory only experienced an oscillating magnetic field with directions never fully rotating. Hence, no net movement was induced in those tubes (a schematic drawing can be found in Figure 4a and in Movie S2).
An actuation sequence was applied to a phantom with two tubes as follows: Actuation of AMM in the bottom tubeactuation of AMM in both tubes (no gradient field)actuation of AMM in the top tubeactuation of AMM in both tubes in the backward direction (changing the rotation direction of the rotating field vector). Video frames shortly before and at the end of each sequence are shown in Figure 4b. The video can be found in Supporting Information (Movie S3).
Further experiments were performed with more complex movements. Figure 4c shows video frames of the selective actuation in nonparallel tubes. The associated video can be found in Supporting Information (Movie S4). For such actuation in arbitrary directions, the plane of rotation of the field vector needs to be adapted to the intended direction of movement (full description can be found in the Supporting Information).
The videos and video frames from Figure 4 prove that individual swarms were selectively steered. The selection occurred as intended by the actuation sequences, described above.
Imaging AMM with MPI. The final goal is to ensure that the AMM can indeed be imaged using MPI. The magnetic properties indicate a positive answer, but the practical proof is shown below. A single tube was positioned inside the scanner, and a homogeneous rotating field (10 Hz and 6 mT, no spatially selective control) was applied. Figure 5 shows the sagittal, coronal, and axial plane of the reconstructed images as well as a volume representation before and after an actuation experiment (3D views in Movies S5 and S6). Details about the imaging parameters and the image reconstruction can be found in Supporting Information.

■ DISCUSSION AND CONCLUSIONS
While the behavior of micro-and nanobot swarms (with a relatively low number of individual units) on surfaces is becoming better understood, 33−36 centimeter-scale locomotion strategies with nanometer-scale constituents have not been investigated so far, such that the swarming behavior of magnetic particles became of great interest. 37,38 Rather than the development of a specific microbot, we propose a new kind of large-scale locomotion strategy that inherently allows for spatially selective control and imaging of a microbot swarm in a tubular structure by MPI. Additionally, our presented model highlights some critical parameters of the system, such as the Mason number, the volume fraction of particles, and the height of the cloud.
While the locomotion strategy proposed here is limited to a 2D surface, it is likely that AMM can also be formed using magnetic micro-propellers, similarly to a previous study where different models of locomotion could be achieved with a single swarming material. 39 Such propellers can then swim against gravity and move rapidly over surfaces. The biocompatibility of AMM must be investigated carefully in future studies. No coating has been used in our studies, which is often a fundamental constituent of established drug agents. 40 The biodegradation is likely to happen in the liver and spleen as has been reported for magnetite nanoparticles. 41 MPI is an imaging technique under preclinical investigation, although first attempts toward clinical scanners have been made. 42 The visualization with MPI is especially advantageous since the scanner can not only be used for imaging the distribution of AMM but also for selective steering. Although AMM is visible in MPI, the image quality is reduced compared to the typically used tracer materials. However, the images show that live tracking of AMM is possible when imaging and actuation sequences are alternated faster.
Application scenarios of our technique include the formation and control of AMM with different kinds of therapeutic drugs. As an example, an AMM effect could be achieved with biodegradable magnetic microspheres (polymeric spheres, including magnetic nanoparticles and a drug). These can be actively guided to a target location and then thermally activated using hyperthermia to increase the drug and nanoparticle release. This process can again be monitored using the difference in the MPI signal of incorporated and free magnetic nanoparticles. 43,44 Also possible is the application in the inner ear for targeted drug delivery. 45 Another application scenario includes the guidance of AMM into vessel branches with occlusions. Such branches hardly take up passively transported drugs due to the hydrodynamics of such a system. 46,47 The limit of the spatial selectivity of actuation is the magnetic field gradient. A higher gradient introduces relevant dragging forces onto the nanoparticles, tearing them away from surfaces and impeding the locomotion process. This could, however, be utilized to keep certain particles in the desired position. The gradient proposed here of 0.6 T m −1 constitutes a compromise between spatial selectivity and interference of the AMM formation process on the ground of the tubes. In future studies, the size and shape of the nanoparticles will be tuned to allow for larger gradients to achieve more precise spatial control and better imaging results. Furthermore, for the steering of AMM in longer tubes, the FFP trajectory needs to be adapted such that the center of the ellipsoid is moved with the speed of AMM. As already shown here, it is possible to change the plane of rotation such that the AMM can be steered around the corners or into vessel branches of choice.
In summary, we propose a new kind of high-speed propulsion mechanism of magnetic nanoparticles for biomedical applications. This study creates a new direction in active magnetic matter research, which includes the investigation physics of the system, leading to the observed high movement speeds on the one hand and research on biomedical applications on the other hand.