Active generation and magnetic actuation of microrobotic swarms in bio-fluids

In nature, various types of animals will form self-organised large-scale structures. Through designing wireless actuation methods, microrobots can emulate natural swarm behaviours, which have drawn extensive attention due to their great potential in biomedical applications. However, as the prerequisite for their in-vivo applications, whether microrobotic swarms can take effect in bio-fluids with complex components has yet to be fully investigated. In this work, we first categorise magnetic active swarms into three types, and individually investigate the generation and navigation behaviours of two types of the swarms in bio-fluids. The influences of viscosities, ionic strengths and mesh-like structures are studied. A strategy is then proposed to select the optimised swarms in different fluidic environments based on their physical properties, and the results are further validated in various bio-fluids. Moreover, we also realise the swarm generation and navigation in bovine eyeballs, which also validates the proposed prediction in the ex-vivo environment.

The nanoparticles are suspended in blue dye, and the suspension is injected into the vitreous humor. (a) The spread nanoparticles, which is indicate by the green contour. (b) After the rotating field is applied, the swarm is generated, which is highlighted by the red circle. (c) -(f) The locomotion of the swarm. The direction of the translational velocity of the swarm is shown by the black arrows, the rotation of the swarm is indicated by the red arrows, and the contour of the dyed region is represented using blue dashed curves. The yellow arrows show the major change of the dyed contour. The scale bar indicates 2 mm. A particle chain actuated by a rotating magnetic field in fluid will generate a local fluidic vortex, as shown by the blue arrows in Figure 1a. The vorticity ⃗ of a flow field with velocity distribution 7 7⃗ is defined by: where , , and B are the three components of 7 7⃗ along the three axes of Cartesian coordinate. In a twodimensional vortex (in x-y plane), because the flow is confined in the plane, only the z-component of the vorticity is non-zero, Supplementary Equation 1 can be simplified to: (2) The merging of vortices induced by rotating particle chains is the main reason for the generation of a fluidicinduced swarm, as shown in Supplementary Figure 1a III -V. The induced fluidic vortices exerts long-range attractive interaction forces on adjacent particle chains, which gradually reduces the distances among them.
Finally, when the distance of two rotating chains is close enough, the vortices induced by them will merge.
The simulation results of the vortex merging are presented in Supplementary Figure 1b. Initially, two identical vortices are distributed, and driven by the attractive fluidic interaction induced by the advection of vorticity, the vortices move towards each other. When they come into contact, they rapidly deformed into prolate shapes.
Then, an elliptical shape with two filaments of vorticity is formed. Finally, a circular vortex pattern is generated, while the filaments gradually roll-up around the core of the vortex and dissipated. As a result, the chains keep self-rotating following the rotating magnetic field and, meanwhile, they begin to perform coaxial rotation due to the fluidic interaction. After continuing merging processes, the initial great numbers of vortices will merge into one vortex or a few major vortices induced by multiple particle chains, and the fluidic-inducedd swarm is formed. The simulation results validate the merging process of vortices, and therefore, can support the hypothesis that this kind of swarm is generated mainly based on fluidic interactions. The experimental results of the generation of a fluidic-induced swarm is demonstrated in Supplementary Figure 1c. The nanoparticles are dispersed uniformly at the initial state. After a rotating magnetic field is applied, the nanoparticle chains are observed to perform self-rotation at first, then a relatively high concentrated region of nanoparticles is formed, which is the prototype of a fluidic-induced swarm. Finally, most of the particle chains are gathered into the core of the vortex, and a dynamic-equilibrium fluidic-induced swarm is formed with the particle chains rotating synchronically.
The schematic process of the generation of an MF-induced swarm is shown in Supplementary Fig. 1D. We take the initial situation that dispersed nanoparticles form two long particle chains as an example. When the oscillating magnetic field (Figure 1b) is applied, the long chains are firstly broken into several shorter pieces at stage III. Because at this moment, the magnetic field strength is low, and the chain-chain magnetic interactions are not sufficient to actuate the chains. Therefore, the relative locomotion of the chains are maintained. After the field strength reaches the maximal value (stage IV), the interaction among particle chains become stronger, which makes their distribution along x-axis narrower and y-axis longer. Dipole interactions are induced between two paramagnetic particle chains in a magnetic field, and the simulation results are presented in Supplementary Figure 1f. The particle chains will induce local magnetic fields, which influences the external magnetic field. The white arrows indicate the directions of superposed magnetic field, and the colour map shows the field strength that is induced by the particle chains. The simulation results of the induced forces exerted on the chains are shown by the green arrows in Supplementary Figure 1f. The dipole forces tend to re-arrange the particle chains into a long (along y-axis) and narrow (along x-axis) pattern. As a result, the ribbon-like swarm is formed mainly due to the dipole-dipole interactions among the particle chains.
The experimental results of MF-induced swarm are shown in Supplementary Figure 1d. A three-axial Helmholtz electromagnetic coil setup is applied for magnetic actuation, as shown in Supplementary Figure 1e.
The control signal is programmed on the control PC, and the experimental results are observed using the CCD camera. Actuated by the oscillating magnetic fields, the nanoparticles locally gathered into chain-like dynamic patterns. After a series of self-merging processes of subswarms, a ribbon-like swarm is generated, which is With the same amplitude ratio, the ribbon-like swarm tends to have lower aspect ratio if the ionic strength of the fluids is higher. Meanwhile, the swarm begin to form at =3 in 0.2×, 0.4×, 0.6× PBS, and when the ionic strength continues to increase, the lowest amplitude ratio I for triggering the generation of the swarm becomes larger, e.g. I =4, 5, 6 in 0.8×, 1×, 2× PBS, respectively. A high ionic strength enhances particle-particle attractive interactions, and with the same oscillating frequency, the particle chains in fluids with more ions will be longer and bulkier. Therefore, the reconfiguration process of the MF-induced swarms may be hindered, and the chains cannot be broken and re-assembled sufficiently, which makes the aspect ratio smaller. The reason also explains the curves in Supplementary Figure 5. With a higher viscosity, the aspect ratio of the MF-induced swarm will be larger, because particle chains tend to form shorter ones, which makes the reconfiguration process more sufficient. However, because the generation of MF-induced swarm requires fast response of magnetic particle chains in fluids, if the viscosity continues to increase, which prevents the agents from fast reconfiguration, the MF-induced swarm may not be able to form.

Supplementary Note 3: Generation conditions for swarms in bio-fluids.
The generation conditions for the MF-induced swarms in FBS are demonstrated in Supplementary Figure 8.
In FBS, when amplitude ratio γ is low (blue crosses), particles will form massive zig-zag patterns. In the region with green circles, straight patterns which uncontrollably elongate are formed. With the increase of γ (blue diamonds), the particles generate unstable ribbon-like swarms with continuous pattern reconfiguration. A dynamic-stable ribbon-like swarm is formed in the region of red asterisks, which is highlighted by the red area.
Multiple long chain-like patterns will be formed if γ becomes even larger (black crosses).
The generation condition for the medium-induced swarms in HA is demonstrated in Supplementary Figure 9.
When the applied magnetic field strength is not sufficiently strong to actuate the nanoparticle chains, the cases are labeled using blue "×". The medium-induced swarms with a low percentage of central area and loose cores are presented by the green circle. The red area surrounded by the red asterisks indicates the proper conditions for the generation of the medium-induced swarms.

Supplementary Note 4: Reconfiguration of MF-induced swarms in bio-fluids
By tuning input amplitude ratio, the aspect ratio of the MF-induced swarms will change accordingly, and the results are shown in Supplementary Figure 10. In all four bio-fluids, the swarms have larger aspect ratios when the input frequency is higher, and the largest aspect ratio reaches approximately 38, when the swarm is actuated by 30 Hz-frequency fields in FBS. Meanwhile, in DI water, the differences on aspect ratios between cases is larger than those in gastric acid. The average length of nanoparticle chains is a major factor for the swarm reconfiguration, and in DI water, when the amplitude ratio and field strength is fixed, the chain length is only determined by the frequency. In gastric acid, the additional ions in fluids induce attractive electrostatic forces among nanoparticles, which potentially reduces the difference on chain length with different input frequencies.
Therefore, the differences on aspect ratios are smaller in fluids with high ionic strengths.

Supplementary Note 5: Navigated locomotion of an MF-induced swarm in 4× diluted blood.
In this part, we demonstrate the feasibility of making navigated locomotion of MF-induced swarms in 4× diluted blood, as shown in Supplementary Figure 11. The red dashed arrow indicates the moving trajectory of the swarm, and the white arrows schematically indicate the flow field around the swarm.

Supplementary Note 6:
Investigations of MF-induced swarms formed by corona-coated nanoparticles.
The incubation steps are briefly described as follows: The in vitro protein corona was allowed to form by adding magnetite nanoparticles (6.6 mg/mL) into human plasma at a ratio of 1:4 and incubating for 10 minutes at room temperature by gentle shaking. Hereby, we first investigate the effects of partial dilution, which may be cause by the injected particle suspension locally, and the experimental results are shown in Supplementary Figure 13. We first suspend nanoparticles in blue dye, and inject the blue nanoparticle suspension into the vitreous humor. The region of dye indicates the location that may be diluted by the injected solution. After the rotating magnetic field is applied, the spread nanoparticles immediately gathered into a circular swarm, and it can move effectively in the region of dye, as shown in Supplementary Figure 13b and c. In Supplementary Figure 13d It is observed that, the viscoelasticities of these two samples are in the same range. As a result, the locomotion of the swarm will not influence the physical properties of the vitreous humor.
Supplementary Note 8: Actuation of a swarm on a mucosa sample.
We use a piece of porcine intestinal tract as the substrate, and conduct swarm actuation experiments on it. It is noted that, the original mucus layer is remained on the intestinal sample. In our first trial, we directly drop the nanoparticle suspension onto the sample, but when the nanoparticles contact the surface of the intestinal tract, they cannot be actuated again due to the overwhelming sticking surface force. In order to solve this issue, we conduct the following steps.
We first collect some mucus into an open tank with a silica substrate, and 4 µL nanoparticle suspension with a concentration of 6 mg/mL is injected into the mucus. Then a rotating magnetic field is applied, and because mucus is full of mesh-like structures, spread nanoparticles immediately gather into a swarm tangling with the fibres. In this case, the swarm is an ensemble with a relatively stable structure, and meanwhile, the magnetic torque and force induced are significantly enlarged. The swarm is subsequently retracted from the mucus, and injected onto the intestinal sample with a mucus layer. The experimental results is shown in Supplementary   Figure 16. After applying a rotating magnetic field with a pitch angle of 5°, the swarm can be actuated and navigated efficiently due to the large actuation force. As a conclusion, the swarm can also be actuated on a mucosa sample.