Flow tweezing of anisotropic magnetic microrobots in a dynamic magnetic trap for active retention and localized flow sensing

Yuan Liu*^a, Quanliang Cao^bc, Haifeng Xu^a and Gungun Lin*^d
aShenzhen Institute of Advanced Technology, Chinese Academy of Sciences, 1068 Xueyuan Avenue, Shenzhen 518055, Guangdong Province, P. R. China. E-mail: y.liu1@siat.ac.cn
^bWuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan, 430074, China
^cState Key Laboratory of Advanced Electromagnetic Technology, Huazhong University of Science and Technology, Wuhan, 430074, China
^dInstitute for Biomedical Materials and Devices, School of Mathematical and Physical Sciences, Faculty of Science, University of Technology Sydney, 15 Broadway, Ultimo, NSW 2007, Australia. E-mail: gungun.lin@uts.edu.au

First published on 9th August 2024

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Introduction

Controlled transport of microscale functional systems in fluidic flows has key applications in lab-on-chip microfluidic devices,¹ chemical reactors,² and in vivo physiological systems featuring hierarchical networks of capillaries, arteries and veins.^3–9 Traditional wired devices (e.g., differential pressure flowmeter and cantilever-based flowmeter) face difficulties in their manipulation in small and confined spaces.^10–12 Magnetically responsive microrobots with programmed shape and anisotropy have shown significant potential due to their miniaturised fingerprints and untethered manipulation capability.^1,13 Equipped with motion capabilities, such systems function as mobile platforms for applications, including localized sensing,^14,15 drug delivery,^16,17 and cargo transport.^18,19 However, most of the existing systems focus on locomotion in static fluids.^20,21 Efficient control and transport of the systems in dynamic fluidic flows remain elusive.^22,23

Magnetic tweezers possess trapping capability to physically confine a magnetically responsive object in fluids. They are widely established by using a pair of permanent magnets,²⁴ a single magnet,²⁵ or a cylindrical magnet.²³ The trapping magnetic fields of tweezers feature a local maximum of field strength to trap magnetic particles.²⁶ It has been reported that a rotating magnetic field can drive magnetic structures of various morphologies (e.g., magnetic microsphere^27,28 and dimer-shaped microstructures^29,30) into synchronous rotation at low frequencies and further to large-area revolution at high frequencies in unconfined fluids. The magnetic field control strategy enables the localization and retention of magnetically powered devices in the lumina (e.g., intestine³¹ and blood vessels¹) of the human body. Flow in the lumina generates the propelling force to prevent retention. Localized flow sensing provides valuable feedback on flow conditions, facilitating the optimization of magnetic field parameters to enhance device retention. However, achieving effective localized flow sensing poses a significant challenge for mobile microrobots in confined fluidic flows.

Here, we report the dynamic magnetic field tweezing of microrobots for active device retention and localised flow sensing (Fig. 1). The coupling between the magnetic trapping field, the confined fluidic flow field and the microrobotic body results in intriguing in-flow locomotion characteristics. Switchable motion modes are proposed, achieved by balancing the magnetic force and the flow force. The magnetic robot can switch its locomotion mode from “on-trap centre rolling” to “large-area revolution” with varying rotating magnetic field frequencies. The revolution of the particle can be further modulated from “on-trap centre rolling” to “off-trap centre rolling” at varied flow speeds. These motion modes imbue the microrobot with multiple functions. Dynamic magnetic tweezing provides the necessary magnetic force to retain the robot, and off-trap centre rolling enables localized flow sensing. On the trap centre, the motion range of the microrobot can be controlled by adjusting the rolling frequency. Leveraging this manipulation strategy for microrobots using a dynamic rotating magnetic trap shows promise in various applications, including lab-on-chip microfluidic systems, micro-robotic control, and endovascular flow measurements.

Theoretical background

Synchronous to asynchronous rotation

Under a rotating magnetic field, a magnetic structure can undergo synchronous rotation with the field, meaning that the rotation frequency of the particle matches the external field frequency. In a perfect isotropic superparamagnetic spherical structure with a homogeneous distribution of magnetic content, changes in the magnetic moment due to the external magnetic field (i.e., Néel relaxation) occur on a timescale much shorter than typical experimental timescales. As a result, the structure may experience zero torque and could not be rotated by a slowly rotating magnetic field. However, Bean and Livingston reported that a torque can be applied to aligned magnetic nanoparticles due to the anisotropy of the magnetic cores, resulting in anisotropic magnetic susceptibility and the production of torque when the field is not aligned with the easy axis.³² For magnetic beads, the capability of magnetic tweezers to apply torque depends on the beads having a preferred magnetization axis, a topic that remains under debate. Some authors attributed this to the presence of a small permanent magnetization component,³³ while others argued that beads exhibit a “soft” magnetization axis.³⁴ Nonetheless, it is known that the rotation remains in a synchronous regime when the external field frequency is lower than a critical rotation frequency. Above this critical frequency, the particle's rotation may lag behind the external field, when the magnetic force is balanced with or even lower than the fluid drag force at increasing rotational driving frequencies. The transition from synchronous to asynchronous rotation has been utilized in developing sensor platforms based on spherical magnetic beads to detect small changes in the particle diameter due to the presence of external analytes.²

Torsional magnetic tweezers

Magnetic tweezers utilize the principle that external magnetic fields can apply both forces and torques to magnetic structures. Typical magnetic tweezers employed pairs of permanent magnets to generate horizontal in-plane dominant magnetic fields.^35,36 This in-plane magnetic field rigorously constrains the rotation of the magnetic microstructure around a virtual rotation axis for microrobotic manipulation or a tether axis for the study of biomolecular mechanics. In these scenarios, the position of the microstructure is confined to a localized region, known as the trap centre, where the first derivative of the in-plane field changes its sign. Alternative variants of magnetic tweezers, such as free-orbiting magnetic tweezers,^37,38 enable a magnetic microstructure to orbit around a vertical axis. These tweezers utilized a cylindrical magnet to generate a vertically aligned field, allowing the rotation of the magnetic microstructure about the vertical axis to be unconstrained or only weakly constrained by the magnet. To produce an even weaker magnetic trap, a bar magnet is sometimes attached to the cylindrical magnet to introduce a small horizontal field component to the predominantly vertically aligned field. While a magnetic structure is often confined to a localized region by a magnetic trap, particularly when the rotation is symmetric with respect to the rotational axis, recent discoveries by our team have expanded the understanding of such systems.³⁰ By utilizing a pair of permanent disk magnets, we observed that a rod-like magnetic particle composed of two spherical cores can transition into large-area revolution. This phenomenon has been attributed to the off-axis gyration of the anisotropic structure, accompanied by a significant centrifugal force.

Physical models of in-flow sensing with an off-trap centre rolling microrobot

For a rotating magnetic structure in a magnetic trap, a couple of physical forces can be involved. Firstly, the force F exerted on a paramagnetic microrobot by an external magnetic field B is given by the equation: , where m(B) represents the induced magnetization and ∇ is the first derivative/gradient operator. The local maximum of a magnetic field may generate a magnetic trap, the centre of which is characterized by the first derivative switching its sign. The torque exerted by the magnetic field on a magnetic microrobot in magnetic tweezers is described by: Γ_B = m₀ × B, where the direction of m₀ specifies the anisotropic axis of a magnetic structure. Secondly, for an anisotropic microrobot, characterized by either geometric anisotropy or a non-homogeneous distribution of magnetic content, the mismatch between the geometric centre and the centre of mass during rotation may introduce an additional force, namely centrifugal force. This centrifugal force is given by: F = mω²r, where m is the mass, ω is the angular speed, and r is the rotating radius. The centrifugal force increases with the frequency of rotation, potentially driving the structures away from the rotation centre and resulting in large-area revolution.

By trapping a magnetic microrobot in a fluidic channel, the microrobot can experience an apparent “drag force” due to the hydrodynamic fluid flow. When a microrobot is set to roll, the cross-section and orientation of the microrobot dynamically change in response to a rotating magnetic field. Although the fluctuation of the drag force resulting from the changing cross-section during a rolling period could potentially alter the microrobot's position, this variation can be counterbalanced by the magnetic force generated by an elastic magnetic trap that acts like a stiff spring. This is because the magnetic force in a magnetic trap scales with the distance from the trap centre.

Assuming that the fluidic drag force F_d remains constant for a specific rolling speed and that the ‘nominal’ cross-sectional area A is constant, the fluidic drag force can be given by:³⁹

	(1)

where ρ is the density of the fluid, v is the speed, A is the cross-section area, and C_D is the drag coefficient. At a low Reynolds (Re) number (i.e. close to 1 for the flow rate varying from 0 to 50 μL s⁻¹ (0–16 mm s⁻¹)), the drag force can be expressed as:^40,41

Fd = Cμlv	(2)

where C is dependent on the shape of the microrobot, μ is the fluid viscosity, and l is the dimension of the microrobot. According to eqn (1), the drag coefficient can be derived as:

	(3)

By combining eqn (1) and (3), at low Re, the drag coefficient asymptotically varies inversely with Re:^42–44

	(4)

Combining the equations mentioned earlier, the fluidic drag force scales directly with the flow speed: F_d ∝ ν. Additionally, the magnetic force generated in a magnetic trap created by a pair of permanent magnets scales linearly with the distance from the field center, d, which can be confirmed by analyzing the magnetic field distribution of the magnets. Thus, by balancing the magnetic force with the drag force, a microrobot can be maintained at a constant off-center distance at a specific fluid speed. For an off-center distance that scales with the fluid speed: d ∼ v, relationships among the magnetic force, off-center distance, and fluid speed can be established: F_m ∼ v ∼ d. This relationship enables the use of the microrobot's off-center distance to detect fluid speed and magnetic force.

Experimental

Magneto-optical characterization of microrobotic motions

For the tweezing study, we constructed a pair of permanent magnets, each with a diameter of 3 cm and positioned 5 mm apart to produce the desired magnetic field patterns (Fig. 1a). The magnets can be driven by a motor to rotate under varying magnetic field frequencies up to 2000 rpm. For the characterization of the microrobotic motion, a glass capillary with a diameter of 2 mm was placed in the centre of a working plane sitting 3 cm above the magnets. A microfluidic syringe pump (Harvard Apparatus Pico Plus Elite) was used to pump a phosphate-buffered saline solution containing the microrobots into the glass capillary tube. The flow rate was regulated from 0 μL s⁻¹ to 100 μL s⁻¹. The magnetic tweezing setup was installed on the stage of a wide-field optical microscope (Olympus MVX 10) and equipped with a high-speed camera (Andor Zyla) to capture the motion trajectory of the microrobot under a rotating magnetic field. The size ratio of the microrobot relative to the channel cross-section is an important factor for the robot design. When the microrobots' dimension is close to the cross-section, the stress from the wall of an extremely narrow channel cannot change the shape of a rigid microrobot and restricts its locomotion, which easily causes blockage in the flow channel. The dimension of microrobots needs to be much less than the dimension of the flow channel. Therefore, we injected a microrobot with dimensions of 400 μm × 600 μm × 150 μm in a flow channel with a 2 mm inner diameter.

Fabrication of microrobots

Magnetic microrobots were fabricated by embedding aligned iron oxide superparamagnetic nanoparticles in a polyethylene glycol diacrylate (PEG-DA, MW700, 455008, Sigma-Aldrich) polymer matrix. A magnetic field-assisted photolithography approach was utilized. This methodology involved the application of a magnetic field provided by a bar permanent magnet to guide the assembly of superparamagnetic nanoparticles through short-range dipolar interactions in the PEG-DA hydrogel, thereby establishing a magnetic anisotropy axis aligned with the direction determined by the applied magnetic field. In practice, 7 wt% of iron oxide magnetic nanoparticles (Sigma-Aldrich, Cat. no: 544884) were thoroughly mixed with 70 wt% PEG-DA hydrogel monomers and 1% w/w photo-initiator (2-hydroxy-2-methylpropiophenone, 405655, Sigma-Aldrich) by vortexing for 5 minutes to form a magnetic-hydrogel premix. Then, 10 μL of the magnetic-hydrogel premix was added to a chamber enclosed by cover slips of 170 μm thickness. After the premix was added, the chamber was covered with another cover slip. This created a microrobot with a thickness defined by the chamber. The chamber wall thickness could be adjusted by changing the number of stacked cover slips. A photomask was fabricated by laser patterning of a positive resist covered on top of a Cr-coated glass plate. The mask was aligned with the chamber containing the hydrogel premix and exposed under UV light at 365 nm to transfer the geometry of the photomask onto the hydrogel structures. The shape of the microrobot was defined by computer-aided design, specifying geometric features on a photomask. The dimensions of the resulting plate-like robots ranged from dozens of microns to millimeters.

Using bright-field optical microscopy, we can observe magnetic nanoparticle stripes with a preferred orientation, manifesting as dark regions aligned along the applied magnetic field direction. The regions with no or fewer particles exhibit much brighter contrast. Comparison between microrobots with and without aligned magnetic nanoparticles clearly reveals the preferred orientation axis of the magnetic nanoparticles in the microrobot (Fig. 1b).

Results and discussion

We utilized a 3D Hall sensor to measure the magnetic flux density at the midpoint between two magnets, determining it to be approximately 50 mT. This measurement corresponds to a Z-axis distance of 3 cm from the surface of the magnets. To verify the 3D distribution of the magnetic field emanating from the magnets as configured in Fig. 1a, we further conducted COMSOL simulations with results shown in Fig. 1c. A Cartesian coordinate system was established to facilitate discussions. In this case, the magnets are aligned along the X-axis, and the three magnetic field components are computed for the X–Y working plane (WP) located 3 cm above the magnets. The simulations revealed that the in-plane X component (B_x) of the magnetic field exhibited a local maximum strength at the field centre (Fig. 1b). The first derivative of B_x (∇B_x) changes its sign at the field centre, suggesting that the magnetic force generated by the horizontal X-component of the field enables trapping of the microrobot. In contrast, the magnitudes of the in-plane Y component and the out-of-plane Z component of the magnetic fields were near zero, significantly weaker than the in-plane X component. Hereby we can denote the X-component of the field as ‘the primary in-plane field’. Notably, the first derivative of the Z-component of the magnetic field is maximal at the field centre and gradually decreases as one moves away from the centre. This gradient creates an unbalanced vertical magnetic lifting force across the microrobot's body. The impact of this unbalanced z-axis lift force is that it causes one end of the microrobot to lift, resulting in its thin sidewall in touch with the bottom of the substrate.

To investigate the locomotion of microrobots in a confined fluidic flow, we injected a microrobot in a glass capillary channel with a 2 mm inner diameter which was placed at the centre between the pair of the permanent magnets. One side of the glass capillary flow channel was connected with a syringe pump for liquid injection. It was shown that the microrobot exhibited two primary motion modes as illustrated in Fig. 2a. The microrobot was initially trapped at the centre of the rotating magnetic field and rotated synchronously with a low-frequency magnetic field (Fig. 2a and b). By increasing the rotation frequency of the magnetic field, the localised synchronous locomotion was transitioned to large-area revolution. The phenomenon could be explained by the interplay between a magnetic trapping force arising from ‘the primary in-plane component’ of the magnetic field, a rolling friction force, and a centrifugal force experienced by the microrobot (Fig. 2c). The centrifugal force arising from the mismatch between the geometric rotation centre and the mass centre pushes the microrobot off the centre position, leading to the swing of the microrobot around the centre of the field. This force is balanced by the magnetic trap force originating from the gradient of the X-component of the magnetic field that scales within 1 cm-distance away from the field centre (Fig. 2b). For instance, the microrobot measured with dimensions of 400 μm × 600 μm × 150 μm can rotate around its centre at low frequencies of 0–1000 rpm. When the rotating frequency is further increased above 1000 rpm, the centrifugal force could overcome the friction force, leading to the swing of the microrobot off the centre with modulated trajectory ranges (off-axis diameter: ∼2 mm for 1000 rpm, ∼2.5 mm for 1100 rpm and ∼4 mm for 1500 rpm) (Fig. 2c). At the transition frequency of 1000 rpm, the centrifugal force experienced by the microrobot was estimated to be about 2.26 nN (F_c = mrw², in which m is the weight, r is the off-axis radius, and w is the angular speed of revolution). Here the mass of the microrobot was obtained based on the volume of the microrobots and the composition of 70 wt% PEG-DA hydrogel and 7 wt% iron oxide magnetic nanoparticles. The radius was defined by the difference between the robot's centre of mass and its geometrical rotation centre. When the microrobot does the revolution locomotion, the trajectory is elliptical rather than circular due to space limitations. Owing to the stiffness of the magnetic trap, by adjusting the rotating frequency of the field, the motion modes can be dynamically switched between on-trap rolling and large-scale revolution.

Active retention and fluidic sensing of magnetic microrobots

To study the locomotion of microrobots in fluidic flow, we monitor the motion dynamics of microrobots at varying flow rates with and without a magnetic field. Fig. 3a shows that without applying a rotating magnetic field, a statically trapped microrobot was abruptly washed off from the centre at a higher flow rate of 80 μL s⁻¹ when the flow rate was gradually increased from 0. This suggests that a significant static friction force is present. By computing the fluidic drag force using eqn (1) and balancing it with the static friction force, the latter force was estimated to be as high as 30 nN, which prevents the microrobot from displacing at varying flow rates. In contrast, when the microrobot was set to roll, it was pushed away gradually from the centre at varying flow rates until an equilibrium position is achieved, as shown in the right panel of Fig. 3a. The ‘stable’ position suggests that our assumption of a constant averaged ‘drag force’ under rolling motion is valid. In this respect, the off-centre distance, d, was observed to scale with the flow speed (ν), in line with our theoretical analysis in the prior section. The results highlighted the importance of the rolling motion of a microrobot, which significantly reduces the friction force experienced by the robot.

We demonstrated 4 major modes of motion with respect to varying flow rates and rotating field frequencies, which include “on-centre rolling”, “off-centre rolling”, “large-area revolution” and “flowed off” (Fig. 3b and c). At a zero rotating field, the microrobot was either trapped at the centre or being flowed off. With a rotating magnetic field, the microrobot rolled in the centre of the magnetic potential well and may undergo a “large-area revolution” in the lower flow rate range from 0–30 μL s⁻¹. At a high rotating speed (>1000 rpm), the microrobot may switch from “large-area revolution” to “off-centre rolling” before it was flowed off the trap. In a confined fluidic flow field, there was a large dynamic range where the microrobot performed “off-centre rolling” at varying rotation speeds from 200 rpm to 1000 rpm and flow rates from 0 to 40 μL s⁻¹.

We systematically characterized the off-centre distance with respect to the change of flow rate and the rotating field frequency, respectively. It is shown in Fig. 3b that there is a good linear relationship between the off-centre distance and the flow rate, in line with our previous theoretical analysis revealing d ∼ v. We further found that a higher rotating speed leads to a smaller off-centre distance and renders a smaller magnetic force exerted on the microrobot (Fig. 3c), as the magnetic force scales with the off-centre distance (F_m ∼ d ∼ v) as a typical feature of the magnetic trap. For example, the microrobot with a 200 rpm rotation speed travelled 6.5 mm at a flow rate of 40 μL s⁻¹, while it only travelled 3.5 mm in distance at a rotation speed of 800 rpm. As the magnetic force is reduced, a small flow speed is sufficient to transit the particle from an “off-centre rolling” state to a “flowed off” state. The transition speed for 200 rpm was about 62 μL s⁻¹, while the transition speed for 800 rpm was reduced to 48 μL s⁻¹. The scaling relationship between the microrobot's off-centre distance and the flow speed equips the microrobot a flow-sensing capability, the range of which can be modulated by the rotation frequency of the magnetic field. The switchable motion modes endow the microrobot with multiple functions, including retention-based trap centre rolling, large-area motion based on revolution, and flow sensing based on off-trap centre rolling (Fig. 3d and e). The decrease of the off-centre distance with the increase of the rotating field frequency suggests that there exists an additional propulsion force in a direction against the flow.

Propulsion movement under magnetic tweezing

Indeed, Fig. 4 shows that the rotation of anisotropic structures in a magnetic trap caused in-flow directional movement of the microrobot. In the absence of fluidic flow, the microrobot was observed to propel, and the motion distance increases with the rotation speed from 200 rpm to 800 rpm (Fig. 4a). A linear relationship was observed between the rotating field speed and the off-centre distance (Fig. 4b). As the magnetic trapping force was balanced out with the propulsion force in an equilibrium state, the analysis indicates that the associated propulsion force scales with the rotating speed of the microrobot. The microrobot walked 2.24 mm at 1000 rpm rolling speed and the propelling force can be computed to be 25 nN at 1000 rpm rotation frequency (Fig. 4b).

To further confirm the origin of the propelling force, we exchanged the flow direction and found that the propelling force exhibits a directional bias against the flow direction (defined in Fig. 4c and d). However, the opposing propulsion force appears to have different magnitudes when the flow direction is switched. This suggests that the propelling force could be stemming from a non-reciprocal movement of the structure which is nonsymmetric with respect to the magnetic field direction. There might exist a preferred flow direction that facilitates the non-reciprocal movement of the structure that yielded an optimum propulsion force. Since the directions of the fluidic flow and propelling force oppose each other, the propelling force may attenuate the flow effect, resulting in shorter displacement distances towards the field centre (Fig. 4e). Our results (Fig. 4f and g) further indicate that the relative directions between the rotation magnetic field and the flow should be leveraged to acquire a large flow responsive range when operating a flow-sensing microrobot. For instance, the maximum flow rate is 61.9 μL s⁻¹ with a 7.8 mm distance (200 rpm distance) for flow from the right to left. On the other hand, the microrobot can respond to the flow direction, thereby functioning as a vector flow sensor for measuring both the flow rate and direction.

Flow profile measurement with microrobots in a curved flow channel

We further utilised the off-centre rolling phenomenon for flow sensing within a confined flow channel. Given the dynamic changes in the flow conditions typical of natural cavities in the human body, we fabricated a curved flow channel through high-temperature treatment of glass capillaries (Fig. 5a). The curved channel features a relatively smaller channel diameter of 1.5 mm. The microrobot structures can be transported to different locations marked by A, B, C, D and E by shifting the trap centre of the magnetic field. By varying the speed and recording the points of transition from off-centre rolling to flowing outside, we observed that microparticle structures with a speed of 600 rpm require about 55 μL s⁻¹ speed to be pushed outside. The fluidic speed along the profile, obtained from COMSOL simulation, is depicted in Fig. 5c. The magnetic microrobots are manipulated to the desired positions by altering the trapping centre. To convert the off-center distance to flow speed, we performed a calibration of the off-center distance versus the flow speed and the rotation magnetic field frequency (which also defines the rolling speed), as shown in Fig. 3b. For a specific rolling speed, the off-center distance scales with the flow rate. Based on the linear relationship between the off-center distance and the flow speed, we performed a linear fitting of the curve to obtain the scaling constant. We utilized two types of microrobot structures (400 μm × 600 μm ×150 μm, and 200 μm × 300 μm × 100 μm) to measure the flow profile. Fig. 5d illustrates the flow profiles tested by the two types of magnetic microrobots. The magnetic microrobots were demonstrated with against-flow and localized flow sensing capabilities. The smaller microrobot exhibited higher resolution, resulting in a testing result more closely aligning with simulation outcomes. This flow-sensing method, based on dynamic magnetic trapping, holds promise for localized flow profile measurement with micro-scale resolution in complex and confined channels.

Conclusion

We have demonstrated that dynamic magnetic tweezing enables active trapping and retention of magnetic microrobots in confined fluidic flows. We have uncovered unconventional motion modes exhibited by magnetic microrobots under the effect of dynamic magnetic tweezing fields within confined fluidic flows. The interplay between the rotating magnetic trap and the flow fluid results in the elastic displacement of the microrobot from the field centre, the distance of which can be modulated by the magnetic field frequency and flow speeds. Through the coupling of the magnetic field and fluidic field, multiple motion modes are realized, encompassing on-trap centre rolling, large-area revolution, off-trap centre rolling, and flowed-off. Moreover, off-trap centre rolling facilitates local sensing of the flow rate and flow direction around the magnetic microrobot. The manipulation scheme exhibits an intriguing flow field responsive characteristic, holding potential for localised sensing in micro-scale and confined spaces, as well as for in vivo localized endovascular blood velocity measurement. It is worth noting that, for potential use in blood vessel, additional development is still needed. Several medical imaging techniques are available to visualize the location of microrobots in vivo,⁴⁵ including magnetic resonance imaging (MRI), X-ray imaging, ultrasound imaging, magnetic particle imaging, and fluorescence imaging. However, these techniques face trade-offs among system complexity, imaging resolution, depth, and acquisition speed. Our recent work has demonstrated the incorporation of near-infrared (NIR-II, 1000–1700 nm) emitting probes into microrobots, enabling imaging depths of approximately 5 mm and facilitating the tracking of single microrobots in the stomach of a mouse.¹⁵ However, there is a need to extend the imaging depth towards the ideal range of 10–50 cm for human use. Achieving this goal may involve enhancing the quantum efficiency and brightness of the probes, developing methods to load a high density of NIR probes into a single robot, and optimizing NIR working wavelengths to minimize tissue extinction loss. Additionally, there have been research efforts to explore MRI for manipulating and tracking magnetic microrobots simultaneously.⁴⁶ It is envisioned that the current research could benefit further from the development of MRI that could generate the magnetic field profiles reported in this work for in-flow tweezing and sensing applications.

Data availability

The authors confirm that the data supporting the findings of this study are available within the article.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

Y. L. acknowledges financial support from the National Natural Science Foundation of China (52203152), the Shenzhen Outstanding Talents Training Fund (RCBS20221008093222008), and the Shenzhen Science and Technology Program (JSGGKQTD20221101115654021). G. L. acknowledges financial support from the Australian Research Council DECRA Fellowship (DE230100079).

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