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Bioinspired acousto-magnetic microswarm robots with upstream motility


The ability to propel against flows, that is, to perform positive rheotaxis, can provide exciting opportunities for applications in targeted therapeutics and non-invasive surgery. So far no biocompatible technologies exist for navigating microparticles upstream when they are in a background fluid flow. Inspired by many naturally occurring microswimmers—such as bacteria, spermatozoa and plankton—that utilize the no-slip boundary conditions of the wall to exhibit upstream propulsion, here we report on the design and characterization of self-assembled microswarms that can execute upstream motility in a combination of external acoustic and magnetic fields. Both acoustic and magnetic fields are safe to humans, non-invasive, can penetrate deeply into the human body and are well-developed in clinical settings. The combination of both fields can overcome the limitations encountered by single actuation methods. The design criteria of the acoustically induced reaction force of the microswarms, which is needed to perform rolling-type motion, are discussed. We show quantitative agreement between experimental data and our model that captures the rolling behaviour. The upstream capability provides a design strategy for delivering small drug molecules to hard-to-reach sites and represents a fundamental step towards the realization of micro- and nanosystem navigation against the blood flow.

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Fig. 1: Bioinspired upstream motion in an acoustic and magnetic field.
Fig. 2: Estimation of the acoustic-induced reaction force.
Fig. 3: Microswarm formation.
Fig. 4: Upstream rolling model of the microswarm.
Fig. 5: Microswarm rheotaxis in combined acoustic and magnetic fields.

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Data availability

The authors declare that data supporting the findings of this study are available within the paper and its Supplementary Information. Source data are provided with this paper.


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This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme grant agreement no. 853309 (SONOBOTS) and grant agreement no. 743217 (SOMBOT). In addition, the work has been supported by ETH Zurich Career Seed Grant (grant no. 14 17-2) and DFG Priority Programme SPP 1726, Microswimmers—“From single particle motion to collective behaviour.”

Author information

Authors and Affiliations



D.A. initiated, designed, and supervised the project. D.A contributed to the experimental design and scientific presentation. D.H., M.G., A.S. and D.A. performed all of the experiments and data analysis. A.S., D.R., D.A. and J.H. developed the theoretical studies. D.A. wrote the manuscript with contribution from all authors. All authors contributed to the scientific discussion.

Corresponding authors

Correspondence to Daniel Ahmed or Bradley J. Nelson.

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Competing interests

The authors declare no competing interests.

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Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1

Fabrication of the acoustofluidic device.

Extended Data Fig. 2 Ultrasound manipulation system.

(a) Schematic demonstrates the ultrasound particle manipulation setup. (b) A micrograph shows trapped microparticles in pressure nodes arrays when exposed to an ultrasound at ~2.1 MHz and 12 V, respectively.

Extended Data Fig. 3

Experimental setup of microparticle manipulation in acoustic and magnetic field.

Extended Data Fig. 4

An electromagnetic setup purchased from MagnebotiX AG (Zurich, Switzerland) with eight independently controlled coils was integrated with the inverted microscope to generate a rotating magnetic field.

Extended Data Fig. 5

Swarm stability against thermal fluctuation A plot demonstrates the ratio of the thermal to magnetic forces versus the radius of superparamagnetic particles. Magnetic forces dominate over the thermal effects for particles with radii 3 μm.

Extended Data Fig. 6

Poiseuille flow profile Experimental characterization of the Poiseuille flow profile within the circular channel.

Extended Data Fig. 7

Upstream motion Upstream migration of swarm of microparticles in a combined acoustic and magnetic field where the pressure node lies outside the capillary, see also Supplementary Movie 6.

Supplementary information

Supplementary Information

Supplementary Notes 1–5, Extended Data Figs. 1–7, Tables 1 and 2, legends for Supplementary Videos 1–9 and references.

Supplementary Video 1

Fluorescent microparticles getting trapped in the acoustic pressure nodes.

Supplementary Video 2

Acoustic switching of microparticles from the centre to the sidewall of the channel. Recorded at 15 fps and played at 60 fps.

Supplementary Video 3

An array of trapped microparticles was acoustically shifted. Recorded at 15 fps and played at 30 fps.

Supplementary Video 4

Formation of microswarms in an acoustic and magnetic field. The top panel shows microswarm configuration sandwiched between two glass slides and in the absence of an acoustic field. The middle panel shows microswarm structures in the acoustic pressure node. The bottom panel demonstrates microswarms formation in the pressure node when imposed upon an external flow field.

Supplementary Video 5

Recruitment of microswarm near a wall in the presence of an acoustic field.

Supplementary Video 6

Upstream migration of microparticles in a combined acoustic and magnetic field with the pressure node outside the capillary. Recorded at 15 fps and played at 60 fps.

Supplementary Video 7

Upstream migration of microparticles with the pressure node lies inside the capillary.

Supplementary Video 8

Deformation of the microswarm when the acoustic field is turned on and off.

Supplementary Video 9

Ultrasound manipulation of polystyrene particles (of 5.5 µm) under pulsatile flow. An external flow of 150 µl min–1 (corresponds to 200 mm s–1) with a periodic flow of 1 Hz is developed along a 1.55 mm outer diameter capillary. A pair of piezoelectric transducers were bonded across the channel and were actuated at 5.1 MHz, 20 VPP. The video is recorded at 7 fps and played at 15 fps.

Supplementary Software 1

Supplementary Software 2

Supplementary Software 3

Source data

Source Data Fig. 2

Source data for Fig. 2b,c.

Source Data Fig. 5

Source data for Fig. 5b,c.

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Ahmed, D., Sukhov, A., Hauri, D. et al. Bioinspired acousto-magnetic microswarm robots with upstream motility. Nat Mach Intell 3, 116–124 (2021).

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