Starfish-inspired Ultrasound Ciliary Bands for Microrobotic Systems

Cilia are short, hair-like appendages ubiquitous in various biological systems, which have evolved to manipulate and gather food in liquids at regimes where viscosity dominates inertia. Inspired by these natural systems, synthetic cilia have been developed and cleverly utilized in microfluidics and microrobotics to achieve functionalities such as propulsion, liquid pumping and mixing, and particle manipulation. In this article, we present the first demonstration of ultrasound-activated synthetic ciliary bands that mimic the natural arrangements of ciliary bands on the surface of starfish larva. Our system leverages nonlinear acoustics at microscales to drive bulk fluid motion via acoustically actuated small-amplitude oscillations of synthetic cilia. By arranging the planar ciliary bands angled towards (+) or away (–) from each other, we achieve bulk fluid motion akin to a flow source or sink. We further combine these flow characteristics with a novel physical principle to circumvent the scallop theorem and realize acoustic-based propulsion at microscales. Finally, inspired by the feeding mechanism of a starfish larva, we demonstrate an analogous microparticle trap by arranging + and – ciliary bands adjacent to each other.


Introduction
Cilia are short, hair-like appendages present in numerous biological living systems. They can be found on the surfaces of many organisms, including algae and invertebrate larvae, which are naturally evolved to manipulate and gather food in liquids, where viscosity dominates inertia.
Ciliated surfaces are also present in most mammals' respiratory tracts, where they trap and move particulates towards the nostrils. Ciliated surfaces are further manifested in the Fallopian tube to transport the ovum towards the uterus. Recent studies on the larval stages of marine invertebrates, such as Patiria miniate (starfish), have elicited that these invertebrates can adjust the orientation of cilia in their ciliary bands (i.e., densely packed cilia) to control the direction of liquid flow; i.e. an analogous fluid source and sink are developed for their propulsion and feeding mechanisms 1 . Inspired by nature's cilia and their functions, engineered synthetic cilia and ciliary bands are of great interest for lab-on-chip devices and microrobotic systems. In particular, they promise solutions for many fundamental functions including propulsion, liquid pumping and mixing, and particle manipulation-all difficult to realize at microscale due to a lack of inertia.
Artificial cilia are commonly driven by external fields, such as electric, magnetic, light, and pressure fields. Magnetically-driven cilia, in particular, have become popular due to their relatively simple and easy operation. For example, the motion of artificial cilia has been demonstrated with a handheld magnet applied to arrays of composite magnetic-polymeric nanorod arrays 2 . In another method, magnetism-based self-assembled cilia are first formed in a chain through the dipole-dipole interaction of superparamagnetic particles immersed in liquid, and subsequently rotated via a rotating magnetic field 3 . These and similar concepts have been implemented for fluid pumping and particle transport 4 . In addition, 1D and 2D arrangements of magnetic cilia have been shown to exhibit metachronal waves and used for various applications in fluid and particle transport and soft robotics 5,6 . In alternative approaches, electrostaticallyactivated cilia are created with metal-coated polymeric films for mixing applications at low Reynolds number; light-driven cilia are fabricated using azo-benzene doped liquid crystals 7 ; and cilia containing multiple pneumatically-controlled actuators 8 are developed to generate propulsion in liquid 9 .
While several different approaches have been developed to exploit artificial cilia for biomedical applications, acoustically-activated cilia have received little attentiona surprising trend given the widespread use of ultrasound in biomedical and clinical systems. In particular, while the acoustic vibration of individual synthetic cilia has been employed for liquid pumping 9 , the interaction of multiple cilia in close proximity i.e. in ciliary bands (as observed in biological systems), remains largely unexplored. Inspired by the natural arrangements of the cilia on the surface of starfish larva, we developed ultrasound-activated ciliary bands. Notably, cilia and ciliary bands activated by ultrasound are particularly attractive because ultrasound is safe to most biological systems, non-invasive, penetrates deep in the body of an animal model, and is widely used in clinical settings. Ultrasound-based ciliary bands promise to be an extremely versatile tool for various lab-on-chip applications and developing micro-and nanorobots for in vivo applications. This article presents the first demonstration of ultrasound-activated synthetic ciliary bands to realize multi-functional microrobotic systems. When our synthetic polymeric ciliary bands are exposed to an acoustic field, they undergo small-amplitude oscillation and execute a bulk liquid flow. When the ultrasound-actuated planar ciliary bands are angled toward each other (+), the fluid is pushed away from the surface on which the bands are housed, mimicking a flow source. In contrast, when the cilia are angled away from each other (-), the liquid is forced in toward the surface, mimicking a flow sink.
Achieving externally-controlled propulsion at the microscale represents another significant challenge to realizing micro-and nanorobotic manipulation systems for in vivo use.
The well-known scallop theorem states that the reciprocal motion of a two-state motor submerged in a Newtonian liquid at low Reynolds number results in no net motion. To date, only a few studies have been carried out that used reciprocal motion for propulsion at the microscale.
One example is the "micro-scallop," which uses a magnetic field oscillating at 0.5 Hz to perform reciprocal-motion-based propulsion in non-Newtonian shear-thinning and -thickening gels 10 . In another study, periodic motion of a rigid body introduced nonlinearities through interfacial deformation, thus generating propulsion under low-Reynolds number flow fields 11 . In this work, we leveraged nonlinear acoustics in conjunction with a source/sink arrangement of ciliary bands to develop a new physical principle of propulsion for acoustic-based microrobots. Specifically, we present a unique approach to micro-propulsion that overcomes the scallop theorem by using high-frequency reciprocal oscillation of ciliary bands to locally induce considerable inertial forces and consequent propulsion. Thus, we render the contingency of the scallop theorem invalid by introducing inertia in an otherwise viscous dominated flow regime 12 . Finally, by arranging + and ciliary bands, i.e. a source and sink, adjacent to each other, we demonstrate a microparticle trap mimicking the feeding mechanism of starfish larva.

Bioinspired Ciliary Bands
Inspired by the remarkable natural arrangements of ciliary bands on the surface of invertebrate larvae, we developed new designs for ultrasound-based ciliary bands that leverage the same physical principles. To validate our concept, we fabricated "+" and "-" arrangements of cilia using ultraviolet (UV) photopolymerization method and performed experiments to characterize their behaviour in an acoustic field. The UV photopolymerization method was developed under an inverted microscope. In short, masks containing the ciliary band designs were placed at the field stop of the microscope. UV light passes through a 20x objective and polymerized the polyethylene glycol and photoinitiator solution sandwiched between two glass slides (Fig. S1).
The fabricated + andciliary bands comprised two to eight cilia on each side. Each cilium had a length, base thickness, and height of L ≈ 100 µm, W ≈ 15 − 35 µm, and H ≈ 50 µm (Fig. S2), respectively, and as a set were arranged in series with separation of 20 − 40 µm. After fabrication, the ciliary bands were placed in an acoustic chamber filled with liquid solution containing tracer particles. A piezo transducer, which generated the acoustic field, was bonded next to the acoustic chamber and connected to an electronic function generator (Fig. S3). The entire setup was mounted on an inverted microscope, and experimental results were captured using light-sensitive and high-speed cameras.
Over the course of the experiment, the acoustic field's excitation frequency was modulated from 20 − 100 kHz while maintaining an applied peak-to-peak voltage of 1 − 25 V PP .
When exposed to such an acoustic field, a ciliary band undergoes small-amplitude oscillations ( Fig. S4), which result in a time-averaged steady flow field characterized by a pair of counterrotating vortices in the surrounding liquid, also referred as acoustic streaming 13 . This acoustic streaming is driven by the dissipation of acoustic energy flux inside the fluid system that occurs, in general, both within and outside of the viscous boundary layer. However, for devices where the characteristic dimensions are much smaller compared to the acoustic wavelength (L ≪ λ), the acoustic streaming is primarily driven by the viscous dissipations within the boundary layer. To understand the behaviour of a + ciliary band, we first looked at particle transport in the right half array of the + ciliary band when exposed to ultrasound. The tracer particles, as indicated by red, green, and blue trajectories in Fig. 2a, rapidly hop from the tip of one cilium to another, with particles achieving velocities as high as 10 mm/s when they approach the tip. The ciliary array's direction dictates the flow direction, i.e. the flow is guided from right-to-left along the right ciliary array ( Fig. 2b and Movie S1). The rapid motion of particles along that array produces a clockwise (CW) vortex in the right half of the ciliary band; similar fluid flow along the left half produces a counter-clockwise (CCW) vortex. Thus, an analogous acoustic source is formed due to build-up of the two counter-rotating vortices, producing an outward flow at the centre of the + ciliary band, as shown in Fig. 3a. Fig. 3b likewise illustrates the liquid flow field near aciliary band. In contrast to Fig. 3a, the flow field for aciliary band is analogous to a fluid sink and produces an inward flow at the centre (see also Movie S2). In a control experiment, when a straight ciliary array was exposed to an acoustic field, we observed no significant particle transport or fluid flow from one cilium to another ( Fig. S5 and Movie S3).
Instead, the tracer particles were trapped in small vortices around each cilia tip. Therefore, angulated ciliary array is responsible for the tangential streaming in the direction of the cilia tips, which is critical to developing the acoustic analogous source and sink.
The strength of the flow produced from + andultrasound ciliary bands is determined by the intensity of the ambient acoustic field, which is controlled by adjusting the voltage applied to the piezoelectric transducer. Specifically, the streaming is driven by force and mass sources that depend quadratically on the first-order pressure and velocity, which in turn, depend linearly on the applied displacement amplitude 14 . Furthermore, prior numerical and experimental investigations have revealed that, for small values of signal power, the displacement amplitude depends linearly on the applied voltage 14,15 . Consequently, the streaming is expected to scale quadratically with the applied voltage (i.e., streaming velocity ∝ V PP 2 ). To investigate this scaling, we employed particle image velocimetry to measure the average velocities normal to the ciliary bands at sites indicated by magenta boxes in Fig. 3a and 3b. Fig. 3c and 3d show that this quadratic relation is reasonably well satisfied by the ciliary bands. We note that the vertical streaming velocity of the + ciliary band is larger compared to theconfiguration; likely due to the closer placement of the innermost cilia tips of the + ciliary band, which leads to each half band contributing more to the vertical streaming.
We reproduced the streaming flow patterns via numerical simulations based on the established perturbation approach 14,16 . Briefly, the perturbation approach expresses the fluid response to acoustic actuation as a sum of the first-order harmonic fields ( 1 , p 1 , ρ 1 ) and the second-order steady fields ( 2 , p 2 , ρ 2 ), e.g., = ε + ε 2 + ⋯, where ε is an appropriate smallness parameter 16 . This approach represents the steady flow field induced by the ciliary bands of the microrobot in a fluid by a second-order system of equations ( 2 , p 2 , ρ 2 ), which, in turn, is driven by the body force and mass source terms stemming from nonlinear interactions of the time-harmonic first-order fields ( , p 1 , ρ 1 ). Further details of the theoretical and numerical formulation can be found in Supplementary text. The numerical simulations yielded the same qualitative flow patterns ( Fig. 3e and 3f) as the experimental results and therefore can serve as a useful tool in assessing the flow patterns for different configurations of ciliary arrays.
Engineering ciliary bands did not show any evidence of resonance characteristics.
Nonetheless, we observed frequency dependent behaviour of our system. Specifically, we observed that the performance of the system, with regards to generation of streaming, was best at 68.5 kHz. This can be attributed to the fact that the piezo transducer's oscillation amplitude coupled with glass slide is maximum at this frequency, which is likely to be one of the resonances of the piezo/glass system, see also supporting where ∆s is the oscillation amplitude, and the separation of time and length scales between the acoustic actuation and streaming flow (see also eq. 4). Therefore, these ciliary bands can generate motion as long as their oscillation frequency is sufficiently high to introduce inertia in the second-order equations.

Bioinspired Microrobot
Microrobots could facilitate specialized tasks in medicine 17 , including surgical procedures and drug delivery to hard-to-access sites in vivo. Chemical 18-26 and external field-driven, such as magnetic [27][28][29][30][31][32][33][34][35] , light [36][37][38] , electrical 39 , biohybrid [40][41][42] or ultrasound 43-48 -microrobots are attractive because they do not require an onboard power supply or intricate moving parts and allow wireless control of the microrobot. Nonlinear ultrasound provides an alternate and attractive method to generate propulsion in vivo. In this section, we analyse the swimming motion of our bioinspired microrobot. The applied ultrasound has a wavelength on the order of a centimetre (~22 cm), which is at least two orders of magnitude larger than the microrobot (~280 µm). As a result, the swimmer is subjected to uniform pressure on all sides. This expectation is further corroborated by a control experiment performed on a swimmer lacking ciliary bands and under acoustic actuation of different frequencies and amplitudes (Fig. S7); the lack of resultant motion of the device suggests (i) a nearly-uniform acoustic pressure field, with no significant net force on the swimmer, and (ii) the radiation force of the acoustic wave from the piezo transducer does not contribute to any motion.
We designed + andciliary bands on the left and right sides, respectively, of the soft robot, as shown in the schematic in Fig. 4a. As the microrobot is released and exposed to This value also suggests that the system is viscous-dominated and thus must not exhibit any noticeable motion, per the scallop theorem. However, since ultrasound causes the ciliary band to oscillate, we must consider the Reynolds number associated with the oscillation of the cilia.
For ultrasound actuated systems, the steady flow field is driven by the nonlinear interactions of the harmonic first-order response of the fluid. This can also be deduced from the perturbation expansion approach where the second-order system of equations is driven by time-averaged nonlinear first-order terms that scale with Re (see also Supplementary text). Depending on Re , these first-order response dependent forcing terms (second and third term on the left-hand side of Eq. S7 in Supplementary text) can introduce sufficient inertia in the system to achieve swimming, even for reciprocal motion, rendering the Scallop theorem inapplicable.
The first-order fluid response is represented by the linearized Navier-Stokes equations, Eq.
S4 and S5) and can be expressed in terms of the non-dimensional frequency Reynolds number.
We begin by defining the following non-dimensional quantities: where ρ, ṽ, t̃ and μ denote the characteristic scales for the first order velocity, density, time, and viscosity, respectively. Using these non-dimensional quantities, the first-order momentum equation can be expressed as The total time-averaged acoustic propulsive force , experienced by the microrobot can be expressed as where Ω 1 represents the surface of the microrobot. Here, the first term accounts for the contribution from the stress 〈 〉 developed by localized acoustic microstreaming, while the second term represents the nonlinear interactions of the first-order harmonic velocity response.
As revealed by our scaling analysis, both the first-order response as well as the forcing terms for the second-order equations depend on Re . Therefore, each of the terms on the right-hand side of Eq. 5, can be tuned by modifying Re . Consequently, propulsion can be achieved by tuning Re . Therefore, the starfish larva-inspired microrobot circumvents the scallop theorem by introducing high-frequency oscillation of ciliary bands which induces inertial forces and subsequent propulsion.

Microparticle Transport
Next, we introduce a microparticle trapping strategy inspired by the feeding mechanism of a starfish larvae 1 . Briefly, this mechanism is characterized by the juxtaposition of ciliary arrays that beat in reverse, generating a specific flow field that facilitates the transport of particles and nutrients to the larva's surface for subsequent capture. Correspondingly, we design an analogous structure that incorporates a combinatorial arrangement of + andciliary bands, as shown in Fig. 5a.
When a synthetic band with this arrangement is exposed to ultrasound, microparticles in close vicinity of the + ciliary band are initially attracted to and travelled along the left ciliary array, then at the centre of the + ciliary band are pushed away at velocities of up to 2 mm/s (Movie S7). Were this a stand-alone + ciliary band, the trajectories of these particles would have followed the symmetrical vortices, as in Fig. 3a. However, the presence of an adjacentciliary band breaks the symmetry of a stand-alone + ciliary band and instead pulls these particles towards the right half of the + ciliary band. Subsequently, in accordance with the source-like flow profile generated by a + ciliary band, these particles move away from the + ciliary band.
Given that the strength of the source diminishes with distance from the + ciliary band, the effect of the adjacent sink becomes more prominent as the microparticles progress, causing them to be transported towards theciliary band, as shown in Fig. 5b. Fig. 5c and 5d demonstrate the trajectory and velocity behaviour of microparticles exposed to the trapping flow field provoked by a trapping ciliary band configuration. As expected, the particle decelerates as it moves away from the + band, then accelerates upon approach towards theband. Overall, this arrangement of adjacent + andciliary bands allow the migration of microparticles from one ciliary band to another. Combined with an efficient capture strategy that further siphons these particles into the body of the synthetic structure, this transport mechanism can be used to design efficient microrobotic systems that can attract and capture particles of interest from the surrounding flow field.

Discussion
We developed ultrasound-activated synthetic ciliary bands inspired by the natural ciliary arrangements on the surface of starfish larva. When our planar ciliary bands are angled toward each other (+), fluid is pushed away from the surface on which the cilia are arranged. In contrast, when the cilia are angled away from each other (-), liquid is forced in toward the bands. Thus, we have developed an ultrasound-actuated ciliary arrangement mimicking a source and sink in an artificial system. We further incorporated these aspects to develop a new physical and design principle for acoustic-based microrobots. Our starfish larva-inspired microrobot overcomes the scallop theorem due to its ciliary bands, as their high-frequency oscillations induce inertial forces and consequent propulsion, rendering the contingency of the theorem invalid. Finally, by placing + andciliary bands adjacent to each other, we demonstrate a microparticle transport mechanism analogous to a starfish larva's feeding mechanism.
Since microorganisms live in an environment where inertial effects are negligible, their cilia must produce nonlinear whip-like motion, i.e., an asymmetric beat pattern is executed to overcome the reversibility of low-Re flows, as required by the scallop theorem. The ultrasound cilia and ciliary bands are unique in comparison to natures' cilia. Specifically, unlike natural cilia, ultrasound cilia undergo reciprocal motion to produce a flow. This apparent contradiction with the scallop theorem can be attributed to the oscillation frequency of ultrasound cilia that is at least three orders of magnitude higher than its natural counterpart. As revealed by our theoretical analysis, it is this separation of time scales between the (second-order) fluid response and the (firs-order) acoustic actuation that is responsible for the bulk fluid motion, despite the reciprocal motion of cilia. Interestingly, when synthetic cilia were exposed to lowfrequency ultrasound between 1 to 100 Hz (see also Fig. S4), individual particles demonstrate to and fro motion without any net displacement, further confirming the crucial role of excitation frequency.
We believe the present work introduces a new design space for externally-actuated fielddriven microrobots and the engineering of cilia and ciliary bands that are not exclusive to ultrasound-based systems. Engineering cilia that could produce reciprocal motion in order to introduce inertia are much simpler in terms of their fabrication and operation. The concept can be transferred to non-ultrasound methods, for example in magnetic field-driven systems. Recent studies on magnetism-based synthetic cilia mimic the nonreciprocal whip-like beating pattern of biological cilia; however, engineering these devices requires multi-step fabrication, and they are challenging to scale down to the microscale. Achieving reciprocal motion in the kHz domain with magnetically-doped engineered cilia may introduce inertia at microscales but may be challenging due to (i) the need to rapidly switch the magnetic field and (ii) magnetic hysteresis, the retention of magnetic alignment after a field is removed. In addition to magnetic-field driven systems, light-driven liquid crystal-doped polymeric structures have been shown to generate fast movement and to enable rapid switching in the kHz domain, and thus could become a potential candidate mechanism for propulsion via reciprocal motion.
In our current experiments, depending on the fabrication of the ciliary bands and the corresponding oscillation patterns, we observed smaller counter-rotating vortices at the innermost cilia, in addition to the larger counter-rotating vortices above the ciliary bands (Fig.  S8). Future work will aim to thoroughly investigate the oscillation patterns of the cilia, including the effect of different fabrication processes and material stiffness. We look forward to studying the performance of our ultrasound-based ciliary bands in terms of fluid flow, propulsion, and particle transport near walls and in confined channels in biologically-relevant fluid mediums under physiologically-relevant conditions, including non-pulsatile and pulsatile flow. An immediate next step also involves investigating their performance in non-Newtonian liquids such as blood, viscoelastic mediums, and shear-thinning gels. Currently, the angle of our ciliary bands are fixed, we plan that a light-activated liquid crystal polymer can be used to dynamically change the orientations of ciliary bands, i.e. switch from + toarrangements and vice versa, thereby enabling the development of a robotic system that closely mimics its natural counterparts in propulsion and feeding (trapping) mechanisms. Finally, the concept of + andciliary bands can be utilized in lab-on-a-chip systems to realize label-free trapping, fluid mixing and pumping at low Reynolds fluid low, and separation of particles for portable diagnostics applications.

Materials and Methods
Fabrication Method. Ciliary bands were fabricated using a custom-built projection UV photolithography method developed on an inverted microscope (Fig. S1)  Ciliary array Fig. 2 | Tangential flow along angled ciliary array when exposed to ultrasound. a. Image sequences demonstrate ~6 µm tracer particles, indicated by red, green, and blue lines, travelling along one cilium tip to the next from right-to-left in the direction the tips are angled at excitation frequency and amplitude of 33.7 kHz and 5 V PP , respectively (see also Movie S1). b. Velocity analysis of the tracers revealed a cyclic acceleration/deceleration pattern. Particles reached maximum speeds when they approached a ciliary tip, followed by a deceleration phase. Scale bar, 50 µm.