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• W3117698753 abstract "•Ultrahigh-frequency (≥100 MHz) ultrasonic transducer to manipulate microspheres•The broad bandwidth and highly focused transducer differentiate microparticles•FEA modeling and calculation indicate the force for selectively trapping•The forbidden band theory of acoustic radiation force is proposed for trapping Acoustic micro-beams produced by highly focused ultrasound transducer have been investigated for micro-particle and cell manipulation. Here we report the selective trapping of microspheres via the acoustic force using the single acoustical beam. The forbidden band theory of acoustic radiation force trapping is proposed, which indicates that the trapping of particles via the acoustic beam is directly related to the particle diameter-to-beam wavelength ratio as well as excitation frequency of the ultrasonic acoustic tweezers. Three tightly focused LiNbO3 transducers with different center frequencies were fabricated for use as selective single beam acoustic tweezers (SBATs). These SBATs were capable of selectively manipulating microspheres of sizes 5–45 μm by adjusting the wavelength of acoustic beam. Our observations could introduce new avenues for research in biology and biophysics by promoting the development of a tool for selectively manipulating microspheres or cells of certain selected sizes, by carefully setting the acoustic beam shape and wavelength. Acoustic micro-beams produced by highly focused ultrasound transducer have been investigated for micro-particle and cell manipulation. Here we report the selective trapping of microspheres via the acoustic force using the single acoustical beam. The forbidden band theory of acoustic radiation force trapping is proposed, which indicates that the trapping of particles via the acoustic beam is directly related to the particle diameter-to-beam wavelength ratio as well as excitation frequency of the ultrasonic acoustic tweezers. Three tightly focused LiNbO3 transducers with different center frequencies were fabricated for use as selective single beam acoustic tweezers (SBATs). These SBATs were capable of selectively manipulating microspheres of sizes 5–45 μm by adjusting the wavelength of acoustic beam. Our observations could introduce new avenues for research in biology and biophysics by promoting the development of a tool for selectively manipulating microspheres or cells of certain selected sizes, by carefully setting the acoustic beam shape and wavelength. Particle manipulation by a contactless method has numerous applications in biophysical and biomedical research areas (Lam et al., 2012Lam K. Hsu H. Li Y. Lee C. Lin A. Zhou Q. Kim E. Shung K. Ultrahigh frequency lensless ultrasonic transducers for acoustic tweezers application.Biotechnol. Bioeng. 2012; 110: 881-886Crossref PubMed Scopus (79) Google Scholar; Tomasi et al., 2020Tomasi R. Sart S. Champetier T. Baroud C. Individual control and Quantification of 3D spheroids in a high-density microfluidic droplet array.Cell Rep. 2020; 31: 107670Abstract Full Text Full Text PDF PubMed Scopus (11) Google Scholar; Yu and Miyako, 2018Yu Y. Miyako E. Alternating-Magnetic-field-mediated wireless manipulations of a liquid metal for therapeutic bioengineering.Iscience. 2018; 3: 134-148Abstract Full Text Full Text PDF PubMed Scopus (26) Google Scholar; Diamantaki et al., 2018Diamantaki M. Coletta S. Nasr K. Zeraati R. Laturnus S. Berens P. Preston-Ferrer P. Burgalossi A. Manipulating hippocampal place cell activity by single-cell stimulation in freely moving mice.Cell Rep. 2018; 23: 32-38Abstract Full Text Full Text PDF PubMed Scopus (22) Google Scholar; Patnode et al., 2019Patnode M. Beller Z. Han N. Cheng J. Peters S. Terrapon N. Henrissat B. Le Gall S. Saulnier L. Hayashi D. et al.Interspecies competition impacts targeted manipulation of human gut bacteria by fiber-derived glycans.Cell. 2019; 179: 59-73.e13Abstract Full Text Full Text PDF PubMed Scopus (57) Google Scholar; Ozcelik et al., 2018Ozcelik A. Rufo J. Guo F. Gu Y. Li P. Lata J. Huang T. Acoustic tweezers for the life sciences.Nat. Methods. 2018; 15: 1021-1028Crossref PubMed Scopus (194) Google Scholar; Melde et al., 2016Melde K. Mark A. Qiu T. Fischer P. Holograms for acoustics.Nature. 2016; 537: 518-522Crossref PubMed Scopus (259) Google Scholar). Optical tweezer is an outstanding example capable of trapping and manipulating various types of microparticles (Yu and Miyako, 2018Yu Y. Miyako E. Alternating-Magnetic-field-mediated wireless manipulations of a liquid metal for therapeutic bioengineering.Iscience. 2018; 3: 134-148Abstract Full Text Full Text PDF PubMed Scopus (26) Google Scholar; Maragò et al., 2013Maragò O. Jones P. Gucciardi P. Volpe G. Ferrari A. Optical trapping and manipulation of nanostructures.Nat. Nanotechnol. 2013; 8: 807-819Crossref PubMed Scopus (615) Google Scholar; Ashkin et al., 1986Ashkin A. Dziedzic J. Bjorkholm J. Chu S. Observation of a single-beam gradient force optical trap for dielectric particles.Opt. Lett. 1986; 11: 288Crossref PubMed Scopus (5317) Google Scholar; Grier, 2003Grier D. A revolution in optical manipulation.Nature. 2003; 424: 810-816Crossref PubMed Scopus (3838) Google Scholar; Kotamarthi et al., 2020Kotamarthi H. Sauer R. Baker T. The non-dominant AAA+ ring in the ClpAP protease functions as an anti-stalling motor to accelerate protein unfolding and translocation.Cell Rep. 2020; 30: 2644-2654.e3Abstract Full Text Full Text PDF PubMed Scopus (6) Google Scholar). It has been utilized to measure the elastic properties of the DNA molecular chain (Fazal and Block, 2011Fazal F. Block S. Optical tweezers study life under tension.Nat. Photon. 2011; 5: 318-321Crossref PubMed Scopus (259) Google Scholar), rotate the microspheres or cells in many fields (Padgett and Bowman, 2011Padgett M. Bowman R. Tweezers with a twist.Nat. Photon. 2011; 5: 343-348Crossref Scopus (1141) Google Scholar), and assemble 1D, 2D, and 3D array structures of embryonic stem cells (Kirkham et al., 2015Kirkham G. Britchford E. Upton T. Ware J. Gibson G. Devaud Y. Ehrbar M. Padgett M. Allen S. Buttery L. et al.Precision assembly of complex cellular microenvironments using holographic optical tweezers.Sci. Rep. 2015; 5: 1-7Crossref Scopus (57) Google Scholar). However, the focused lasers used to realize optical tweezers could cause local heating and photodamage in biological samples because of the high energy it generates. In addition, the applied force by optical tweezer is small, of the order of ~pN or ~ fN (Quinto-Su, 2014Quinto-Su P. A microscopic steam engine implemented in an optical tweezer.Nat. Commun. 2014; 5: 1-7Crossref Google Scholar; Keloth et al., 2018Keloth A. Anderson O. Risbridger D. Paterson L. Single cell isolation using optical tweezers.Micromachines. 2018; 9: 434Google Scholar). These problems can be avoided by using acoustic tweezers because acoustic energy is unlikely to damage biological samples (Neuman and Nagy, 2008Neuman K. Nagy A. Single-molecule force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy.Nat. Methods. 2008; 5: 491-505Crossref PubMed Scopus (1510) Google Scholar; Choe et al., 2011Choe Y. Kim J. Shung K. Kim E. Microparticle trapping in an ultrasonic Bessel beam.Appl. Phys. Lett. 2011; 99: 233704Crossref PubMed Scopus (58) Google Scholar; Liu and Hu, 2009Liu Y. Hu J. Ultrasonic trapping of small particles by a vibrating rod.IEEE Trans. Ultrason. Ferroelectr. Freq. Control. 2009; 56: 798-805Crossref PubMed Scopus (8) Google Scholar; Marston, 2006Marston P. Axial radiation force of a Bessel beam on a sphere and direction reversal of the force.J. Acoust. Soc. Am. 2006; 120: 3518-3524Crossref PubMed Scopus (225) Google Scholar; Wu, 1991Wu J. Acoustical tweezers.J. Acoust. Soc. Am. 1991; 89: 2140-2143Crossref PubMed Scopus (296) Google Scholar). Moreover, these acoustic instruments are not only much easier to set up but also incur lower costs than their optical counterparts. Recently, single beam acoustic tweezers (SBATs), analogous to optical tweezers for trapping and manipulating the individual particle with an acoustic micro-beam (Lee et al., 2005Lee J. Ha K. Shung K. A theoretical study of the feasibility of acoustical tweezers: ray acoustics approach.The J. Acoust. Soc. America. 2005; 117: 3273-3280Crossref PubMed Scopus (95) Google Scholar, Lee et al., 2009Lee J. Teh S. Lee A. Kim H. Lee C. Shung K. Single beam acoustic trapping.Appl. Phys. Lett. 2009; 95: 073701Crossref PubMed Scopus (171) Google Scholar; Lee and Shung, 2006Lee J. Shung K. Effect of ultrasonic attenuation on the feasibility of acoustic tweezers.Ultrasound Med. Biol. 2006; 32: 1575-1583Abstract Full Text Full Text PDF PubMed Scopus (37) Google Scholar; Zhu et al., 2016Zhu B. Xu J. Li Y. Wang T. Xiong K. Lee C. Yang X. Shiiba M. Takeuchi S. Zhou Q. et al.Micro-particle manipulation by single beam acoustic tweezers based on hydrothermal PZT thick film.AIP Adv. 2016; 6: 035102Crossref PubMed Scopus (25) Google Scholar; , (Baudoin et al., 2020bBaudoin M. Thomas J. Sahely R. Gerbedoen J. Gong Z. Sivery A. Matar O. Smagin N. Favreau P. Vlandas A. Spatially selective manipulation of cells with single-beam acoustical tweezers.Nat. Commun. 2020; 11: 1-10Crossref PubMed Scopus (18) Google Scholar); Kamsma et al., 2018Kamsma D. Bochet P. Oswald F. Alblas N. Goyard S. Wuite G. Peterman E. Rose T. Single-cell acoustic force spectroscopy: resolving kinetics and strength of T cell adhesion to fibronectin.Cell Rep. 2018; 24: 3008-3016Abstract Full Text Full Text PDF PubMed Scopus (10) Google Scholar; Sitters et al., 2014Sitters G. Kamsma D. Thalhammer G. Ritsch-Marte M. Peterman E. Wuite G. Acoustic force spectroscopy.Nat. Methods. 2014; 12: 47-50Crossref PubMed Scopus (108) Google Scholar) have attracted considerable attention. Over the past decade, acoustic trapping using SBATs has been investigated both theoretically and experimentally. Owing to the advances of high-frequency ultrasound transducer fabrication process, the performance of acoustic tweezers has been considerably improved over time. Transducers capable of operating at 200 MHz have also been developed, and are shown in Figure 1A, which has enabled the trapping of cells with sizes 15–20 μm (Lee et al., 2011Lee J. Lee C. Kim H. Jakob A. Lemor R. Teh S. Lee A. Shung K. Targeted cell immobilization by ultrasound microbeam.Biotechnol. Bioeng. 2011; 108: 1643-1650Crossref PubMed Scopus (61) Google Scholar), as well as microspheres with diameters 5 and 10 μm (Marston, 2006Marston P. Axial radiation force of a Bessel beam on a sphere and direction reversal of the force.J. Acoust. Soc. Am. 2006; 120: 3518-3524Crossref PubMed Scopus (225) Google Scholar). The performance of acoustic trapping with SBATs is influenced by various factors, including the acoustic characteristics of the medium, excitation frequency of the transducer, distribution of the acoustic field, and the size, shape, and material properties of the particles themselves. In general, the smaller the particles that are needed to be trapped, the higher the SBAT frequency must be. These provide a simple logic for selecting and differentiating the trapping object by its size range from 5 to 50 μm by tuning the frequency used from 100 to 300 MHz. Besides the well-known influence of size-to-wavelength, we propose the “forbidden band” of acoustic trapping. Thus, trapping of particles whose diameters are in the range of the acoustic wavelength is not possible due to the positive gradient of acoustic radiation force (ARF). Figure 1B shows the schematic diagram of the size-selectivity manipulation of single microspheres of different sizes. However, several problems still need to be addressed to realize trapping microsphere using transducers. First, it is difficult for a typical SBAT to achieve a -6 dB bandwidth of more than 30%, which means that the frequency range in which the transducer can be excited is small, and thus the range of particle sizes to trap using the SBAT is limited. Nevertheless, the broad bandwidth and highly focused transducers for SBAT applications are quite challenging to manufacture, particularly of one operating in the ultrahigh frequency range (>100 MHz). In addition, the SBAT needs to show characteristic features, e.g., a low f-number and a cylindrical symmetry of the acoustic beam, to meet the requirements of biomedical and biological applications (see Figure S1 and Table S1 in Supplemental information for detailed definition of these parameters). Based on our prior work, size-selective manipulation of single particles in the range 3–100 μm can be achieved with frequencies between 150 and 400 MHz (Chen et al., 2017Chen X. Lam K. Chen R. Chen Z. Yu P. Chen Z. Shung K. Zhou Q. An adjustable multi-scale single beam acoustic tweezers based on ultrahigh frequency ultrasonic transducer.Biotechnol. Bioeng. 2017; 114: 2637-2647Crossref PubMed Scopus (10) Google Scholar). However, the range of the trapping was successful or failed using the different ultrahigh frequency ultrasonic transducers with different f-number has not been previously reported, and it is very important to explain and quantify the trapping ability of the focusing transducers with different characterization for the various the acoustic contrast between microspheres or cells and medium, which would be of significant importance both in research and industrial applications. In this work, we combined experimental and theoretical investigations to give the phenomenon and explanation of size selectivity of acoustic radiation force trapping via the highly focused transducers. Three high-performance (with low f-number and broad bandwidth) ultrahigh frequency ultrasound transducers are designed and fabricated for generating tightly focused ultrasound beam. We find that there is a grabbing band corresponding to size of the microparticle and ultrasound frequency within a certain range. The forbidden band is given by calculation of acoustic radiation force for microsphere and verified by experiment. This platform can be used to manipulate and differentiate specific microparticles without disturbing other particles. To realize individual particle mobilization of elastic micro-particles suspended in liquids, the ultrasound beam width of single-beam acoustic tweezers should be close to the particle size with a highly focused ultrasonic beam that can produce sufficient specific force for trapping and manipulating a micro-particle of interest. Tightly focused LiNbO3 transducers (LN100, LN200, and LN300) with center frequency around 100 MHz, 200 MHz, and 300 MHz were evaluated and used to trap microspheres of 5–15 μm at their focus. All the transducers show high sensitivity and relatively broad −6 dB bandwidth. The ultrahigh center frequency, broad bandwidth, high sensitivity, and small f# make the transducers suitable for SBAT applications. The receive-echo response, corresponding frequency spectrum, as well as the lateral beam profile of the LiNbO3 focused transducers are shown in Figure S1, and a beam width equal to 16.4, 6.6, and 6.4 μm was obtained by transducers “LN_100”, “LN_200,” and “LN_300,” respectively, in detecting a spatial point target at full width at half maximum (FWHM, −6 dB). The schematic structure of the transducers is shown in Figure 2A; these transducers have f# values close to 1.0 with the theoretical values for the beam width of −6 dB lateral beam being 12.4, 6.4, and 6.2 μm (= f# × wavelength) for LN_100, LN_200, and LN_300 at 104, 207, and 275 MHz in water (sound velocity is 1,540 m/s), respectively (see Table S1). The map of acoustics pressure was achieved using finite element method (FEM) in the COMSOL environment. The COMSOL model is constructed in a two-dimensional axisymmetric coordinate system, and the plane wave radiation is set at the boundary of the propagation medium. Here, we focus on the case of the LN_200 transducer, and the aperture size of the piezoelectric element is 0.8 × 0.8 mm2 with the measured center frequency of 207 MHz and the −6 dB bandwidth of 44.2%. In the FEM, the ultrahigh frequency focused LN_200 transducer with a piezoelectric layer (15 μm) and its matching layer (2.5 μm) in the form of double-layer rings are attached to the hemispherical water area (1.2 mm diameter) and focal plane at z = 0. The maximum calculation grid size of water area is set to one-fifth wavelength in the water at excitation frequency. The LN_200 transducer is operated at a frequency of 200–300 MHz corresponding to a wavelength of 7.7–5.1 μm in water. The acoustic pressure waveforms were simulated at each point in a hemisphere and a rectangle on the xz plane in increments of λ/15 for different frequencies and quarter circles. Moreover, the principle setup and the model parameters (2D-axisymmetric coordinate system, boundary conditions, relative resolution) are the same for all three transducers. A cross-section of the computational model and calculated results for the acoustic field, e.g., magnitude and phase of acoustic pressure as well as the angular spectrum, are shown in Figure 2. Based on these results, it can be observed that beam focusing is achieved almost at the focal position (z = 0 mm) of the needle transducer, while the lateral −6 dB beam width of the pressure amplitude at the focal point is 6.56 μm in Figure 2G, which is in agreement with the theoretical value (6.2 μm) based on f-number and wavelength. Using the finite element analysis software, the aforementioned three tightly focused transducers (LN_100, LN_200, and LN_300) were modeled and simulated (see Figure S2), and the simulated -6 dB lateral beam widths of 17.9, 7.0, and 6.7 μm agree with the experimental value of 16.4, 6.4, and 6.2 μm at central frequency. Sound field distribution and lateral beam characteristics at the focus of the three transducers are given in the Figure S3. The lateral component of the radiation force determines whether the particles can be manipulated to move them in the lateral direction; owing to the symmetry of the acoustic field, only a certain direction needs to be considered. Then, the acoustic radiation forces on the microspheres can be calculated as detailed in Transparent Methods. The spherical scatterer (polystyrene microsphere) and the medium (water) are used in calculation with the following parameters:ρ = 1,000 kg/m3, c = 1,540 m/s, ρs = 1,040 kg/m3, cl = 2,330 m/s, and ct = 1,100 m/s. The lateral component of the acoustic radiation force Fx was calculated (based on Equations S3–S9 in Transparent methods) for different particles sizes (5–15 μm) and for frequencies between 200 and 300 MHz. Their distribution at 250 MHz was plotted; these results are shown in Figure 3, and these parameters correspond to size-to-wavelength ratios from 0.8 to 2.4. Qualitative different behavior of the radiation force can be observed depending on the particle size. For particles with 5 μm (Figures 3A) and 15 μm (Figure 3C) diameter the radiation force is directed toward the center of the acoustic beam (x = 0). This attractive force allows for particle trapping even if the transducer is slightly moved in the lateral direction. In contrast to this, radiation force acting on the 10-μm particle is directed away from the acoustic beam axis pushing the particle off the focal area. These calculations indicate that the manipulation of particles of different sizes using the transducer produces two different behaviors, namely, pulling back or pushing away, leading to selective trapping. The capability of LiNbO3 ultrahigh frequency microbeam devices for size-selective trapping of a single microsphere was demonstrated via calculation of the acoustic force at 250 MHz with the LN_200 transducer. To further understand the selective trapping of particles, we repeated the simulation of the distribution of acoustic pressure produced by the transducer using FEM and the calculation of acoustic force for microspheres with different radii for three different ultrasound transducers at different frequencies. To better scan and get the corresponding relationship diagram, the result Fx of the abovementioned formula is taken as the corresponding one-dimensional drawing group in the middle axial direction (Fx,y=0). Supposing there are two cases of the microsphere under the focus beam (can trap or cannot trap), these two cases can be defined by the following discriminant:dFx,y=0dx|x=0>0ordFx,y=0dx|x=0<0?(Equation 1) dFx,y=0dx|x=0=C∗Re{∑n=0∞ψn∑m=−nnAnm(ΔHnmΔHn+1,m+1∗−ΔHn,−mΔHn+1,−m−1∗)}xs(Equation 2) ΔHnm=∬kx2+ky2≤k2(eikxxs−1)dkxdkyS(kx,ky)Ynm∗(θk,ϕk)where the C is 1/(8π2ρc2k2) and xs is defined as the size of the calculation grid (1/20λ) in the x direction in FEM. When dFx,y=0dx|x=0>0, as described in Figure 3B, the corresponding microsphere will move away from the focus beam center. Otherwise, Figures 3A and 3C conform to the condition of dFx,y=0dx|x=0<0 and the microsphere will be trapped at the center by acoustic radiation force. The discriminating factor dFx,y=0dx|x=0 values as a function of d and frequency of the three focused transducers are all calculated as shown in Figure 4(A1–C1). With the change of the size of the microsphere (d) and the excitation frequency (f), the three transducers all show the “Forbidden band” in which the discriminating factor becomes positive and meets the condition of dFx,y=0dx|x=0>0. To characterize the band gap more clearly, both dFx,y=0dx|x=0 are depicted in the gray scale diagram and the x coordinates are normalized to d/lambda, as shown in Figure 4, which set the A is dFx,y=0dx|x=0>0 and B is dFx,y=0dx|x=0<0. When given a transducer (f# and DOF), trapped particles, and medium (acoustic property of c and ρ), “Forbidden band” could be defined and based on the size-to-wavelength ratio. In this case, the theoretical widths of the “Forbidden band” of three transducers are 1.41 d/λ from 1.01 to 2.42 d/λ, 0.99 d/λ from 1.28 to 2.17 d/λ, and 0.99 d/λ from 1.28 to 2.17 d/λ, respectively. Furthermore, we designed corresponding experiments to verify this theory. All the three LiNbO3 ultrasonic transducers are capable of efficient excitation over a large range of frequencies owing to their high sensitivity and relatively wide bandwidth. In particular, we operate the LN_200 and LN_300 transducers at frequencies of 200–300 MHz and LN_100 transducer at 80–130 MHz. Thus, by modifying the excitation frequency and selecting microspheres with different diameters, we could quantitatively obtain the dependence of trapping effect on excitation frequency and microsphere diameter and compare experimental discrete points with theoretical calculations of the distribution of effective trapping as shown in Figure 4(A2–C2). This shows the dependence of trapping results on the excitation frequency and microsphere diameter to wavelength ratio along with the theoretically calculated frequency (f) and ratio (d/λ) ranges, wherein the gray area indicates that the particles were pushed away, whereas the white area indicates that the particles were trapped. Multiple microspheres are typically trapped simultaneously when d/λ < 0.5, owing to the beam width and small particle size. However, this case was not considered in current study. As illustrated in Figure 4A, the LN_100 transducer was unable to manipulate microspheres when the particle size-to-wavelength ratio was 1.17–2.48 d/λ, which agrees with the corresponding theoretical range of 1.08–2.49 d/λ. However, the microspheres could be trapped and manipulated via the SBAT at frequencies outside of this range. As shown in Figures 4B and 4C, for the LN_200 and LN_300 transducers, the theoretical range of the particle size-to-wavelength ratio for which particle manipulation was not possible is about 1.28–2.17 d/λ, which is also close to the experimentally obtained range of 1.36–2.34 d/λ and 1.35–2.04 d/λ for the two different transducers, respectively. The forbidden band theory of acoustic radiation force trapping and widths of the forbidden band for all three transducers are little different because they have different center frequencies and f-numbers. This result indicates that trapping of SBAT is not possible in the range about 1.1 d/λ here the d is the diameter of the target object microsphere and the λ is the wavelength of the medium. This is because a positive gradient of ARF will occur at the focus when the excitation frequency and the size of microsphere achieves nearly 1 d/λ~2 d/λ. Thus, SBATs could be developed for selectively manipulating microspheres of certain sizes by carefully selecting the excitation frequency. The LN_200 transducer was selected for the experimental demonstration to visually depict the size selectivity of SBAT devices; the transducer, was operated at 250 MHz. At 250 MHz, the LN_200 transducer was capable of manipulating a single microsphere with a diameter of 5 or 15 μm; however, it was unable to trap a single microsphere of 10 μm diameter. Figure 5 and Video S1show examples of manipulation of single microspheres of different sizes using this transducer. The bright area with a red circle is the projection of the transducer. Microspheres of three different sizes (5, 10, and 15 μm) were used. The red dashed line or red dot is shown as a reference in Figure 5 to illustrate the position shift of the microspheres. The LN_200 transducer was excited by a sinusoidal burst in different conditions: a driving frequency of 250 MHz; the excitation voltages of 3.6 V, 2.4 V, and 1.2 V for 15, 10, and 5 μm microspheres, respectively; and a duty cycle of 1%. The panels in Figure 5 labeled “A” show the manipulation of a single 5-μm microsphere (yellow circle) that was trapped and manipulated by moving the transducer device. Similarly, the panels labeled “D” are for the 15-μm microsphere. However, for the 10-μm microsphere, the observation was different, in particular, the microsphere moved away from the center of the focus immediately after the transducer was switched on. Our calculation and experimental results provide a deeper understanding of SBATs, which can be used to broaden their applications. https://www.cell.com/cms/asset/16eb5225-ef8b-4cf9-b5e5-da2a99832b9c/mmc2.mp4Loading ... Download .mp4 (1.65 MB) Help with .mp4 files Video S1. Experiment of two different particles trappingThe 5-μm particles trapping and transport and 10-μm particles transport and scattering. To estimate the forbidden band in the application of SBAT for cell trapping, the calculations of the force using LN_200 at 250 MHz with different size of cells were performed. As the acoustic properties of the cells are different from the polystyrene spheres used earlier, we chose the two cells with different density and compressibility and the cell size from 5 to 15 μm, which is reported in the literature (Augustsson et al., 2016Augustsson P. Karlsen J. Su H. Bruus H. Voldman J. Iso-acoustic focusing of cells for size-insensitive acousto-mechanical phenotyping.Nat. Commun. 2016; 7: 1-9Crossref Scopus (108) Google Scholar; Baudoin et al., 2020aBaudoin M. Thomas J. Sahely R. Gerbedoen J. Gong Z. Sivery A. Matar O. Smagin N. Favreau P. Vlandas A. Spatially selective manipulation of cells with single-beam acoustical tweezers.Nat. Commun. 2020; 11: 4244Crossref PubMed Google Scholar, Baudoin et al., 2020bBaudoin M. Thomas J. Sahely R. Gerbedoen J. Gong Z. Sivery A. Matar O. Smagin N. Favreau P. Vlandas A. Spatially selective manipulation of cells with single-beam acoustical tweezers.Nat. Commun. 2020; 11: 1-10Crossref PubMed Scopus (18) Google Scholar). Table 1 shows the density and compressibility of two cells (cell 1 and cell 2) with the extreme values. Figures 6A–6C show the simulation of the ARF and ΔF under the two conditions (trapped ΔF > 0 and not trapped ΔF < 0) when the size of cell increasing, where F1 and F2 are defined as the extreme value of Fx at x < 0 and x > 0 and the ΔF is the interpolation of F1 and F2. The ΔF of two different cells are shown in Figure 6D, and the white area represents the positive area (trapping) and gray area the negative area (not trapping).Table 1The acoustic properties of the cells for trappingCell density (kg/m3)Cell compressibility (×10−10 Pa−1)Acoustic impedance (MRayl)Cell 11,0004.41.51Cell 21,2103.31.91 Open table in a new tab Furthermore, the value of ΔF for two cells is different due to the different acoustic properties, and they all show the same “forbidden band” corresponding to the different sizes (about 7–12 μm). This result demonstrates that the same forbidden band also exists in cells with different acoustic property and constitutes a cornerstone of size selectivity of SBAT for biological applications. In conclusion, size selectivity of SBATs at a cellular level was demonstrated via trapping experiments using tightly focused LiNbO3 transducers with different center frequencies. These transducers are suitable for SBAT applications because they can operate at an ultrahigh frequency and have broad bandwidth, high sensitivity, and small f#. Our experimental trapping results demonstrated that the ratio of particle size-to-wavelength is an important determinant of acoustic trapping. The SBAT devices were found to be capable of selectively manipulating microspheres of certain sizes by adjusting the wavelength of the acoustic beam accordingly; this was, verified via both simulation and theoretical calculation. Additionally, the results are also valid for acoustically trapping cells typically characterized by a lower acoustic contrast compared with polystyrene particles used in the current study and the ARF trapping of live cells in terms of composition, shape, and physical properties would be the next step of our research. These trapping results are promising for the application of SBATs in biomedical and biophysical research. In conclusion, the present work constitutes another important cornerstone toward widespread applications of SBAT for biological and chemical research applications. This study presents the dependency of trapping capability of high-frequency focused ultrasonic beam on the working frequency and particle diameter, which is useful in the selective manipulation of cells and other small particles. Two main limitations are as follows: (1) The particles trapped in the article are spheres or ellipsoids so that they can be substituted into Equations (1) and (2) to calculate the acoustic radiation force. If the particles have irregular shapes, you need to use the FEM to model and simulate the incident sound field and its scattering field and calculate the sound radiation force by integrating the sound field. (2) The trapped particles selected for the experiment in the article are PDMS, which is uniform and not easy to deform. Suppose the “Forbidden Band” effects are used to manipulate real cells. In that case, it is essential to characterize the material's acoustic and mechanical properties and then substitute it into the formula. More importantly, the cell's deformation also needs to be considered because this affects the distribution of the scattered field and the direction and magnitude of the final force will change. It is also necessary to perform accurate sound field analysis on the focusing transducer used as acoustic tweezers. If the frequency (≥100 MHz) is too high (in this article), the sound field distribution can only be obtained by FEM, not by an experimental hydrophone test. Further information and requests for resources and reagents should be directed to and will be fulfilled by the Lead Contact, Prof. Chunlong Fei ( [email protected] ). This study did not generate new unique materials. All data associated with the study are included in the paper. All methods can be found in the accompanying Transparent methods supplemental file. Financial support from the National Natural Science Foundation of China of China (No: 61974110 ), the Natural Science Foundations of Shaanxi Province (No: 2020JM-205 ), the Shaanxi Provincial Association of Science and Technology Young Talents Support Project (No: 20190105 ), Shenzhen Science technology and fundamental research and discipline layout project (No: JCYJ20170818153048647), and the National Key Research and Development Program of China (No: 2017YFC0109703 ) are greatly appreciated. Conceptualization, C.F. and Y.Y.; Methodology, Z.L., D.W., Z.Q., and D.C.; Investigation, D.L., Q.Z., and Z.C.; Software, Z.L., R.W., and C.H.; Writing – Original Draft, Z.L., D.W., and C.F.; Writing – Review & Editing, Z.L., C.F., Z.Q., and D.W.; Supervision, C.F.; Funding Acquisition, C.F. and Y.Y. The authors declare no competing interests. Download .pdf (.77 MB) Help with pdf files Document S1. Transparent methods, Figures S1–S3, and Table S1" @default.
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• W3117698753 title "The forbidden band and size selectivity of acoustic radiation force trapping" @default.
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