Filtered Lebedev quadrature method for robust and efficient beam shape coefficient estimation in acoustic tweezers calibration.

Acoustic tweezers offer a contactless, three-dimensional, and selective approach to trapping objects by harnessing the acoustic radiation force. Precise control of this technique requires accurate calibration of the force, which depends on the object's properties and the spherical harmonics expansion of the incident field through the beam shape coefficients. Previous studies showed that these coefficients can be determined using either the Lebedev quadrature or the angular spectrum methods. However, the former is highly susceptible to noise, while the latter demands extensive implementation time due to the number of required measurement points. A filtered method with a reduced number of points is introduced to address these limitations. Initially, we emphasize the implicit filtering in the angular spectrum method, allowing relative noise insensitivity. Subsequently, we present its unfiltered version, enabling force estimation of a standing field. Finally, we develop a filtered method based on the Lebedev quadrature, requiring fewer points, and apply it to focused vortex beams. Numerical evaluation of the radiation force demonstrates the method's resilience to noise and a reduced need for points compared to previous methods. The filtered Lebedev method paves the way for characterizing high-frequency acoustic tweezers, where measurement constraints necessitate rapid and robust beam shape coefficient estimation techniques.

Spatially selective manipulation of cells with single-beam acoustical tweezers.

Acoustical tweezers open major prospects in microbiology for cells and microorganisms contactless manipulation, organization and mechanical properties testing since they are biocompatible, label-free and have the potential to exert forces several orders of magnitude larger than their optical counterpart at equivalent power. Yet, these perspectives have so far been hindered by the absence of spatial selectivity of existing acoustical tweezers - i.e., the ability to select and move objects individually - and/or their limited resolution restricting their use to large particle manipulation only and/or finally the limited forces that they could apply. Here, we report precise selective manipulation and positioning of individual human cells in a standard microscopy environment with trapping forces up to ~200 pN without altering their viability. These results are obtained with miniaturized acoustical tweezers combining holography with active materials to synthesize specific wavefields called focused acoustical vortices designed to produce stiff localized traps with reduced acoustic power.

Computation of the radiation force exerted by the acoustic tweezers using pressure field measurements.

Acoustic tweezers allow for manipulation of small objects like elastic spheres with a force generated by the radiation pressure which arises from the nonlinear interaction between the incident and scattered waves by the object. The accurate control of the object by acoustic tweezers requires the study of the components of the three-dimensional (3D) force. If the physical properties of the elastic sphere are known, then the 3D components of the force can be calculated thanks to a decomposition of the incident acoustic field in the spherical functions basis. This study proposes evaluating the expansion coefficients. Three methods are used and compared. The first one consists of measuring the acoustic field on a spherical surface centered on the theoretical position of the object and to calculate the spherical functions decomposition by Lebedev quadratures. The second method is based on the measurement of the acoustic field at random points in a spherical volume and on the resolution of the inverse problem by a sparse method called the orthogonal matching pursuit. In the third method, the incident beam is measured on a transverse plane, decomposed into a sum of plane waves, and then the expansion coefficients are calculated. The results of the three methods will be presented and compared.

Folding a focalized acoustical vortex on a flat holographic transducer: Miniaturized selective acoustical tweezers.

Acoustical tweezers based on focalized acoustical vortices hold the promise of precise contactless manipulation of millimeter down to submicrometer particles, microorganisms, and cells with unprecedented combined selectivity and trapping force. Yet, the widespread dissemination of this technology has been hindered by severe limitations of current systems in terms of performance and/or miniaturization and integrability. Here, we unleash the potential of focalized acoustical vortices by developing the first flat, compact, paired single electrode focalized acoustical tweezers. These tweezers rely on spiraling transducers obtained by folding a spherical acoustical vortex on a flat piezoelectric substrate. We demonstrate the ability of these tweezers to grab and displace micrometric objects in a standard microfluidic environment with unique selectivity. The simplicity of this system and its scalability to higher frequencies open tremendous perspectives in microbiology, microrobotics, and microscopy.

Orbital Angular Momentum Transfer to Stably Trapped Elastic Particles in Acoustical Vortex Beams.

The controlled rotation of solid particles trapped in a liquid by an ultrasonic vortex beam is observed. Single polystyrene beads, or clusters, can be trapped against gravity while simultaneously rotated. The induced rotation of a single particle is compared to a torque balance model accounting for the acoustic response of the particle. The measured torque (∼10 pN m for a driving acoustic power ∼40 W/cm^{2}) suggests two dominating dissipation mechanisms of the acoustic orbital angular momentum responsible for the observed rotation. The first takes place in the bulk of the absorbing particle, while the second arises as dissipation in the viscous boundary layer in the surrounding fluid. Importantly, the dissipation processes affect both the dipolar and quadrupolar particle vibration modes suggesting that the restriction to the well-known Rayleigh scattering regime is invalid to model the total torque even for spheres much smaller than the sound wavelength. The findings show that a precise knowledge of the probe elastic absorption properties is crucial to perform rheological measurements with maneuverable trapped spheres in viscous liquids. Further results suggest that the external rotational steady flow must be included in the balance and can play an important role in other liquids.

Observation of a Single-Beam Gradient Force Acoustical Trap for Elastic Particles: Acoustical Tweezers.

We demonstrate the trapping of elastic particles by the large gradient force of a single acoustical beam in three dimensions. Acoustical tweezers can push, pull and accurately control both the position and the forces exerted on a unique particle. Forces in excess of 1 micronewton were exerted on polystyrene beads in the submillimeter range. A beam intensity less than 50 W/cm^{2} was required, ensuring damage-free trapping conditions. The large spectrum of frequencies covered by coherent ultrasonic sources provides a wide variety of manipulation possibilities from macroscopic to microscopic length scales. Our observations could open the way to important applications, in particular, in biology and biophysics at the cellular scale and for the design of acoustical machines in microfluidic environments.

SAW Synthesis With IDTs Array and the Inverse Filter: Toward a Versatile SAW Toolbox for Microfluidics and Biological Applications.

Surface acoustic waves (SAWs) are versatile tools to manipulate fluids at small scales for microfluidics and biological applications. A nonexhaustive list of operations that can be performed with SAW includes sessile droplet displacement, atomization, division, and merging but also the actuation of fluids embedded in microchannels or the manipulation of suspended particles. However, each of these operations requires a specific design of the wave generation system, the so-called interdigitated transducers (IDTs). Depending on the application, it might indeed be necessary to generate focused or plane, propagating or standing, and aligned or shifted waves. Furthermore, the possibilities offered by more complex wave fields such as acoustical vortices for particle tweezing and liquid twisting cannot be explored with classical IDTs. In this paper, we show that the inverse filter technique coupled with an IDTs array enables us to synthesize all classical wave fields used in microfluidics and biological applications with a single multifunctional platform. It also enables us to generate swirling SAWs, whose potential for the on-chip synthesis of tailored acoustical vortices has been demonstrated lately. The possibilities offered by this platform are illustrated by performing many operations successively on sessile droplets with the same system.

Sound propagation in dilute suspensions of spheres: Analytical comparison between coupled phase model and multiple scattering theory.

Sound propagation in dilute suspensions of small spheres is studied using two models: a hydrodynamic model based on the coupled phase equations and an acoustic model based on the ECAH (ECAH: Epstein-Carhart-Allegra-Hawley) multiple scattering theory. The aim is to compare both models through the study of three fundamental kinds of particles: rigid particles, elastic spheres, and viscous droplets. The hydrodynamic model is based on a Rayleigh-Plesset-like equation generalized to elastic spheres and viscous droplets. The hydrodynamic forces for elastic spheres are introduced by analogy with those of droplets. The ECAH theory is also modified in order to take into account the velocity of rigid particles. Analytical calculations performed for long wavelength, low dilution, and weak absorption in the ambient fluid show that both models are strictly equivalent for the three kinds of particles studied. The analytical calculations show that dilatational and translational mechanisms are modeled in the same way by both models. The effective parameters of dilute suspensions are also calculated.

Properties of theranostic nanoparticles determined in suspension by ultrasonic spectroscopy.

In the context of growing use of nanoparticles, it is important to be able to characterize all their physical properties in order to understand their behavior, to optimize them, and to control their quality. We showed that ultrasonic spectroscopy provides many of the desired properties. To do so, we used as an example nanocapsules made of a polymer shell encaspulating a liquid perfluorocarbon core and designed them for theranostic applications. Frequency-dependent measurements of both ultrasound velocity and attenuation were performed on nanocapsule suspensions. Then the desired properties were extracted by analyzing the experimental data using a recently developed model that relates the speed of sound and attenuation of a suspension to the geometrical and viscoelastic properties of the nanocapsules.

Taming the degeneration of Bessel beams at an anisotropic-isotropic interface: Toward three-dimensional control of confined vortical waves.

Despite their self-reconstruction properties in heterogeneous media, Bessel beams are known to degenerate when they are refracted from an isotropic to an anisotropic medium. In this paper, we study the converse situation wherein an anisotropic Bessel beam is refracted into an isotropic medium. It is shown that these anisotropic Bessel beams also degenerate, leading to confined vortical waves that may serve as localized particle trap for acoustical tweezers. The linear nature of this degeneration allows the three-dimensional control of this trap position by wavefront correction. Theory is confronted to experiments performed in the field of acoustics. A swirling surface acoustic wave is synthesized at the surface of a piezoelectric crystal by a microelectromechanical integrated system and radiated inside a miniature liquid vessel. The wavefront correction is operated with inverse filter technique. This work opens perspectives for contactless on-chip manipulation devices.

Cyclones and attractive streaming generated by acoustical vortices.

Acoustical and optical vortices have attracted great interest due to their ability to capture and manipulate particles with the use of radiation pressure. Here we show that acoustical vortices can also induce axial vortical flow reminiscent of cyclones, whose topology can be controlled by adjusting the properties of the acoustical beam. In confined geometry, the phase singularity enables generating "attractive streaming" with the flow directed toward the transducer. This opens perspectives for contactless vortical flow control.

Influence of shell compressibility on the ultrasonic properties of polydispersed suspensions of nanometric encapsulated droplets.

Liquid droplets of nanometric size encapsulated by a polymer shell are envisioned for targeted drug delivery in therapeutic applications. Unlike standard micrometric gas-filled contrast agents used for medical imaging, these particles present a thick shell and a weakly compressible core. Hence, their dynamical behavior may be out of the range of validity of the models available for the description of encapsulated bubbles. In the present paper, a model for the ultrasound dispersion and absorption in a suspension of nanodroplets is proposed, accounting for both dilatational and translational motions of the particle. The radial motion is modeled by a generalized Rayleigh-Plesset-like equation which takes into account the compressibility of the viscoelastic shell, as well as the one of the core. The effect of the polydispersity of particles in size and shell thickness is introduced in the coupled balance equations which govern the motion of the particles in the surrounding fluid. Both effects of shell compressibility and polydispersity are quantified through the dispersion and absorption curves obtained on a wide ultrasonic frequency range. Finally, some results for larger gas-filled particles are also provided, revealing the limit of the role of the shell compressibility.

Three-dimensional acoustic radiation force on an arbitrarily located elastic sphere.

This work aims to model the acoustic radiation forces acting on an elastic sphere placed in an inviscid fluid. An expression of the axial and transverse forces exerted on the sphere is derived. The analysis is based on the scattering of an arbitrary acoustic field expanded in the spherical coordinate system centered on the spherical scatterer. The sphere is allowed to be arbitrarily located. The special case of high order Bessel beams, acoustical vortices, are considered. These types of beams have a helicoidal wave front, i.e., a screw-type phase singularity and hence, the beam has a central dark core of zero amplitude surrounded by an intense ring. Depending on the sphere's radius, different radial equilibrium positions may exist and the sphere can be set in rotation around the beam axis by an azimuthal force. This confirms the pseudo-angular moment transfer from the beam to the sphere. Cases where the axial force is directed opposite to the direction of the beam propagation are investigated and the potential use of Bessel beams as tractor beams is demonstrated. Numerical results provide an impetus for further designing acoustical tweezers for potential applications in particle entrapment and remote controlled manipulation.

A model for ultrasound absorption and dispersion in dilute suspensions of nanometric contrast agents.

Ultrasound dispersion and absorption are examined in dilute suspensions of contrast agents of nanometric size, with a typical radius around 100 nm. These kinds of contrast agents are designed for targeted delivery of drugs for cancer treatment. Compared to standard contrast agents used for imaging, particles are of smaller size to pass through the endothelial barrier, their shell, made up of biocompatible polymer, is stiffer to undergo a longer lifetime, and they have a liquid core instead of a gaseous one. Ultrasound propagation in dilute suspension is modeled by combining two modes for particle oscillations. The first one is a dilatational mode assuming an incompressible shell with a rheological behavior of Kelvin-Voigt or Maxwell type. The second one is a translational mode induced by visco-inertial interaction with the ambient fluid. The relative importance of these two modes of interaction on both dispersion and absorption is quantified and analyzed for a model system and for two radii (75 and 150 nm) and the two rheological models. The influence of shell parameters (Young modulus, viscosity, and relative thickness) is finally discussed.

Sound, infrasound, and sonic boom absorption by atmospheric clouds.

This study quantifies the influence of atmospheric clouds on propagation of sound and infrasound, based on an existing model [Gubaidulin and Nigmatulin, Int. J. Multiphase Flow 26, 207-228 (2000)]. Clouds are considered as a dilute and polydisperse suspension of liquid water droplets within a mixture of dry air and water vapor, both considered as perfect gases. The model is limited to low and medium altitude clouds, with a small ice content. Four physical mechanisms are taken into account: viscoinertial effects, heat transfer, water phase changes (evaporation and condensation), and vapor diffusion. Physical properties of atmospheric clouds (altitude, thickness, water content and droplet size distribution) are collected, along with values of the thermodynamical coefficients. Different types of clouds have been selected. Quantitative evaluation shows that, for low audible and infrasound frequencies, absorption within clouds is several orders of magnitude larger than classical absorption. The importance of phase changes and vapor diffusion is outlined. Finally, numerical simulations for nonlinear propagation of sonic booms indicate that, for thick clouds, attenuation can lead to a very large decay of the boom at the ground level.

Scattering of ultrasonic shock waves in suspensions of silica nanoparticles.

Experiments are carried out to assess, for the first time, the validity of a generalized Burgers' equation, introduced first by Davidson [J. Acoust. Soc. Am. 54, 1331-1342 (1973)] to compute the nonlinear propagation of finite amplitude acoustical waves in suspensions of "rigid" particles. Silica nanoparticles of two sizes (33 and 69 nm) have been synthesized in a water-ethanol mixture and precisely characterized via electron microscopy. An acoustical beam of high amplitude is generated at 1 MHz inside a water tank, leading to the formation of acoustical shock waves through nonlinear steepening. The signal is then measured after propagation in a cylinder containing either a reference solution or suspensions of nanoparticles. In this way, a "nonlinear attenuation" is obtained and compared to the numerical solution of a generalized Burgers' equation adapted to the case of hydrosols. An excellent agreement (corresponding to an error on the particles size estimation of 3 nm) is achieved in the frequency range from 1 to 40 MHz. Both visco-inertial and thermal scattering are significant in the present case, whereas thermal effects can generally be neglected for most hydrosols. This is due to the value of the specific heat ratio of water-ethanol mixture which significantly differs from unity.

Inhibition of ovulation by NOMAC/E2, a novel monophasic oral contraceptive combining nomegestrol acetate and 17ß-oestradiol: a double-blind, randomised, dose-finding pilot study.

OBJECTIVE: To explore the optimal dose of the progestogen, nomegestrol acetate (NOMAC), required in a monophasic oral contraceptive, in combination with 1.5 mg 17ß-oestradiol (E(2)), to inhibit ovulation. METHODS: A double-blind, randomised study assessing 41 normally cycling women (aged 18-35 years) over two screening cycles, one control cycle and one consecutive treatment cycle; 38 women completed the treatment period. Subjects received 0.625 mg NOMAC/1.5 mg E(2) (n = 9), 1.25 mg NOMAC/1.5 mg E(2) (n = 10), 2.5 mg NOMAC/1.5 mg E(2) (n = 10) or 2.5 mg NOMAC alone (n = 9) for 21 days. RESULTS: During the treatment cycle, ovulation was suppressed in all treatment groups. The lowest plasma E(2) levels were observed with 2.5 mg NOMAC given alone. Addition of 1.5 mg E(2) to 2.5 mg NOMAC resulted in statistically significant increases in E(2) levels and decreases in mean follicle-stimulating hormone and luteinising hormone levels. In the three NOMAC/E(2) combination groups, a statistically significant inverse correlation was found between E(2) plasma levels and NOMAC dose. CONCLUSION: The dose of 2.5 mg NOMAC was confirmed to be optimal to inhibit both ovulation and follicular maturation. The antigonadotropic effect of 2.5 mg NOMAC was reinforced when combined with 1.5 mg E(2).

Haemostatic effects of a new combined oral contraceptive, nomegestrol acetate/17ß-estradiol, compared with those of levonorgestrel/ethinyl estradiol. A double-blind, randomised study.

Use of oral contraceptives (OC) that combine a progestogen with synthetic ethinyl estradiol (EE) is associated with increased risk of venous thromboembolism. NOMAC/E2 is a new monophasic OC that combines nomegestrol acetate (NOMAC), a highly selective progestogen, with 17ß-estradiol (E2). The study objective was to compare the effects on markers of haemostasis of NOMAC/E2 (2.5 mg/1.5 mg) versus the second-generation OC, levonorgestrel (LNG)/EE (100 µg/20 µg). Healthy women (age 18-38 years) received once-daily treatment for three consecutive 28-day cycles in a double-blind, randomised study: either NOMAC/E2 for 24 days with a four-day placebo interval (n=45) or LNG/EE for 21 days with a seven-day placebo interval (n=45) per cycle. Mean changes from baseline to end-of-treatment in coagulation markers, including prothrombin fragment 1+2 (primary endpoint), fibrinolysis markers and platelet functions were assessed. Mean prothrombin fragment 1+2 levels (primary endpoint) did not increase with NOMAC/E2 compared with LNG/EE ( -0.02 vs. +0.08 nM, p<0.01). Other significant differences between NOMAC/E2 and LNG/EE were mean changes in antithrombin (+0.3% vs. -4.4%, p<0.001), activated protein C resistance - normalised ratio (+0.20 vs. +0.46, p<0.01), D-dimer ( -53 vs. +43 ng/ml, p<0.001), plasminogen (+6% vs. +30%, p<0.0001) and plasminogen activator inhibitor-1 ( -3.1 vs. -8.0 ng/ml, p<0.001). There was no effect of either treatment on platelet aggregation. The NOMAC/E2 pill regimen has fewer adverse effects on blood biological coagulation and fibrinolysis markers than LNG/EE. This suggests that NOMAC/E2 could have a more favourable venous thromboembolism risk profile than LNG/EE; further epidemiological data are required to confirm this.

Transverse shift of helical beams and subdiffraction imaging.

An imaging technique is here proposed to overcome the classical "diffraction limit" by using helical beams. This technique and the analysis presented are valid for all kinds of waves (either optical or acoustical) as long as the field can be considered as scalar. We show that the stable structure of such phase singularities turns out to be appropriate to measure both the position and the diameter of subdiffraction circular apertures. The property used is a shift of the scattered vortex. Its location is obtained with a very high resolution thanks to a nonclassical correlation method exploiting the superoscillating property of a vortex near its axis. This theoretical analysis is supported by acoustic experiments performed underwater evidencing subdiffraction imaging.

Generalization of helicoidal beams for short pulses.

A generalization to the transient regime is developed for waves with a phase singularity of the screw type. These singular waves are commonly called vortices for all kind of waves as, for instance, optical vortex or acoustical vortex. We generalize the definition of vortices to get an azimuthal velocity invariant for all the frequency components contained in the broad spectrum of a short pulse. This generalization leads to a modification of the orbital angular momentum definition. Another generalization is introduced by considering helicoidal waves with a finite number of turns. We demonstrate that, in this last case, the topological charge is no longer an integer. This provides a physical interpretation to vortices of fractional charge that are involved here to take into account the diffraction occurring at both tips of the now finite helical wave front. We show that shortening the pulse implies an angular localization of the wave energy and, as a consequence, a spreading of the angular momentum amplitude due to the uncertainty principle.