Acoustic Pressure Field Research Articles

SIMUS: An open-source simulator for medical ultrasound imaging. Part I: Theory & examples

Background and ObjectiveComputational ultrasound imaging has become a well-established methodology in the ultrasound community. Simulations of ultrasound sequences and images allow the study of innovative techniques in terms of emission strategy, beamforming, and probe design. There is a wide spectrum of software dedicated to ultrasound imaging, each having its specificities in its applications and the numerical method. MethodsWe describe in this two-part paper a new ultrasound simulator (SIMUS) for MATLAB, which belongs to the MATLAB UltraSound Toolbox (MUST). The SIMUS software simulates acoustic pressure fields and radiofrequency RF signals for uniform linear or convex probes. SIMUS is an open-source software whose features are 1) ease of use, 2) time-harmonic analysis, 3) pedagogy. The main goal was to offer a comprehensive turnkey tool, along with a detailed theory for pedagogical and research purposes. ResultsThis article describes in detail the underlying linear theory of SIMUS and provides examples of simulated acoustic fields and ultrasound images. The accompanying article (part II) is devoted to the comparison of SIMUS with several software packages: Field II, k-Wave, FOCUS, and the Verasonics simulator. The MATLAB open codes for the simulator SIMUS are distributed under the terms of the GNU Lesser General Public License, and can be downloaded from https://www.biomecardio.com/MUST. ConclusionsThe simulations described in this part and in the accompanying paper (Part II) show that SIMUS can be used for realistic simulations in medical ultrasound imaging.

EXTRACTION OF PRESSURE AND TEMPERATURE DISTRIBUTION OF HIGH INTENSITY FOCUSED ULTRASOUND CONSIDERING NONLINEAR PROPAGATION

The aim of this study is the extraction of acoustic pressure distribution in the target tissue layers based on the nonlinear behavior of waves. The nonlinear behavior effect of high intensity focused ultrasound (HIFU) on the temperature distribution of the tissue was extracted and compared with the linear behavior. The acoustic pressure field was calculated using the Westervelt equation and was coupled with Pennes thermal transfer equation. The simulations were performed for three layers of skin, fat and muscle using Comsol software. The disagreement between two linear and nonlinear models was analyzed with Kolmogorov–Smirnov test. The pressure and temperature distributions were calculated in nonlinear model by changing the acoustical parameters of the transducer including intensity, effective radiation area, focal length and sonication time. Model results were validated with experimental results with 98% correlation coefficient ([Formula: see text]). There is no significant difference between the pressure amplitude and temperature distribution in linear and nonlinear models at low intensity ([Formula: see text]), but with increasing intensity to 10[Formula: see text]W/cm2, in nonlinear model, maximum pressure and maximum temperature increased 40% and 20% compared with linear model. For input intensities of 1.5, 2, 8 and 10[Formula: see text]W/cm2, the maximum pressure (at focal point) increased 10%, 12%, 22%, 40% and maximum temperature increased 1%, 2%, 12%, 20% in nonlinear model compared to linear model. At 0.8[Formula: see text]cm2 and 1.5[Formula: see text]cm2 effective radiation area, the maximum acoustic pressure and temperature in nonlinear model increased from 12[Formula: see text]MPa to 30[Formula: see text]MPa and 43∘C to 79∘C, respectively. By decreasing the focal lengths from 10[Formula: see text]mm to 7.5[Formula: see text]mm, the maximum temperature increased from 45∘C to 87∘C. It is concluded a change in the input parameters of the transducer; it can be very effective in treating. The results emphasize the effects of nonlinear propagation and acoustical radiation parameters to improve the HIFU treatment.

On the acoustic performance of double degree of freedom helmholtz resonator based acoustic liners

This study investigates the acoustic performance of double degree of freedom Helmholtz resonators and multi cell acoustic liners made of these resonators, both experimentally and through finite element analysis. The dimensions of the resonator internal cavities were varied to assess the effect of the volume ratio on the acoustic performance of the system. Experiments were performed using a grazing flow impedance tube and instrumented 3D printed modular resonators, which can be switched between a single and double degree of freedom resonating cavity configuration. An aluminium acoustic liner with 16 modular resonating cavities was also used in experiments. The effect of the volume ratio is investigated by presenting the transmission loss and transmission coefficient induced and the changes in sound pressure level within the resonator. The underlying sound attenuation mechanisms are further elaborated through the finite element analysis results of the acoustic pressure and velocity fields in the different resonator configurations. The results showed that as the volume ratio is increased, the difference between the first and second resonance frequencies tends to have a convex behaviour. This may indicate the presence of an optimum volume ratio of the two internal cavities for a broad bandwidth of sound absorption. Moreover, the finite element analysis results showed that increasing the volume ratio increased both the transmission loss induced and the bandwidth of frequencies attenuated at the first resonance frequency due to an in-phase velocity magnitude relation, for both the neck and septum of the resonator. Conversely, for the second resonance frequency, there is an out-of-phase relation between the neck and septum velocity magnitudes. In addition to the single resonator analysis, the acoustic performance of liner configurations with 16 resonators was also investigated. The results showed an increase in the bandwidth of attenuated frequencies when each resonating cavity had a different volume ratio, as compared to a fixed volume ratio. In addition, the order of the resonators of different volume ratio in the liner arrangement did not seem to have a significant effect on the overall sound attenuation performance.

Elastic Orbital Angular Momentum.

We identify that flexural guided elastic waves in elastic pipes carry a well-defined orbital angular momentum associated with the compressional dilatational potential. This enables the transfer of elastic orbital angular momentum, that we numerically demonstrate, through the coupling of the compressional potential in a pipe to the acoustic pressure field in a surrounding fluid in contact with the pipe.

Development of an innovative noise generation system for turboprop aircraft fuselage testing

This paper presents the development of a cabin noise testing equipment that will be used to evaluate the interior noise of regional aircraft as well as to aid the development of noise reduction techniques. The innovative noise generation system consists of three loudspeaker arrays positioned around the fuselage circumference to synthesize a pressure field that is similar to the pressure field seen by the fuselage during a flight. The acoustic pressure field generated by the loudspeakers is measured by a number of microphones scattered on the fuselage surface. These microphone signals are then fed back to the controller with the purpose of minimising the error between the target pressure field and the measured one by means of an iterative learning approach. The number and location of the microphones used in the control loop are selected through a pre-test optimisation analysis, which aims to reduce the time and cost of the set-up. A small-scale electroacoustic demonstrator has been built to develop the feedback control approach. A frequency domain multi-input multi-output feedback controller is used to replicate the random pressure field generated by the turbulent boundary layer excitation. The multi-harmonics of the propeller induced excitation are then added to the time histories of the broadband noise using a time waveform replication technique. Different arrangements of the driving signal distribution are investigated, and the results are then presented in terms of accuracy of the pressure field reproduction.

On the influence of the nozzle exhaust initial conditions on the near field acoustic pressure

In this paper, the acoustic pressure generated in the near field of a single stream cold jet is investigated. The analysis is focused on the effect of the initial conditions at the nozzle exit parametrized by considering two different turbulence levels and two different boundary layer thicknesses. The study has been performed by processing a numerical database obtained by large-eddy simulations (LES) of a jet flow at M = 0.9 and Re = 105. Pressure time series are obtained from pointwise virtual probes located in several radial and axial positions in the jet near-field. The acoustic pressure is extracted by the application of a consolidated wavelet-based procedure and the achieved acoustic signals are analyzed in terms of global quantities as well as by computing wavelet-reconstructed Fourier spectra. The results show that both the boundary-layer thickness and the turbulence level significantly affect the acoustic pressure in terms of its intensity and directivity whereas the distribution of energy in the frequency domain depends appreciably, only on the boundary-layer thickness.

Experimental acoustic scene analysis using One-Eighth spherical fraction microphone array.

This paper investigates the performance of one-eighth Spherical Fraction Microphone Array through experimental measurement to analyze acoustic scenes in one-eighth of space. The array geometry is designed to be placed in a room corner at the junction of three acoustically rigid walls. Two prototypes are built with 8 and 16 microphones, respectively. The sampling strategy is discussed and a spatial aliasing analysis is carried out both analytically and by numerical simulations. The array performances are evaluated through Spherical Fraction Beamforming (SFB). This approach is based on the decomposition of the acoustic pressure field in a rigid bounded domain. The localization angular error and Directivity Index criterion are evaluated for both arrays. In a first experiment, the arrays are mounted in an eighth of space built inside an anechoic room. The results are compared with simulation and show consistency. The theoretical limitations of SFB in a rigid bounded one-eighth of space are retrieved experimentally. These limitations are also observed in a real configuration: an office room. Further investigations on SFB are also conducted in the case of a virtual scene constructed with two sound sources.

Fundamental Approaches to Robust Differential Beamforming With High Directivity Factors

Differential beamforming, which measures the spatial derivatives of the acoustic pressure field, can be used in a wide range of small devices that require high-fidelity sound and speech acquisition as it can achieve frequency-invariant spatial responses with high directivity factors (DFs). Since a differential process is inherently sensitive to sensors' self noise and other array imperfections, the most challenging problem in the design of any differential beamformer is how to achieve the maximum possible DF while maintaining a proper level of robustness for practical usage. While significant efforts have been made on this topic, the problem remains unsolved and further study is indispensable. This paper is devoted to dealing with this challenging problem. It presents a study on theory and methods to achieve the optimal and fundamental compromise between the white noise gain (WNG), which quantifies how robust is the beamformer, and the DF in differential beamforming. The major contributions of this work are as follows. 1) We show and prove that any null constrained fixed beamformer can be decomposed as the sum of two orthogonal filters, i.e., the maximum WNG (MWNG) beamformer and a reduced-rank one. Based on this decomposition, we develop three kinds of differential beamformers from the WNG perspective, which can achieve a flexible and optimal compromise between DF and WNG. 2) We show that a transformed null constrained beamformer can also be decomposed as the sum of two orthogonal filters, i.e., the transformed maximum DF (MDF) beamformer and another reduced-rank one. Based on this decomposition, we also develop three kinds of differential beamformers, which can obtain the desired level of DF while using the rest of the degrees of freedom to maximize the WNG. Simulations are performed to validate the theoretical analysis and developed differential beamformers.

Segmented ROSI method: Beamforming method for investigating turbomachinery noise sources along segmented trajectories

The rotating source identifier (ROSI) beamforming method is a method designed for localizing rotating noise sources in a uniform flow based on out-of-flow acoustic pressure field measurement data. It has been developed for sources moving along a circular trajectory, such as turbomachinery blades. The original ROSI method processes the measured acoustic signals over a long time segment to reconstruct the noise sources, providing time-averaged results for each noise source. By doing so, it does not take into consideration certain features of the noise sources, such as the directivity of the trailing edge and leading-edge noise sources. A further development of the ROSI method is presented herein, which separates the sound-pressure signal of one revolution into multiple segments. In this way, the beamforming maps can provide one with a better understanding of the differences between the noise sources as a function of angular position. This method will be referred to herein as the segmented ROSI method. The goal of this further development is to improve the capability of the method in identifying the position-dependent modulations of the various noise sources as they are moving along their trajectories, rotating around the axis. The investigation presents the theory behind the new segmented ROSI method along with simulation and measurement-based test cases which help in comparing the new method to the original ROSI method. The results show that the novel method provides a strong tool for investigating turbomachinery noise sources that vary along segments of their trajectories. It is therefore expected that the tool will be useful in cases that look at turbomachinery from an angle and cases where the loading of the blades changes as a function of angular position.

Mathematical modeling of monochromatic acoustic wave diffraction on a system of bodies and on flat screens

Some problems of diffraction of a monochromatic acoustic wave on surfaces of complex shapes are considered. To solve such problems, an approach is applied, in which the problem is reduced to a boundary hypersingular integral equation, where the integral is understood in the sense of a finite value according to Hadamard. Such approach allows solving diffraction problems both on solid objects and on thin screens. To solve the integral equation, the method of piecewise constant approximations and collocations, developed in the previous works of the author, is used. In the present study, examples of modeling the diffraction of an acoustic wave by bodies with partial filling are given. It is shown how the filling of bodies influences the acoustic pressure field, and the field direction patterns are given. An example of applying this approach to solving the problem of sound propagation in an urban area is also given: the diffraction of an acoustic wave from a point source on a system of buildings is considered. The presented results demonstrate that this method allows constructing reflected fields and analyze their characteristics on surfaces of complex shapes.

Multi-frequency sonoreactor characterisation in the frequency domain using a semi-empirical bubbly liquid model

Recently, multi-frequency systems were reported to improve performance in power ultrasound applications. In line with this, digital prototyping of multi-frequency sonoreactors also started gaining interest. However, the conventional method of simulating multi-frequency acoustic pressure fields in the time-domain led to many challenges and limitations. In this study, a multi-frequency sonoreactor was characterised using frequency domain simulations in 2-D. The studied system consists of a hexagonal sonoreactor capable of operating at 28, 40 and 70 kHz. Four frequency combinations were studied: 28–40, 28–70, 40–70 and 28–40–70 kHz. A semi-empirical, modified Commander and Prosperetti model was used to describe the bubbly-liquid effects in the sonoreactor. The root-mean-squared acoustic pressure was compared against experimental validation results using sonochemiluminescence (SCL) images and was noted to show good qualitative agreement with SCL results in terms of antinode predictions. The empirical phase speed calculated from SCL measurements was found to be important to circumvent uncertainties in bubble parameter specifications which reduces error in the simulations. Additionally, simulation results also highlighted the importance of geometry in the context of optimising the standing wave magnitudes for each working frequency due to the effects of constructive and destructive interference.

In-situ observations and acoustic measurements upon fragmentation of free-floating intermetallics under ultrasonic cavitation in water

Grain refinement in alloys is a well-known effect of ultrasonic melt processing. Fragmentation of primary crystals by cavitation-induced action in liquid metals is considered as one of the main driving mechanisms for producing finer and equiaxed grain structures. However, in-situ observations of the fragmentation process are generally complex and difficult to follow in opaque liquid metals, especially for the free-floating crystals. In the present study, we develop a transparent test rig to observe in real time the fragmentation potential of free-floating primary Al3Zr particles under ultrasonic excitation in water (an established analogue medium to liquid aluminium for cavitation studies). An effective treatment domain was identified and fragmentation time determined using acoustic pressure field mapping. For the first time, real-time high-speed imaging captured the dynamic interaction of shock waves from the collapsing bubbles with floating intermetallic particles that led to their fragmentation. The breakage sequence as well as the cavitation erosion pattern were studied by means of post-treatment microscopic characterisation of the fragments. Fragment size distribution and crack patterns on the fractured surface were then analysed and quantified. Application of ultrasound is shown to rapidly (<10 s) reduce intermetallic size (from 5 mm down to 10 μm), thereby increasing the number of potential nucleation sites for the grain refinement of aluminium alloys during melt treatment.

Evolvable Acoustic Field Generated by a Transducer with 3D-Printed Fresnel Lens.

Evolvable acoustic fields are considered an effective method for solving technical problems related to fields such as biological imaging, particle manipulation, drug therapy and intervention. However, because of technical difficulties and the limited technology available for realizing flexible adjustments of sound fields, few studies have reported on this aspect in recent years. Herein, we propose a novel solution, using a Fresnel lens-focused ultrasonic transducer for generating excited-signal-dependent acoustic pressure patterns. Finite element analysis (FEA) is used to predict the performance of a transducer with a Fresnel lens. The Fresnel lens is printed using 3D additive manufacturing. Normalized intensity maps of the acoustic pressure fields are characterized from the Fresnel lens-focused transducer under various numbers of excited-signal cycles. The results demonstrate that under different cycle excitations, a temporal evolution acoustic intensity can be generated and regulated by an ultrasound transducer with a 3D Fresnel lens. This acoustical pattern control method is not only simple to realize but also has considerable application prospects.

Periodic Rayleigh streaming vortices and Eckart flow arising from traveling-wave-based diffractive acoustic fields.

Recent studies have demonstrated that periodic time-averaged acoustic fields can be produced from traveling surface acoustic waves (SAWs) in microfluidic devices. This is caused by diffractive effects arising from a spatially limited transducer. This permits the generation of acoustic patterns evocative of those produced from standing waves, but instead with the application of a traveling wave. While acoustic pressure fields in such systems have been investigated, acoustic streaming from diffractive fields has not. In this work we examine this phenomenon and demonstrate the appearance of geometry-dependent acoustic vortices, and demonstrate that periodic, identically rotating Rayleigh streaming vortices result from the imposition of a traveling SAW. This is also characterized by a channel-spanning flow that bridges between adjacent vortices along the channel top and bottom. We find that the channel dimensions determine the types of streaming that develops; while Eckart streaming has been previously presumed to be a distinguishing feature of traveling-wave actuation, we show that Rayleigh streaming vortices also results. This has implications for microfluidic actuation, where traveling acoustic waves have applications in microscale mixing, separation, and patterning.

Differential luminescent imaging method for pressure field measurement

A differential luminescent imaging method is applied to a pressure-sensitive paint (PSP) measurement to capture a quasi-steady acoustic pressure field. Conventionally, PSP measurements capture an absolute luminescent intensity and convert it to pressure. When the mean component of the absolute luminescent intensity occupies a substantial portion of the dynamic range of the image acquisition device, it leads to a coarse signal resolution. Differential luminescent imaging, utilizing two-color luminescent intensities and a differential amplifier, extracts the fluctuation component from the absolute luminescent intensity. The developed differential luminescent imaging system gives a point-wise pressure measurement. These measurements are combined to produce a spatially resolved image. It is capable of resolving the periodic pressure wave over the acoustic field where the resolution of a conventional PSP measurement falls into one digital count. This comparison to a conventional PSP measurement is given as a reference by which to evaluate the spatiotemporal resolution of the differential luminescent imaging method.

Acoustic and phase portrait analysis of leading-edge roughness element on laminar separation bubbles at low Reynolds number flow

Since laminar separation bubbles are neutrally shaped on the suction side of full-span wings in low Reynolds number flows, a roughness element can be used to improve the performance of micro aerial vehicles. The purpose of this article was to investigate the leading-edge roughness element’s effect and its location on upstream of the laminar separation bubble from phase portrait point of view. Therefore, passive control might have an acoustic side effect, especially when the bubble might burst and increase noise. Consequently, the effect of the leading-edge roughness element features on the bubble’s behavior is considered on the acoustic pressure field and the vortices behind the NASA-LS0417 cross-section. The consequences express that the distribution of roughness in the appropriate dimensions and location could contribute to increasing the performance of the airfoil and the interaction of vortices produced by roughness elements with shear layers on the suction side has increased the sound frequency in the relevant sound pressure level (SPL). The results have demonstrated that vortex shedding frequency was increased in the presence of roughness compared to the smooth airfoil. Also, more complexity of the phase portrait circuits was found, retrieved from velocity gradient limitation. Likewise, the highest SPL is related to the state where the separation bubble phenomenon is on the surface versus placing roughness elements on the leading edge leads to a negative amount of SPL.

Multi-view videogrammetry for the estimate of plate sound radiation

This paper explores the possibility of estimating the acoustic pressure field resulting from the vibrations of thin structures using photogrammetric techniques. In particular, the performance of measurement systems using two or more cameras to estimate the displacement of 3D markers placed on the surface of a plate are analyzed by simulation. The projection of the markers on the image plane of each camera is calculated assuming a perfectly calibrated system, in which the errors in the 3D reconstruction of the marker positions are substantially determined by the intrinsic pixellation intrinsic to the measurement process. The acoustic pressure in space is finally calculated, starting from the position of the markers, by means of the Rayleigh integral. The accuracy of the estimate is evaluated by varying the geometry of the cameras setup, their resolution and their number. The results presented show that the estimation of the acoustic radiation is substantially more accurate than the accuracy with which the vibration is estimated. The effect is due to the smoothing operation intrinsically linked to the Rayleigh integration procedure. This study demonstrates the effectiveness of optical systems with multiple, relatively low-cost low-resolution cameras for the measurement of the acoustic pressure field generated by flexural vibrations of distributed structures.

Normal mode energy estimation based on reconstructing the incoherent beamformed outputs from a horizontal array.

The acoustic pressure field in many underwater environments is well described by a superposition of normal modes. The normal modes can be used for source localization and environmental inversion. However, the wavenumber resolution of traditional normal mode filtering methods for a small-aperture horizontal array is usually not sufficient to identify individual modes in a shallow water waveguide. This paper proposes an original method of normal mode energy estimation to remove the energy leakage between modes. The modal energy is defined as the square of the modal amplitude. This method is to reconstruct the incoherent beamformed outputs in wavenumber domain for a horizontally moving source. The adaptive beamforming is used to suppress interference and improve output signal-to-noise ratio. The uncertainty of modal phase velocity has also been considered in this method. The proposed method can provide more accurate estimates of modal energy for a small-aperture horizontal array than the traditional mode filtering methods, such as the matched filter, the least squares mode filter, the regularized-least squares mode filter, and the maximum a posteriori mode filter, in simulations and experiments.

Stochastic sound propagation using dynamically orthogonal parabolic equations

Accurate modeling of underwater acoustic propagation is challenging due to the complex ocean physics and acoustic dynamics and the need for resolving the wavelength of the propagating acoustic wave over large distances. These challenges are further amplified by the incomplete knowledge of the ocean environment and the acoustic parameters. These complexities thus lead to many sources of uncertainties in the governing models. In this work, we use our stochastic Dynamically Orthogonal (DO) framework to represent these uncertainties probabilistically in the acoustic Parabolic Equation (PE). These equations optimally represent the dominant uncertainties in the sound speed, density, bathymetry, and acoustic pressure fields. Starting from the governing PE, we derive range-evolution DO differential equations for the mean field, stochastic modes, and coefficients, hence preserving the nonlinearities and capturing the non-Gaussian statistics. The DO equations are implemented for the narrow-angle PE and higher-order Padé wide-angle PEs and are applied in range-dependent canonical test cases and realistic ocean environments with uncertain source location, source frequency, sound speed, and/or bathymetry fields. We highlight the computational advantages of our framework by comparing it to Monte Carlo predictions and show convergence of the probability density functions as the number of samples and/or modes is increased.

From macroscale to microscale characterization of droplet breakup regimes using a micromachined ultrasonic droplet generator

Controllable, uniform droplet generation is critical to many industrial processes and biomedical applications (e.g., materials synthesis, cell handling, and aerosol drug delivery). We have developed an ultrasonic droplet generator that can enable dynamic control over the droplet size distribution in the 2–75 μm range. The system uses a bulk piezoelectric transducer to generate a standing acoustic pressure field that drives fluid transport through an array of microscopic orifices. Our previous work suggests that certain resonances lead to variability in the pressure gradient at the orifices, affecting the droplet size distribution of the resultant spray. Here, we present a parametric study relating ejection uniformity to orifice size, operating frequency, and drive amplitude. We introduce a new system configuration that allows high-resolution stroboscopic imaging of the liquid-gas interface evolution at each orifice. Although the entire micronozzle array remains acoustically active, we use orifice size to control the flow resistance, restricting ejection to a single preselected orifice. Observed ejection regimes resemble classical descriptions of jet breakup (Rayleigh, wind-induced, and atomization), depending on drive voltage. A regime map is created using 5, 10, and 15 μm orifices for 0.5–2.0 MHz actuation from threshold ejection amplitude to the point of chaotic wind-induced breakup.