Finite amplitude measurements of the nonlinear parameter B/A for liquid mixtures spanning a range relevant to tissue harmonic mode

Field-deployable measurement technique for absolute acoustic nonlinearity parameter values

Over the past two decades, several researchers have demonstrated that changes in the acoustic nonlinearity parameter β can be related to changes in material properties due to mechanical and/or thermal degradation processes. Generally, a piezoelectric sensor-based detection method is used to measure changes in β values because it is operationally simpler than the complex capacitive detection method. However, this method is limited to measuring only relative changes in β values; whereas, the absolute β values of components in service often need to be measured in the field to quantify the degradation level. Accordingly, a novel field-deployable method for measuring absolute β values was developed in this study. Nonlinear ultrasonic experiments were conducted using capacitive detection, conventional piezoelectric sensor-based detection, and proposed detection methods, and the results were compared. The β values of a copper single-crystal sample measured using the new and the capacitive detection methods were 2.49 and 2.1, respectively, and those obtained using the conventional piezoelectric sensor-based detection method ranged between 90 and 130. The test results confirm that the proposed field-deployable measurement method produces more consistent absolute β values without involving the complexity of the capacitive detection method.

A review on B/A measurement methods with a clinical perspective

The nonlinear parameter of ultrasound B/A has shown to be a useful diagnostic parameter, reflecting medium content, structure, and temperature. Despite its recognized values, B/A is not yet used as a diagnostic tool in the clinic due to the limitations of current measurement and imaging techniques. This review presents an extensive and comprehensive overview of the techniques developed for B/A measurement of liquid and liquid-like media (e.g., tissue), identifying the methods that are most promising from a clinical perspective. This work summarizes the progress made in the field and the typical challenges on the way to B/A estimation. Limitations and problems with the current techniques are identified, suggesting directions that may lead to further improvement. Since the basic theory of the physics behind the measurement strategies is presented, it is also suited for a reader who is new to nonlinear ultrasound.

Determination of the Ultrasonic Non-linearity Parameter B/A versus Frequency for Water

For tissue characterization, it is desirable to determine B/A using high-frequency transducers. Moreover, an accurate estimate of B/A at elevated frequencies (or at least the assumption of frequency independence of B/A) is required to evaluate the safety of high-frequency systems. However, common finite-amplitude approaches become increasingly inaccurate at high frequencies. In this article, a practical variation of the finite-amplitude method is proposed which combines experiments with numerical simulations of the Khokhlov-Zabolotskaya-Kuznetsov equation and can be used at elevated frequencies. The results at low frequencies show that the proposed approach is accurate with lower uncertainties compared with the finite-amplitude method because it avoids assumptions and approximations. The measured values of B/A versus frequency for water at 2.25-20 MHz show that there is no statistically significant variation in B/A values with frequency, and therefore the assumption of frequency independence of B/A is realistic.

Experimental Configuration to Determine the Nonlinear Parameter β in PMMA and CFRP with the Finite Amplitude Method

Parameters to measure nonlinearity in polymethylmethacrylate (PMMA) and carbon fiber reinforced polymer (CFRP) materials have been determined with nonlinear ultrasound (NLUS). The nonlinear parameter β has been determined using the variation of the Finite Amplitude Method (FAM) with harmonic generation. Using this as a reference, the first contribution of this work consists of deducting the experimental configuration necessary to measure this nonlinear parameter in a correct and feasible way. Excitation level, frequency of the wave generated, number of cycles analysed and the distances transducer-specimen and specimen-hydrophone have been determined in both materials. The second contribution is a semi-analytical model that allows to obtain the nonlinear parameter in materials by removing water contribution and considering geometric and viscous attenuation, using the data obtained in an immersion tank. Finally, an application of this model has been carried out in PMMA in order to determinate the nonlinear parameter in this material. From the results, we confirm that the configuration determined in this paper to obtain the parameter β decreases the noise in the measurements.

Ultrasonic sensor concept to fit a ventricular assist device cannula evaluated using geometrically accurate heart phantoms

Future left ventricular assist devices (LVADs) are expected to respond to the physiologic need of patients; however, they still lack reliable pressure or volume sensors for feedback control. In the clinic, echocardiography systems are routinely used to measure left ventricular (LV) volume. Until now, echocardiography in this form was never integrated in LVADs due to its computational complexity. The aim of this study was to demonstrate the applicability of a simplified ultrasonic sensor to fit an LVAD cannula and to show the achievable accuracy in vitro. Our approach requires only two ultrasonic transducers because we estimated the LV volume with the LV end-diastolic diameter commonly used in clinical assessments. In order to optimize the accuracy, we assessed the optimal design parameters considering over 50 orientations of the two ultrasonic transducers. A test bench was equipped with five talcum-infused silicone heart phantoms, in which the intra-ventricular surface replicated papillary muscles and trabeculae carnae. The end-diastolic LV filling volumes of the five heart phantoms ranged from 180 to 480 mL. This reference volume was altered by ±40 mL with a syringe pump. Based on the calibrated measurements acquired by the two ultrasonic transducers, the LV volume was estimated well. However, the accuracies obtained are strongly dependent on the choice of the design parameters. Orientations toward the septum perform better, as they interfere less with the papillary muscles. The optimized design is valid for all hearts. Considering this, the Bland-Altman analysis reports the LV volume accuracy as a bias of ±10% and limits of agreement of 0%-40% in all but the smallest heart. The simplicity of traditional echocardiography systems was reduced by two orders of magnitude in technical complexity, while achieving a comparable accuracy to 2D echocardiography requiring a calibration of absolute volume only. Hence, our approach exploits the established benefits of echocardiography and makes them applicable as an LV volume sensor for LVADs.

Improvement of pulse-echo harmonic generation from a traction-free boundary through phase shift of a dual element transducer

The practical implementation of nonlinear ultrasonic technique has been limited to the through-transmission setup for measuring the second harmonic component induced by the nonlinearity or microstructural changes of test material. A more practical technique such as the pulse-echo testing has been ruled out because a traction-free reflecting boundary destructively alters the nonlinear generation process. A focusing acoustic beam or rigid boundary condition was often employed for biomedical imaging and fluid nonlinearity in the pulse-echo inspection. In this article, we further explore a more general and efficient method to improve the generation of the second harmonic component in the pulse-echo mode with traction-free surface. A dual element planar transdcer with optimal phase shift of the input signal in one element relative to another is proposed for this purpose. The validity of the phase shift concept is confirmed by comparing the enhanced generation of second harmonic amplitudes and the resulting nonlinear parameters with the rigid-boundary case equivalent to the conventional through-transmission setup.

Acoustic nonlinearity parameter measurements in a pulse-echo setup with the stress-free reflection boundary

This paper describes the acoustic nonlinearity parameter (β) determination for fluids using a pulse-echo method with the stress-free boundary. A newly derived β formula requires the measurement of the fundamental and second harmonic displacements with appropriate corrections for attenuation, diffraction, and boundary reflection. Measurements are composed of two steps: receiver calibration and harmonic generation. The β values calculated for water at several distances between the planar transducer and the water-air interface are in good agreement with literature, providing a validation for the method.

Calibration of focused ultrasonic transducers and absolute measurements of fluid nonlinearity with diffraction and attenuation corrections

This paper presents analytical and experimental techniques for absolute determination of the acoustic nonlinearity parameter (β) in fluids using focused transducers. When focused transducers are used for β measurements, the geometrical and mechanical calibrations are generally required for accurate determination of the receiver transfer function from which the absolute pressure can be calculated. The fundamental and second harmonic wave amplitudes in harmonic generation measurements should be modified to account for beam diffraction and material absorption. All these issues are resolved in this study and the proposed technique is validated through the β measurement in water. An experimental method is developed to determine the effective radius and focal length of focused transducers. A simplified self-reciprocity calibration procedure for a broadband focused receiver is described. The diffraction and attenuation corrections for the fundamental and second harmonic waves are explicitly derived using the multi-Gaussian beam model, and the effects on the β determination are discussed. When the diffraction and attenuation corrections are all properly made, the measurement of β over a large range of propagation distances is possible with errors less than 8%.

Determination of acoustical nonlinear parameter β of water using the finite amplitude method

The acoustic nonlinearity of water is investigated using a variation of the finite amplitude method with harmonic generation. The finite amplitude method provides information on the coefficient of nonlinearity, β, through the ratio of the amplitude of the fundamental and that of the second harmonic. The pressure of both the fundamental, p1, and that of the second harmonic, p2, are determined experimentally at different transmitter-receiver separation distances, eliminating the need for knowledge of the sound absorption in the medium. It was found that the experimental relationship between the slope of p2(x)/p1(2)(x) and transmitter-receiver separation distance, x, follows a linear relationship only in the near-field, in good agreement with theoretical predictions. A β of 3.5±0.1 is determined for water at room temperature, in good agreement with previous results from both the isentropic equation of state and finite amplitude method.

Extensions of nonlinear B/A parameter imaging methods for echo mode

This paper investigates nonlinear B/A parameter imaging in ultrasound echo mode. First, the B/A estimation methods which can be extended to echo mode are identified. The finite amplitude approaches are found to be excellent candidates to assess the nonlinear parameter because of their experimental simplicity, supported by a strong mathematical background. Second, three nonlinear coefficient measurement methods, thus far proposed for applications in homogeneous media, are extended to heterogeneous media. In particular, the simulations show that the extended comparative method (ECM) offers the best results when the probe diffraction effects are taken into consideration. The first experimental images obtained by applying the ECM for two different phantoms are also presented, showing the feasibility of B/A imaging.

Determination of volume fractions in multicomponent mixtures using ultrasound frequency analysis

Controlling the composition of mixtures is critical for quality control in a wide variety of applications. There is a need for rapid, on-site measurements to optimize processes in real time. Ultrasound easily penetrates opaque samples and containers, yet currently provides minimal chemical information. We have developed a general approach to determine the volume fraction of a liquid in mixtures with multiple components. Ultrasound waves propagating through a medium undergo distortion processes that are characteristic of the chemical bonding composition. The distortion of the waveform can be measured in the ultrasound frequency profile. An ultrasound pulse-through configuration with matching 5 MHz transducers was used to analyze mixtures of water, methanol, and ethanol. Multilinear regression analysis was used to determine the volume fraction of all components in a series of mixtures. Using this technique, volume fractions were determined simultaneously with correlation coefficients (r(2)) greater than 0.98 in two-component mixtures. Determination of volume fractions in three-component mixtures ranging from 65-100% water also showed correlation coefficients of 0.91 for methanol and 0.94 for ethanol. This technique is attractive for process monitoring due to the short measurement time and the simple methodology that excludes sample pretreatment.

Demonstration of second-harmonic IVUS feasibility with focused broadband miniature transducers

Focused broadband miniature polyvinylidene fluoride-trifluoroethylene (PVDF TrFE) ultrasonic transducers were investigated for intravascular (IVUS) second-harmonic imaging. Modeling and experimental studies demonstrated that focused transducers, unlike conventional flat transducers, build up second harmonic peak pressures faster and stronger, leading to an increased SNR of second harmonic content within the coronary geometry. Experimental results demonstrated that focused second harmonic pressures could be controlled to occur at specific depths by controlling the f-number of the transducer. The experimental results were in good agreement with the modeled results. Experiments were conducted using three imaging modalities: fundamental 20 MHz (F20), second harmonic 40 MHz (H40), and fundamental 40 MHz (F40). The lateral resolutions for a 1-mm transducer (f-number 3.2) at F20, F40, and H40 were experimentally measured to be 162, 123, and 124 microm, respectively, which agreed well with the theoretical calculations with <<8% error. Lateral resolution was further characterized in the three modes, using a micromachined phantom consisting of fixed bars and spaces with widths ranging from 20 to 160 microm. H40 exhibited better lateral resolution, clearly displaying 40- and 60-microm bars with about 4 dB and 7 dB greater signal strength compared with F20. Ex vivo human aorta images were obtained in the second-harmonic imaging mode to show the feasibility of high resolution second-harmonic IVUS using focused transducers.

Finite amplitude method for measuring the nonlinearity parameter BA in small-volume samples using focused ultrasound

On the basis of finite amplitude and comparative methods, the acoustic nonlinearity parameter BA of a liquid sample of as small as 0.1 ml is measured using an 18.6-MHz focused Gaussian beam. The sample fills the space between a polystyrene plate and a tungsten reflector set about 1 mm apart from each other within the focal region. The sound speed c and attenuation coefficient alpha are determined using the time of flight and the insertion loss of the sound passing through the sample, respectively. The density rho is estimated from the reflection coefficient at the interface between the polystyrene plate and the sample, where the transformation from longitudinal to transverse waves is considered. To compensate for the effect of velocity dispersion on the second harmonic generation, the relative phase of the second harmonic sound is also measured using dual-frequency sound. By summarizing all the linear properties and amplitude data of the second harmonic component in the sound transmitted through the sample, the BA value is finally determined. The measurement is validated through the experiments on nondispersive liquids and weakly dispersive biological samples with known BA values.

Plane wave source with minimal harmonic distortion for investigating nonlinear acoustic properties

The objective of this investigation is to introduce and validate a practical ultrasound source to be used in the investigation of the nonlinear material properties of liquids and soft tissues studied in vitro. Methods based on the progressive distortion of finite amplitude ultrasonic waves in the low megahertz frequency range are most easily implemented under the assumption of plane wave propagation. However, achieving an approximately planar ultrasonic field over substantial propagation distances can be challenging. Furthermore, undesired harmonic distortion of the ultrasonic field prior to insonification of the specified region of interest represents another serious limitation. This paper introduces an approach based on the use of the ultrasonic field emanating from a stainless-steel delay line. Both simulation and direct experimental measurement demonstrate that such a field exhibits relatively planar wave fronts to a good approximation (such that a 3-mm-diam receiver would be exposed to no more than 3 dB of loss across its face) and is free from the significant harmonic distortion that would occur in a conventional water path.