Interaction of macro- and microvascular function underlies brachial artery flow-mediated dilation in humans.

Brachial artery flow-mediated dilation (BAFMD) is induced by hyperemic wall shear rate (WSR) following forearm ischemia. In older adults, there appears to be a reduced brachial hyperemic WSR and altered stimulus-response relationship compared with young adults. However, it is unclear if an altered forearm microvascular response to ischemia influences brachial hyperemic WSR in older adults. We determined associations between brachial hyperemic WSR and forearm skeletal muscle oxygen saturation in young and older adults. Healthy young (n = 17, 29 ± 7 yr) and older (n = 32, 65 ± 4 yr) adults participated in the study. BAFMD by a multigate spectral Doppler system and forearm skeletal muscle oxygen saturation by near-infrared spectroscopy were concurrently measured. When compared with the young, older adults showed reduced oxygen extraction kinetics (OE, 0.15 [0.12-0.17] vs. 0.09 [0.05-0.12]%s-1) and magnitude (So2deficit, 3,810 ± 1,420 vs. 2,723 ± 1,240%s) during ischemia, as well as oxygen resaturation kinetics (So2slope, 2.5 ± 0.7 vs. 1.7 ± 0.7%s-1) upon reperfusion (all P < 0.05). When OE in the young and So2slope in older adults were stratified by their median values, young adults with OE above the median had greater hyperemic WSR parameters compared with those below the median (P < 0.05), but So2slope in older adults did not show clear differences in hyperemic WSR parameters between those above/below the median. This study demonstrates that, in addition to a reduced microvascular response to ischemia, there may be a dissociation between microvascular response to ischemia and brachial hyperemic WSR in older adults, which may result in a further impairment of BAFMD in this cohort.NEW & NOTEWORTHY Microvascular response to ischemia and subsequent reperfusion is diminished in older adults compared with the young. Furthermore, there appears to be a dissociation between the microvascular response to ischemia and brachial hyperemic WSR in older adults, which may further disturb the BAFMD process in this cohort. A reduced BAFMD in older adults may be a result of multiple alterations occurring both at macro- and microcirculation.

High-Frame-Rate Volumetric Porcine Renal Vasculature Imaging.

OBJECTIVE: The aim of this study was to assess the feasibility and imaging options of contrast-enhanced volumetric ultrasound kidney vasculature imaging in a porcine model using a prototype sparse spiral array. METHODS: Transcutaneous freehand in vivo imaging of two healthy porcine kidneys was performed according to three protocols with different microbubble concentrations and transmission sequences. Combining high-frame-rate transmission sequences with our previously described spatial coherence beamformer, we determined the ability to produce detailed volumetric images of the vasculature. We also determined power, color and spectral Doppler, as well as super-resolved microvasculature in a volume. The results were compared against a clinical 2-D ultrasound machine. RESULTS: Three-dimensional visualization of the kidney vasculature structure and blood flow was possible with our method. Good structural agreement was found between the visualized vasculature structure and the 2-D reference. Microvasculature patterns in the kidney cortex were visible with super-resolution processing. Blood flow velocity estimations were within a physiological range and pattern, also in agreement with the 2-D reference results. CONCLUSION: Volumetric imaging of the kidney vasculature was possible using a prototype sparse spiral array. Reliable structural and temporal information could be extracted from these imaging results.

3-D Coherent Multi-Transducer Ultrasound Imaging with Sparse Spiral Arrays.

Coherent multi-transducer ultrasound (CoMTUS) creates an extended effective aperture through the coherent combination of multiple arrays, which results in images with enhanced resolution, extended field-of-view, and higher sensitivity. The subwavelength localization accuracy of the multiple transducers required to coherently beamform the data is achieved by using the echoes backscattered from targeted points. In this study, CoMTUS is implemented and demonstrated for the first time in 3-D imaging using a pair of 256-element 2-D sparse spiral arrays, which keep the channel count low and limit the amount of data to be processed. The imaging performance of the method was investigated using both simulations and phantom tests. The feasibility of free-hand operation is also experimentally demonstrated. Results show that, in comparison to a single dense array system using the same total number of active elements, the proposed CoMTUS system improves spatial resolution (up to 10 times) in the direction where both arrays are aligned, contrast-to-noise-ratio (CNR, up to 46%), and generalized CNR (up to 15%). Overall, CoMTUS shows a narrower main lobe and higher contrast-to-noise ratio, which results in an increased dynamic range and better target detectability.

Sparse 2-D PZT-on-PCB Arrays With Density Tapering.

Two-dimensional (2-D) arrays offer volumetric imaging capabilities without the need for probe translation or rotation. A sparse array with elements seeded in a tapering spiral pattern enables one-to-one connection to an ultrasound machine, thus allowing flexible transmission and reception strategies. To test the concept of sparse spiral array imaging, we have designed, realized, and characterized two prototype probes designed at 2.5-MHz low-frequency (LF) and 5-MHz high-frequency (HF) center frequencies. Both probes share the same electronic design, based on piezoelectric ceramics and rapid prototyping with printed circuit board substrates to wire the elements to external connectors. Different center frequencies were achieved by adjusting the piezoelectric layer thickness. The LF and HF prototype probes had 88% and 95% of working elements, producing peak pressures of 21 and 96 kPa/V when focused at 5 and 3 cm, respectively. The one-way -3-dB bandwidths were 26% and 32%. These results, together with experimental tests on tissue-mimicking phantoms, show that the probes are viable for volumetric imaging.

Unfocused Field Analysis of a Density-Tapered Spiral Array for High-Volume-Rate 3-D Ultrasound Imaging.

Spiral array transducers with a sparse 2-D aperture have demonstrated their potential in realizing 3-D ultrasound imaging with reduced data rates. Nevertheless, their feasibility in high-volume-rate imaging based on unfocused transmissions has yet to be established. From a metrology standpoint, it is essential to characterize the acoustic field of unfocused transmissions from spiral arrays not only to assess their safety but also to identify the root cause of imaging irregularities due to the array's sparse aperture. Here, we present a field profile analysis of unfocused transmissions from a density-tapered spiral array transducer (256 hexagonal elements, 220- [Formula: see text] element diameter, and 1-cm aperture diameter) through both simulations and hydrophone measurements. We investigated plane- and diverging-wave transmissions (five-cycle, 7.5-MHz pulses) from 0° to 10° steering for their beam intensity characteristics and wavefront arrival time profiles. Unfocused firings were also tested for B-mode imaging performance (ten compounded angles, -5° to 5° span). The array was found to produce unfocused transmissions with a peak negative pressure of 93.9 kPa at 2 cm depth. All transmissions steered up to 5° were free of secondary lobes within 12 dB of the main beam peak intensity. All wavefront arrival time profiles were found to closely match the expected profiles with maximum root-mean-squared errors of [Formula: see text] for plane wave (PW) and [Formula: see text] for diverging wave. The B-mode images showed good spatial resolution with a penetration depth of 22 mm in PW imaging. Overall, these results demonstrate that the density-tapered spiral array can facilitate unfocused transmissions below regulatory limits (mechanical index: 0.034; spatial-peak, pulse-average intensity: 0.298 W/cm2) and with suppressed secondary lobes while maintaining smooth wavefronts.

Design, Implementation, and Medical Applications of 2-D Ultrasound Sparse Arrays.

An ultrasound sparse array consists of a sparse distribution of elements over a 2-D aperture. Such an array is typically characterized by a limited number of elements, which in most cases is compatible with the channel number of the available scanners. Sparse arrays represent an attractive alternative to full 2-D arrays that may require the control of thousands of elements through expensive application-specific integrated circuits (ASICs). However, their massive use is hindered by two main drawbacks: the possible beam profile deterioration, which may worsen the image contrast, and the limited signal-to-noise ratio (SNR), which may result too low for some applications. This article reviews the work done for three decades on 2-D ultrasound sparse arrays for medical applications. First, random, optimized, and deterministic design methods are reviewed together with their main influencing factors. Then, experimental 2-D sparse array implementations based on piezoelectric and capacitive micromachined ultrasonic transducer (CMUT) technologies are presented. Sample applications to 3-D (Doppler) imaging, super-resolution imaging, photo-acoustic imaging, and therapy are reported. The final sections discuss the main shortcomings associated with the use of sparse arrays, the related countermeasures, and the next steps envisaged in the development of innovative arrays.

Experimental and simulation study of harmonic components generated by plane and focused waves.

Although there is increasing interest in the use of plane waves (PW) in high-frame-rate imaging, not much experimental data is available about their behavior in terms of nonlinear propagation. This paper presents a detailed study of fundamental and harmonic components of the ultrasound beam associated to PW transmission from a linear array. Simulations and hydrophone measurements of PW propagation in water were performed and compared to the results obtained for focused waves (FWs) at various levels of peak negative pressure (PNP). Experimental results confirm that, at comparable PNP, the amplitudes of the harmonics reached by PWs are always higher, over extended regions, than those achieved with FW. For example, at MI = 0.2 the PW second harmonic turns out to be 9 dB higher at 25 mm depth (i.e. in the focal region), and 20 dB higher at 40 mm depth. Simulations additionally show that when ultrasound waves propagate through blood or muscle, the situation is in general reversed but, at low MI, the second harmonic amplitude can still be higher in PW than in FW. Furthermore, it is shown that increasing the array aperture size yields higher harmonic growth in PW compared to FW.

High Frame Rate Volumetric Imaging of Microbubbles Using a Sparse Array and Spatial Coherence Beamforming.

Volumetric ultrasound imaging of blood flow with microbubbles enables a more complete visualization of the microvasculature. Sparse arrays are ideal candidates to perform volumetric imaging at reduced manufacturing complexity and cable count. However, due to the small number of transducer elements, sparse arrays often come with high clutter levels, especially when wide beams are transmitted to increase the frame rate. In this study, we demonstrate with a prototype sparse array probe and a diverging wave transmission strategy, that a uniform transmission field can be achieved. With the implementation of a spatial coherence beamformer, the background clutter signal can be effectively suppressed, leading to a signal to background ratio improvement of 25 dB. With this approach, we demonstrate the volumetric visualization of single microbubbles in a tissue-mimicking phantom as well as vasculature mapping in a live chicken embryo chorioallantoic membrane.

In Vitro and In Vivo Multispectral Photoacoustic Imaging for the Evaluation of Chromophore Concentration.

Multispectral photoacoustic imaging is a powerful noninvasive medical imaging technique that provides access to functional information. In this study, a set of methods is proposed and validated, with experimental multispectral photoacoustic images used to estimate the concentration of chromophores. The unmixing techniques used in this paper consist of two steps: (1) automatic extraction of the reference spectrum of each pure chromophore; and (2) abundance calculation of each pure chromophore from the estimated reference spectra. The compared strategies bring positivity and sum-to-one constraints, from the hyperspectral remote sensing field to multispectral photoacoustic, to evaluate chromophore concentration. Particularly, the study extracts the endmembers and compares the algorithms from the hyperspectral remote sensing domain and a dedicated algorithm for segmentation of multispectral photoacoustic data to this end. First, these strategies are tested with dilution and mixing of chromophores on colored 4% agar phantom data. Then, some preliminary in vivo experiments are performed. These consist of estimations of the oxygen saturation rate (sO2) in mouse tumors. This article proposes then a proof-of-concept of the interest to bring hyperspectral remote sensing algorithms to multispectral photoacoustic imaging for the estimation of chromophore concentration.

On the Depth-Dependent Accuracy of Plane-Wave-Based Vector Velocity Measurements With Linear Arrays.

High-frame-rate vector Doppler methods are used to measure blood velocities over large 2-D regions, but their accuracy is often estimated over a short range of depths. This article thoroughly examines the dependence of velocity measurement accuracy on the target position. Simulations were carried out on flat and parabolic flow profiles, for different Doppler angles, and considering a 2-D vector flow imaging (2-D VFI) method based on plane wave transmission and speckle tracking. The results were also compared with those obtained by the reference spectral Doppler (SD) method. Although, as expected, the bias and standard deviation generally tend to worsen at increasing depths, the measurements also show the following. First, the errors are much lower for the flat profile (from ≈ -4 ± 3% at 20 mm to ≈ -17 ± 4% at 100 mm) than for the parabolic profile (from ≈ -4 ± 3% to ≈ -38 ±%). Second, only part of the relative estimation error is related to the inherent low resolution of the 2-D VFI method. For example, even for SD, the error bias increases (on average) from -0.7% (20 mm) to -17% (60 mm) up to -26% (100 mm). Third, conversely, the beam divergence associated with the linear array acoustic lens was found to have a great impact on the velocity measurements. By simply removing such lens, the average bias for 2-D VFI at 60 and 100 mm dropped down to -9.4% and -19.4%, respectively. In conclusion, the results indicate that the transmission beam broadening on the elevation plane, which is not limited by reception dynamic focusing, is the main cause of velocity underestimation in the presence of high spatial gradients.

Real-Time High Frame Rate Color Flow Mapping System.

Plane wave (PW) transmission (TX) can be profitably used to improve the performance of color flow mapping (CFM) systems by increasing the autocorrelation ensemble length (EL) and/or the frame rate (FR). Although high-end scanners tend to include imaging schemes using PW TX and parallel receive beams, high frame rate (HFR) CFM has been so far experimentally implemented mostly through research platforms that transmit PWs and beamform/process the received channel data off-line. In this article, full real-time implementation of PW CFM with continuous-time clutter filtering and extended FR/EL is reported. The field-programmable gate arrays (FPGAs) and digital signal processors (DSPs) onboard the ULA-OP 256 research scanner were programmed to perform high-speed parallel beamforming and autocorrelation-based CFM processing, respectively. Different strategies were tested, in which the TX of PWs for CFM is either continuous or interleaved with the TX of packets of B-mode pulses. A fourth-order Chebyshev continuous-time high-pass filter with programmable cutoff frequency was implemented and its clutter rejection performance was positively compared with that obtained when operating on packet data. CFM FRs up to 575 were obtained. The possibility of programming the autocorrelation EL up to 64 permitted to detect flow with high sensitivity and accuracy (average relative errors down to 0.4% ± 8.4%). In vivo HFR movies are presented, showing the dynamics of flow in the common carotid artery, which highlight the presence of secondary flow components.

Real-Time 3-D Spectral Doppler Analysis With a Sparse Spiral Array.

2-D sparse arrays may push the development of low-cost 3-D systems, not needing to control thousands of elements by expensive application-specific integrated circuits (ASICs). However, there is still some concern about their suitability in applications, such as Doppler investigation, which inherently involve poor signal-to-noise ratios (SNRs). In this article, a novel real-time 3-D pulsed-wave (PW) Doppler system, based on a 256-element 2-D spiral array, is presented. Coded transmission (TX) and matched filtering were implemented to improve the system SNR. Standard sonograms as well as multigate spectral Doppler (MSD) profiles, along lines that can be arbitrarily located in different planes, are presented. The performance of the system was assessed quantitatively on experimental data obtained from a straight tube flow phantom. An SNR increase of 11.4 dB was measured by transmitting linear chirps instead of standard sinusoidal bursts. For a qualitative assessment of the system performance in more realistic conditions, an anthropomorphic phantom of the carotid arteries was used. Finally, real-time B-mode and MSD images were obtained from healthy volunteers.

Virtual Real-Time for High PRF Multiline Vector Doppler on ULA-OP 256.

The recent development of high-frame-rate (HFR) imaging/Doppler methods based on the transmission of plane or diverging waves has proposed new challenges to echographic data management and display. Due to the huge amount of data that need to be processed at very high speed, the pulse repetition frequency (PRF) is typically limited to hundreds hertz or few kilohertz. In Doppler applications, a PRF limitation may result unacceptable since it inherently translates to a corresponding limitation in the maximum detectable velocity. In this article, the ULA-OP 256 implementation of a novel ultrasound modality, called virtual real-time (VRT), is described. First, for a given HFR RT modality, the scanner displays the processed results while saving channel data into an internal buffer. Then, ULA-OP 256 switches to VRT mode, according to which the raw data stored in the buffer are immediately reprocessed by the same hardware used in RT. In the two phases, the ULA-OP 256 calculation power can be differently distributed to increase the acquisition frame rate or the quality of processing results. VRT was here used to extend the PRF limit in a multiline vector Doppler (MLVD) application. In RT, the PRF was maximized at the expense of the display quality; in VRT, data were reprocessed at a lower rate in a high-quality display format, which provides more detailed flow information. Experiments are reported in which the MLVD technique is shown capable of working at 16-kHz PRF, so that flow jet velocities higher up to 3 m/s can be detected.

The effect of size range on ultrasound-induced translations in microbubble populations.

Microbubble translations driven by ultrasound-induced radiation forces can be beneficial for applications in ultrasound molecular imaging and drug delivery. Here, the effect of size range in microbubble populations on their translations is investigated experimentally and theoretically. The displacements within five distinct size-isolated microbubble populations are driven by a standard ultrasound-imaging probe at frequencies ranging from 3 to 7 MHz, and measured using the multi-gate spectral Doppler approach. Peak microbubble displacements, reaching up to 10 µm per pulse, are found to describe transient phenomena from the resonant proportion of each bubble population. The overall trend of the statistical behavior of the bubble displacements, quantified by the total number of identified displacements, reveals significant differences between the bubble populations as a function of the transmission frequency. A good agreement is found between the experiments and theory that includes a model parameter fit, which is further supported by separate measurements of individual microbubbles to characterize the viscoelasticity of their stabilizing lipid shell. These findings may help to tune the microbubble size distribution and ultrasound transmission parameters to optimize the radiation-force translations. They also demonstrate a simple technique to characterize the microbubble shell viscosity, the fitted model parameter, from freely floating microbubble populations using a standard ultrasound-imaging probe.

Doppler Ultrasound Technology for Fetal Heart Rate Monitoring: A Review.

Fetal well-being is commonly assessed by monitoring the fetal heart rate (fHR). In clinical practice, the de facto standard technology for fHR monitoring is based on the Doppler ultrasound (US). Continuous monitoring of the fHR before and during labor is performed using a US transducer fixed on the maternal abdomen. The continuous fHR monitoring, together with simultaneous monitoring of the uterine activity, is referred to as cardiotocography (CTG). In contrast, for intermittent measurements of the fHR, a handheld Doppler US transducer is typically used. In this article, the technology of Doppler US for continuous fHR monitoring and intermittent fHR measurements is described, with emphasis on fHR monitoring for CTG. Special attention is dedicated to the measurement environment, which includes the clinical setting in which fHR monitoring is commonly performed. In addition, to understand the signal content of acquired Doppler US signals, the anatomy and physiology of the fetal heart and the surrounding maternal abdomen are described. The challenges encountered in these measurements have led to different technological strategies, which are presented and critically discussed, with a focus on the US transducer geometry, Doppler signal processing, and fHR extraction methods.

3-D Super-Resolution Ultrasound Imaging With a 2-D Sparse Array.

High-frame-rate 3-D ultrasound imaging technology combined with super-resolution processing method can visualize 3-D microvascular structures by overcoming the diffraction-limited resolution in every spatial direction. However, 3-D super-resolution ultrasound imaging using a full 2-D array requires a system with a large number of independent channels, the design of which might be impractical due to the high cost, complexity, and volume of data produced. In this study, a 2-D sparse array was designed and fabricated with 512 elements chosen from a density-tapered 2-D spiral layout. High-frame-rate volumetric imaging was performed using two synchronized ULA-OP 256 research scanners. Volumetric images were constructed by coherently compounding nine-angle plane waves acquired at a pulse repetition frequency of 4500 Hz. Localization-based 3-D super-resolution images of two touching subwavelength tubes were generated from 6000 volumes acquired in 12 s. Finally, this work demonstrates the feasibility of 3-D super-resolution imaging and super-resolved velocity mapping using a customized 2-D sparse array transducer.

Spectral Doppler Measurements With 2-D Sparse Arrays.

The 2-D sparse arrays, in which a few hundreds of elements are distributed on the probe surface according to an optimization procedure, represent an alternative to full 2-D arrays, including thousands of elements usually organized in a grid. Sparse arrays have already been used in B-mode imaging tests, but their application to Doppler investigations has not been reported yet. Since the sparsity of the elements influences the acoustic field, a corresponding influence on the mean frequency (Fm), bandwidth (BW), and signal-to-noise ratio (SNR) of the Doppler spectra is expected. This article aims to assess, by simulations and experiments, to what extent the use of a sparse rather than a full gridded 2-D array has an impact on spectral Doppler measurements. Parabolic flows were investigated by a 3 MHz, 1024-element gridded array and by a sparse array; the latter was obtained by properly selecting a subgroup of 256 elements from the full array. Simulations show that the mean Doppler frequency does not change between the sparse and the full array while there are significant differences on the BW (average reduction of 17.2% for the sparse array, due to different apertures of the two probes) and on the signal power (Ps) (22 dB, due to the different number of active elements). These results are confirmed by flow phantom experiments, which also highlight that the most critical difference between sparse and full gridded array in Doppler measurements is in terms of SNR (-16.8 dB).

A Comparison of Coherence-Based Beamforming Techniques in High-Frame-Rate Ultrasound Imaging With Multi-Line Transmission.

One of the current challenges in ultrasound imaging is achieving higher frame rates, particularly in cardiac applications, where tracking the heart motion and other rapid events can provide potential valuable diagnostic information. The main drawback of ultrasound high-frame-rate strategies is that usually they partly sacrifice image quality in order to speed up the acquisition time. In particular, multi-line transmission (MLT), which consists in transmitting multiple ultrasound beams simultaneously in different directions, has been proven able to improve frame rates in echocardiography, unfortunately generating artifacts due to inter-beam crosstalk interferences. This work investigates the possibility to effectively suppress crosstalk artifacts in MLT while improving image quality by applying beamforming techniques based on backscattered signals spatial coherence. Several coherence-based algorithms (i.e., short-lag filtered-delay multiply and sum beamforming, coherence and generalized coherence factor, phase and sign coherence, and nonlinear beamforming with p th root compression) are implemented and compared, and their performance trends are evaluated when varying their design parameters. Indeed, experimental results of phantom and in vivo cardiac acquisitions demonstrate that this class of algorithms can provide significant benefits compared with delay and sum, well-suppressing artifacts (up to 48.5-dB lower crosstalk), and increasing image resolution (by up to 46.3%) and contrast (by up to 30 dB in terms of contrast ratio and 12.6% for generalized contrast-to-noise ratio) at the same time.

High-Frame-Rate Tri-Plane Echocardiography With Spiral Arrays: From Simulation to Real-Time Implementation.

Major cardiovascular diseases (CVDs) are associated with (regional) dysfunction of the left ventricle. Despite the 3-D nature of the heart and its dynamics, the assessment of myocardial function is still largely based on 2-D ultrasound imaging, thereby making diagnosis heavily susceptible to the operator's expertise. Unfortunately, to date, 3-D echocardiography cannot provide adequate spatiotemporal resolution in real-time. Hence, tri-plane imaging has been introduced as a compromise between 2-D and true volumetric ultrasound imaging. However, tri-plane imaging typically requires high-end ultrasound systems equipped with fully populated matrix array probes embedded with expensive and little flexible electronics for two-stage beamforming. This article presents an advanced ultrasound system for real-time, high frame rate (HFR), and tri-plane echocardiography based on low element count sparse arrays, i.e., the so-called spiral arrays. The system was simulated, experimentally validated, and implemented for real-time operation on the ULA-OP 256 system. Five different array configurations were tested together with four different scan sequences, including multi-line and planar diverging wave transmission. In particular, the former can be exploited to achieve, in tri-plane imaging, the same temporal resolution currently used in clinical 2-D echocardiography, at the expenses of contrast (-3.5 dB) and signal-to-noise ratio (SNR) (-8.7 dB). On the other hand, the transmission of planar diverging waves boosts the frame rate up to 250 Hz, but further compromises contrast (-10.5 dB), SNR (-9.7 dB), and lateral resolution (+46%). In conclusion, despite an unavoidable loss in image quality and sensitivity due to the limited number of elements, HFR tri-plane imaging with spiral arrays is shown to be feasible in real-time and may enable real-time functional analysis of all left ventricular segments of the heart.

Microbubble Radiation Force-Induced Translation in Plane-Wave Versus Focused Transmission Modes.

Due to the primary radiation force, microbubble displacement has been observed previously in the focal region of single-element and array ultrasound probes. This effect has been harnessed to increase the contact between the microbubbles and targeted endothelium for drug delivery and ultrasound molecular imaging. In this study, microbubble displacements associated with plane-wave (PW) transmission are thoroughly investigated and compared to those obtained in focused-wave (FW) transmission over a range of pulse repetition frequencies, burst lengths (BLs), peak negative pressures, and transmission frequencies. In PW mode, the displacements, depending upon the experimental conditions, are in some cases consistently higher (e.g., by 28%, when the longest BL was used at PRF = 4 kHz), and the axial displacements are spatially more uniform compared to FW mode. Statistical analysis on the measured displacements reveals a slightly different frequency dependence of statistical quantities compared to transient peak microbubble displacements, which may suggest the need to consider the size range within the tested microbubble population.