Microbubble radiation force-induced translation in plane-wave versus focused transmission modes

Abstract

Microbubble displacement due to the primary radiation force 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 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, peak negative pressures and transmission frequencies. In PW mode, the displacements, depending on the experimental conditions, are in some cases consistently higher (e.g. by 28%, when the longest burst length 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.

1. Introduction

An acoustic wave can impart radiation force on a particle to translate it in the direction of wave propagation. In ultrasonics, this phenomenon offers the tantalizing possibility of controlling the position of intravascular microbubbles in vivo by an external probe. Several earlier studies have provided the theoretical framework for calculating the primary radiation force in an ultrasound field, either in linearized [1], [2] or in non-linearized equations [3]. Although those derivations assumed a plane wave, all experiments were performed with a focused ultrasound wave. Radiation force effects associated with focused transmission have been used to improve targeted microbubble binding and adhesion to the endothelium in ultrasound molecular imaging [4]–[6] and to enhance ultrasound-guided drug delivery [7].

Microbubble ultrasound contrast agents are being used increasingly together with plane wave (PW) transmission [8] to improve contrast echocardiography or arterial flow quantification. In addition, this approach has allowed resolution of structures more than one order-of-magnitude smaller than the system point spread function in super-resolution microvascular imaging studies [9]–[11]. Since PW transmission is typically performed at a high pulse repetition frequency (PRF), which is the ideal condition to produce large microbubble displacements [2], it is worth identifying the conditions in which the radiation force associated with PW mode might influence the results of the Doppler flow investigation method, and determining how such artifacts could be avoided. On the other hand, PW transmission may also be attractive to facilitate more uniform contact between microbubbles and endothelium throughout the tissue volume for molecular imaging or targeted drug delivery. It is thus important to learn how to finely control the transmission parameters in order to produce the desired microbubble displacements in PW mode, and to understand which major differences, advantages or drawbacks may exist compared to the standard focused wave (FW) transmission.

In an earlier study, we introduced the methodology to qualitatively evaluate radiation force effects in PW mode [12]. Our preliminary findings showed that comparable maximum microbubble displacements are obtained in PW and FW modes when the same peak negative pressure (PNP), PRF and burst length (BL) are used [13]. It was also observed that such displacements are typically larger and almost uniform at different depths in PW mode, while they are notably peaked at the focal point in FW mode.

The aim of this study was to experimentally evaluate which differences occur between focused and plane wave transmission in terms of local microbubble displacement. Comprehensive tests were performed with a refined experimental procedure. We report results obtained in both PW and FW transmission modes by varying all transmission parameters (including the center frequency, F₀) over suitable ranges. Furthermore, the displacements along “lateral” scan lines (i.e., not coincident with the transmission beam axis) are also evaluated for both modes. The statistical significance of the measured displacements is also examined. The results are discussed to provide guidelines for better control of ultrasound radiation force associated with PW transmission.

The paper is organized as follows: Section II describes microbubble synthesis, the experimental setup, details on the ultrasound pulse-echo acquisitions, and data processing methods. Section III presents and discusses the main results for the measured microbubble displacements as a function of various transmission parameters. Finally, concluding remarks are given in Section IV.

II. Methods

A. Microbubble synthesis

Microbubbles were prepared using 1,2-distearoyl-sn-glycero-3-phosphocholine (DSPC) as the main phospholipid shell component and 1,2-distearoyl-sn-glycero-3-phospho-ethanolamine-N-[amino(polyethylene glycol)-2000] (DSPE-PEG2000) as an emulsifier (Avanti Polar Lipids, Alabaster, AL, USA). The lipid and emulsifier were mixed at a molar ratio of 9:1 in chloroform, stirred homogeneously at 200 rpm and dried for 4 h under vacuum. The resulting lipid film was dispersed in 0.2-μm filtered phosphate buffer saline (PBS; Sigma-Aldrich, St. Louis, MO, USA) to a concentration of 2 mg/mL. The dispersion was then heated to 60 °C, (5 °C above the main phase transition temperature of DSPC) under continuous stirring at 200 rpm until the lipids formed a nearly homogenous suspension. The suspension was further subjected to low-power (20% amplitude) probe sonication, with the probe submerged below the gas/water surface, for 15 min to form a clear solution containing only small unilamellar vesicles. The sonicator probe was then moved to the gas/water interface. Perfluorobutane (PFB; FluoroMed, L.P., Round Rock, TX, USA) gas was flowed over the suspension surface for approximately 10 s, and the power amplitude of probe sonicator was set to the maximum (100%). The lipid suspension was then sonicated for ~8 s to generate a milky white suspension containing microbubbles and macroscopic foam. The suspension was immediately sealed and kept in an ice bath for ~5 min. Once the microbubble suspension cooled down to room temperature, the suspension was collected in 30-mL syringes and concentrated by centrifugation at 150 relative centrifugal force (rcf) for 2 min. The concentrated cake contained a polydisperse (0.5 to 20-μm diameter) population of microbubbles. Therefore, differential centrifugation [14] was used to isolate a narrow size range with a mean diameter of ~3.4 μm (Fig. 1a). This size range was chosen as a tradeoff between production yield, stability and echogenicity [15]. The polydisperse microbubble cake was diluted with PBS and subjected to 90 rcf for 1 min, and supernatant (cake) containing microbubbles with diameter > 3 μm was collected. The cake was re-suspended in PBS and centrifuged at 50 rcf for 1 min, and the infranatant containing microbubbles smaller than 4 μm was retained. The collected infranatant contained microbubbles in the size range of 3–4 μm diameter. This suspension was then centrifuged at 90 rcf for 5 min to obtain a concentrated microbubble product. The centrifugation steps were repeated several times to increase the total amount of size-isolated microbubbles and refine the distribution. The concentrated 3–4 μm microbubble cake was stored in a 2-mL vial with headspace filled with PFB and diluted as required just prior to experimentation. The microbubble size distribution and concentration were measured with a Multisizer III (Beckman Coulter Life Sciences, Indianapolis, IN, USA) using a 30-μm aperture, which measures particles between 0.8 to 18 μm in diameter. To sample, an aliquot of 0.5 μL of homogeneously mixed microbubble suspension was added to 10 mL Isoton (Beckman Coulter). Measurements with only Isoton (no microbubbles) were taken as blank.

Fig. 1.

(a) Number- and volume-weighted size distributions of the microbubble population averaged over nine measurements, shown as mean ± standard deviation. (b) Schematic of the experimental set-up.

B. Ultrasound set-up

The size-isolated microbubbles were diluted with deionized water to a concentration of approximately 5×10⁴ bubbles/mL. This concentration was chosen to maximize the signal-to-noise ratio while avoiding attenuation. 800 mL of the suspension was placed in a 1-L beaker with sound-absorbing rubber angled at the bottom to minimize reflections from the bottom glass surface (Fig. 1b). The microbubbles were insonified by an LA332 array probe (Esaote, Florence, Italy) driven by the 64-channel ULA-OP open scanner [16]. The LA332 is a 144-element linear array with 0.245-mm pitch, 4.6-MHz center frequency and 100% (−6 dB) bandwidth. The elements are covered by a silicon lens, which sets an elevational focus at about 23 mm.

By exciting the 64 central-probe elements with sinusoidal bursts, the ULA-OP was programmed to produce either PW or FW transmissions of variable frequency, amplitude and length. In FW mode, the TX focus was always set coincident with the elevational focal depth (23 mm).and a Hamming apodization function was used.

The PNPs obtained in the two modes were measured in water by a calibrated needle hydrophone (Onda, HGL-0400) and then equalized by adjusting the probe transmission amplitudes. Fig. 2 shows the acoustic pressures measured along the axial dimension (Z-axis) and in the lateral-axial (XZ) plane for both PW and FW modes, when the excitation signals were set to produce 200-kPa PNP at 4 MHz. Fig.2 was obtained for BL = 2 μs. For longer BLs, only a slightly different pattern of the sound field for PW TX was observed.

Fig. 2.

Equalized pressure fields measured along the beam axis (top) and over the normalized dB scale XZ plane in FW (bottom, left) and PW (bottom, right) modes, when 4 MHz pulses with 2 μs BL were transmitted at 4 kHz PRF.

C. Imaging acquisitions

During each acquisition, the microbubble suspension was insonified in either PW or FW mode by maintaining the transmission parameters listed in Table 1.

TABLE I.

Transmission parameters

Acquisition Parameter	Acronym	Range
Center frequency	F0	3–7 MHz
Pulse Repetition Frequency	PRF	1–7 kHz
Burst Length	BL	1–10 μs
Peak Negative Pressure	PNP	100–330 kPa

Between each consecutive acquisition, the microbubble suspension was manually stirred, followed by a waiting time of one minute to allow fluid motion to dissipate. The suspension was monitored between each acquisition by analyzing a 1-mL aliquot with an Accusizer 780AD (Particle Sizing Systems, Santa Barbara, CA, USA). This prevented significant concentration and size distribution changes between different acquisitions. If the bubble concentration changed by 10% or if there were significant changes in the measured size distribution, the microbubble suspension was replaced by a new one.

In transmission (TX), for both FW and PW modes, the active aperture was always coincident with the 64 central elements of the probe. In FW mode, in particular, the focal depth was coincident with the elevational focus (≈ 23 mm; F# = 2.8). In reception (RX), the selection of the active aperture was programmable, depending on the experimental goals. In most cases, the TX and RX apertures were coincident, and microbubble displacements along the probe axis were investigated. Only in the experiments addressed to evaluate the radiation force effects along lines parallel to the probe axis, the RX aperture was dynamically changed, as discussed in Sec.III.C, [dummy_incomplate para]

In all cases, the echo signals received by the 64 active elements were digitized at 50 MHz with 12-bit resolution, dynamically focused and weighted in real-time to produce one beamformed radiofrequency signal. This signal was then real-time quadrature demodulated, low-pass filtered and undersampled over a 10–60-mm depth range. For each setup configuration (PW or FW, F₀, PRF, BL, PNP), the RX data following 240,000 TX events were recorded, until the memory onboard ULA-OP was completely filled; we used this maximum number to increase the statistical meaning of the measurements. The acquired data were then downloaded into a file by the ULA-OP software.

D. Post-processing

Every file was post-processed through Matlab (Mathworks, Natick, MA, USA) by applying a multi-gate spectral Doppler (MSD) approach [17]. The samples corresponding to each depth over the range 10–60 mm were grouped into (slowtime) blocks of size 512 with 32-sample overlap. Each block was weighted by a Hanning window and transformed to the frequency domain through a 512-point Fast Fourier Transform (FFT). For each acquisition, multiple consecutive MSD profiles showing the Doppler spectra detected at all investigated depths were thus obtained.

a). Peak microbubble displacements

For each MSD profile, output power spectral densities below a fixed amplitude threshold (A_TH) were zeroed, eliminating the background noise (black region in Fig. 3). A_TH was heuristically chosen to be 20 dB higher than the root-mean-squared noise level, which was estimated through reference measurements in water without bubbles and low enough to preserve the spectral contributions produced by microbubble scattering. For each depth (d), the frequency of the highest residual spectral component was detected over the full acquisition period, and this value was considered as the local peak frequency, f_pk. Such frequency can be converted to velocity, v_pk, through the classic Doppler equation:

$$v_{pk}(d)=\frac{f_{pk}(d)c}{2F_0}$$ (1)

where c is the speed of sound in water.

Fig. 3.

Average MSD profiles obtained in two acquisitions at F0 = 4 MHz, PRF = 4 kHz, BL = 10μs, PNP = 200 kPa, for (a) FW and (b) PW TX mode. The estimated maximum PMD values (dotted white line) and a smoothing polynomial regression (pink solid line) are overlapped.

Here, v_pk(d) represents the peak microbubble velocity during the acquisition period, at depth d, that is presumably obtained by microbubbles in the most favorable circumstances for highest displacement at that depth: driven at resonance, and located in the elevational center of the beam. The peak velocity can also be written in terms of (axial) Peak Microbubble Displacement (PMD) per TX pulse, after a division by the PRF:

$$PMD(d)=\frac{f_{pk}(d)c}{2F_{0}PRF}$$ (2)

The PMD(d) values, smoothened by a 7th-order polynomial regression curve could then be overlapped to the average MSD profiles, as in Fig. 3.

b). Statistical analysis of microbubble displacements

Peak microbubble displacements are representative of a single portion of microbubble population: those microbubbles that are most sensitive to the particular acoustic parameters (e.g., microbubbles nearest to resonance). The distribution of sizes ensures that some fraction of microbubbles within the ROI will likely be near resonance. In order to consider all displacements produced by a full microbubble population, the following approach was developed: Individual microbubble displacements (hereinafter called “events”) at a single depth were identified from the corresponding spectrum as the local maxima above the fixed amplitude threshold A_TH and with a minimum width of 2 pixels. The selected depth was 2.5 cm, corresponding to a region where the PNP is close to the maximum value for both transmission modes. The events were identified at each instant and counted across the entire acquisition. An empirical displacement threshold (D_TH) of 0.6 μm/pulse was chosen to exclude the numerous slow-moving bubbles that were difficult to distinguish from one another. Therefore, only peaks above D_TH were counted.

The original counted events were weighed to account for multiple counts per single event, which happens more to the slow-moving bubbles compared to the fast ones. The multiple counting results from the BL and the bubble displacement during the FFT window yielding an apparent particle length on the MSD display in the axial dimension. The weighing function is defined as,

$$W(D)=\frac{32D}{0.6\times 512D+c\times \frac{BL}{2}}$$ (3)

where D is the bubble displacement. The numbers 32 and 512 represent the sliding step size and the size of the FFT window, respectively. The correction factor of 0.6 accounts for the Hanning window applied prior to FFT (which reduces the effective time window), and c × BL/2 represents the length of an echo produced by a single bubble due to the BL and sound speed. The weighting does not account for the appearance and disappearance of microbubbles from the acquisition plane, which can happen due to streaming induced by ultrasound, lateral displacements due to a residual fluid convection, or bubble destruction. These would require more sophisticated tracking algorithms, which we have chosen not to implement here for the sake of simplicity.

The term “counts” hereinafter indicates the number of counted events (i.e. above the threshold D_TH) weighed as explained above. For each acquisition, a counts histogram like those shown in Fig. 4 was obtained. As can be seen in this example, peak microbubble displacements can be biased by rare events. Likewise, mean displacements are not suitable either because the number distributions can have a skewed profile. The median value, D_M, however, is well suited to describe the displacements from a statistical point of view. D_M represents the “middle” displacement value separating the distribution and therefore represents a “typical” displacement that is less sensitive to rare events than PMD. Another useful statistical quantity is the total number of displacements, or counts, over a certain displacement threshold D_TH, observed during the entire acquisition.

Fig. 4.

Sample microbubble displacement histograms obtained for PW at two different TX frequencies.

III. Results and Discussion

A. Peak microbubble displacements

Following single-element transducer work by Vos et al. [3], we chose to first focus our analysis on the spatial and temporal peak microbubble displacements, PMD_MAX as this measurement can be directly extracted from the MSD data. Figures 5–8 show the measured PMD_MAXs as a function of BL, PRF, PNP and F₀ for both FW and PW modes, while fixing the other parameters.

Fig. 5.

PMD_MAX vs. BL for PW and FW modes (F₀ = 4 MHz, PRF = 4 kHz, PNP = 200 kPa). The error bars represent the standard deviation over multiple (minimum three) measurements, and the dashed lines show linear fits to the data.

Fig. 8.

PMD_MAX vs. driving frequency for PW and FW modes (PNP = 200 kPa, BL = 10 μs, PRF = 4 kHz). The error bars represent the standard deviation over multiple (minimum three) measurements.

The PMD_MAX increased linearly with the BL for both TX modes, as shown in Fig. 5, obtained at 4 MHz and 200-kPa PNP. The same proportionality was also verified at 6 MHz and other pressures (e.g., 260 kPa). This linear increase of the PMD_MAX per pulse with ultrasound BL for both FW and PW confirmed that a longer duration of radiation force yields larger overall displacements. It also suggests that history effects, which could increase the time the bubble needs to reach a steady velocity from the beginning of the burst, are not significant in these conditions.

Although the overall microbubble displacement increases with the PRF [2], the displacement per pulse is expected to be independent of the PRF in the absence of streaming effects. Figure 6 shows the PMD_MAX as a function of pulse repetition frequency.

Fig. 6.

PMD _MAX vs. PRF for PW and FW modes (F₀ = 4 MHz, PNP = 200 kPa, BL = 10 μs). The error bars represent the standard deviation over multiple (minimum three) measurements.

In both transmission modes, the PMD_MAX per pulse remained nearly constant, although a slight decrease could be noticed between 1 and 2-kHz PRF. This decrease was independent of the sequence (short-to-long or long-to-short) of PRF values. The lack of hysteresis indicated that history of PRF (e.g., alterations in the bubble concentration or spatial distribution due to streaming) did not affect this measurement. One explanation is the increased probability of destroying near-resonance microbubbles at higher PRF, leading to a slight under-estimation of the peak microbubble displacement.

According to Vos et al. [3], when neglecting the contributions of buoyancy and added mass, the radiation force was expected to be quadratic with peak negative pressure in lieu of microbubble destruction, streaming etc. This behavior is confirmed by Fig. 7, which shows that PMD_MAX increased monotonically with PNP, approximately following a square relation. We observed displacements up to 20 μm/pulse at 330-kPa PNP. Similar trends were obtained for other frequencies in the range 3 to 7 MHz.

Fig. 7.

PMD _MAX vs. PNP for PW and FW modes (F₀ = 4 MHz, BL = 10 μs, PRF = 4 kHz). The error bars represent the standard deviation over multiple (minimum three) measurements, and the dashed lines show square fits to the data.

Overall, the maximum displacement appeared to decrease with increasing frequency (see Fig. 8). However, the frequency behavior of PMD_MAX is difficult to interpret given that, as said above, peak displacements may be governed by rare events for the microbubble population within the ultrasound beam. The PMD_MAX is expected to result from the resonant proportion of the population, and when driven at their respective favorable frequencies, smaller bubbles (resonant at high frequencies) are expected to displace less compared to larger bubbles at low frequencies.

According to theory [3], a 4.5-μm bubble is expected to resonate (and therefore displace the most) at a frequency around 2 MHz, while a 2-μm bubble resonates at around 8 MHz. Our bubble population contains some of both bubble sizes despite the relatively narrow size distribution (see Fig. 1). The body forces experienced by these two bubble sizes at resonance have different magnitudes, yielding thus different PMDs. This would explain the decreasing behavior of PMD_MAX in Fig. 8. We verified that smaller bubbles produced sufficient signal to exclude detection threshold effects by successfully measuring displacements within a bubble population with a diameter range of 1–2 μm (data not shown).

B. Statistical analysis of microbubble displacements

To investigate specific behavior of the microbubble population within the acoustic field, we used the statistical approach outlined in Section IIb. Figure 9 shows an example of number distributions of all identified displacements at a depth of 2.5 cm and at different frequencies. The variation in the histograms at different driving frequencies highlights the need to describe the displacements of a given bubble population using statistical quantities. Here, we observe that the fraction of microbubbles displacing above the threshold decreased with increasing frequency.

Fig. 9.

Number distributions of displacements for PW mode at different driving frequencies (PRF = 4 kHz, PNP = 200 kPa).

Fig. 10 shows the median microbubble displacement (D_M) as a function of the BL, PRF, PNP and F₀. As expected, the median displacements were lower (up to 10 μm/pulse) than the corresponding PMD_MAX values (up to 20 μm/pulse). The trends of the median displacements with the different TX parameters are generally consistent with those observed for PMDs, see Figures 5–8, confirming that, overall, PW mode appears to provide slightly larger median displacements than FW mode. The main difference between the observed PMD_MAX and the median displacements is that the latter no longer followed a square relation with PNP, with smaller values than expected and higher fluctuations (larger error bars) beyond 250 kPa PNP.

Fig. 10.

Median microbubble displacements vs. BL, PRF, PNP and F₀ for PW and FW modes (default values are F₀ = 4 MHz, PNP = 200 kPa, BL = 10 μs, PRF = 4 kHz). The medians were taken for displacements above the threshold value D_{T H} of 0.6 μm/pulse. The error bars represent the standard deviation over multiple (minimum three) measurements.

This may be explained by the statistical value being more sensitive to bubble destruction at higher PNPs compared to transient PMDs, as destroyed bubbles do not contribute to subsequent counts. For PW this effect is particularly strong as, unlike for FW, bubbles are destroyed at a wider range of depths (cf. Fig. 2) and may do so before reaching the depth at which the measurements were taken. Furthermore, the relative difference between high and low frequencies is slightly larger for the median displacement compared to PMD_MAX (see Fig. 8), which could be explained by the former’s sensitivity to the narrow size distribution of the bubble population. 3–4 μm-diameter bubbles are expected to resonate between 3 and 4-MHz frequencies [3] and therefore yield statistically important displacements, while PMD_MAX values are always produced by resonant bubbles regardless of their proportion within the population.

Fig. 11 shows the counts as a function of the four TX parameters. The total number of counts followed similar trends as the PMD_MAX and median displacements with varying BL, PRF and PNP. It was noted, however, that for high PNP, significant differences in the counts were found between the different runs in PW mode, manifested by fluctuations in the data and large standard deviations at PNP > 240 kPa. The counts for PW were even lower than for FW for some cases at these high pressures. Similarly to the trend observed for the median displacements, this could result from bubble destruction. Indeed, after a typical measurement with PW at high PNP, the monitored size distribution and concentration of the microbubble solution was found to change. Also, at high PNP, one could observe spectral lines on the MSD display resulting from the broadband emission typical for bubble bursting.

Fig. 11.

Number of counted microbubble displacements vs. BL, PRF, PNP and F₀ for PW and FW (default values are F₀ = 4 MHz, PNP = 200 kPa, BL = 10 μs, PRF = 4 kHz). Counts were taken above the threshold value D_{T H} of 0.6 μm/pulse. The error bars represent the standard deviation over multiple (minimum three) measurements.

For transmissions at frequencies above 5 MHz for both PW and FW, the counts remained approximately constant, while lower frequencies yielded a significantly greater number of displacements. The relative difference between the counts at high and low frequencies is further enhanced compared to PMD_MAX and median displacements, implying a strong sensitivity to the size distribution of the microbubble population. PW yielded up to 4 times as many counts compared to FW.

If one roughly approximates the size of the volume comprising a counted bubble event as the pitch × pitch × depth resolution, that is, 0.245 mm × 0.245 mm × 0.4 mm = 2.4×10⁻⁴ mL, a concentration of 5×10⁴ bubbles/mL would mean that approximately one bubble is expected to be within that volume for every echo. For 240,000 echoes, the same number of bubbles is expected to be counted within the volume. An average of 3×10⁴ counted displacements in an acquisition in the default conditions therefore implies that approximately 13% of the bubble population has displaced more than D_TH.

C. Displacements along lateral scan lines

In order to extend to a wider region of interest (ROI) the investigation of microbubble displacements produced by FWs or PWs, 56 RX scan lines spaced by 0.245 mm were considered. The same TX aperture, independent of the RX strategy, produced all TX beams. The first RX scan line was displaced by 28×0.245 mm from the probe axis. The 64-element RX aperture was accordingly set symmetrical to that scan line to facilitate the RX beamforming. The procedure was repeated for 56 TX events by moving the scan line and the RX aperture by one pitch after each TX event. This permitted us to evaluate the effects of the same TX modality over an ROI of width 56×0.245mm = 13.72 mm.

Figure 12 shows the spatial-temporal peak, median displacements and total number of counts measured for FW and PW transmissions and covering the axial (depth) and lateral dimensions covering a surface of 50 mm × 16 mm. Here, nine acquisitions were averaged, and X=0 mm corresponds to the transmission beam axis. The displacements were in good correlation with the axial and lateral beamplots provided in Fig. 2. For FW, the highest displacements occurred at the focus in the location of the highest PNP, while for PW the microbubbles translated in a more uniform manner across the whole field. Note that the effect of pressure variation in the elevation direction due to the acoustic lens is expected to be similar to that produced by the TX focus along the X-axis.

Fig. 12.

PMDMAX, median and number of microbubble displacement plots in the axial (Z) and lateral (X) dimensions for focused (left) and plane wave (right) (F₀ = 4 MHz, PNP = 200 kPa, BL = 10 μs, PRF = 4 kHz).

One apparent difference between the displacement and PNP beamplots was the width of the focal area for FW, which was significantly larger for the displacements than for the PNP. Moderate displacements (D > 2 μm) were measured away from the beam axis in locations where the PNP had relatively insignificant values (PNP < 20 kPa). Such discrepancy could result from streaming effects, which may be expected for relatively long transmissions.

D. General comments on the results

All results presented in this paper have been obtained in water, with or without (the latter in case of one-way beam measurements) suspended microbubbles. It is expected that propagation through human tissues has two major consequences. According to Fig. 7, attenuation would limit the local PNP values and thus, almost quadratically, the associated displacements. Additionally, the mean frequency reduction at increasing depths may involve an increase of median displacements in a microbubble population. However, as shown in Figs. 8 and 10, such increase may become significant only at very large depths.

Previous studies provided a theoretical framework and experimental validation for calculating microbubble displacements [1], [2]. In Vos et al. [3], phospholipid-coated microbubble displacement was experimentally found to be 6 μm/pulse when driven with a 150 kPa burst and 16 μm/pulse with a 290 kPa burst, 4 MHz, in a focused ultrasound field. A theoretical model was parametrically fit to the experimental values and provided a good match for a wide range of acoustic driving parameters. The acoustic parameters underlying the data in Fig. 7 were similar to those in Vos et al., albeit with a slightly shorter pulse length in the current study (10 μs vs. 12.5 μs), providing 4 μm/pulse at 150 kPa and 13 μm/pulse at 290 kPa. After correction for the pulse length, these values are equal within round-off error. Thus, the model presented by Vos et al. [3] can be used to describe the current experimental results. Of note, as the model theoretically assumed a plane wave ultrasound field while it was validated in a focused ultrasound field, it would not predict any differences between microbubble displacements in FW vs. PW excitation.

Interestingly, while the overall trends of the PMDs with the different TX parameters were the same for the two different TX modes, higher displacements were consistently induced by PW compared to FW transmission mode. This could be due to PW having a higher probability to push a resonant bubble of a favorable size and location, as overall PW pushes bubbles over a greater volume along the axial dimension (as shown by the velocity profiles in Fig. 2). Furthermore, since PW leads to insonation over a greater fluid volume, higher streaming velocity in the liquid can be expected.

Some assumptions were made to give physical meaning to the magnitudes estimated by our algorithms. The main assumptions were that: i) The peak frequency shifts providing the peak microbubble displacements estimated from an FFT are produced by bubbles that are moving at the maximum speed, ii) the acquisition is sufficiently long to provide a significant statistical meaning, iii) the concentration and spatial distribution of the bubble suspension remains constant during the acquisition process, iv) the physical properties of the microbubbles remain stable [3], and v) the acoustical attenuation is negligible.

The phenomenon of bubble destruction was monitored empirically by observing the instantaneous multigate spectral plots: destruction manifests itself dramatically in the frequency domain as a spectral enlargement followed by the disappearance of the signal. It was negligible at lower pressures but appeared to be significant beyond approximately 240-kPa PNP, especially for PW where the bubble destructions could occur at a wider range of depths. The effect of microbubble destruction was particularly visible in the number of the counted bubble displacements at high pressures, as shown in Fig. 11.

The PMD_MAX may not be representative of bubble populations which contain multiple bubble diameters at various locations within the sound field. A PMD could be a result of a rare event from the resonant fraction of the population, as highlighted by the number distributions in Fig. 4. To highlight relations between the transmit frequency and the displacements within a specific bubble population, statistical quantities such as the median displacement were therefore considered. Given the complexity of phenomena involved, the relative “number” of events becomes significant to avoid overestimation of microbubble displacement by a single rare event. Conversely, statistical counts represent the overall number of displacements within a population, which may be higher if the transmission happens close to the resonance frequency of a larger fraction of the population. This will be verified by testing microbubble populations of different size distributions in a future study. Such considerations are important for in vivo applications employing radiation force.

The main limitation of the statistical quantities as described here (median displacement and counts) is their sensitivity to the unavoidable threshold, DTH. The true median displacements are expected to be significantly lower than those displayed in Fig. 10 (and counts much higher than in Fig. 11), but it is difficult to distinguish the individual, slowly moving bubbles that cluster near the zero-frequency-shift axis (central line in Fig. 3). Even in the absence of a threshold, countable peaks are not easily measurable. However, characterizing the slowly moving fraction of the bubble population is of less interest for the relevant applications.

IV. Conclusion

In general, the measured microbubble displacements in response to the transmitted ultrasound pulses were consistent with the expected behavior. Overall, Figs. 5, 6 and 7 suggest that in standard imaging mode (typically using short, wideband transmission bursts), especially when the effects of blood viscosity are considered [18], no significant displacements are expected in either FW and PW modes.

In order to obtain appreciable displacements, as required in ultrasound-guided drug delivery or endothelial molecular imaging, narrowband TX pulses capable of generating at least 200-kPa PNP should be used. overall, the results confirm that for a given PNP, PW displaces larger numbers of bubbles, in a more uniform manner, both in the axial and lateral dimensions, and at greater extent. Thus, PW will likely be superior for applications employing ultrasound radiation force on microbubbles to achieve ligand-receptor binding or local drug delivery.

Our comparison was based on conditions that guaranteed that the mechanical index was the same for both TX modalities. This assumption involves higher source pressure for PW TX, with possible consequences in terms of a higher temperature on the probe surface and patient’s skin. These aspects [19], [20] should be carefully considered in future studies. Further research will also be done to model the microbubble behavior and engineer the microbubble shell viscoelasticity to tune microbubble displacements. Such microbubble-selective translation could open a new avenue for multicolor ultrasound molecular imaging.

Biography

Francesco Guidi was born in Portoferraio (LI), Italy, in 1964. He graduated from the University of Florence, Italy, with the M.Sc. degree in Electronics Engineering and subsequently he received his Ph.D. degree in “Electronic Systems Engineering”. After working in a national company on the design of a real time radiologic image processing system, he joined the National Institute of Nuclear Physics (INFN) where he was involved in the design of real time software for solid state particle detectors. Since 1992, he has held a position at the Information Engineering Department of the University of Florence. His research interests include the development of electronic systems and real-time methods for ultrasound blood flow estimation and the investigation of acoustic properties of ultrasound contrast agents. On these topics, ha has authored nearly 90 papers.

Outi Supponen is an Assistant Professor in the Mechanical Engineering Department at McGill University, Canada. She received her MEng degree in Aeronautical Engineering from Imperial College London, UK, in 2013, and her PhD degree in Mechanics from Ecole Polytechnique Fédérale de Lausanne, Switzerland, in 2017. From 2018 to 2019, she was a Postdoctoral Fellow at University of Colorado Boulder, USA. Her research interests include cavitation, microbubbles and underwater acoustics.

Awaneesh Upadhyay received his Bachelor of Engineering degree in Computer Science and Engineering at the College of Engineering and Technology in Muzaffarnagar, India, in 2001, his MSc. in theoretical computer science at the Chennai Mathematical Institute in 2005, and his M.Tech. in nano-science and technology at the University School of Basic and Advance Sciences, Indraprashth University, Delhi, in 2010. In May 2018, Awaneesh completed his Ph.D. in chemical engineering at the Indian Institute of Technology, Gandhinagar, on the topic of ultrasound contrast agents. Since July 2018, he has been a postdoctoral scholar conducting research on ultrasound contrast agents in Mark Borden’s lab at the University of Colorado Boulder.

Hendrik J. Vos (M âŁ^~14) received the M.Sc. degree in Applied Physics from Delft University of Technology, Delft, The Netherlands in 2004, and his Ph.D. degree with the Department of Biomedical Engineering at Erasmus MC, Rotterdam, The Netherlands, in 2010. He worked as a Postmaster Researcher with the University of Florence, Italy, and as a contract researcher for the petrochemical industry on cutting-edge ultrasonic solutions. He currently is assistant professor with Erasmus MC, and received a Dutch NWO-TTW-VIDI personal grant in 2018. His research interests include acoustical array technology for biomedical imaging in all its aspects: transducers, 2-D and 3-D beamforming, cardiac shear waves, ultrafast Doppler, contrast imaging, and related subclinical and clinical studies.

Correct address:

Biomedical Engineering, Thorax Center, Erasmus MC, University Medical Center Rotterdam, PO BOX 2040, 3000-CA, Rotterdam, the Netherlands.

Mark Andrew Borden received his B.S. degree in chemical engineering from the University of Arizona in 1999 and his Ph.D. degree in chemical engineering from the University of California, Davis in 2003. He then did a postdoc in biomedical engineering under Kathy Ferrara at UC Davis and radiology under Bob Gillies at the Arizona Cancer Canter until 2007, when he took the position of assistant professor of chemical engineering at Columbia University in New York City. In 2010, he moved his lab to beautiful Boulder, Colorado, where he is now a professor of mechanical engineering, fellow of materials science and director of biomedical engineering at the University of Colorado. In 2016, he spent sabbatical under Piero Tortoli at the University of Florence. Dr. Borden has authored over 100 papers, book chapters and patents on microbubbles, nanodrops and their biomedical applications. Dr. Borden is a member of the IEEE International Ultrasonics Symposium Technical Program Committee, the scientific committee for the European Contrast Ultrasound Symposium, and the NIH Biomaterials and Biointerfaces (BMBI) study section. He was the recipient of the James D. Watson Investigator Award and the NSF CAREER Award.

Piero Tortoli (M’91-SM’96-F’19) received the Laurea degree in electronics engineering from the University of Florence, Italy, in 1978. Since then, he has been on the faculty of the Electronics and Telecommunications (now Information Engineering) Department of the University of Florence, where he is currently full Professor of Electronics, leading a group of about 10 researchers in the Microelectronics Systems Design Laboratory. His research interests include the development of open ultrasound research systems and novel imaging/Doppler methods. On these topics, he has authored more than 280 papers.

Professor Tortoli is Fellow member of IEEE and AIMBE. He has served on the IEEE International Ultrasonics Symposium Technical Program Committee since 1999 and is currently Associate Editor of the IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control. He chaired the 22nd International Symposium on Acoustical Imaging (1995), the 12th New England Doppler Conference (2003), established the Artimino Conference on Medical Ultrasound in 2011 and organized it again in 2017. In 2000, he was named an Honorary member of the Polish Academy of Sciences. Since 2016 he is an elected member of the Academic Senate at the University of Florence.