Sensitivity improvement of subharmonic-based pressure measurement using phospholipid-coated monodisperse microbubbles

Highlights

• •A flow-focusing microfluidic chip for monodisperse microbubbles (MM) generation.
• •An optimal frequency was identified for achieving maximal subharmonic for MM.
• •Three distinct regimes were found in subharmonic-PNP relationship for MM.
• •Subharmonic amplitude decreased monotonically with overpressure at all PNPs for MM.
• •MM can greatly improve the sensitivity of subharmonic-based pressure measurements.

Abstract

The use of the subharmonic signal from microbubbles exposed to ultrasound is a promising safe and cost-effective approach for the non-invasive measurement of blood pressure. Achieving a high sensitivity of the subharmonic amplitude to the ambient overpressure is crucial for clinical applications. However, currently used microbubbles have a wide size distribution and diverse shell properties. This causes uncertainty in the response of the subharmonic amplitude to changes in ambient pressure, which limits the sensitivity. The aim of this study was to use monodisperse microbubbles to improve the sensitivity of subharmonic-based pressure measurements. With the same shell materials and gas core, we used a flow-focusing microfluidic chip and a mechanical agitation method to fabricate monodisperse (∼2.45-µm mean radius and 4.7 % polydisperse index) and polydisperse microbubbles (∼1.51-µm mean radius and 48.4 % polydisperse index), respectively. We varied the ultrasound parameters (i.e., the frequency, peak negative pressure (PNP) and pulse length), and found that there was an optimal excitation frequency (2.8 MHz) for achieving maximal subharmonic emission for monodisperse microbubbles, but not for polydisperse microbubbles. Three distinct regimes (occurrence, growth, and saturation) were identified in the response of the subharmonic amplitude to increasing PNP for both monodisperse and polydisperse microbubbles. For the polydisperse microbubbles, the subharmonic amplitude decreased either monotonically or non-monotonically with ambient overpressure, depending on the PNP. By contrast, for the monodisperse microbubbles, there was only a monotonic decrease at all PNPs. The maximum sensitivity (1.18 dB/kPa, R² = 0.97) of the subharmonic amplitude to ambient overpressure for the monodisperse microbubbles was ∼6.5 times higher than that for the polydisperse microbubbles (0.18 dB/kPa, R² = 0.88). These results show that monodisperse microbubbles can achieve a more consistent response of the subharmonic signal to changes in ambient overpressure and greatly improve the measurement sensitivity.

1. Introduction

Typical ultrasound contrast agents are shell-encapsulated, gas-filled microbubbles with a diameter of less than 10 µm [1], [2]. Under the excitation of ultrasound waves, microbubbles enhance the intensity of the fundamental frequency in the scattering signal or generate nonlinear harmonic signals, thereby improving the sensitivity and signal-to-noise ratio of ultrasound imaging [3], [4]. Cavitating microbubbles can open biological tissue barriers (e.g., the plasma membrane, and intracellular tight junctions) via microstreaming and microjets, thereby improving the efficiency of macromolecular delivery in cancer and gene therapy [5], [6]. Previous studies have found that the amplitude of the subharmonic signal from microbubbles is sensitive to changes in ambient overpressure [7], [8], [9]. Accordingly, a technique that uses the subharmonic signal for pressure estimation, called subharmonic-aided pressure estimation (SHAPE), has been proposed. Recent in vivo and pre-clinical studies (e.g., for the measurement of cardiovascular pressure, portal hypertension, aortic pressure, portal vein pressure, and tumor interstitial fluid pressure) showed SHAPE to be translatable as a safe and cost-effective technology for the non-invasive estimation of the blood pressure in clinical applications [10], [11], [12], [13], [14], [15].

Achieving higher sensitivity of the subharmonic amplitude to the ambient pressure is crucial for SHAPE-based clinical applications. Many studies using numerical calculations and experimental measurements have analyzed the influence of the acoustic parameters (e.g., peak negative pressure (PNP), central frequency, pulse length, and pulse shape) on the sensitivity of SHAPE [16], [17], [18], [19], [20], [21]. The PNP commonly dictates the subharmonic amplitude from microbubbles. There are three distinct regimes (i.e., occurrence, growth, and saturation) in the response of the subharmonic signal to changing PNP. Most studies found that the relationship between the subharmonic amplitude and ambient overpressure depends on the threshold PNP for eliciting a subharmonic response [18], [22], [23]. For low PNPs below this threshold, the subharmonic response increases first at lower ambient overpressure, and then decreases or saturates at higher ambient overpressure (i.e., the response is non-monotonic) [16], [17], [24]. For high PNPs in the growth and saturation regimes, the subharmonic response decreases with ambient overpressure in monotonic manner [16], [18], [25]. Using the PNP within the growth regime, the subharmonic signal amplitude has the highest sensitivity to ambient pressure changes [26], [27]. For a given PNP, the excitation frequency f plays a crucial role in determining subharmonic amplitude. The threshold PNP for subharmonic occurrence is dependent on f [18]. At higher frequencies, the subharmonic threshold, and the growth and saturation curves shift to higher PNPs [18]. Simulations determined that when gas bubble is excited at twice resonance frequency f₀ (f/f₀ = 2), the threshold PNP is minimal or the subharmonic amplitude is maximal under the fixed PNP [28]. Some simulations have also determined that the subharmonic amplitude increases when 1.4 < f/f₀ < 1.6, and then approaching maximum when f/f₀ ≈ 1.6, followed by a decrease for a higher f/f₀ [29], [30]. Thus, the sensitivity of the subharmonic amplitude to changes in ambient overpressure depends on both PNP and f. For a given PNP and f, the subharmonic amplitude also depends on the pulse length, with a longer pulse length providing higher sensitivity to ambient pressure [31]. This may be because a longer pulse length increases the efficiency of non-linear oscillations in microbubbles. In addition, the subharmonic amplitude is strongly affected by the pulse shape. A two-frequency compound pulse can enhance the subharmonic response, whereas a greater smoothness of the shaped pulses inhibits subharmonic emission [32]. The use of wide-bandwidth excitation, such as a chirp signal, rather than traditional sinusoidal excitation, as well as increasing the bandwidth, can improve the sensitivity for SHAPE [20], [33], [34].

To optimize the sensitivity of the subharmonic amplitude to changes in ambient pressure, it is important to deeply understand the mechanisms on the relationship between subharmonic response and ambient overpressure. Previous reports proposed that the different trends observed in the relationship between subharmonic amplitude and overpressure may be due to different types of subharmonics from microbubbles in different states [16], [35]. For the non-monotonically changing regime, increasing overpressure decreases the microbubble size. This results in a decrease in surface tension and causes the microbubbles to transition from an elastic state to a buckling state [36]. The oscillations of microbubbles shift more toward compression than expansion [16], [37], [38]. Previous studies identified that compression-only behavior from microbubbles in the buckling state enhances the subharmonic signal with increasing overpressure under a low PNP [16], [39]. For the monotonically decreasing regime, the decrease in the subharmonic amplitude with increasing overpressure is attributed to the restriction of microbubble activity (expansion-only behavior) or microbubble destruction [16], [17], [36]. In addition, increasing ambient overpressure decrease the bubble size (increase f₀), therefore decreasing f/f₀. If the changing f/f₀ moves to the value (∼1.6) corresponding to the maximum subharmonic amplitude, the subharmonic response exhibits an increasing trend with the increasing overpressure. Conversely, if the changing f/f₀ moves away from this value, the subharmonic response shows a decreasing trend. At f/f₀ near the value that gives the maximum subharmonic amplitude, complex non-monotonic variation in the subharmonic response occurs [20], [29], [30].

Currently used microbubbles (whether commercial or non-commercial) have a polydisperse size distribution. Theoretically, the measured subharmonic response can be seen as the aggregation of the responses from every bubble in the population. The relative contribution of each bubble size depends on the relative number of bubbles of that size [19]. A change in the overpressure may cause different variations of the resonance frequency of microbubbles with different size. Thus, the subharmonic response in some bubbles in a population increases whereas that of other bubbles decreases. The aggregation of these effects determines the eventual relationship between the subharmonic amplitude and the ambient overpressure [16], [18], [19]. Moreover, microbubbles with different sizes exhibit disparate shell parameters, such as initial surface tension and viscoelasticity [40]. Therefore, these microbubbles exhibit different dynamic behavior (e.g., compression-only or asymmetric oscillation), which may result in an uncertain relationship between the subharmonic amplitude and ambient overpressure [3]. Microbubbles with a narrow size distribution have approximately the same resonance frequency and initial shell properties [3], [41], and are therefore expected to give a relatively uniform and highly sensitive response of the subharmonic amplitude to ambient pressure [42].

In this study, monodisperse and polydisperse microbubbles with the same shell materials and gas core were fabricated using a flow-focusing microfluidic chip and a high-speed agitation method, respectively. Based on an experimental setup for subharmonic measurement, an optimal excitation frequency was first selected according to the frequency response of the monodisperse and polydisperse microbubbles. Subsequently, the relationship between the subharmonic amplitude and PNP was analyzed to achieve a maximal subharmonic response. Finally, the sensitivity of the subharmonic amplitude to ambient overpressure was analyzed at different PNPs to verify the advantages of monodisperse microbubbles in pressure measurement.

2. Materials and methods

2.1. Fabrication of polydisperse and monodisperse microbubbles

2.1.1. Formation of the liposome solution

Two types of phospholipid (1,2-distearoyl-sn-glycero-3-phosphocholine (DSPC) and1,2-dipalmitoyl-sn-glycero-3-phosphoethanolamine-N-[methoxy(polyethyleneglycol)-5000] (DPPE-PEG5k) (Lipoid, Germany)) were used to prepare the dispersed liposome solution. First, DSPC and DPPE-PEG5k powder were mixed in a 9:1 M ratio, and then dissolved in a mixture of chloroform and methanol with a volume ratio of 2:1, forming a phospholipid solution. The flask containing the phospholipid solution was mounted on a rotavapor (ZX98-1, Chengxian Instrument Equipment Co., Ltd, China), which was operated at a fixed rotation rate and with a temperature of 60 °C. The inner pressure was reduced to ∼0 Pa to rapidly evaporate the solvent. After 2 h, a uniform lipid film formed. Subsequently, phosphate-buffered saline solution was added, and the film was hydrated at 60 °C for 1 h to form the liposome solution, in which the mass concentration of DSPC was 1 mg/mL. The liposome solution was stored at 4 °C for use.

2.1.2. Fabrication of the flow-focusing microfluidic chip

Soft lithography was used to fabricate the microfluidic chip. Briefly, a silicon wafer was spin-coated with photoresist, and the channel structure, which consisted of three channels—a continuous phase (width of 80 µm), a dispersed phase (width of 80 µm), and an outlet (width of 21 µm)—was exposed to UV light through a mask. Polydimethylsiloxane (PDMS) (Sylgard 184, Dow Corning, USA) with a 10:1 ratio (prepolymer and curing agent) was poured onto the silicon wafer and baked at 65 °C. Finally, the PDMS colloids were cut separately and bonded to a glass slide to form the flow-focusing microfluidic chip.

2.1.3. Generation of polydisperse microbubbles

The liposome solution was rehydrated at 60 °C for 30 min, and then 300 µL solution was transferred to a sealed 2-mLtube filled with C₃F₈ gas (XingdaoTechnology Co., Ltd, China). For generating polydisperse microbubbles, high-speed mechanical agitation was performed by a oscillator at 1800 oscillations/min for 30 s [43], [44]. To reduce multiple scattering effects, the polydisperse microbubbles were diluted to ∼30,000 microbubbles/mL for experiments (also please see the reason for selecting concentration in section 2.1.4).

2.1.4. Generation of monodisperse microbubbles

The setup for generating monodisperse microbubbles is shown in Fig. 1. Tween 20 was added to the liposome solution to eliminate the coalescence of microbubbles in the outlet channel and thus reduce the polydispersity index (PDI) of the microbubbles [45]. The liposome solution was then rehydrated at 60 °C for 30 min. The continuous phase was driven by an automatic pressure controller (Pressure Controller Light, Zhiwei Technology Co., Ltd, China), and its flow rate was precisely regulated at 40 ± 5 µL/min by a flowmeter-based feedback controller (FS4, Zhiwei Technology Co., Ltd, China). The C₃F₈ gas pressure of the dispersed phase was controlled at 400 ± 10 mbar using the same pressure controller. A microscope (ECLIPSE Ti, Nikon, Japan) with a high-speed CCD camera with maximal 200,000 frames/s (AcutEye-1M-3500, Ketianjian Technology Co., Ltd, China) was used to observe and record the formation of monodisperse microbubbles. The bubble production rate was calculated by counting the number of newly added microbubbles at the orifice in 30 video frames, and dividing by the time elapsed. The estimated production rate was ∼40000 bubbles per second. The monodisperse microbubbles were harvested in a sealed vial filled with C₃F₈ gas from the outlet channel, and then stored at 4 °C. 24 h after harvesting, monodisperse microbubbles were diluted to for experiments. Note that the relationship between the microbubble concentration and subharmonic amplitude was measured before experiments (Data not shown). The subharmonic amplitude didn’t significantly vary under the microbubble concentration below 50,000 microbubbles/mL, but rapidly decreased after the microbubble concentration reached 100,000 microbubbles/mL. The multiple scattering from high microbubble concentration would result in the decrease in subharmonic amplitude. Thus, ∼30,000 microbubbles/mL was selected for experiments.

Fig. 1.

Monodisperse microbubbles were fabricated using a flow-focusing microfluidic chip. Both the rate of continuous phase and the pressure of disperse phase were controlled by a pressure controller. The microscope and high-speed camera were used to real-time record the generation of monodisperse microbubbles.

2.1.5. Size distribution and PDI calculation

To measure the size distribution of the microbubbles, we used ImageJ (National Institutes of Health, USA) software. The microscopic images of the microbubbles were first binarized. Then, the area of each bubble in the images was calculated from the total area of pixels that made up the microbubbles (the area of a pixel was 0.33 × 0.33 µm²), thus obtaining the microbubble radius (R). About 2000 microbubbles in five microscopic images were used to obtain the size distribution of microbubbles. Finally, the PDI was calculated by $\sqrt{\sum {(R-\overline{R})}^2/n}/\overline{R}$($\overline{R}$ is the mean radius of the counted microbubbles) [46].

2.2. Experimental setup for subharmonic measurement

2.2.1. In vitro pressure-measurement system

A customized cubic framework with four empty sides and two solid top and bottom sides (20 × 20 × 20 mm³) was made with white resin. Four acoustically transparent polyester membranes with a thickness of 75 µm were screwed on four hollow sides, forming a sealed container with an inlet and an outlet, as shown in Fig. 2A and 2B. A magnetic stirrer was placed in the bottom of the container to stir the solution and form a uniform microbubble distribution during the measurements. During the experiment, T-shaped valve was opened, and the microbubbles were driven into the container through the outlet by a syringe. We note that no obvious air bubbles were produced during this process to eliminate random strong reflection. After T-shaped valve was closed, the ambient pressure inside the container was regulated by a syringe pump (AJ5803, Angel Electronic Equipment Co., Ltd, China) through air compression and real-time measurements were made using a pressure gauge (MIK-Y290,0–50 kPa, Asmik Sensor Technology Co., Ltd, China). Subsequently, a closed circuit with known ambient pressure was formed through a 3-way connector. The ambient overpressure applied to the microbubbles ranged from 0 to 24 kPa, which corresponds to the blood pressure range of humans.

Fig. 2.

A. Schematic representation of the designed setup for subharmonic-aided pressure measurement. Microbubble suspension was added into a customized container, of which four sides, as acoustic window, were sealed with four acoustically transparent polyester membranes. The pressure within the container was regulated by syringe pump and measured by a pressure gage. B. The customized container entity for microbubbles suspension.

2.2.2. Acoustic-emission and receiving modules

The setup for subharmonic measurement is shown in Fig. 2. To excite the acoustic response of the microbubbles, a focused transducer (Advanced Devices, Wakefield, MA) with a center frequency of 3.5-MHz, 50-mm focal length, and 15-mm diameter was driven by a sinusoidal pulse sequence produced by a waveform generator (33220A, Agilent Technologies, USA), and then amplified by a 50-dB RF amplifier (E&I 2100L; Electronics &Innovation Ltd, USA) to generate acoustic waves with the desired frequency, PNP, and pulse length at a pulse repetition frequency of 10 Hz. We note that absorber (UA-1, Institute of Acoustics, Chinese Academy of Sciences, China) were placed on one side and the bottom of the water tank to eliminate the reflections from these surfaces. Before the experiments, a series of calibration measurements was performed using a needle hydrophone. The amplitudes of the sinusoidal signals at a specific frequency bandwidth (2 to 4 MHz at an interval of 0.2 MHz) were calibrated to achieve the same PNP output at the focal region. The relationship between the amplitude of the sinusoidal signal and the PNP at a fixed frequency of 2.8 MHz was also calibrated. Further details of the calibration are not provided.

The scattering signals of the microbubbles in the container were received by another plane transducer (Advanced Devices, Wakefield, MA) with a 5-MHz center frequency and 15-mm diameter, the position of which was spatially vertical to the emitting transducer and 50 mm from the center of the container. The received signals were amplified by a pulse receiver (5077PR, Olympus, USA) with 20-dB gain, sampled using a high-speed A/D converter (Spectrum, Germany) with a sampling frequency of 65 MHz, and then transferred to a computer via a PCIE-bus for processing.

2.2.3. Extraction and calculation of the subharmonic signal

To obtain the frequency spectrum of the scattering signals, the sampled signals X_i(n) (n = 0, 1, ···, 1024–1; i = 1, 2, ···, 30) (n is the number of sampling points in a sampling period; i is the number of the sampling period) were processed by fast Fourier transform:

$$X_i\left(k\right)=\sum _{n=0}^{N-1}{x}_i\left(n\right)e^{-j\frac{2\pi }{N}kn}(k=0,1,···,1024-1)$$ (1)

where k is the frequency point. Then, the power spectrum, P, was obtained by

$$P_i\left(k\right)={X_i\left(k\right)}^2$$ (2)

The signal in a bandwidth of 0.14 MHz centered on half of the excitation frequency was extracted as the subharmonic signal, as shown in Fig. 3. The amplitude of the subharmonic (S_i) in a sampling period was calculated by

$$S_i={\sum }_{j=1}^3{P}_i(j)$$ (3)

where j is the number of frequency points in the bandwidth [47]. Then, the subharmonic amplitude in all sampling periods can be obtained by

$$S={\sum }_{i=1}^{30}{S}_i$$ (4)

The corresponding subharmonic reduction ($S_{\mathrm{r}}$) under the defined overpressure was calculated by

$$S_r=S_m-S_c$$ (5)

where S_m and S_c are the subharmonic amplitude from the microbubbles and saline solution under the same acoustic parameters and ambient overpressure, respectively.

Fig. 3.

Typical frequency spectra for explaining the subharmonic calculation. The black and red curves refer to the spectrum of the scattering signals from the saline solution and microbubbles solution at 2.8-MHz frequency, 30-cycles pulse length, and 124 kPa peak negative pressure, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

2.3. Data analysis

After the fresh microbubble suspension was injected into the container under a specific ambient overpressure, it was repeatedly excited three times by acoustic waves with fixed acoustic parameters. Thus, three groups of scattered signals were recorded. The above process was repeated three times and a total of nine groups of scattering signals were recorded. Finally, the subharmonic amplitudes from the nine groups were averaged to obtain the mean value and deviation under the specific acoustic parameters and ambient overpressure. The measured data points in the plot of subharmonic amplitude as a function of overpressure relationship were linearly fitted to determine the measurement sensitivity and linear correction coefficient. Finally, One-way ANOVA was used to determine whether the relationship between subharmonic response and ambient overpressure was statistically significant.

3. Results

3.1. Size distribution of the microbubbles

Under a continuous-phase flow rate of 40 µL/min and dispersed-phase pressure of 400 mbar, the microbubbles were stably and uniformly generated via the focusing microfluidic system, as shown in Fig. 4A. The microscopic images of the monodisperse microbubbles 24 h after harvesting are shown in Fig. 4B1, in which a uniform bubble size can be observed. Fig. 4B1 also shows the harvested monodisperse microbubble suspension located on the upper layer of the solution. The PDI at 2, 24, and 48 h after harvesting was 7.2 %, 4.7 %, and 9.1 %, respectively (Fig. 4C1), which is indicative of good microbubble stability. The monodisperse microbubbles 24 h after harvesting were used for the experiments, and the calculated mean radius was ∼2.45 µm. By contrast, the microscopic image of the polydisperse microbubbles in Fig. 4B2 exhibits a non-uniform size distribution. The mean radius and PDI of the polydisperse bubbles were ∼1.51 µm and 48.4 %, respectively (Fig. 4C2).

Fig. 4.

A. Monodisperse microbubbles were formed in the outlet passage of a flow-focusing microfluidic chip. B1, B2. The microscopic images and suspension solution of monodisperse 24 h after harvesting (B1) and polydisperse microbubbles 1 h after harvesting (B2). Bars = 20 µm. C1, C2. The size distribution of monodisperse microbubbles 2, 24 and 48 h after harvesting (C1) and polydisperse microbubbles 1 h after harvesting (C2).

3.2. Relationship between the subharmonic amplitude and frequency

Fig. 5 exhibits the relationships between the subharmonic amplitude of the monodisperse microbubbles and the excitation frequency (from 2 to 4 MHz with 0.2-MHz increment) at different PNPs (160, 250, and 350 kPa) and a fixed pulse length of 10 cycles. As shown in Fig. 5A1, the subharmonic amplitude exhibited a non-monotonic change with increasing excitation frequency. More specifically, the subharmonic amplitude gradually increased with excitation frequency from 2 to 2.6 MHz, reaching a maximum at ∼2.6 MHz (under 160 and 250 kPa) or ∼2.8 MHz (under 350 kPa), and then decreased as the excitation frequency was further increased from 3 to 4 MHz. The corresponding frequency spectra of the scattering signals in Fig. 5B1 show at PNP of 350 kPa, the subharmonic emission at 2.8 MHz was far larger than that at 2.4 and 3.4 MHz. These results show that for monodisperse microbubbles, there was a maximal subharmonic response dependent on the excitation frequency.

Fig. 5.

A1. At PNPs of 160, 250, and 350 kPa and a pulse length of 10 cycles, the relationship between subharmonic amplitude and the excitation frequency in monodisperse microbubbles at the overpressure of 0 kPa. A2. At PNPs of 100, 150, and 200 kPa and a pulse length of 30 cycles, the relationship between subharmonic amplitude and the excitation frequency in polydisperse microbubbles at the overpressure of 0 kPa. B1. At different frequencies, the frequency spectra of the scattering signals from monodisperse microbubbles at PNP of 350 kPa and a pulse length of 10 cycles. B2. At different frequencies, the frequency spectra of the scattering signals from polydisperse microbubbles at PNP of 200 kPa and a pulse length of 30 cycles.

For polydisperse microbubbles at PNPs of 100, 150, and 200 kPa and a pulse length of 30 cycles, there was a monotonic decrease in the subharmonic amplitude with excitation frequency, as shown in Fig. 5A2. Specifically, at 100 kPa, the subharmonic amplitude linearly decreased for excitation frequencies between 2 and 3 MHz, before slightly increasing and then plateauing at frequencies above 3 MHz. At PNPs of 150 and 200 kPa, the subharmonic amplitude linearly decreased with excitation frequency from 2 to 4 MHz. The corresponding frequency spectra in Fig. 5B2 shows that the subharmonic emissions decreased from −43.8 to −53.1 dB as the frequency was increased from 2.4 to 3.4 MHz. These results show that, within the frequency bandwidth of this study, there was no specific frequency that produced a well-defined maximum subharmonic amplitude for polydisperse microbubbles. Here note that 10-cycles and 30-cycles pulse length were used for experiments on monodisperse and polydisperse bubbles, respectively. In our preliminary experiment, when using 10-cycle pulse length, at some frequency points, the amplitude of subharmonic was very small or even not significant under the used PNPs for polydisperse microbubbles. However, using 30-cycle pulse length could ensure relatively large subharmonic amplitude for polydisperse microbubbles. This should be because the longer pulse increases the efficiency of nonlinear vibration of microbubbles, resulting in larger subharmonic amplitude [31].

3.3. Relationship between the subharmonic amplitude and PNP

After optimizing the excitation frequency as described above, we applied a 2.8-MHz frequency and 30-cycle pulse length to analyze the change of the subharmonic amplitude with PNP at atmosphere pressure (i.e., zero overpressure) for both monodisperse or polydisperse microbubbles. Fig. 6A1 and 6A2 show that with increasing PNP, there were three distinct regimes (occurrence, growth, and saturation) in the subharmonic response for both monodisperse and polydisperse microbubbles. Here we defined an increase of 3 dB relative to the control in the subharmonic amplitude as subharmonic occurrence. Before the occurrence regime, the subharmonic amplitude approached the noise level. Fig. 6B1 and 6B2 also show that no subharmonic emission occurred for monodisperse and polydisperse microbubbles at PNP of 65 kPa. The subharmonic amplitudes of both monodisperse and polydisperse microbubbles exhibited a steep rise after the PNP reached a certain threshold. However, the occurrence threshold (∼110 kPa) of the subharmonic signal from the monodisperse microbubbles was less than that (∼130 kPa) of the polydisperse microbubbles. In the growth regime, the subharmonic amplitude of the monodisperse and polydisperse microbubbles gradually increased with PNP in the range of 110–300 kPa and 130–210 kPa, respectively. A strong subharmonic signal emerged in the frequency spectra from monodisperse and polydisperse microbubbles at PNP of 143 kPa, as shown in Fig. 6B1 and 6B2. In the saturation regime, the subharmonic amplitude plateaued above ∼300 and ∼200 kPa for the monodisperse and polydisperse microbubbles, respectively. The representative frequency spectra in Fig. 6B1 and 6B2 exhibited strong subharmonic emission from the monodisperse microbubbles at PNP of 300 kPa and polydisperse microbubbles at PNP of 221 kPa.

Fig. 6.

A1 and A2. At frequency of 2.8 MHz and pulse length of 30 cycles, the relationship between subharmonic amplitude and PNP in monodisperse (A1) and polydisperse (A2) microbubbles at the overpressure of 0 kPa. B1 and B2. Corresponding frequency spectrum of the scattering signals from monodisperse (B1) and polydisperse (B2) microbubbles at different PNPs. Translucent shading indicates the deviation around the mean value.

3.4. Relationship between the subharmonic amplitude and overpressure for different pulse lengths

We next analyzed the relationship between subharmonic amplitude and overpressure at different pulse lengths (10, 30, and 50 cycles) and PNPs (100, 200, and 300 kPa for monodisperse microbubbles; 100, 150, and 200 kPa for polydisperse microbubbles) and a fixed frequency of 2.8 MHz.

For the monodisperse microbubbles, the lowest PNP used (100 kPa) was below the threshold pressure for subharmonic occurrence for all pulse lengths. The subharmonic amplitude relative to that at zero overpressure was nearly unchanged at overpressures up to 24 kPa with only limited fluctuation (<±1 dB) (Fig. 7A1). Table 1 shows that the sensitivities and correction coefficients of the relationship between the subharmonic amplitude and overpressure were low under these conditions. Thus, a 100-kPa PNP in the occurrence regime is not appropriate for measuring the overpressure for monodisperse microbubbles. For the polydisperse microbubbles, the subharmonic amplitude did not significantly vary with overpressure for a 10-cycle pulse length; however, a non-monotonic change was observed for pulse lengths of 30 and 50 cycles, as shown in Fig. 8A1. Specifically, the subharmonic amplitude first increased with increasing overpressure, and then approximately plateaued (under a 50-cycle pulse length) or gradually decreased (under a 30-cycle pulse length). The small sensitivities and correction coefficients of the relationship between subharmonic amplitude and overpressure in different overpressure ranges are shown in Table 2.

Fig. 7.

A1-A3. For monodisperse microbubbles, the relationship between the reduction of subharmonic amplitude and the ambient overpressure at PNPs of 100 kPa (A1), 200 kPa (A2), and 300 kPa (A3) and pulse length of 10, 30, and 50 cycles and frequency of 2.8 MHz. B. At the overpressure of 3, 12 and 21 kPa, the representative frequency spectra of the scattering signals of monodisperse microbubbles at 200-kPa PNP, 30-cycle pulse length and 2.8-MHz frequency. Translucent shading indicates the deviation around the mean value. Control refers to the saline solution group excited by 200-kPa PNP, 30-cycle pulse length and 2.8-MHz frequency.

Table 1.

At different excitation conditions, the sensitivity of subharmonic amplitude to ambient overpressure in monodisperse microbubbles.

PNP (kPa)	Pulse length (cycles)	Overpressure (kPa)	Sensitivity (dB/kPa)	R2	p
	10	0–24	−0.01	0.18	0.15
100	30	0–24	−0.01	0.40	0.02
	50	0–24	−0.01	0.26	0.0013
	10	0–24	−0.26	0.91	<0.001
200	30	0–24	−0.88	0.97	<0.001
	50	0–24	−1.18	0.97	<0.001
	10	0–24	−0.26	0.90	<0.001
300	30	0–24	−0.78	0.96	<0.001
	50	0–24	−0.89	0.90	<0.001

Fig. 8.

A1-A3. For polydisperse microbubbles, the relationship between the reduction of subharmonic amplitude and the ambient overpressure at PNPs of 100 kPa (A1), 150 kPa (A2), and 200 kPa (A3) and pulse length of 10, 30, and 50 cycles and frequency of 2.8 MHz. B. At the overpressure of 3, 12 and 21 kPa, the representative frequency spectra of the scattering signals of polydisperse microbubbles excited by 150-kPa PNP, 30-cycle pulse length and 2.8-MHz frequency. Translucent shading indicates the deviation around the mean value. Control refers to the saline solution group excited by 150-kPa PNP, 30-cycle pulse length and 2.8-MHz frequency.

Table 2.

At different excitation conditions, the sensitivity of subharmonic amplitude to ambient overpressure in polydisperse microbubbles.

PNP (kPa)	Pulse length (Cycles)	Overpressure (kPa)	Sensitivity (dB/kPa)	R2	p
100	10	0–12	0.03	0.57	0.84
		12–24	−0.01	0.50	0.92
	30	0–12	0.18	0.97	<0.001
		12–24	−0.11	0.87	<0.001
	50	0–12	0.34	0.9	<0.001
		12–24	0	0	0.0013
	10	0–24	−0.09	0.84	<0.001
150	30	0–24	−0.15	0.90	<0.001
	50	0–24	−0.18	0.88	<0.001
	10	0–24	−0.03	0.35	0.18
200	30	0–24	−0.03	0.21	<0.001
	50	0–24	−0.04	0.27	<0.001

For the monodisperse microbubbles at PNP (200 kPa) in the growth regime, the subharmonic amplitude decreased monotonically with ambient pressures from 0 to 24 kPa for all pulse lengths (p < 0.001), as shown in Fig. 7A2. The representative frequency spectra for a 30-cycle pulse length in Fig. 7B shows that the subharmonic emission at PNP of 200 kPa reduced from −48.1 dB to −63.2 dB when the overpressure was increased from 3 to 21 kPa. The correlation coefficients (R²) of the fitted lines for the relationship between subharmonic amplitude and overpressure in Fig. 7A2 were 0.91, 0.97, and 0.97 for pulse lengths of 10, 30, and 50 cycles, indicative of strong linearity. From the slopes of the fitted lines, the sensitivities under pulse lengths of 10, 30, and 50 cycles were − 0.26, −0.88, and − 1.18 dB/kPa, respectively, as listed in Table 1. These results also show that the sensitivity of the subharmonic amplitude to overpressure was dependent on the pulse length. For polydisperse microbubbles, a monotonic decrease was also observed in the subharmonic amplitude with increasing overpressure from 0 to 24 kPa under different pulse lengths (p < 0.001), as shown in Fig. 8A2. The frequency spectra in Fig. 8B shows the reduction in the subharmonic emission with overpressure at PNP of 200 kPa for a pulse length of 30 cycles. The sensitivity of the subharmonic amplitude to overpressure was − 0.09, −0.15, and − 0.18 dB/kPa under pulse lengths of 10, 30, and 50 cycles, respectively (Table 2). These sensitivities were far lower than those observed using the monodisperse microbubbles.

For the PNP in the saturation regime, there was a monotonic decrease of the subharmonic amplitude of monodisperse microbubbles with overpressure for all pulse lengths (p < 0.001) (Fig. 7A3). This trend was similar to that obtained for the PNP in the growth regime. All correlation coefficients (0.91, 0.97, and 0.97) of the fitted lines under different pulse lengths indicated strong linearity. The sensitivities of the subharmonic amplitude to overpressure significantly increased with increasing pulse length (−0.26, −0.78, and − 0.89 dB/kPa for pulse lengths of 10, 30, and 50 cycles, respectively), as listed in Table 1. However, for the polydisperse microbubbles, the subharmonic amplitude only slightly decreased with increasing overpressure from 0 to 24 kPa for all pulse lengths (Fig. 8A3). The sensitivities of the subharmonic amplitude to overpressure were lower under such situations, as shown in Table 2.

4. Discussion

4.1. Optimal frequency to achieve a maximal subharmonic response using monodisperse microbubbles

For the monodisperse microbubbles used in this study (mean radius of 2.45 µm and PDI of 4.7 %), the subharmonic amplitude changed non-monotonically with excitation frequency in the range of 2–4 MHz. This trend is consistent with theoretical calculations for a single free-bubble model [19], [48]. Because each bubble in a monodisperse population has approximately the same size, shell properties (e.g., viscoelastic properties), and resonance frequency, and produces a similar acoustic response under a fixed PNP and ambient pressure, monodisperse microbubbles could act as a uniform model to validate the theoretical results [3], [49]. Theoretically, the amplitude of the subharmonic response is dependent on f/f₀, and reaches a maximum value when the excitation frequency is 1.6–2.0 times the resonance frequency [19]. The theoretical resonance frequency of the monodisperse microbubbles used in this study is approximately 2.25 MHz. Thus, 3.6–4.5 MHz (f≈(1.6–2.0) × f₀ = (1.6–2.0) × 2.25 MHz) would be the theoretical demarcation point of the ascending and descending regimes in the relationship between the subharmonic amplitude and frequency (i.e., the point at which the maximal subharmonic response is attained). However, our results show that the maximal subharmonic amplitude occurred at ∼2.8 MHz. This discrepancy with the theoretical prediction can be explained as follows. Previous studies found that the resonance frequency shifts to smaller values with increasing PNP. The higher the used PNP is, the smaller the shifting amount is [46], [50]. The relationship between acoustic attenuation and excitation frequency at different PNPs in Fig. 9 is consistent with this conclusion. Fig. 9 shows that the resonance frequency shifted from ∼2.40 to ∼1.40 MHz when the PNP was increased from 3 to 120 kPa. Thus, 2.8 MHz (≈1.4×∼2 MHz) is consistent with the previous theoretical conclusion, and would be the optimal excitation frequency for achieving the maximal subharmonic response.

Fig. 9.

At PNPs of 3, 30, 60, 90, and 120 kPa and a fixed 12-cycle pulse length, the relationship between the excitation frequency (1.1–3 MHz with 0.1-MHz increment) and the attenuation in monodisperse microbubbles. Translucent shading indicates the deviation around the mean value.

For the polydisperse microbubbles (mean radius of 1.51 µm and PDI of 48.4 %), the subharmonic amplitude decreased monotonically with excitation frequency. Thus, we infer that the threshold of subharmonic emission increased with increasing frequency. This is consistent with a recent study that found that the curves in the occurrence, growth, and saturation regimes, and the threshold for a certain subharmonic response shift to higher PNPs at higher frequencies [18], [25]. We propose that this monotonic trend observed in this study is because the maximal subharmonic response might not have been triggered by the used frequency bandwidth (2–4 MHz). Dependent on the f/f₀, the subharmonic response may differ among microbubbles with different size in polydisperse population [19]. Thus, it is unlikely to observe a well-defined peak in the sensitivity of the subharmonic amplitude to frequency.

4.2. Optimal PNP and PL to achieve maximal sensitivity of the subharmonic amplitude to overpressure using monodisperse microbubbles

Although three distinct regimes (occurrence, growth, and saturation) were identified in the response of the subharmonic amplitude to increasing PNP for both monodisperse and polydisperse microbubbles, we also note that the threshold PNP for subharmonics occurrence was lower for monodisperse microbubbles compared to polydisperse microbubbles, and the subharmonic amplitude for monodisperse microbubbles saturated at a higher PNP than that for polydisperse microbubbles. The main reason is that the initial surface tension of the used monodisperse microbubbles may be lower than that of most of polydisperse microbubbles. Thus, under a given low PNP, the compression-only behavior of microbubbles dominates the subharmonic generation [18], [37], [38]. The lower the surface tension, the easier it is for monodisperse microbubbles to enter a buckling state. Therefore, lower threshold PNP is required for subharmonic generation of monodisperse microbubbles. Under a given high PNP, expansion-only behavior plays a decisive role in subharmonic generation. The lower the surface tension, the more difficult it is for monodisperse microbubbles to enter a rupture state[37], [52], resulting in higher PNP for subharmonic saturation of monodisperse microbubbles. However, the initial surface tension of monodisperse and polydisperse microbubbles remains unknown in this study. The above suppose needs to be further verified in the future studies. In addition, note that the stability of the microbubbles was characterized by measuring the scattering intensity of microbubbles at 60-kPa PNP, 30 cycles pulse length and 2.8-MHz frequency before experiments. No significant change was observed in the scattering intensity of the microbubble suspension with the time during 5 h (Data not shown). Hence, the microbubble concentration doesn’t significantly change during the experiments, and the variations in the observed acoustic behaviors aren’t related to the microbubble concentration.

Three PNPs (one in each of the three regimes) were selected to determine the value that gave the maximal sensitivity of the subharmonic response to overpressure. With the lowest PNP (which was below the threshold for eliciting a subharmonic response) for the monodisperse microbubbles, no significant change was found in the subharmonic amplitude with a change in overpressure. Previous studies determined that the relationship between the subharmonic amplitude and the overpressure depends on the initial surface tension at low PNP, and a low PNP may cause microbubbles to enter into a compression-only state [16], [37], [38]. A lower surface tension of the shell results in a larger subharmonic amplitude for low PNPs [18], [37], [38]. However, the initial surface tension of the monodisperse bubbles used in this study is not known. If the initial surface tension of monodisperse bubbles were sufficiently large (Please note that this larger surface tension may still be smaller than that of polydisperse bubbles), they may not shift from the elastic to buckling state even at high overpressure. Accordingly, the lowest PNP used in this study may not have been sufficient to trigger subharmonic emission at high overpressures. We also think that if the initial surface tension of the monodisperse bubbles could be minimized by modifying the shell materials, there would be a larger change in the subharmonic response with overpressure for the lower PNP.

For the polydisperse microbubbles, there was a non-monotonic change in the subharmonic amplitude with respect to overpressure. This is consistent with previous simulation and experimental results for the relationship between subharmonic amplitude and overpressure for SonoVue microbubbles. However, previous studies also reported some seemingly contradictory results, in which subharmonic amplitude exhibit less reduction or a large increase for the same increase in ambient overpressure [16], [51]. Because there may be some differences in lipid concentrations and arrangements on the shell among the bubbles in polydisperse population, the surface tension of microbubbles in polydisperse population may vary significantly[16], [52]. Thus, under the lowest PNP, bubbles with lower surface tension approaching the bucking state were easily triggered to generate subharmonic emission, in contrast with those with higher surface tension away from the bucking state. The aggregation of these different effects determines the subharmonic amplitude first increase with the increasing overpressure. When the overpressure was increased to a level at which most bubbles entered the bucking state, the subharmonic emission plateaued.

For the higher PNP (i.e., in the growth regime), for both monodisperse and polydisperse microbubbles, the subharmonic amplitude decreased monotonically with overpressure. These results are consistent with previous reports using commercial microbubbles [16], [18], [23], [25]. In contrast with the polydisperse bubble population, the degree of bubble-size reduction caused by overpressure was approximately same in the monodisperse population, the resulting decrease in f/f₀ might further reduce the subharmonic amplitude. Our results also showed that a far higher sensitivity (1.18 dB/kPa, R² = 0.97) of subharmonic amplitude to overpressure was achieved when using monodisperse bubbles than polydisperse bubbles (0.18 dB/kPa, R² = 0.88). Some reports attributed the reduction in the subharmonic amplitude with increasing overpressure to the decrease in the bubbles size caused by a greater extent of shell destruction [19], [35]. However, a recent study found that the sensitivity of the fundamental response was almost constant for all PNPs [18]. Our results also showed that the intensity of the scattering signal remained unchanged after each excitation from 30 consecutive pulses (data not shown). This suggests that microbubble destruction may not be the main reason for this finding. Furthermore, previous studies also found that under higher PNP, bubble behavior transitions from compression-only to expansion-only, and that the subharmonic amplitude from expansion-only bubbles decreases with increasing overpressure because expansion is inhibited at higher overpressure [37], [52]. Under the assumption of this expansion-only state at higher PNP, we also suppose that the descending trend in subharmonic amplitude to overpressure at higher PNP might be related to the initial surface tension. Specifically, at low overpressure, the surface tension is higher than at high overpressure and closer to that of the rupture state. Thus, under a given high PNP and low overpressure, microbubbles easily transition to the rupture state and exhibit expansion-only behavior, thus generating a stronger subharmonic response. This explanation needs to be validated in future studies. For the highest PNP (i.e., in the saturation regime), the subharmonic amplitude decreased monotonically with overpressure for the monodisperse microbubbles but changed only slightly for the polydisperse microbubbles. This finding is consistent with those of previous studies, which attributed it to gas dissolution, phospholipid shedding, or shell destruction [16].

4.3. Future possibilities for improving the sensitivity of subharmonic-aided pressure measurement

This study is a preliminarily investigation of the advantages of monodisperse microbubbles in SHAPE. We note that the shell materials and gas core of the monodisperse microbubbles used in this work are completely different from those of the commercial microbubbles that have been used in most previous studies. Therefore, the results cannot be directly compared.

To develop strategies for improving the sensitivity of the subharmonic response to changes in overpressure for clinical applications, it is essential to further reveal the mechanism underlying this response. Our results showed that monodisperse microbubbles could serve as a uniform and reliable model for clarifying this mechanism. During the fabrication of monodisperse microbubbles using a flow-focusing microfluidic chip, the lipid molecules are sheared by a high-speed disperse phase to form a phospholipid monolayer shell, which then wraps around the gas to form bubbles[46], [50]. Because the velocity and pressure of the continuous and dispersed phases in the flow-focusing microfluidic chip are constant, theoretically, the number of the lipid molecules wrapped in each bubble is the same, and the surface tension and viscoelastic characteristics are similar for each bubble[46], [50]. Previous studies revealed that the subharmonic response of phospholipid-coated microbubbles is determined by the initial surface tension, which is directly related to the types and relative proportions of phospholipids [16], [18]. By regulating the velocity and pressure of the continuous and dispersed phases, or the shell materials and their proportions, the shell properties of monodisperse bubbles can be specifically designed and controlled. That is to say, a desired initial surface tension and shell viscoelasticity could be achieved. Thus, under different acoustic parameters (i.e., PNP, pulse length, and frequency), the effect of initial tension surface or viscoelasticity on the relationship between the subharmonic amplitude and overpressure could be qualitatively analyzed. Such strategies could further improve the sensitivity of subharmonic-based pressure measurement in the future applications.

4.4. Some limitations of this study

Note that Tween 20 was added to eliminate the coalescence of microbubbles during the fabrication of monodisperse microbubbles. We think that Tween 20 should be incorporated into the shell of monodisperse microbubbles. Thus, the composition of the shell is slightly different between monodisperse microbubbles and polydisperse microbubbles. We also suppose that this difference may cause different viscoelastic properties of shell between monodisperse and polydisperse microbubbles, resulting in different acoustic responses between them, for example, the amplitude of subharmonic response. However, to our knowledge, almost no studies investigate the influence of Tween 20 on the viscoelastic properties of shell. Therefore, the role of Tween 20 on the stability and viscoelastic properties of shell needs to be further investigated in the future studies. In addition, as the mentioned above, the surface tension of the fabricated monodisperse microbubbles is unknown in this study. The mechanisms on the relationship between surface tension and subharmonic amplitude under the specific PNP can’t deeply revealed. If the surface tension of shell is precisely measured by some advanced methods, this will help determine the mechanisms of subharmonic occurrence and optimize the composition of the shell for achieving maximal sensitivity of subharmonic response. Finally, this study investigates the subharmonic response of monodisperse microbubbles in the static environment. However, in clinical applications, both the velocity of blood flow and the diameter of vessel in blood flow environments would be related to the subharmonic properties of monodisperse microbubbles. Thus, to develop the clinical applications of SHAPE using monodisperse microbubbles, it is necessary to investigate the relationship between acoustic parameters and the subharmonic response of monodisperse microbubbles in the blood flow environment in the next studies.

5. Conclusions

To achieve high sensitivity of subharmonic-based pressure measurement, we compared the subharmonic responses from monodisperse and polydisperse microbubbles. An optimal excitation frequency, which can elicit maximal subharmonic emission, was identified for the monodisperse microbubbles but not for the polydisperse microbubbles. For both monodisperse and polydisperse microbubbles, three regimes (occurrence, growth, and saturation) were identified in the subharmonic response to PNP. For the polydisperse microbubbles, the subharmonic amplitude changed either monotonically or non-monotonically depending on the PNP. However, there was only a monotonic decrease in the subharmonic amplitude with overpressure for monodisperse microbubbles. Moreover, the sensitivity of the subharmonic amplitude to overpressure was far higher in monodisperse microbubbles (1.18 dB/kPa, R² = 0.97) than in polydisperse microbubbles (0.18 dB/kPa, R² = 0.88). These results show that monodisperse microbubbles have a significant advantage over polydisperse microbubbles, and could greatly improve the sensitivity of subharmonic-based pressure measurement.

CRediT authorship contribution statement

Pengcheng Wang: Software, Investigation, Formal analysis. Chunjie Tan: Investigation. Xiang Ji: Methodology. Jingfeng Bai: Resources. Alfred C.H. Yu: Resources. Peng Qin: Writing – review & editing, Writing – original draft, Supervision, Funding acquisition, Conceptualization.

Declaration of competing interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Peng Qin reports financial support was provided by National Natural Science Foundation of China. Peng Qin reports financial support was provided by Shanghai Jiao Tong University. If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.