Contrast-enhanced Ultrasound Imaging Using Capacitive Micromachined Ultrasonic Transducers

Capacitive micromachined ultrasonic transducers (CMUTs) have a nonlinear relationship between the applied voltage and the emitted signal, which is detrimental to conventional contrast enhanced ultrasound (CEUS) techniques. Instead, a three-pulse amplitude modulation (AM) sequence has been proposed, which is not adversely aﬀected by the emitted harmonics. In this paper, this is shown theoretically, and the performance of the sequence is veriﬁed using a 4 . 8 MHz linear CMUT array, and a comparable lead zirconate titanate (PZT) array, across 6 V to 60 V applied AC voltage. CEUS images of the contrast agent SonoVue ﬂowing through a 3D printed hydrogel phantom showed an average enhancement in contrast-to-tissue ratio (CTR) between B-mode and CEUS images of 49 . 9 dB and 37 . 4 dB for the PZT array and CMUT, respectively. Furthermore, hydrophone recordings of the emitted signals showed that the nonlinear emissions from the CMUT did not signiﬁcantly degrade the cancellation in the compounded AM signal, leaving an average of 2 % of the emitted power between


Introduction
Recently, capacitive micromachined ultrasonic transducers (CMUTs) have become available as an alternative to the more conventional piezoelectric transducers [1,2]. CMUTs offer sensitivity features that are particularly suitable for microbubble contrast-enhancement imaging, with low transmit pressure, yet high receive sensitivity [1]. Contrast enhanced ultrasound (CEUS) imaging with microbubble contrast agents is used clinically to study the blood's wash-in and wash-out time in organs [3], to quantify the blood-flow velocity using time-intensity curves [4], and, most recently, to image blood-flow through capillaries beyond the diffraction limit, through super-resolution ultrasound imaging (SRI) [5,6]. CEUS imaging with a CMUT is a combination of two nonlinear processes; the spectral content of the emission from a CMUT is nonlinearly related to its excitation voltage [7], and the spectral content of the scattering of the excitation by the microbubble contrast agents is nonlinearly related to the acoustic pressure [8]. This combination poses some challenges to the conventional CEUS techniques, and the viability of CEUS imaging using CMUTs has been questioned [9]. CMUTs emit ultrasound by applying an AC voltage potential across thin plates suspended on top of nanometer to micrometer sized cavities. The technology offers great design flexibility [10], making it possible to produce transducers with several advantageous features for CEUS imaging. Firstly, the transducer can achieve wide bandwidth, resulting in high axial resolu-* Correspondence: shoy@dtu.dk 1 Center for Fast Ultrasound Imaging, Department of Health Technology, Technical University of Denmark, Kgs. Lyngby, Denmark Full list of author information is available at the end of the article tion [10]. For SRI, where separation of the microbubbles within each image frame is essential, this could enable SRI with a higher number of resolved microbubbles within each frame, and thus a lower acquisition time. The wide bandwidth would also facilitate detection of higher harmonics scattered by the microbubbles, often utilized in the pulse inversion (PI) technique. Secondly, CMUTs can produce a low emitted pressure, suitable for exciting microbubbles without destroying them [11], whilst maintaining a high receive sensitivity [12]. However, the drawback of CMUT technology is that the electrostatic force driving the excitation causes the emitted signal to contain considerable harmonic components [13]. The amount of harmonic content produced by the transducer is dependent on the ratio of the applied AC voltage to the applied DC voltage [7], which renders the transducer incapable of removing of tissue-generated signals using conventional CEUS techniques.
CEUS imaging achieves high contrast by removing the signal scattered by the tissue from that scattered by the microbubbles. The most common techniques used to remove the tissue signal are PI, amplitude modulation (AM), and singular value decomposition (SVD). The first two utilize the fact that when a bubble is insonified, it will scatter the sound nonlinearly [14]. SVD is a spatiotemporal filtering technique, which utilizes the bubble's high scattered intensity and temporally transient behavior to separate the bubbles from the tissue [5]. These techniques are thus capable of removing the linearly scattered signals caused by the tissue surrounding the contrast agents. PI combines the responses from two excitations with opposite signs [15]. Conventionally, AM is achieved by combining the response from two excitations, one with half the amplitude of the next [16]. Both the difference in amplitude and difference in polarity will cause the CMUT to emit harmonics that differ between the emissions, which conventional AM and PI will not be able to remove.
Using such sequences with CMUTs will therefore result in poor contrast in the CEUS images [17,18]. Several attempts have been made to overcome this issue by altering the frequency content of the emitted pulse [19,20], but such approaches are not necessarily compatible with the bipolar pulsers often found in commercial scanners. Moreover, these methods rely on all elements in the probe behaving identically, which is often not the case. However, Fouan and Bouakaz [18] have proposed that CEUS imaging can be obtained

Emission from a CMUT
The propagation of sound waves from a CMUT array is induced by applying an AC voltage, V AC , across the CMUT cells. This causes a time-varying deflection, driven by electrostatic force on the cell plates. [22]. The acoustic pressure radiated from a circular cell plate is proportional to the resulting displacement of the plate [23], and the relationship between the applied voltage and the displacement is governed by a nonlinear differential equation [24]. Analytic evaluation of this equation is not straight forward, but several authors have studied the relationship numerically [22,24,25].
It has been shown that the emitted sound pressure from CMUTs contain harmonics to the applied excitation frequency [24,26]. Thus, when the applied V AC is a simple sinusoid at some excitation frequency, ω 0 , the resulting emitted pressure, p(t), can be expressed 22 23  as p(t) = α 0 sin (ω 0 t) Here, t is time, α is some amplitude, h is a harmonic index, φ is a phase difference. Since α h can be any real number, including zero, this notation is applicable even when only certain harmonics are present in the emitted signal. A compact form of (1) is given in (2) CMUTs are therefore said to be inherently nonlinear.
However, it will here be shown that the nature of the harmonics does not affect the effectiveness of the threepulse AM sequence.

The amplitude modulation technique
When the microbubbles are insonified with an ultrasound pulse, the reflections contain harmonics of the incident frequency. Eckersley et al. [11] show that the nonlinear reflections can be modeled as a polynomial expansion of the incident wave, as Here, y(t) is the reflected signal, p i (t) is the incident pressure wave on the bubble, and a i are reflection co- where y AM is the remaining three-pulse amplitude modulation signal, and y A , y B , y C are the scattered signals caused by the three emissions. If instead, only 2 emissions are used the combination is made as

Amplitude modulation with a CMUT
By assuming that no distortion of the signal occurs between the emission and the bubble position, we can apply (6) to the tree emissions given in (3) -(5) before applying (7). By expressing the pressure waves in their compact form and limiting the polynomial expansion to third order for simplicity, this gives Then, by expanding to the long form of (3) -(5), setting α 0 = 1, working through the algebra (shown in more detail in the appendix) gives Two important observations can be made about (10).
Firstly, it reveals a subtle, but, essential property of AM imaging; the remaining signal lacks any linearly scattered components, yet, the last term of (10) con- This shows that when the emitted signals are reflected only linearly, the AM compounding cancels all of these terms. Some emitted harmonics remain in the y AM sig-nal, but, these terms all carry the reflection coefficients a 2 or a 3 , meaning that the signals have been nonlinearly scattered by the microbubble. Notably, the fact that these emitted harmonics remain in the y AM signal has not impaired the efficiency of the AM theory.
Moreover, although the amplitude and phase of the emitted harmonics will be affected by the amplitude of V AC , this does not affect the cancellation of linearly scattered signals. Because of this, when using the AM modality to image in vivo with a CMUT, it is possible to filter out linear scattering from tissue whilst attaining reflections from the microbubbles at the emitted frequency. Thus, it is shown theoretically that CEUS imaging with a CMUT using the three-pulse AM sequence is achievable.

Methods
To verify the outcome of the theoretical evaluation shown in Section 2, the ability of a linear CMUT array to cancel received linear components while preserving nonlinearly scattered signal was assessed using three measurement set-ups. Firstly, an experimental set-up was designed to quantify CTR. Section 3.1 outlines the design of the set-up. Contrast enhanced AM images were collected using a synthetic aperture imaging sequence on a CMUT and a PZT probe, further described in Section 3.2. Subsequently, the CTR was calculated for all the collected images, as detailed in Section 3.3. Secondly, Section 3.4 describes how the emitted signal from the transducers were recorded using a hydrophone, and used to determine the peaknegative-pressure (PNP) and the power annihilation ratio. Lastly, Section 3.5 describes how the signal-tonoise ratio of the two probes were evaluated to fairly compare the CMUT's and PZT arrays's performance.

CEUS imaging set-up
The experimental set-up used to quantify CTR consisted of a microflow phantom and a block of tissue-

Image acquisition
The phantom and tissue-mimicking material was imaged using a linear CMUT [30] and, as a reference, a commercial linear PZT array of equivalent design dimensions, using a Verasonics research scanner (Verasonics Vantage 256). The specifications of the probes are given in Table 1. The set-up was imaged using a synthetic aperture sequence [31] with low intensity diverging wave propagation. A summary of the sequence parameters are given in Table 2. The transducers emit-    consisted of emissions from n = 13 virtual sources placed 16 mm behind the transducer surface. The lateral positions of the virtual sources were given by The sequence was used to quantify how the CTR in the resulting images vary with the applied AC voltage.
The lowest V AC was 6 V, at which the imaging system approaches its noise floor. For the CMUT, V AC was then increased in steps of 10 V until the maximum tolerable AC voltage of the probe, as given in Table 1, was reached. Additionally, a constant DC voltage of 190 V was applied to the CMUT, as specified in [30].
For the PZT array, the same voltage range was used, from 6 V to the probe's maximum tolerable voltage.
But, the step size was reduced to 3 V between 6 V and

Calculation of CTR
The collected data from both probes were matched filtered and beamformed using delay-and-sum beamforming. CEUS images were composed using both (7) and (8). The two-pulse AM sequence, which was also studied by the authors in [32], is included for comparison with the three-pulse AM proposed by Fouan and Bouakaz [18], to study how an additional emission in the minor sequence affects the image quality. In addition, the data from every full amplitude emission in the minor sequence was used to compose B-mode images, for comparison. For each composed image, the CTR was calculated as where P B is the average power of the signal scattered by the bubbles and P T M M is the average power scattered by the tissue-mimicking material. The average power was calculated as

Hydrophone recordings
The derivation of (10) assumes that the same signal corresponding to each virtual source, given by (11).
The hydrophone recorded the minor sequence using all the applied AC voltages, from each virtual source.
Then, the sequence's ability to cancel linear terms was quantified by defining an annihilated power ratio as Here, the numerator contains the remaining AM signal subtracted from the full emitted signal and thus gives the power of the annihilated signal. For each xposition and applied V AC , the recordings of the minor sequence were used to compose the compounded emitted AM signal, p AM , according to (7), and the annihilated power ratio. This evaluation will be affected by nonlinear propagation in the water. The evaluation was therefore performed using both the PZT array and CMUT for comparison, to distinguish effects caused by nonlinear propagation from the effects caused by nonlinear excitation.
In addition, the measured hydrophone signals were used to quantify the PNP caused by each applied V AC for both transducers. The minimum of the recording of the full emission was found from the recording beneath each virtual source and averaged to give the PNP.

Quantifying signal-to-noise ratio
Because the imaging performance of a CMUT and a PZT transducer are to be compared, it is prevalent to also quantify and compare the signal-to-noise ra- where y is the image line and y represents the average of the image line across the 10 acquisitions. Although the theory of the three-pulse AM sequence, presented in Section 2, predicts that CTR should not degrade as the amount nonlinearity in the emitted signal rises with the applied AC voltage, it is expected that the CTR varies with AC voltage due to the nature of the microbubble contrast agents. As the applied voltage increases, so does the PNP of the emitted signal, which affects both the power and the spectral content of the scattered signal from the microbubbles [33]. Therefore, to fully understand the observed variation in CTR seen in Fig. 4 The compounded AM signals were computed from the collected hydrophone recordings, using (7), and the annihilated power ratio was calculated as in (14). Finally, the SNR of the image acquisition using the two probes at varying AC voltages were calculated according to (15). The measured SNR is given in Table 3.

Results
Generally, it is seen that the SNR of the CMUT probe  is lower than the PZT transducer, with a mean difference of 16 dB across 6 V to 56 V applied AC voltage.
Further discussion of the data will be given in Section 5.

Discussion
As predicted by the theory laid out in Section 2,    The CTR of the CEUS images follows the expected trend; it increases initially, before starting to decrease at higher voltages. This progression is caused by the back-scattering properties of microbubbles. At low pressures, the nonlinear component of the backscattering from microbubbles is proportional to the incident acoustic pressure [33,34], and Emmer et al. [35] showed that SonoVue exhibits a low pressure threshold, under which the bubbles do not scatter nonlinearly. On the other hand, at high pressures, the CTR is expected to drop because the microbubbles start   CEUS Contrast enhanced ultrasound.
ROI Region-of-interest.
SNR Signal-to-noise ratio.
SRI Super-resolution ultrasound imaging.
SVD singular value decomposition.
VS Virtual source.

Ethics approval and consent to participate
Not applicable.

Consent for publication
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Availability of data and material
The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request.

Competing interests
The authors declare that they have no competing interests.

Acknowledgments
Not applicable.

Appendix
The tree emissions given in (3) -(5) can be written on the compact form seen in (2) as p B (t) = 0.5 p L + 0.5 p C (t) = 0.5 p L + 0.5 ∞ h=2 p H .