Nonlinear X-Wave Ultrasound Imaging of Acoustic Biomolecules

The basic physics of sound waves enables ultrasound to visualize biological tissues with high spatial and temporal resolution. Recently, this capability was enhanced with the development of acoustic biomolecules—proteins with physical properties enabling them to scatter sound. The expression of these unique air-filled proteins, known as gas vesicles (GVs), in cells allows ultrasound to image cellular functions such as gene expression in vivo, providing ultrasound with its analog of optical fluorescent proteins. Acoustical methods for the in vivo detection of GVs are now required to maximize the impact of this technology in biology and medicine. We previously engineered GVs exhibiting a nonlinear scattering behavior in response to acoustic pressures above 300 kPa and showed that amplitude-modulated (AM) ultrasound pulse sequences that excite both the linear and nonlinear GV scattering regimes were highly effective at distinguishing GVs from linear scatterers like soft biological tissues. Unfortunately, the in vivo specificity of AM ultrasound imaging is systematically compromised by the nonlinearity added by the GVs to propagating waves, resulting in strong image artifacts from linear scatterers downstream of GV inclusions. To address this issue, we present an imaging paradigm, cross-amplitude modulation (xAM), which relies on cross-propagating plane-wave transmissions of finite aperture X waves to achieve quasi-artifact-free in vivo imaging of GVs. The xAM method derives from counterpropagating wave interaction theory, which predicts that, in media exhibiting quadratic elastic nonlinearity like biological tissue, the nonlinear interaction of counterpropagating acoustic waves is inefficient. By transmitting cross-propagating plane waves, we minimize cumulative nonlinear interaction effects due to collinear wave propagation while generating a transient wave-amplitude modulation at the two plane waves’ intersection. In both simulations and experiments, we show that residual xAM nonlinearity due to wave propagation decreases as the plane-wave cross-propagation angle increases. We demonstrate in tissue-mimicking phantoms that imaging artifacts distal to GV inclusions decrease as the plane-wave cross-propagation angle opens, nearing complete extinction at angles above 16.5 degrees. Finally, we demonstrate that xAM enables highly specific in vivo imaging of GVs located in the gastrointestinal tract, a target of prime interest for future cellular imaging. These results advance the physical facet of the emerging field of biomolecular ultrasound and are also relevant to synthetic ultrasound contrast agents.

Popular Summary

Ultrasound is a widespread technique in biomedical imaging, and recently developed biomolecular contrast agents are extending its ability to visualize the function of specific cells deep inside the body. To maximize the impact of these new contrast agents, methods are needed to distinguish their signals from those of background tissues. Here, we introduce an imaging method based on the transmission of cross-propagating ultrasound plane waves that retrieves nonlinear echoes arising from biomolecular contrast agents and enables their detection in the body.

A standard ultrasound pulse sequence consists of transmitting low-amplitude wave pulses followed by high-amplitude ones to elicit the linear and nonlinear responses of the contrast agent. When received, the lower-amplitude echoes are rescaled and subtracted from the high-amplitude ones, and the residual nonlinearity reveals the location of the contrast agents. Unfortunately, the high-amplitude pulses are often distorted by the contrast agent medium, which introduces artifacts in the ultrasound image.

To overcome this limitation, we transmit simultaneously two plane waves that form an angle with respect to the imaging array and propagate in an X shape. Along the line where the waves intersect, the wave amplitude gets modulated by a factor of 2. Because the waves travel in different directions, transient segments of each wave front contribute to the modulation, which prevents the buildup of pulse-shape distortions.

This approach produces artifact-free ultrasound images of biomolecular contrast agents with easy-to-generate angles of $15°$ or higher, facilitating the development of ultrasound as a technique that can visualize not only anatomy but also cellular functions such as gene expression.

Figure 1

Sketch of the two nonlinear phenomena that take place while imaging a biological medium containing acoustic biomolecules. (a) Propagation history of a single plane wave: Nonlinear frequency components accumulate with depth as the wave propagates through tissue before being attenuated. This phenomenon, amplified during the near-collinear interaction of two wavefronts, leads to nonlinear propagation artifacts distal to GV inclusions. (b) Nonlinear scattering behavior of GVs insonified above their buckling pressure, enabling their detection with an AM code.

Figure 2

Simulation of the xAM sequence for $\theta =18°$ in a homogeneous and isotropic water medium. (a) Half-aperture plane-wave transmission at an 18° angle with respect to the transducer array. (b) Axisymmetric half-aperture plane-wave transmission at an 18° angle with the other half of the array. (c) Cross-propagating plane-wave transmission at an 18° angle using both half-apertures. (d) Simulated waveforms at the bisector intersection for $z=3.6\mathrm{mm}$. The cross-propagating plane-wave peak positive pressure is 747 kPa (blue curve), while the residue peak positive pressure (green curve) is 0.13 kPa, or 0.02% of the cross-propagating plane-wave peak positive pressure.

Figure 3

Simulation of nonlinear plane-wave interaction as a function of the cross-propagation angle $\theta$. (a) Peak positive pressure of the xAM residual as a function of depth for five cross-propagation angles. (b) Peak positive pressure of the xAM residual as a function of $\theta$ at depths $z$ equal to 4 mm and 6 mm.

Figure 4

xAM images of the cross section of a subwavelength nickel wire as a function of the cross-propagation angle $\theta$. (a) Images reconstructed from the three component transmissions of the pAM code and xAM code at angles ranging from 1.5° to 21°. The wire is positioned at a depth of 4 mm. Each image depth ranges from 3.0 mm to 4.5 mm and each width from $-1.5\mathrm{mm}$ to 1.5 mm. Scale bar: 1 mm. (b) Peak AM residual signal as a function of the xAM sequence angle $\theta$. The xAM signals are labeled in orange; the pAM signal is labeled with a gray square symbol. Values in dB represent the peak value of the residual signal relative to the peak value of the noise.

Figure 5

In vitro pAM and xAM images of a hGV inclusion in a tissue-mimicking phantom. (a) Left panel: Schematic of the phantom configuration. The linearly scattering tissue-mimicking medium is shown in gray, the hGV inclusion in blue, and the anechoic agar-filled inclusion in black. ROIs are shown for contrast (C), tissue (T), and artifact (A) quantification. Right panel: Set of pAM and xAM images of a representative well positioned at $z=4\mathrm{mm}$. Separate images spanning depths of 3 mm to 9 mm are concatenated. Scale bar: 1 mm. White dotted line: $Z_X$ at $\theta =21°$. (b) CTR as a function of $\theta$. (c) ATR as a function of $\theta$. (d) CAR as a function of $\theta$. $N=6$. Error bars: standard error of the mean (SEM).

Figure 6

In vivo pAM and xAM imaging of acoustic biomolecules. (a) Schematic of the experiment. A concentric mixture of nonlinearly scattering hGVs and linearly scattering wtGVs is injected in a mouse gastrointestinal (GI) tract and imaged with pAM and xAM. (b) pBMode image, $\mathrm{focus}=4\mathrm{mm}$, $f-\mathrm{number}=2.0$. (c) pAM image, arrows point to the artifact (A). (d) xBMode, $\theta =19.5°$. (e) xAM image. The pAM and xAM dynamic ranges are displayed relative to their respective BMode ranges. All image depths range from $z=2\mathrm{mm}$ to $Z_X=9.2\mathrm{mm}$. (f) Comparison of xAM and pAM in terms of mean CTR and CAR. $N=3$. ROIs for CTR and CAR measurements are reported in Fig. 8, Appendix pp1.

Figure 7

Linear array aperture geometry and directivity. (a) Ultrasound imaging linear array configuration. Here, $\theta$ is the cross-propagation angle, $p$ the pitch of the linear transducer array, $x_1$ the first element of the active aperture (blue elements), $x_b$ the element along the aperture, and $x_n$ an arbitrary element along the array. Note that $d_{tx}$ is the distance from the planar wavefront to a point along the bisector, and $d_{rx}$ is the return distance to the array. Silent elements are labeled in orange. (b) Directivity of an individual element of the linear transducer array ($p=0.1\mathrm{mm}$, $f=15.6\mathrm{MHz}$). The red dotted line indicates the $-3\mathrm{dB}$ acoustic pressure level.

Figure 8

Tissue (T), contrast (C), and artifact (A) regions of interest used for the ratios displayed in Fig. 6.

Figure 9

Analytical and simulated cross-propagating plane-wave intersection velocity as a function of $\theta$.

Figure 10

Comparison of coherently compounded and single-acquisition xAM images of the hGV inclusion in the tissue-mimicking phantom reported in Fig. 5. (a) A set of xAM images from the experiment depicted in Fig. 5. (b) The same images with coherent compounding applied to successive sets of four acquisitions. (c) Contrast-to-tissue ratio of single-acquisition xAM compared with coherently compounded data as a function of angle. (d) Artifact-to-tissue ratio. (e) Contrast-to-artifact ratio. Here, $n=6$. Error bars are not shown for ease of comparison.