Nonlinear X-wave ultrasound imaging of acoustic biomolecules

Abstract

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 both excite 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 counter-propagating wave interaction theory which predicts that, in media exhibiting quadratic elastic nonlinearity like biological tissue, the nonlinear interaction of counter-propagating 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. We show in both simulations and experiments 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.

Keywords: Acoustics; Biological Physics; Nonlinear Dynamics.

FIG. 7.

Linear array aperture geometry and directivity. (a) Ultrasound imaging linear array configuration. θ is the cross-propagation angle, p the pitch of the linear transducer array, x₁ 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. 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 labelled in orange. (b) Directivity of an individual element of the linear transducer array (p = 0.1 mm, f = 15.6 MHz). The red dotted line indicates the – 3 dB acoustic pressure level.

FIG. 8.

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

FIG. S1.

Analytical and simulated cross-propagating plane-waves intersection velocity as a function of θ.

FIG. S2.

Comparison of coherently compounded and to single-acquisition xAM images the in vitro data at 4 mm. (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. n = 6. Error bars not shown for ease of comparison.

FIG. 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 amplitude modulation (AM) code.

FIG. 2.

Simulation of the xAM sequence for θ = 18° in a homogeneous/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-waves transmission at an 18° angle using both half-apertures. (d) Simulated waveforms at the bisector intersection for z = 3.6 mm. The cross-propagating plane-waves peak positive pressure was 747 kPa (blue curve), while the residue peak positive pressure (green curve) was 0.13 kPa, or 0.02% of the cross-propagating plane-waves peak positive pressure.

FIG. 3.

Simulation of nonlinear plane-wave interaction as a function of the cross-propagation angle θ. (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 θ at depths z equals 4 mm and 6 mm.

FIG. 4.

xAM images of the cross section of a subwavelength nickel wire as a function of the cross-propagation angle θ. (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 was positioned at a depth of 4 mm. Each image depth ranges from 3.0 mm to 4.5 mm and width from −1.5 mm to 1.5 mm. Scale bar: 1 mm. (b) Peak AM residual signal as a function of the xAM sequence angle θ. xAM signals are labelled in orange, the pAM signal is labelled with a gray square symbol. Values in dB represent the peak value of the residual signal relative to the peak value of the noise.

FIG. 5.

In vitro pAM and xAM images of an hGV inclusion in a tissue-mimicking phantom. (a) Left, schematic of the phantom configuration: linearly scattering tissue-mimicking medium in gray, hGV inclusion in blue, anechoic agar-filled inclusion in black, and ROIs for contrast (C), tissue (T) and artifact (A) quantification. Right, set of pAM and xAM images of a representative well positioned at z = 4 mm. Separate images spanning depths of 3 mm to 9 mm are concatenated. Scale bar: 1 mm. White dotted line: Z_X at θ = 21°. (b) Contrast-to-tissue ratio (CTR) as a function of θ. (c) Artifact-to-tissue ratio (ATR) as a function of θ. (d) Contrast-to-artifact ratio (CAR) as a function of θ. N = 6. Error bars: SEM.

FIG. 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 was injected in a mouse gastrointestinal (GI) tract and imaged with pAM and xAM. (b) pBMode image, focus = 4 mm, f-number = 2.0. (c) pAM image, arrows point at the artifact (A). (d) xBMode, θ = 19.5° (e) xAM image. pAM and xAM dynamic ranges are displayed relative to their respective BMode ranges. All images depth ranged from z = 2 mm to Z_X = 9.2 mm. (f) Comparison of xAM and pAM in terms of mean contrast-to-tissue ratios (CTR) and contrast-to-artifact ratios (CAR). N = 3. ROIs for CTR and CAR measurements are reported in Fig. 8, Appendix A.