Cubic nonlinearity and surface shock waves in soft tissue-like materials.

The cubic nonlinearity of shear wave propagation plays a significant role in brain injury biomechanics. However, soft materials, like the brain, also support the propagation of surface waves, which produce a combination of longitudinal and transverse deformation. The order of the nonlinearity of surface waves in soft materials is still unknown. Here, we directly observe nonlinear Scholte waves propagating in an interface formed by an incompressible gelatin tissue-mimicking phantom and a water layer using ultrasound imaging operated as fast as 16667 frames per second. A two-dimensional correlation-based tracking algorithm was utilized to extract movies of the movement produced by the surface wave. Our results show that the initially nearly monochromatic wave becomes progressively distorted with the propagation due to nonlinearity. The distortion of the wave and its frequency spectrum indicate a high content of odd harmonics when compared with even harmonics. Additionally, by fitting our experimental data to a minimalist one-dimensional model based on the wave speed variation as a function of the perturbation amplitude, we found a cubic nonlinear parameter 46 times larger than the quadratic nonlinear parameter. Overall, the wave distortion, the harmonic development, and the dependence of the wave speed with the amplitude prove that cubic nonlinearity is essential to modeling nonlinear Scholte wave propagation.

Modeling Ultrasound Propagation in the Moving Brain: Applications to Shear Shock Waves and Traumatic Brain Injury.

Traumatic brain injury (TBI) studies on the living human brain are experimentally infeasible due to ethical reasons and the elastic properties of the brain degrade rapidly postmortem. We present a simulation approach that models ultrasound propagation in the human brain, while it is moving due to the complex shear shock wave deformation from a traumatic impact. Finite difference simulations can model ultrasound propagation in complex media such as human tissue. Recently, we have shown that the fullwave finite difference approach can also be used to represent displacements that are much smaller than the grid size, such as the motion encountered in shear wave propagation from ultrasound elastography. However, this subresolution displacement model, called impedance flow, was only implemented and validated for acoustical media composed of randomly distributed scatterers. Herein, we propose a generalization of the impedance flow method that describes the continuous subresolution motion of structured acoustical maps, and in particular of acoustical maps of the human brain. It is shown that the average error in simulating subresolution displacements using impedance flow is small when compared to the acoustical wavelength ( λ /1702). The method is then applied to acoustical maps of the human brain with a motion that is imposed by the propagation of a shear shock wave. This motion is determined numerically with a custom piecewise parabolic method that is calibrated to ex vivo observations of shear shocks in the porcine brain. Then the fullwave simulation tool is used to model transmit-receive imaging sequences based on an L7-4 imaging transducer. The simulated radio frequency data are beamformed using a conventional delay-and-sum method and a normalized cross-correlation method designed for shock wave tracking is used to determine the tissue motion. This overall process is an in silico reproduction of the experiments that were previously performed to observe shear shock waves in fresh porcine brain. It is shown that the proposed generalized impedance flow method accurately captures the shear wave motion in terms of the wave profile, shock front characteristics, odd harmonic spectrum generation, and acceleration at the shear shock front. We expect that this approach will lead to improvements in image sequence design that takes into account the aberration and multiple reflections from the brain and in the design of tracking algorithms that can more accurately capture the complex brain motion that occurs during a traumatic impact. These methods of modeling ultrasound propagation in moving media can also be applied to other displacements, such as those generated by shear wave elastography or blood flow.

Superharmonic Ultrasound for Motion-Independent Localization Microscopy: Applications to Microvascular Imaging From Low to High Flow Rates.

Recent advances in high frame rate biomedical ultrasound have led to the development of ultrasound localization microscopy (ULM), a method of imaging microbubble (MB) contrast agents beyond the diffraction limit of conventional coherent imaging techniques. By localizing and tracking the positions of thousands of individual MBs, ultrahigh resolution vascular maps are generated which can be further analyzed to study disease. Isolating bubble echoes from tissue signal is a key requirement for super-resolution imaging which relies on the spatiotemporal separability and localization of the bubble signals. To date, this has been accomplished either during acquisition using contrast imaging sequences or post-beamforming by applying a spatiotemporal filter to the B-mode images. Superharmonic imaging (SHI) is another contrast imaging method that separates bubbles from tissue based on their strongly nonlinear acoustic properties. This approach is highly sensitive, and, unlike spatiotemporal filters, it does not require decorrelation of contrast agent signals. Since this superharmonic method does not rely on bubble velocity, it can detect completely stationary and moving bubbles alike. In this work, we apply SHI to ULM and demonstrate an average improvement in SNR of 10.3-dB in vitro when compared with the standard singular value decomposition filter approach and an increase in SNR at low flow ( [Formula: see text]/frame) from 5 to 16.5 dB. Additionally, we apply this method to imaging a rodent kidney in vivo and measure vessels as small as [Formula: see text] in diameter after motion correction.

Quantitative sub-resolution blood velocity estimation using ultrasound localization microscopy ex-vivo and in-vivo.

Super-resolution ultrasound imaging relies on the sub-wavelength localization of microbubble contrast agents. By tracking individual microbubbles, the velocity and flow within microvessels can be estimated. It has been shown that the average flow velocity, within a microvessel ranging from tens to hundreds of microns in diameter, can be measured. However, a 2D super-resolution image can only localize bubbles with sub-wavelength resolution in the imaging plane whereas the resolution in the elevation plane is limited by conventional beamwidth physics. Since ultrasound imaging integrates echoes over the elevation dimension, velocity estimates at a single location in the imaging plane include information throughout the imaging slice thickness. This slice thickness is typically a few orders or magnitude larger than the super-resolution limit. It is shown here that in order to estimate the velocity, a spatial integration over the elevation direction must be considered. This operation yields a multiplicative correction factor that compensates for the elevation integration. A correlation-based velocity estimation technique is then presented. Calibrated microtube phantom experiments are used to validate the proposed velocity estimation method and the proposed elevation integration correction factor. It is shown that velocity measurements are in excellent agreement with theoretical predictions within the considered range of flow rates (10 to 90 µl/min) in a microtube with a diameter of 200 µm. Then, the proposed technique is applied to two in-vivo mouse tail experiments imaged with a low frequency human clinical transducer (ATL L7-4) with human clinical concentrations of microbubbles. In the first experiment, a vein was visible with a diameter of 140 µm and a peak flow velocity of 0.8 mm s-1. In the second experiment, a vein was observed in the super-resolved image with a diameter of 120 µm and with maximum local velocity of ≈4.4 mm s-1. It is shown that the parabolic flow profiles within these micro-vessels are resolvable.

Super-Resolution Imaging Through the Human Skull.

High-resolution transcranial ultrasound imaging in humans has been a persistent challenge for ultrasound due to the imaging degradation effects from aberration and reverberation. These mechanisms depend strongly on skull morphology and have high variability across individuals. Here, we demonstrate the feasibility of human transcranial super-resolution imaging using a geometrical focusing approach to efficiently concentrate energy at the region of interest, and a phase correction focusing approach that takes the skull morphology into account. It is shown that using the proposed focused super-resolution method, we can image a 208- [Formula: see text] microtube behind a human skull phantom in both an out-of-plane and an in-plane configuration. Individual phase correction profiles for the temporal region of the human skull were calculated and subsequently applied to transmit-receive a custom focused super-resolution imaging sequence through a human skull phantom, targeting the 208- [Formula: see text] diameter microtube at 68.5 mm in depth and at 2.5 MHz. Microbubble contrast agents were diluted to a concentration of 1.6×106 bubbles/mL and perfused through the microtube. It is shown that by correcting for the skull aberration, the RF signal amplitude from the tube improved by a factor of 1.6 in the out-of-plane focused emission case. The lateral registration error of the tube's position, which in the uncorrected case was 990 [Formula: see text], was reduced to as low as 50 [Formula: see text] in the corrected case as measured in the B-mode images. Sensitivity in microbubble detection for the phase-corrected case increased by a factor of 1.48 in the out-of-plane imaging case, while, in the in-plane target case, it improved by a factor of 1.31 while achieving an axial registration correction from an initial 1885- [Formula: see text] error for the uncorrected emission, to a 284- [Formula: see text] error for the corrected counterpart. These findings suggest that super-resolution imaging may be used far more generally as a clinical imaging modality in the brain.

Piecewise parabolic method for propagation of shear shock waves in relaxing soft solids: One-dimensional case.

Shear shock waves can be generated spontaneously deep within the brain during a traumatic injury. This recently observed behavior could be a primary mechanism for the generation of traumatic brain injuries. However, shear shock wave physics and its numerical modeling are relatively unstudied. Existing numerical solvers used in biomechanics are not designed for the extremely large Mach numbers (greater than 1) observed in the brain. Furthermore, soft solids, such as the brain, have a complex nonclassical viscoleastic response, which must be accurately modeled to capture the nonlinear wave behavior. Here, we develop a 1D inviscid velocity-stress-like system to model the propagation of shear shock waves in a homogeneous medium. Then a generalized Maxwell body is used to model a relaxing medium that can describe experimentally determined attenuation laws. Finally, the resulting system is solved numerically with the piecewise parabolic method, a high-order finite volume method. The nonlinear and the relaxing components of this method are validated with theoretical predictions. Comparisons between numerical solutions obtained for the proposed model and the experiments of plane shear shock wave propagation based on high frame-rate ultrasound imaging and tracking are shown to be in excellent agreement.

Adaptive Multifocus Beamforming for Contrast-Enhanced-Super-Resolution Ultrasound Imaging in Deep Tissue.

Contrast-enhanced-super-resolution ultrasound imaging, also referred to as ultrasound localization microscopy, can resolve vessels that are smaller than the diffraction limit and has recently been able to generate super-resolved vascular images of shallow in vivo structures in small animals. To fully translate this technology to the clinic, it is advantageous to be able to detect microbubbles at deeper locations in tissue while maintaining a short acquisition time. Current implementations of this imaging method rely on plane-wave imaging. This method has the advantage of maximizing the frame rate, which is important due to the large amount of frames required for super-resolution processing. However, the wide planar beam used to illuminate the field of view produces poor contrast and low sensitivity bubble detection. Here, we propose an "adaptive multifocus" sequence, a new ultrasound imaging sequence that combines the high frame rate feature of a plane wave with the increased bubble detection sensitivity of a focused beam. This sequence simultaneously sonicates two or more foci with a single emission, hence retaining a high frame rate, yet achieving improved sensitivity to microbubbles. In the limit of one target, the beam reduces to a conventional focused transmission; and for an infinite number of targets, it converges to plane-wave imaging. Numerical simulations, using the full-wave code, are performed to compare the point spread function of the proposed sequence to that generated by the plane-wave emission. Our numerical results predict an improvement of up to 15 dB in the signal-to-noise ratio. Ex vivo experiments of a tissue-embedded microtube phantom are used to generate super-resolved images and to compare the adaptive beamforming approach to plane-wave imaging. These experimental results show that the adaptive multifocus sequence successfully detects 744 microbubble events at 60 mm when they are undetectable by the plane-wave sequence under the same imaging conditions. At a shallower depth of 44 mm, the proposed adaptive multifocus method detects 6.9 times more bubbles than plane-wave imaging (1763 versus 257 bubble events).

3-D Ultrasound Localization Microscopy for Identifying Microvascular Morphology Features of Tumor Angiogenesis at a Resolution Beyond the Diffraction Limit of Conventional Ultrasound.

Angiogenesis has been known as a hallmark of solid tumor cancers for decades, yet ultrasound has been limited in its ability to detect the microvascular changes associated with malignancy. Here, we demonstrate the potential of 'ultrasound localization microscopy' applied volumetrically in combination with quantitative analysis of microvascular morphology, as an approach to overcome this limitation. This pilot study demonstrates our ability to image complex microvascular patterns associated with tumor angiogenesis in-vivo at a resolution of tens of microns - substantially better than the diffraction limit of traditional clinical ultrasound, yet using an 8 MHz clinical ultrasound probe. Furthermore, it is observed that data from healthy and tumor-bearing tissue exhibit significant differences in microvascular pattern and density. Results suggests that with continued development of these novel technologies, ultrasound has the potential to detect biomarkers of cancer based on the microvascular 'fingerprint' of malignant angiogenesis rather than through imaging of blood flow dynamics or the tumor mass itself.

Creep of sound paths in consolidated granular material detected through coda wave interferometry.

The time evolution of the contact force structure of a consolidated granular material subjected to a constant stress is monitored using the coda wave interferometry method. In addition, the nature of the aging and rejuvenation processes are investigated. These processes are interpreted in terms of affine and nonaffine structural path deformations. During the later stages of creep, the rearrangements of subgrains are so small that they only produce affine deformations in the contact paths, without any significant changes in the structural configuration. As a result, the strain path distribution follows the macroscopic strain. Conversely, in the presence of ultrasonic perturbations, the nonaffine grain buckling mechanism dominates, producing relatively drastic changes in the structural configuration accompanied by path deformations of the order of the grain size. This plastic mechanism induces material rejuvenation that is observed macroscopically as an ultrasonically accelerated creep.

Effect of packing fraction on shear band formation in a granular material forced by a penetrometer.

Granular ensembles subjected to confinement forces can reach metastable states that often break down via formation of shear bands for sufficiently high deviatoric stress. In this article we investigate the flow induced in a granular ensemble that is perturbed by a vertically moving finger in a quasiplanar geometry. The flow exhibits spiral-like shear bands and evolves discontinuously in time, in concert with an oscillating penetration force. We characterize the nature of this nucleation-relaxation type process for loose to dense packing fractions. The nucleation dynamics is reasonably well described by a simple Mohr-Coulomb failure criterium in which the friction coefficient is a function of packing fraction. We contrast our findings with the recent work of Gravish et al. [Phys. Rev. Lett. 105, 128301 (2010)].

Ultrasound induces aging in granular materials.

Aging and rejuvenation have been identified as the general mechanisms that rule the time evolution of granular materials subjected to some external confinement pressure. In creep experiments performed in a triaxial configuration, we obtained evidence that relatively high intensity ultrasound waves propagating through the material induce both weakening and significant plasticity. In the framework of glassy materials, it is shown that the effect of ultrasound can be simply accounted for by a general variable, the fluidity, whose dynamics are described by an effective aging parameter that strongly decreases with sound amplitude and vanishes at the yield stress limit. The response from step perturbations in ultrasound intensity provided a method to assess the effective-viscosity jumps which are direct evidence of acoustic fluidization.