Search

Elastic properties of materials can be measured by observing shear wave propagation following localized, impulsive excitations and relating the propagation velocity to a model of the material. However, characterization of anisotropic materials is difficult because of the number of elasticity constants in the material model and the complex dependence of propagation velocity relative to the excitation axis, material symmetries, and propagation directions. In this study, we develop a model of wave propagation following impulsive excitation in an incompressible, transversely isotropic (TI) material such as muscle. Wave motion is described in terms of three propagation modes identified by their polarization relative to the material symmetry axis and propagation direction. Phase velocities for these propagation modes are expressed in terms of five elasticity constants needed to describe a general TI material, and also in terms of three constants after the application of two constraints that hold in the limit of an incompressible material. Group propagation velocities are derived from the phase velocities to describe the propagation of wave packets away from the excitation region following localized excitation. The theoretical model is compared to the results of finite element (FE) simulations performed using a nearly incompressible material model with the five elasticity constants chosen to preserve the essential properties of the material in the incompressible limit. Propagation velocities calculated from the FE displacement data show complex structure that agrees quantitatively with the theoretical model and demonstrates the possibility of measuring all three elasticity constants needed to characterize an incompressible, TI material., (© 2013 Elsevier Ltd. All rights reserved.)

The speed at which shear waves propagate in tissue can be used to quantify the shear modulus of the tissue. As many groups have shown, shear waves can be generated within tissues using focused, impulsive, acoustic radiation force excitations, and the resulting displacement response can be ultrasonically tracked through time. The goals of the work herein are twofold: (i) to develop and validate an algorithm to quantify shear wave speed from radiation force-induced, ultrasonically-detected displacement data that is robust in the presence of poor displacement signal-to-noise ratio and (ii) to apply this algorithm to in vivo datasets acquired in human volunteers to demonstrate the clinical feasibility of using this method to quantify the shear modulus of liver tissue in longitudinal studies. The ultimate clinical application of this work is noninvasive quantification of liver stiffness in the setting of fibrosis and steatosis. In the proposed algorithm, time-to-peak displacement data in response to impulsive acoustic radiation force outside the region of excitation are used to characterize the shear wave speed of a material, which is used to reconstruct the material's shear modulus. The algorithm is developed and validated using finite element method simulations. By using this algorithm on simulated displacement fields, reconstructions for materials with shear moduli (mu) ranging from 1.3-5 kPa are accurate to within 0.3 kPa, whereas stiffer shear moduli ranging from 10-16 kPa are accurate to within 1.0 kPa. Ultrasonically tracking the displacement data, which introduces jitter in the displacement estimates, does not impede the use of this algorithm to reconstruct accurate shear moduli. By using in vivo data acquired intercostally in 20 volunteers with body mass indices ranging from normal to obese, liver shear moduli have been reconstructed between 0.9 and 3.0 kPa, with an average precision of +/-0.4 kPa. These reconstructed liver moduli are consistent with those reported in the literature (mu = 0.75-2.5 kPa) with a similar precision (+/-0.3 kPa). Repeated intercostal liver shear modulus reconstructions were performed on nine different days in two volunteers over a 105-day period, yielding an average shear modulus of 1.9 +/- 0.50 kPa (1.3-2.5 kPa) in the first volunteer and 1.8 +/- 0.4 kPa (1.1-3.0 kPa) in the second volunteer. The simulation and in vivo data to date demonstrate that this method is capable of generating accurate and repeatable liver stiffness measurements and appears promising as a clinical tool for quantifying liver stiffness.

Radiation force-based techniques have been developed by several groups for imaging the mechanical properties of tissue. Acoustic Radiation Force Impulse (ARFI) imaging is one such method that uses commercially available scanners to generate localized radiation forces in tissue. The response of the tissue to the radiation force is determined using conventional B-mode imaging pulses to track micron-scale displacements in tissue. Current research in ARFI imaging is focused on producing real-time images of tissue displacements and related mechanical properties. Obstacles to producing a real-time ARFI imaging modality include data acquisition, processing power, data transfer rates, heating of the transducer, and patient safety concerns. We propose a parallel receive beamforming technique to reduce transducer heating and patient acoustic exposure, and to facilitate data acquisition for real-time ARFI imaging. Custom beam sequencing was used with a commercially available scanner to track tissue displacements with parallel-receive beamforming in tissue-mimicking phantoms. Using simulations, the effects of material properties on parallel tracking are observed. Transducer and tissue heating for parallel tracking are compared to standard ARFI beam sequencing. The effects of tracking beam position and size of the tracked region are also discussed in relation to the size and temporal response of the region of applied force, and the impact on ARFI image contrast and signal-to-noise ratio are quantified.

Acoustic radiation force impulse imaging has been used clinically to study the dynamic response of lesions relative to their background material to focused, impulsive acoustic radiation force excitations through the generation of dynamic displacement field images. Dynamic displacement data are typically displayed as a set of parametric images, including displacement immediately after excitation, maximum displacement, time to peak displacement, and recovery time from peak displacement. To date, however, no definitive trends have been established between these parametric images and the tissues' mechanical properties. This work demonstrates that displacement magnitude, time to peak displacement, and recovery time are all inversely related to the Young's modulus in homogeneous elastic media. Experimentally, pulse repetition frequency during displacement tracking limits stiffness resolution using the time to peak displacement parameter. The excitation pulse duration also impacts the time to peak parameter, with longer pulses reducing the inertial effects present during impulsive excitations. Material density affects tissue dynamics, but is not expected to play a significant role in biological tissues. The presence of an elastic spherical inclusion in the imaged medium significantly alters the tissue dynamics in response to impulsive, focused acoustic radiation force excitations. Times to peak displacement for excitations within and outside an elastic inclusion are still indicative of local material stiffness; however, recovery times are altered due to the reflection and transmission of shear waves at the inclusion boundaries. These shear wave interactions cause stiffer inclusions to appear to be displaced longer than the more compliant background material. The magnitude of shear waves reflected at elastic lesion boundaries is dependent on the stiffness contrast between the inclusion and the background material, and the stiffness and size of the inclusion dictate when shear wave reflections within the lesion will interfere with one another. Jitter and bias associated with the ultrasonic displacement tracking also impact the estimation of a tissue's dynamic response to acoustic radiation force excitation.

The use of ultrasonic methods to track the tissue deformation generated by acoustic radiation force is subject to jitter and displacement underestimation errors, with displacement underestimation being primarily caused by lateral and elevation shearing within the point spread function (PSF) of the ultrasonic beam. Models have been developed using finite element methods and Field II, a linear acoustic field simulation package, to study the impact of focal configuration, tracking frequency, and material properties on the accuracy of ultrasonically tracking the tissue deformation generated by acoustic radiation force excitations. These models demonstrate that lateral and elevation shearing underneath the PSF of the tracking beam leads to displacement underestimation in the focal zone. Displacement underestimation can be reduced by using tracking beams that are narrower than the spatial extent of the displacement fields. Displacement underestimation and jitter decrease with time after excitation as shear wave propagation away from the region of excitation reduces shearing in the lateral and elevation dimensions. The use of higher tracking frequencies in broadband transducers, along with 2D focusing in the elevation dimension, will reduce jitter and improve displacement tracking accuracy. Relative displacement underestimation remains constant as a function of applied force, whereas jitter increases with applied force. Underdeveloped speckle (SNR < 1.91) leads to greater levels of jitter and peak displacement underestimation. Axial shearing is minimal over the tracking kernel lengths used in acoustic radiation force impulse imaging and thus does not impact displacement tracking.

Several groups are studying acoustic radiation force and its ability to image the mechanical properties of tissue. Acoustic radiation force impulse (ARFI) imaging is one modality using standard diagnostic ultrasound scanners to generate localized, impulsive, acoustic radiation forces in tissue. The dynamic response of tissue is measured via conventional ultrasonic speckle-tracking methods and provides information about the mechanical properties of tissue. A finite-element method (FEM) model has been developed that simulates the dynamic response of tissues, with and without spherical inclusions, to an impulsive acoustic radiation force excitation from a linear array transducer. These FEM models were validated with calibrated phantoms. Shear wave speed, and therefore elasticity, dictates tissue relaxation following ARFI excitation, but Poisson's ratio and density do not significantly alter tissue relaxation rates. Increased acoustic attenuation in tissue increases the relative amount of tissue displacement in the near field compared with the focal depth, but relaxation rates are not altered. Applications of this model include improving image quality, and distilling material and structural information from tissue's dynamic response to ARFI excitation. Future work on these models includes incorporation of viscous material properties and modeling the ultrasonic tracking of displaced scatterers.

Several laboratories are investigating the use of acoustic radiation force to image the mechanical properties of tissue. Acoustic Radiation Force Impulse (ARFI) imaging is one approach that uses brief, high-intensity, focused ultrasound pulses to generate radiation force in tissue. This radiation force generates tissue displacements that are tracked using conventional correlation-based ultrasound methods. The tissue response provides a mechanism to discern mechanical properties of the tissue. The acoustic energy that is absorbed by tissue generates radiation force and tissue heating. A finite element methods model of acoustic heating has been developed that models the thermal response of different tissues during short duration radiation force application. The beam sequences and focal configurations used during ARFI imaging are modeled herein; the results of these thermal models can be extended to the heating due to absorption associated with other radiation force-based imaging modalities. ARFI-induced thermal diffusivity patterns are functions of the transducer f-number, the tissue absorption, and the temporal and spatial spacing of adjacent ARFI interrogations. Cooling time constants are on the order of several seconds. Tissue displacement due to thermal expansion is negligible for ARFI imaging. Changes in sound speed due to temperature changes can be appreciable. These thermal models demonstrate that ARFI imaging of soft tissue is safe, although thermal response must be monitored when ARFI beam sequences are being developed.

Acoustic radiation force impulse (ARFI) imaging is a novel imaging modality in which pulses from a diagnostic ultrasound scanner are used to displace tissue and track its motion. The region displaced has lateral and elevational dimensions of similar scale to the ultrasound beams used to track the motion. Therefore, there is a range of tissue displacements present within the tracking beam, leading to decorrelation of the echo signal. Expressions are derived for the expected value of the displacement estimate and the cross-correlation at the expected displacement. Numerical simulations confirm the analytical model.

The early detection of breast cancer reduces patient mortality. The most common method of breast cancer detection is palpation. However, lesions that lie deep within the breast are difficult to palpate when they are small. Thus, a method of remote palpation, which may allow the detection of small lesions lying deep within the breast, is currently under investigation. In this method, acoustic radiation force is used to apply localized forces within tissue (to tissue volumes on the order of 2 mm3) and the resulting tissue displacements are mapped using ultrasonic correlation based methods. A volume of tissue that is stiffer than the surrounding medium (i.e., a lesion) distributes the force throughout the tissue beneath it, resulting in larger regions of displacement, and smaller maximum displacements. The resulting displacement maps may be used to image tissue stiffness. A finite-element-model (FEM) of acoustic remote palpation is presented in this paper. Using this model, a parametric analysis of the affect of varying tissue and acoustic beam characteristics on radiation force induced tissue displacements is performed. The results are used to evaluate the potential of acoustic remote palpation to provide useful diagnostic information in a clinical setting. The potential for using a single diagnostic transducer to both generate radiation force and track the resulting displacements is investigated.