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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, while 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 (ARFI) imaging and thus does not impact displacement tracking.

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Acoustic Radiation Force Impulse (ARFI) 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 tissue's mechanical properties. This work demonstrates that displacement magnitude, time to peak displacement, and recovery time are all inversely related to the Young's modulus of a 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.

We present a method for determining the shear modulus of an elastic material wherein a spatially-modulated acoustic radiation force is used to generate a disturbance of known spatial frequency (wavelength). The propagation of this initial displacement as a shear wave is measured using ultrasound tracking methods and the temporal frequency of the shear wave is estimated. Given the known wavelength and material density and the measured estimate of temporal frequency, the shear modulus at the point of excitation may be calculated easily. Using this method, the shear moduli of two gelatin phantoms was estimated to be 1.4 and 5.8 kPa, in good agreement with 1.5 and 5.6 kPa values determined though quasistatic material testing.