Dynamic mechanical response of elastic spherical inclusions to impulsive acoustic radiation force excitation

Abstract

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.

Optical coherence tomography detection of shear wave propagation in inhomogeneous tissue equivalent phantoms and ex-vivo carotid artery samples

“…These images provided information to calculate the distance between two measurement points (Δr) and the phase shift (Δφ) between these two tracking locations for each layer which two successive locations can be chosen at a particular depth z (in this work we chose z = 0.2mm in the regions of high concentration and also in the regions of low concentration). At these two locations in the image, phase values are retrieved, then were in turn used to calculate the shear wave speed, shear modulus and Young's modulus [28]. The optical path displacement Z is calculated from the measured phase by using Eq.…”

“…Using this technique, mechanical properties of the phantoms were measured. The ARF excitation for producing transient excitations had previously been implemented to assess the mechanical properties of tissues [25][26][27][28][29]. ARF imaging had also been used in general elasticity imaging methods for the characterization of lesions, muscle screening, and imaging of the calcification of arteries [30][31][32][33][34].…”

On Shear Wave Speed Estimation for Agar-Gelatine Phantom

“…Along a single line, excitation is accomplished and measurement is made, then, another adjacent line is investigated and so on till the image of tissue response is constructed. The tissue response is characterized by a set of parameters; the peak displacement, and the time the tissue takes to reach the peak displacement and the recovery time [23].…”

“…It is used with phantom tissue imaging [24], imaging thermally induced lesions [25], abdominal imaging of lesions [26], human prostate imaging [27] and imaging of cardiovascular vessels [28,29].…”

“…The speed can be estimated from this visualization. Converting 3D visualizations to 2D curves of nodes displacements versus time profiles is more efficient for estimating the speed of the shear wave as proposed in [44]. For more feasibility of the calculations, one of the sides of the curve is selected to calculate the shear wave speed from it, by tracking the peak displacement.…”