Temporal analysis of tissue displacement induced by a transient ultrasound radiation force

Abstract

One of the stress sources that can be used in dynamic elastography imaging methods is the acoustic radiation force. However, displacements of the medium induced by this stress field are generally not fully understood in terms of spatial distribution and temporal evolution. A model has been developed based on the elastodynamic Green's function describing the different acoustic waves generated by focused ultrasound. The function is composed of three terms: two far-field terms, which correspond to a purely longitudinal compression wave and a purely transverse shear wave, and a coupling near-field term which has a longitudinal component and a transverse component. For propagation distances in the shear wavelength range, the predominant term is the near field term. The displacement duration corresponds to the propagation duration of the shear wave between the farthest source point and the observation point. This time therefore depends on the source size and the local shear modulus of the tissue. Evolution of the displacement/time curve profile, which is directly linked to spatial and temporal source profiles, is computed at different radial distances, for different durations of force applications and different shear elastic coefficients. Experimental results performed with an optical interferometric method in a homogeneous tissue-mimicking phantom agreed with the theoretical profiles.

Motion of a solid sphere in a viscoelastic medium in response to applied acoustic radiation force: Theoretical analysis and experimental verification

“…7(a). These results are in agreement with theoretical and experimental results obtained by other groups, 8,17,18,20 where the response to acoustical radiation force was investigated for a medium with different elasticity.…”

“…Using the Taylor expansion of the time-dependent exponential functions around zero, the solution of Eq. (13) for impulsive excitation can be obtained: (16) The displacement reaches its peak at the time t max (17) and the maximum displacement U(t max ) is (18) Note that U(t) and t max are real even if λ 1 and λ 2 are complex.…”

Transient MR elastography (t‐MRE) using ultrasound radiation force: Theory, safety, and initial experiments in vitro

“…The relationship of motion with the duration of the ultrasound pulse and the spatial distribution of the force was investigated in detail by several authors (3,15,26). For the sake of simplicity, we chose an overdamped response to model the transient displacement u(t) at the focus (i.e., we assumed that the medium does not oscillate).…”

“…For the sake of simplicity, we chose an overdamped response to model the transient displacement u(t) at the focus (i.e., we assumed that the medium does not oscillate). The choice of this model was based on the transient displacement waveforms reported in (3,15,26).…”

“…Radiation force is caused by the change of momentum of the ultrasound waves as they propagate, either because of wave absorption or of wave reflection (13)(14)(15)(16)(17)(18). The radiation force is localized and highly directional, its main axis being in the direction of propagation of the ultrasound beam.…”