Guzina, Bojan B.

As shown in a recent study, estimation of the magnitude of the acoustic radiation force (ARF) in isotropic tissue-like solids is the key to measuring a third-order nonlinear modulus of elasticity (C)—responsible for coupling the shear and volumetric constitutive responses of a material. Due to experimental limitations, a direct measurement of the ARF in tissue is however difficult. To overcome this problem, we deploy 3D elastodynamic finite element (EFE) simulations of the ARF experiment in tissue-mimicking phantoms to estimate (i) the “background” shear modulus from the phase of the induced shear waves; (ii) the ARF magnitude from the shear wave amplitude, and (iii) the modulus C from the knowledge of the ARF. In this way, by interpreting the ARF-generated shear waves through the prism of 3D-EFE simulations, we facilitate local estimation of the nonlinear C modulus with spatial resolution equaling the size of the focal region. We call this method the C-Elastography (CE). In this study, the CE technique is applied to gelatin phantoms containing an agar-based inclusion. The profiles of the C-modulus in phantoms tested demonstrate good correlation with the phantom geometry, showing marked (and sharp) C-contrast at push points acting on the inclusion. [Acknowledgment: NIH-Grant EB23113.]

This study concerns the development and preliminary experimental verification of a topological sensitivity–based platform for the material characterization of tissue anomalies exposed by vibroacoustography-type imaging techniques. Vibroacoustography (VA) is a high-resolution imaging method that has been applied to the detection of pathological changes in soft tissues. Although the data provided by this method is related to the mechanical properties of tissue, the viscoelastic parameters of the object cannot be estimated by this imaging method itself. Topological sensitivity (TS) method is a data processing methodology that can be used to estimate the viscoelastic parameters of an object from vibration data. In this study, the concept of topological sensitivity is applied to interpret the vibroacoustography measurements for the purpose of lesion characterization. In the proposed approach, the topological sensitivity function, which signifies the variation of a given cost functional when an infinitesimal inclusion with trial material parameters is placed at the location of a point force, is formulated in terms of the adjoint field. The effectiveness of the resulting formula as a material indicator for lesion characterization is demonstrated by estimating the relative elastic parameters of a well-controlled neoprene sphere embedded in a tissue-mimicking phantom specimen.

Acoustoelasticity is a technique that allows quantification of the elastic nonlinearity coefficients (the so-called third-order moduli) of a material by measuring the variation of the sound speed in different directions (and/or polarizations) versus the applied uniaxial static stress. When dealing with nominally isotropic solids, the variation of the shear wave speed in two orthogonal directions with the applied stress permits the computation of two out of three independent nonlinearity coefficients. To generate the shear wave in an experimental setting, the acoustic radiation force pulse was applied to uniaxially deformed phantoms with strains of up to 30%. The results demonstrate that the compressional-shear coefficient C, which governs the variation of the (linear) shear modulus with hydrostatic pressure was found to vary substantially from one phantom to another, with the highest value observed in an agarose-based phantom. The importance of this nonlinearity parameter resides in the fact that the magnitude of the acoustic radiation force (ARF) in soft solids is proportional to C-1. For consistency, the values of C obtained from the acoustoelasticity experiment are compared to those deduced from the shear wave amplitude via its relationship to the magnitude of the ARF used to generate the shear wave.

The acoustic radiation force (ARF), which signifies the average transfer of momentum from the sound wave to the propagating medium, is nowadays frequently used to compute the mean displacement field in soft tissues due to the action of a focused ultrasound beam. In situations when the sound field used to generate the ARF is modulated, the latter depends on both spatial and temporal derivatives of the acoustic intensity. Unfortunately, the numerical computation of the nonlinear acoustic solution due to modulated focused ultrasound beam is complicated by the presence of two disparate time scales in the formulation. To deal with the problem, the KZK-type spatial scaling is complemented by its dual-time-scale companion, where the temporal coordinate is split into its “fast” and “slow” components, allowing one to track the ultrasound-scale oscillations and modulation-scale variations separately in the solution. In this case, the nonlinear acoustic solution (and consequently the ARF) can be effectively computed in the “fast” frequency domain and “slow” time domain for any given modulation envelope, transient, or steady-state. The proposed developments are both validated by the experimental results and illustrated via numerical examples that show the effectiveness of the computational scheme.