Dontsov, Egor

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.