A Complete Computational Model of Ultrasound Vibro-acoustography

Ultrasound vibro-acoustography is a novel medical imaging modality that combines the high resolution of high-frequency ultrasound with the speckle-free images obtained using lowfrequency methods. This imaging modality relies on the nonlinear interaction of two high frequency beams at slightly different frequencies. We describe the physics of ultrasound vibroacoustography and outline a strategy for its modeling, simulation, and optimal design. NOMENCLATURE φ first-order velocity potential, high frequency φ j subscript j indicates that the field is at frequency ω j c(x) acoustic velocity ω angular frequency ρ density p pressure γ specific heat ratio of the medium ψ second-order velocity potential, low frequency v wavefield velocity T Cauchy stress tensor φ scalar potential for elasticity Φ vector potential for elasticity ~ U vector displacement S elastic interaction source term λ, μ Lamé parameters λ also used for wavelength A square-root of wave operator ·̂ temporal Fourier transform ‖ · ‖ L2-norm kx wavenumber in x-direction kz wavenumber in z-direction z preferential direction for parabolic approximation x = (x1,x2) orthogonal directions for parabolic approximation c0(z) reference velocity independent of x F Fourier transform in x variables λ′,μ′,ρ′ variables within inclusion for integral method λ0,μ0,ρ0 constant parameters outside the inclusion for integral method G Green’s function for integral method F Lippmann-Schwinger source term φ′ scattered field, high frequency φ0 incident field, high frequency