Interpreting attenuation at different excitation amplitudes to estimate strain-dependent interfacial rheological properties of lipid-coated monodisperse microbubbles

Broadband attenuation of ultrasound measured at different excitation pressures being different raises a serious theoretical concern, because the underlying assumption of linear and independent propagation of different frequency components nominally requires attenuation to be independent of excitation. Here, this issue is investigated by examining ultrasound attenuation through a monodisperse lipid-coated microbubble suspension measured at four different acoustic excitation amplitudes. The attenuation data are used to determine interfacial rheological properties (surface tension, surface dilatational elasticity, and surface dilatational viscosity) of the encapsulation according to three different models. Although different models result in similar rheological properties,attenuation measured at different excitation levels (4–110 kPa) leads to different values for them; the dilatation elasticity (0.56 to 0.18 N/m) and viscosity (2.4 × 10⁻⁸ to 1.52 × 10⁻⁸ Ns/m) both decrease with increasing pressure. Numerically simulating the scattered response, nonlinear energy transfer between frequencies are shown to be negligible, thereby demonstrating the linearity in propagation and validating the attenuation analysis. There is a second concern to the characterization arising from shell properties being dependent on excitation amplitude, which is not a proper constitutive variable. It is resolved by arriving at a strain-dependent rheology for the encapsulation. The limitations of the underlying analysis are discussed.

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