  Acoustic characterization of ultrasound contrast agents (UCAs, coated
microbubbles) relies on the attenuation theory that assumes the UCAs oscillate
linearly at sufficiently low excitation pressures. Effective shell parameters
of the UCAs can be estimated by fitting a theoretical attenuation curve to
experimentally measured attenuation data. Depending on the excitation frequency
and properties of the shell, however, an UCA may oscillate nonlinearly even at
sufficiently low excitation pressures violating the assumption in the linear
attenuation theory. Notably, the concern on the estimation of the attenuation
coefficient of a microbubble at resonance using linearized approximation has
long been addressed. In this article, we investigated the attenuation
phenomenon through analyzing the energy dissipation of a single UCA and
propagating waves in an UCA suspension, both of which employed a nonlinear
Rayleigh-Plesset equation. Analytical formulae capable of estimating the
attenuation coefficient due to the weakly nonlinear oscillations of the UCA
were obtained with a relatively rigorous mathematical analysis. The computed
results that were verified by numerical simulations showed the attenuation
coefficient of the UCA at resonance was pressure-dependent and could be
significantly smaller than that predicted by the linear attenuation theory.
Polydispersity of the UCA population enlarged the difference in the estimation
of attenuation between the linear and present second-order nonlinear theories.
