Simulations of insonated contrast agents: Saturation and transient break-up

Abstract

Under insonation contrast agents are known to perform nonlinear pulsations and deform statically, in the form of buckling, or dynamically via parametric mode excitation, and often exhibit jetting and break-up like bubbles without coating. Boundary element simulations are performed in the context of axisymmetry in order to establish the nonlinear evolution of these patterns. The viscoelastic stresses that develop on the coating form the dominant force balance tangentially to the shell-liquid interface, whereas the dynamic overpressure across the shell balances viscoelastic stresses in the normal direction. Strain softening and strain hardening behavior is studied in the presence of shape instabilities for various initial conditions. Simulations recover the pattern of static buckling, subharmonic/harmonic excitation, and dynamic buckling predicted by linear stability. Preferential mode excitation during compression is obtained supercritically for strain softening phospholipid shells while the shell regains its sphericity at expansion. It is a result of energy transfer between the emerging unstable modes and the radial mode, eventually leading to saturated oscillations of shape modes accompanied by asymmetric radial pulsations in favor of compression. Strain softening shells are more prone to sustain saturated pulsations due to the mechanical behavior of the shell. As the sound amplitude increases and before the onset of dynamic buckling, both types of shells exhibit transient break-up via unbalanced growth of a number of unstable shape modes. The effect of pre-stress in lowering the amplitude threshold for shape mode excitation is captured numerically and compared against the predictions of linear stability analysis. The amplitude interval for which sustained shape oscillations are obtained is extended, in the presence of pre-stress, by switching from a strain softening constitutive law to a strain hardening one once the shell curvature increases beyond a certain level. This type of mechanical behavior models the formation of lipid bilayer structures on the shell beyond a certain level of bending, as a result of a lipid monolayer folding transition. In this context a compression only type behavior is obtained in the simulations, which is accompanied by preferential shape deformation during compression at relatively small sound amplitudes in a manner that bears significance on the interpretation of available experimental observations exhibiting similar dynamic behavior. © 2013 American Institute of Physics.