Rayleigh theory of ultrasound scattering applied to liquid-filled contrast nanoparticles.

We present a novel modified theory based upon Rayleigh scattering of ultrasound from composite nanoparticles with a liquid core and solid shell. We derive closed form solutions to the scattering cross-section and have applied this model to an ultrasound contrast agent consisting of a liquid-filled core (perfluorooctyl bromide, PFOB) encapsulated by a polymer shell (poly-caprolactone, PCL). Sensitivity analysis was performed to predict the dependence of the scattering cross-section upon material and dimensional parameters. A rapid increase in the scattering cross-section was achieved by increasing the compressibility of the core, validating the incorporation of high compressibility PFOB; the compressibility of the shell had little impact on the overall scattering cross-section although a more compressible shell is desirable. Changes in the density of the shell and the core result in predicted local minima in the scattering cross-section, approximately corresponding to the PFOB-PCL contrast agent considered; hence, incorporation of a lower shell density could potentially significantly improve the scattering cross-section. A 50% reduction in shell thickness relative to external radius increased the predicted scattering cross-section by 50%. Although it has often been considered that the shell has a negative effect on the echogeneity due to its low compressibility, we have shown that it can potentially play an important role in the echogeneity of the contrast agent. The challenge for the future is to identify suitable shell and core materials that meet the predicted characteristics in order to achieve optimal echogenity.

Ehrenfest model for condensation and evaporation processes in degrading aggregates with multiple bonds.

We present an explicit theory of the degradation and thermal fragmentation kinetics of polymerlike systems and aggregates with multiple bonds in the presence of stochastic evaporation and condensation (restoration) of bonds. The analysis is conducted on the basis of the determination of the first passage time to state zero (fragmented state) in the Ehrenfest diffusion model in continuous time. The main approximations of the developed theory include the assumption that multiple bonds in any link between the primary elements in the aggregate do not interact with each other and that the coagulation rate after thermal fragmentation of the aggregates is negligible (which gives the absorbing zero state in the Ehrenfest model). In particular, it is demonstrated that even small condensation rates (of approximately 10 times smaller than the rates of bond evaporation) may have a significant effect on typical evolution times for the degrading aggregates and can result in a strong accumulation of nanoaggregates in the intermediate fragmentation modes. The simple asymptotic (predominantly exponential) behavior of the obtained solution at large evolution times is analyzed and discussed. The results will be important for the investigation of the degradation kinetics of a variety of polymerlike systems with multiple bonds, including self-arranged structures, polymer networks, different types of nanoclusters and their thermal fragmentation, etc.