The dependence of ultrasound contrast agents backscatter on acoustic pressure: theory versus experiment.

Experimental investigations have not fully explored the interaction between ultrasound beams and microbubble contrast agents. Moreover theoretical investigations have not solved the problem of the microbubble oscillation. A simple in-vitro system based on a commercial scanner (ATL UM9) was used to insonate (3 MHz transmission) diluted contrast suspensions of Definity and Quantison at different acoustic pressures (0.27-1.52 MPa). The experimental data were referred to a blood mimicking fluid in order to extract an estimate of their scattering cross-section. The results were compared with the solutions of the three main bubble oscillatidn models, Rayleigh-Plesset, Herring and Gilmore. Non-linear solutions of the above models were produced numerically using the Mathematica Package Software. The experiments showed that both agents provided a linear increase in scattering cross-section with increasing acoustic pressure. The thick shelled Quantison provided an increasing number of scatterers with increasing acoustic pressure, which proved that free bubbles leaked out of the shell. At high acoustic pressures both Quantison and Definity scattering cross-sections were almost identical, and were probably that of a free bubble. The Rayleigh-Plesset model provided a scattering cross-section almost independent of acoustic pressure. On the contrary the scattering cross-sections calculated by the Herring and Gilmore models solutions displayed a definite dependence on acoustic pressure of an order higher than one, which is slightly higher than the order of dependence exhibited by the experimental data. However, the increase of the experimentally measured scattering cross-section with acoustic pressure was sharper than the calculated one by the above two models. This is most probably due to the fact that the models simulated damped and not free bubble oscillations. In conclusion the Rayleigh-Plesset model was inadequate in describing the bubble oscillations even at small diagnostic acoustic pressures. The Herring and Gilmore models could simulate the dependence of the scattering cross-section of encapsulated microbubbles on acoustic pressure. However the contribution of free bubble oscillations has still to be modelled.

Wave propagation in 0-3/3-3 connectivity composites with complex microstructure.

This work presents a study of the properties of particulate composites. The whole range of particle volume fraction (0-1) and ideal 0-3, 3-3 and intermediate 0-3/3-3 connectivities are analysed. Two different approaches to produce a realistic model of the complex microstructure of the composites are considered. The first one is based on a random location of mono-dispersed particles in the matrix; while the second incorporates a size distribution of the particles based on experimental measurements. Different particle shapes are also considered. A commercial finite element package was used to study the propagation of acoustic plane waves through the composite materials. Due to the complexity of the problem, and as a first step, a two-dimensional model was adopted. The results obtained for the velocity of sound propagation from the finite element technique are compared with those from other theoretical approaches and with experimental data. The study validates the use of this technique to model acoustic wave propagation in 0-3/3-3 connectivity composites. In addition, the finite element calculations, along with the detailed description of the microstructure of the composite, provide valuable information about the micromechanics of the sample and the influence of the microstructure on macroscopic properties.

The geometry and motion of reaction-diffusion waves on closed two-dimensional manifolds.

Chemical or biological systems modelled by reaction diffusion (R.D.) equations which support simple one-dimensional travelling waves (oscillatory or otherwise) may be expected to produce intricate two- or three-dimensional spatial patterns, either stationary or subject to certain motion. Such structures have been observed experimentally. Asymptotic considerations applied to a general class of such systems lead to fundamental restrictions on the existence and geometrical form of possible structures. As a consequence of the geometrical setting, it is a straightforward matter to consider the propagation of waves on closed two-dimensional manifolds. We derive a fundamental equation for R.D. wave propagation on surfaces and discuss its significance. We consider the existence and propagation of rotationally symmetric and double spiral waves on the sphere and on the torus.