Nader Saffari

Microbubble ultrasound contrast agents: A review:

Abstract The superior scattering properties of gas bubbles compared with blood cells have made microbubble ultrasound contrast agents important tools in ultrasound diagnosis. Over the past 2 years they have become the focus of a wide and rapidly expanding field of research, with their benefits being repeatedly demonstrated, both in ultrasound image enhancement, and more recently in drug and gene delivery applications. However, despite considerable investigation, their behaviour is by no means fully understood and, while no definite evidence of harmful effects has been obtained, there remain some concerns as to their safety. In this review the existing theoretical and experimental evidence is examined in order to clarify the extent to which contrast agents are currently understood and to identify areas for future research. In particular the disparity between the conditions considered in theoretical models and those encountered both in vitro, and more importantly in vivo is discussed, together with the controversy regarding the risk of harmful bio-effects.

On the destruction of microbubble ultrasound contrast agents

In recent years, the use of microbubble ultrasound (US) contrast agents as carriers in drug and gene delivery applications has intensified the need for a clear understanding of the processes involved in their destruction. In this study, an analysis of the conditions in the shell of a contrast agent particle has been made, based on the full numerical solution of a modified Rayleigh-Plesset equation. The results indicate that extremely high shell stresses may be expected under typical clinical conditions. Examination of previous experimental evidence in the light of these findings suggests that the shells are almost invariably disrupted, even if they are not visibly destroyed. This has some serious implications, both for targeted delivery processes and reliable assessment of the potential for harmful bioeffects. At present, neither the model nor the experimental data provide an adequate description of contrast agent behaviour. This is due primarily to the lack of information regarding the mechanical response of the shell material and the restriction of the model to the case of small, spherically symmetrical oscillations. Methods for addressing these deficiencies in future work are proposed.

Investigating the significance of multiple scattering in ultrasound contrast agent particle populations

The majority of the existing models describing the behavior of microbubble ultrasound contrast agents consider single, isolated microbubbles suspended in infinite media. The behavior of a microbubble population is predicted by summing the results for single microbubbles and ignoring multiple scattering effects. The aim of this investigation is to determine the significance of multiple scattering in microbubble populations and establish whether an alternative approach is required. In the first part of the work, linear models are derived to identify approximately the conditions under which multiple scattering may be expected. A nonlinear model for sound propagation in a microbubble suspension then is developed and used to examine multiple scattering at higher insonation pressures. Broadband attenuation measurements are described for two different types of microbubble suspension (albumin encapsulated octofluoropropane and copolymer encapsulated isobutane) to ascertain whether or not multiple scattering may be observed experimentally. The results from the simulation work indicate that multiple scattering effects would be discernible at moderate concentrations (10/sup 6/ microbubbles/ml) such as may be present in vivo. The effect upon attenuation in the suspension would be pronounced, however, only if the population contained a sufficient proportion of relatively large (>4 /spl mu/m radius) microbubbles excited at their resonance frequency. This also is found to be the case experimentally. These findings may have important implications for the characterization of ultrasound contrast agents and their use in quantitative diagnostic techniques.

The natural frequencies of microbubble oscillation in elastic vessels

A theoretical model for the dynamics of a bubble in an elastic blood vessel is applied to study numerically the effect of confinement on the free oscillations of a bubble. The vessel wall deformations are described using a lumped-parameter membrane-type model, which is coupled to the Navier-Stokes equations for the fluid motion inside the vessel. It is shown that the bubble oscillations in a finite-length vessel are characterized by a spectrum of frequencies, with distinguishable high-frequency and low-frequency modes. The frequency of the high-frequency mode increases with the vessel elastic modulus and, for a thin-wall vessel, can be higher than the natural frequency of bubble oscillations in an unconfined liquid. In the limiting case of an infinitely stiff vessel wall, the frequency of the low-frequency mode approaches the well-known solution for a bubble confined in a rigid vessel. In order to interpret the results, a simple two-degree-of-freedom model is applied. The results suggest that in order to maximize deposition of acoustic energy, a bubble confined in a long elastic vessel has to be excited at frequencies higher than the natural frequency of the equivalent unconfined bubble.

A first-order k-space model for elastic wave propagation in heterogeneous media.

A pseudospectral model of linear elastic wave propagation is described based on the first order stress-velocity equations of elastodynamics. k-space adjustments to the spectral gradient calculations are derived from the dyadic Greens function solution to the second-order elastic wave equation and used to (a) ensure the solution is exact for homogeneous wave propagation for timesteps of arbitrarily large size, and (b) also allows larger time steps without loss of accuracy in heterogeneous media. The formulation in k-space allows the wavefield to be split easily into compressional and shear parts. A perfectly matched layer (PML) absorbing boundary condition was developed to effectively impose a radiation condition on the wavefield. The staggered grid, which is essential for accurate simulations, is described, along with other practical details of the implementation. The model is verified through comparison with exact solutions for canonical examples and further examples are given to show the efficiency of the method for practical problems. The efficiency of the model is by virtue of the reduced point-per-wavelength requirement, the use of the fast Fourier transform (FFT) to calculate the gradients in k space, and larger time steps made possible by the k-space adjustments.

Modelling of the acoustic field of a multi-element HIFU array scattered by human ribs

The efficacy of high-intensity focused ultrasound (HIFU) for the treatment of a range of different cancers, including those of the liver, prostate and breast, has been demonstrated. As a non-invasive focused therapy, HIFU offers considerable advantages over techniques such as chemotherapy and surgical resection in terms of reduced risk of harmful side effects. Despite this, there are a number of significant challenges which currently hinder its widespread clinical application. One of these challenges is the need to transmit sufficient energy through the rib cage to induce tissue necrosis in the required volume whilst minimizing the formation of side lobes. Multi-element random-phased arrays are currently showing great promise in overcoming the limitations of single-element transducers. Nevertheless, successful treatment of a patient with liver tumours requires a thorough understanding of the way in which the ultrasonic pressure field from a HIFU array is scattered by the rib cage. In order to address this, a boundary element approach based on a generalized minimal residual (GMRES) implementation of the Burton-Miller formulation was used in conjunction with phase conjugation techniques to focus the field of a 256-element random HIFU array behind human ribs at locations requiring intercostal and transcostal treatment. Simulations were carried out on a 3D mesh of quadratic pressure patches generated using CT scan anatomical data for adult ribs 9-12 on the right side. The methodology was validated on spherical and cylindrical scatterers. Field calculations were also carried out for idealized ribs, consisting of arrays of strip-like scatterers, demonstrating effects of splitting at the focus. This method has the advantage of fully accounting for the effect of scattering and diffraction in 3D under continuous wave excitation.

Ultrasonic stimulation of peripheral nervous tissue: an investigation into mechanisms

Neuro-stimulation has wide ranging clinical and research potential but this is currently limited either by low resolution, penetration or by highly invasive procedures. It has been reported in previous studies that ultrasound is able to elicit a neuro-stimulatory effect at a higher resolution than other non-invasive approaches but both the underlying mechanism that makes this possible and the practical details of how it can be implemented are still poorly understood. The current study has identified the main issues that need to be resolved in the field, proposing several different approaches to tackling these areas. An isolated in vitro peripheral nerve bundle was chosen as a simple model to demonstrate and investigate the neuro-stimulatory effect after preliminary results showed successful stimulation in a skin-nerve preparation. Early results from the nerve bundle show successful neurostimulation, indicating that structures in the peripheral nerve axon are sensitive to ultrasound. Further research using this model should reveal more precisely what structures are being affected and how to optimise the effect, helping to inform the design of future procedures and devices used in in vivo applications.

Evolution of ultrasonic impulses in chains of spheres using resonant excitation

It is demonstrated that broad-bandwidth ultrasonic signals containing frequency components in excess of 200 kHz can be created in spherical chains using harmonic excitation at 73 kHz. Multiple reflections created a periodic waveform containing both harmonics and sub-harmonics of the original forcing frequency, due to non-linear Hertzian contact. These discrete frequencies represented some of the many allowed non-linear normal modes of vibration of the whole chain. Excitation at a single fixed frequency could thus be used to produce wide-bandwidth impulses for different lengths of spherical chains. Experimental results were in good agreement with theoretical predictions.

Modelling the effect of acoustic waves on nucleation

A phase transformation in a metastable phase can be affected when it is subjected to a high intensity ultrasound wave. In this study we determined the effect of oscillation in pressure and temperature on a phase transformation using the Gibbs droplet model in a generic format. The developed model is valid for both equilibrium and non-equilibrium clusters formed through a stationary or non-stationary process. We validated the underlying model by comparing the predicted kinetics of water droplet formation from the gas phase against experimental data in the absence of ultrasound. Our results demonstrated better agreement with experimental data in comparison with classical nucleation theory. Then, we determined the thermodynamics and kinetics of nucleation and the early stage of growth of clusters in an isothermal sonocrystallisation process. This new contribution shows that the effect of pressure on the kinetics of nucleation is cluster size-dependent in contrast to classical nucleation theory.

The dynamic excitation of a granular chain for biomedical ultrasound applications: contact mechanics finite element analysis and validation

There has been recent interest in the transmission of acoustic signals along granular chains of spherical beads to produce waveforms of relevance to biomedical ultrasound applications. Hertzian contact between adjacent beads can introduce different harmonic content into the signal as it propagates. This transduction mechanism has the potential to be of use in both diagnostic and therapeutic ultrasound applications, and is the object of the study presented here. Although discrete dynamics models of this behaviour exist, a more comprehensive solution must be sought if changes in shape and deformation of individual beads are to be considered. Thus, the finite element method was used to investigate the dynamics of a granular chain of six, 1 mm diameter chrome steel spherical beads excited at one end using a sinusoidal displacement signal at 73 kHz. Output from this model was compared with the solution provided by the discrete dynamics model, and good overall agreement obtained. In addition, it was able to resolve the complex dynamics of the granular chain, including the multiple collisions which occur. It was demonstrated that under dynamic excitation conditions, the inability of discrete mechanics models to account for elastic deformation of the beads when these lose contact, could lead to discrepancies with experimental observations.