Pierre Gelat

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.

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.

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.

Ultrasonic propagation in finite-length granular chains

A narrowband ultrasound source has been used to generate solitary wave impulses in finite-length chains of spheres. Once the input signal is of sufficient amplitude, both harmonics and sub-harmonics of the input frequency can be generated as non-linear normal modes of the system, allowing a train of impulses to be established from a sinusoidal input. The characteristics of the response have been studied as a function of the physical properties of the chain, the input waveform and the level of static pre-compression. The results agree with the predictions of a theoretical model, based on a set of discrete dynamic equations for the spheres for finite-length chains. Impulses are only created for very small pre-compression forces of the order of 0.01N, where strongly non-linear behaviour is expected.

Relationship between Acoustic Power and Acoustic Radiation Force on Absorbing and Reflecting Targets for Spherically Focusing Radiators

Total acoustic output power is an important parameter required by standards for most ultrasonic medical equipment including high-intensity focused ultrasound (HIFU) systems. Radiation force balances are routinely used; however, radiation force is not strictly dependent on the ultrasound power but, rather, on the wave momentum resolved in one direction. Consequently, measurements based on radiation force become progressively less accurate as the ultrasound wave deviates further from a true plane wave. HIFU transducers can be very strongly focused with F-numbers less than one: under these conditions, the uncertainty associated with use of the radiation force method becomes very significant. International Standards IEC 61161 and IEC 62555 suggest plane-wave correction factors for unfocused transducers radiating onto an ideal absorbing target and focusing corrections for focused transducers radiating onto ideal absorbing targets and onto conical reflecting targets (IEC 61161). Previous models have relied on calculations based on the Rayleigh integral, which is not strictly correct for curved sources. In the work described here, an approach combining finite element methods with a discretization of the Helmholtz equation was developed, making it possible to model the boundary condition at the structure/fluid interface more correctly. This has been used to calculate the relationship between radiation force and total power for both absorbing and conical reflecting targets for transducers ranging from planar to an F-number of 0.5 (hemispherical) and to compare with the recommendations of IEC 61161 and IEC 62555.

The study of chain-like materials for use in biomedical ultrasound

Wave propagation in chain-like materials has been studied previously at low frequencies. The present study has generated these waves at higher frequencies with components >200 kHz, using chains of 1 mm diameter spheres. Resonant ultrasonic horns at 73 kHz have been used as sources of narrowband excitation, which transform into a train of broadband impulses that have the characteristics of solitary waves. These have potential applications in biomedical ultrasound as high amplitude, wide bandwidth impulses.

Numerical and Experimental Study of Mechanisms Involved in Boiling Histotripsy

The aim of boiling histotripsy is to mechanically fractionate tissue as an alternative to thermal ablation for therapeutic applications. In general, the shape of a lesion produced by boiling histotripsy is tadpole like, consisting of a head and a tail. Although many studies have demonstrated the efficacy of boiling histotripsy for fractionating solid tumors, the exact mechanisms underpinning this phenomenon are not yet well understood, particularly the interaction of a boiling vapor bubble with incoming incident shockwaves. To investigate the mechanisms involved in boiling histotripsy, a high-speed camera with a passive cavitation detection system was used to observe the dynamics of bubbles produced in optically transparent tissue-mimicking gel phantoms exposed to the field of a 2.0-MHz high-intensity focused ultrasound (HIFU) transducer. We observed that boiling bubbles were generated in a localized heated region and cavitation clouds were subsequently induced ahead of the expanding bubble. This process was repeated with HIFU pulses and eventually resulted in a tadpole-shaped lesion. A simplified numerical model describing the scattering of the incident ultrasound wave by a vapor bubble was developed to help interpret the experimental observations. Together with the numerical results, these observations suggest that the overall size of a lesion induced by boiling histotripsy is dependent on the sizes of (i) the heated region at the HIFU focus and (ii) the backscattered acoustic field by the original vapor bubble.

Computationally Efficient Boundary Element Methods for High-Frequency Helmholtz Problems in Unbounded Domains

This chapter presents the application of the boundary element method to high-frequency Helmholtz problems in unbounded domains. Based on a standard combined integral equation approach for sound-hard scattering problems we discuss the discretization, preconditioning and fast evaluation of the involved operators. As engineering problem, the propagation of high-intensity focused ultrasound fields into the human rib cage will be considered. Throughout this chapter we present code snippets using the open-source Python boundary element software BEM++ to demonstrate the implementation.

Nonlinear generation of harmonic content within High Intensity Ultrasound signals using granular chains

Applications such as High Intensity Focused Ultrasound (HIFU) conventionally use narrowband signals of high amplitude, which are then focused to a known region within the body. It would be advantageous to be able to broaden the bandwidth, as this could lead to a more spatially-concentrated focal region. One way of increasing the bandwidth is to generate harmonics. The eventual aim of this study is to generate wideband ultrasonic signals with high amplitudes, primarily for therapeutic ultrasound and drug delivery applications. In this paper, a new ultrasonic transducer technology using a one-dimensional chain of spheres is presented to achieve this aim.

The generation of impulses from narrow bandwidth signals using resonant spherical chains

An ultrasonic horn operating at 73 kHz has been used to excite one end of a chain of steel spheres. The signal transmitted along the chain was measured at the far end using a laser vibrometer. Various chain lengths, ranging from 2-10 spheres, have been studied. It was found that a set of solitary wave impulses were generated when a high input amplitude and a minimal pre-compression force was used. Both harmonics and sub-harmonics of the input frequency could be observed. Theoretical models were developed, based on the relevant equations of motion, which modelled the end conditions properly, and their predictions confirmed the experimental observations. Solitary wave impulses were generated only when certain numbers of spheres were used, corresponding to the establishment of resonances in the form of nonlinear normal modes (NNMs). It was found that longer chains led to wider impulse bandwidths. Increased pre-compression tended to damp out this phenomenon, but gave a weakly non-linear state where the time delay of propagation along the chain changed with applied static force. It was thus established that a gated sinusoidal input could be transformed into a set of impulses, of interest in biomedical applications.