A fast full-wave solver for calculating ultrasound propagation in the body.

Therapeutic ultrasound is a promising non-invasive method for inducing various beneficial biological effects in the human body. In cancer treatment applications, high-power ultrasound is focused at a target tissue volume to ablate the malignant tumour. The success of the procedure depends on the ability to accurately focus ultrasound and destroy the target tissue volume through coagulative necrosis whilst preserving the surrounding healthy tissue. Patient-specific treatment planning strategies are therefore being developed to increase the efficacy of such therapies, while reducing any damage to healthy tissue. These strategies require to use high-performance computing methods to solve ultrasound wave propagation in the body quickly and accurately. For realistic clinical scenarios, all numerical methods which employ volumetric meshes require several hours or days to solve the full-wave propagation on a computer cluster. The boundary element method (BEM) is an efficient approach for modelling the wave field because only the boundaries of the hard and soft tissue regions require discretisation. This paper presents a multiple-domain BEM formulation with a novel preconditioner for solving the Helmholtz transmission problem (HTP). This new formulation is efficient at high-frequencies and where high-contrast materials are present. Numerical experiments are performed to solve the HTP in multiple domains comprising: (i) human ribs, an idealised abdominal fat layer and liver tissue, (ii) a human kidney with a perinephric fat layer, exposed to the acoustic field generated by a high-intensity focused ultrasound (HIFU) array transducer. The time required to solve the equations associated with these problems on a single workstation is of the order of minutes. These results demonstrate the great potential of this new BEM formulation for accurately and quickly solving ultrasound wave propagation problems in large anatomical domains which is essential for developing treatment planning strategies.

The dynamic excitation of a granular chain: Contact mechanics finite element analysis and experimental validation.

There is currently interest in transmitting acoustic signals along granular chains to produce waveforms of relevance to biomedical ultrasound applications. The study of such a transduction mechanism is greatly aided by the use of validated theoretical models. In view of this, a finite element analysis is presented in this paper. The dynamics of a granular chain of six, 1 mm diameter chrome steel spherical beads, was excited at one end using a sinusoidal displacement signal at 73 kHz, and terminated by a rigid support. Output from this model was compared with the solution provided by the equivalent discrete dynamics model, and good agreement obtained. An experimental configuration involving the same chain, but terminated by an annular support made of a liquid photopolymer resin was also simulated and the velocity of the last sphere obtained through simulation was compared with laser vibrometer measurement, with good agreement. This model was then extended whereby the granular chain was coupled to an acoustic medium with the properties of water, via a thin vitreous carbon cylinder. Finite element predictions of the acoustic pressure indicate that, for a 73 kHz excitation frequency, harmonic rich acoustic pulses with harmonic content close to 1 MHz are predicted.

Analysis of solitary wave impulses in granular chains using ultrasonic excitation.

The propagation of broad bandwidth solitary wave impulses, generated within granular chains by narrow bandwidth ultrasonic excitation, is studied in detail. Theoretical predictions are compared to experimental results. It is demonstrated that the observed effects result from a sum of a solitary wave traveling out from the source with a wave that reflects from the far end of the chain. It is shown that this combination, when used with an excitation in the form of a long-duration tone burst, encourages the generation of multiple impulses with a characteristic periodicity. This study shows that the properties of the chain structure and the excitation can be adjusted so as to generate ultrasonic solitary wave impulses with a high amplitude and known frequency content, which are of interest in applications such as biomedical ultrasound.

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.

An assessment of the DORT method on simple scatterers using boundary element modelling.

The ability to focus through ribs overcomes an important limitation of a high-intensity focused ultrasound (HIFU) system for the treatment of liver tumours. Whilst it is important to generate high enough acoustic pressures at the treatment location for tissue lesioning, it is also paramount to ensure that the resulting ultrasonic dose on the ribs remains below a specified threshold, since ribs both strongly absorb and reflect ultrasound. The DORT (décomposition de l'opérateur de retournement temporel) method has the ability to focus on and through scatterers immersed in an acoustic medium selectively without requiring prior knowledge of their location or geometry. The method requires a multi-element transducer and is implemented via a singular value decomposition of the measured matrix of inter-element transfer functions. The efficacy of a method of focusing through scatterers is often assessed by comparing the specific absorption rate (SAR) at the surface of the scatterer, and at the focal region. The SAR can be obtained from a knowledge of the acoustic pressure magnitude and the acoustic properties of the medium and scatterer. It is well known that measuring acoustic pressures with a calibrated hydrophone at or near a hard surface presents experimental challenges, potentially resulting in increased measurement uncertainties. Hence, the DORT method is usually assessed experimentally by measuring the SAR at locations on the surface of the scatterer after the latter has been removed from the acoustic medium. This is also likely to generate uncertainties in the acoustic pressure measurement. There is therefore a strong case for assessing the efficacy of the DORT method through a validated theoretical model. The boundary element method (BEM) applied to exterior acoustic scattering problems is well-suited for such an assessment. In this study, BEM was used to implement the DORT method theoretically on locally reacting spherical scatterers, and to assess its focusing capability relative to the spherical focusing case, binarised apodisation based on geometric ray tracing and the phase conjugation method.

A comparison of methods for focusing the field of a HIFU array transducer through human ribs.

A forward model, which predicts the scattering by human ribs of a multi-element high-intensity focused ultrasound transducer, was used to investigate the efficacy of a range of focusing approaches described in the literature. This forward model is based on the boundary element method and was described by Gélat et al (2011 Phys. Med. Biol. 56 5553-81; 2012 Phys. Med. Biol. 57 8471-97). The model has since been improved and features a complex surface impedance condition at the surface of the ribs. The inverse problem of focusing through the ribs was implemented on six transducer array-rib topologies and five methods of focusing were investigated, including spherical focusing, binarized apodization based on geometric ray tracing, phase conjugation and the decomposition of the time-reversal operator method. The excitation frequency was 1 MHz and the array was of spherical-section type. Both human and idealized rib topologies were considered. The merit of each method of focusing was examined. It was concluded that the constrained optimization approach offers greater potential than the other focusing methods in terms of maximizing the ratio of acoustic pressure magnitudes at the focus to those on the surface of the ribs whilst taking full advantage of the dynamic range of the phased array.

The optimization of acoustic fields for ablative therapies of tumours in the upper abdomen.

High intensity focused ultrasound (HIFU) enables highly localized, non-invasive tissue ablation and its efficacy has been demonstrated in the treatment of a range of cancers, including those of the kidney, prostate and breast. HIFU offers the ability to treat deep-seated tumours locally, and potentially bears fewer side effects than more invasive treatment modalities such as resection, chemotherapy and ionizing radiation. There remains however 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 ribcage to ablate tissue at the required foci whilst minimizing the formation of side lobes and sparing healthy tissue. Ribs both absorb and reflect ultrasound strongly. This sometimes results in overheating of bone and overlying tissue during treatment, leading to skin burns. Successful treatment of a patient with tumours in the upper abdomen therefore requires a thorough understanding of the way acoustic and thermal energy is deposited. Previously, a boundary element approach based on a Generalized Minimal Residual (GMRES) implementation of the Burton-Miller formulation was developed to predict the field of a multi-element HIFU array scattered by human ribs, the topology of which was obtained from CT scan data (Gélat et al 2011 Phys. Med. Biol. 56 5553-81). The present paper describes the reformulation of the boundary element equations as a least-squares minimization problem with nonlinear constraints. The methodology has subsequently been tested at an excitation frequency of 1 MHz on a spherical multi-element array in the presence of ribs. A single array-rib geometry was investigated on which a 50% reduction in the maximum acoustic pressure magnitude on the surface of the ribs was achieved with only a 4% reduction in the peak focal pressure compared to the spherical focusing case. This method was then compared with a binarized apodization approach based on ray tracing and against the decomposition of the time-reversal operator (DORT). In both cases, the constrained optimization provided a superior ratio of focal peak pressure to maximum pressure magnitude on the surface of the ribs.

Characterisation and improvement of a reference cylindrical sonoreactor.

This paper describes theoretical and experimental methods for characterising the performance of a 25 kHz sonochemical reactor (RV-25), which is being developed as a reference facility for studying acoustic cavitation at the National Physical Laboratory (NPL). Field measurements, acquired in different locations inside the sonoreactor, are compared with finite element models at different temperatures, showing that relatively small temperature variations can result in significant changes in the acoustic pressure distribution (and consequent cavitation activity). To improve stability, a deeper insight into the way energy is transferred from the power supply to the acoustic field is presented, leading to criteria - based on modal analysis - to dimension and verify an effective temperature control loop. The simultaneous use of measurements and modelling in this work produced guidelines for the design of multi-frequency cylindrical sonoreactors, also described.