We describe and implement a numerical method for modelling the frequency-dependent power-law absorption of ultrasound in tissue, as governed by the first order linear wave equations with a loss taking the form of a fractional time derivative. The (Caputo) fractional time derivative requires the full problem history which is contained within an iterative procedure. The resulting numerical method requires a fixed (static) memory cost irrespective of the number of time steps. The spatial domain is treated by the Fourier spectral method. Numerically comparisons are made against a model for the same power-law absorption with loss described by the fractional-Laplacian operator. One advantage of the fractional time derivative over the fractional-Laplacian operator is the local treatment of the power-law, allowing for a spatially varying frequency power-law.

Existing data on the acoustic properties of low-temperature biological materials is limited and widely dispersed across fields. This makes it difficult to employ this information in the development of ultrasound applications in the medical field, such as cryosurgery and rewarming of cryopreserved tissues. In this review, the low-temperature acoustic properties of biological materials, and the measurement methods used to acquire them were collected from a range of scientific fields. The measurements were reviewed from the acoustic setup to thermal methodologies for samples preparation, temperature monitoring, and system insulation. The collected data contain the longitudinal and shear velocity, and attenuation coefficient of biological soft tissues and biologically relevant substances-water, aqueous solutions, and lipids-in the temperature range down to -50 °C and in the frequency range from 108 kHz to 25 MHz. The multiple reflection method (MRM) was found to be the preferred method for low-temperature samples, with a buffer rod inserted between the transducer and sample to avoid direct contact. Longitudinal velocity changes are observed through the phase transition zone, which is sharp in pure water, and occurs more slowly and at lower temperatures with added solutes. Lipids show longer transition zones with smaller sound velocity changes; with the longitudinal velocity changes observed during phase transition in tissues lying between these two extremes. More general conclusions on the shear velocity and attenuation coefficient at low-temperatures are restricted by the limited data. This review enhance knowledge guiding for further development of ultrasound applications in low-temperature biomedical fields, and may help to increase the precision and standardization of low-temperature acoustic property measurements.

k-Wave is an open-source toolbox for simulating the propagation of acoustic and ultrasound waves in complex and tissue-realistic media that is widely used across academia and industry. In this talk, we present an introduction to k-Wave II. k-Wave-II is a major re-write of the original k-Wave toolbox developed with the following aims: (1) re-engineering the code base to leverage object orientated programming, making it simpler to use for model inversions and coupled physics problems, (2) extending the algorithms to facilitate general boundary conditions on arbitrary surfaces, and to increase performance for narrow-band simulations, (3) improving the development and release process to incorporate good practice and advance long-term sustainability, and (4) improving training, user engagement, and support. We will introduce the new toolbox, discuss current progress, and a provide a road map for future development.

The development of methods to safely rewarm large cryopreserved biological samples remains a barrier to the widespread adoption of cryopreservation. Here, experiments and simulations were performed to demonstrate that ultrasound can increase rewarming rates relative to thermal conduction alone. An ultrasonic rewarming setup based on a custom 444 kHz tubular piezoelectric transducer was designed, characterized, and tested with 2 ml cryovials filled with frozen ground beef. Rewarming rates were characterized in the -20 °C to 5 °C range. Thermal conduction-based rewarming was compared to thermal conduction plus ultrasonic rewarming, demonstrating a tenfold increase in rewarming rate when ultrasound was applied. The maximum recorded rewarming rate with ultrasound was 57° C/min, approximately 2.5 times faster than with thermal conduction alone. Coupled acoustic and thermal simulations were developed and showed good agreement with the heating rates demonstrated experimentally and were also used to demonstrate spatial heating distributions with small (<3° C) temperature differentials throughout the sample when the sample was below 0° C. The experiments and simulations demonstrate the potential for ultrasonic cryovial rewarming with a possible application to large volume rewarming, as faster rewarming rates may improve the viability of cryopreserved tissues and reduce the time needed for cells to regain normal function.

Progress towards fast accurate Ultrasound Tomog-raphy (UST) requires experimental validation of new methods, creating a need for low-cost UST hardware, which can be achieved using in-house manufacture. However, a key challenge for transducer manufacture is controlling the composition and thickness of matching layers. For this work, a new low-cost deposition technique was developed, which is part of the open-UST manufacturing framework. To assess the technique, 8 16-element UST transducer modules were built, and the inter-element variation in their electrical input impedance, impulse response, and transmit-receive response was measured. The acoustic performance was highly uniform with no defective elements. The −40 dB transmit-receive bandwidth was 146 %, with a mean SNR of 60.5 dB, and the standard deviation in amplitude at the 1.21 MHz fundamental frequency, was very low (σ= ± 7.1 %, without using normalisation. The high uniformity is significant, because it means that the elements can be assumed to be identical during image reconstruction, which simplifies the assumptions required, and removes the need for extensive hy-drophone calibration. The open-UST manufacturing framework could therefore lower the barrier to entry for researchers, and accelerate preliminary UST research.

The number of ultrasound detectors required to produce photoacoustic tomography images can be reduced significantly by fully enclosing the imaging target in an acoustically reverberant cavity and exploiting the multiple reflections. This is demonstrated experimentally.

Large-scale nonlinear ultrasound simulations using the open-source k-Wave toolbox are now routinely performed using the MPI version of k-Wave running on traditional CPU-based clusters. However, the all-to-all communications required by the 3D fast Fourier transform (FFT) severely impact performance when scaling to large numbers of compute cores. This can be overcome by using a domain decomposition strategy based on a local Fourier basis. In this work, we analyze the performance and accuracy of using local domain decomposition for running a high-intensity focused ultrasound (HIFU) simulation in the kidney on a single server containing eight NVIDIA P40 graphical processing units (GPUs). Different decompositions and overlap sizes are investigated and compared to a global MPI simulation running on a CPU-based supercomputer using 1280 cores. For a grid size of 960 by 960 by 1280 grid points and an overlap size of 4 grid points, the error in the simulation using local domain decomposition is on the order of 0.1$ compared to the global simulation, which is sufficient for most applications. The financial cost for running the simulation is also reduced by more than an order of magnitude.

The pseudospectral time domain (PSTD) method is popular as a wave equation solver, one of its advantages being that it permits the use of coarse grids, as long as the spatial sampling is greater than two points-per-wavelength. The k-space PSTD method improves on this by incorporating an additional factor to remove the numerical dispersion which arises from the discretisation of the time derivatives. However, the effect of the temporal discretisation of time-varying sources has not previously been considered, although it can lead to substantial errors in the predicted field unless the timestep is sufficiently small to ensure the highest frequency is sampled at many points-per-period. Here, a correction factor is derived which eliminates this source of error, resulting in a k-space PSTD method that retains the spatial sampling advantage of conventional PSTD schemes but is also accurate as long as the temporal sampling is greater than two points-per-period and the CFL number is < 1.

Light absorbing polymer nanocomposites have been widely investigated as a source of broadband and high amplitude ultrasound generated via pulsed laser excitation. Biomedical applications of such sources include both imaging and ablative therapies. Fabrication of light absorbing nanocomposite sources has mostly involved elaborate chemistry. Here, a nanocomposite composed of multi-walled carbon nanotubes mechanically dispersed in polydimethylsiloxane polymer is used. The nanocomposite film was backed on optically clear polydimethylsiloxane and laboratory grade glass slides. The two backed sources were investigated using two lasers whose full-width half maximum durations were 2.6 and 4.0 ns. It was found that the characteristics of the acoustic field generated from the nanocomposite source showed a significant dependence on the backing when the stress confinement criterion is not satisfied.

The k-Wave MATLAB toolbox is widely used to conduct medical ultrasound simulations. It uses a Fourier collocation method to numerically solve the governing model equations, and introduces sources by adding acoustic pressure at points on an orthogonal grid. This approach introduces two errors when sources don't exactly align with the grid. These are phase errors arising from shifting source points to nearby grid nodes, and amplitude errors arising from an angular dependence in the density of source points. These two errors are collectively referred to as 'staircasing'. Staircasing errors can be overcome by considering the band-limited representation of sources that arises from the use of a Fourier collocation method. To do so, sources are discretised by convolving a band-limited point source with the desired source geometry. To validate this approach, a comparison is made with current k-Wave source algorithms and with the FOCUS ultrasound simulation code. The new sources are shown to eliminate staircasing errors.

Ultrasound computed tomography (USCT) is a non-invasive imaging technique that provides information about the acoustic properties of soft tissues in the body, such as the speed of sound (SS) and acoustic attenuation (AA). Knowledge of these properties can improve the discrimination between benign and malignant masses, especially in breast cancer studies. Full wave inversion (FWI) methods for image reconstruction in USCT provide the best image quality compared to more approximate methods. Using FWI, the SS is usually recovered in the time domain, and the AA is usually recovered in the frequency domain. Nevertheless, as both properties can be obtained from the same data, it is desirable to have a common framework to reconstruct both distributions. In this work, an algorithm is proposed to reconstruct both the SS and AA distributions using a time domain FWI methodology based on the fractional Laplacian wave equation, an adjoint field formulation, and a gradient-descent method. The optimization code employs a Compute Unified Device Architecture version of the software k-Wave, which provides high computational efficiency. The performance of the method was evaluated using simulated noisy data from numerical breast phantoms. Errors were less than 0.5% in the recovered SS and 10% in the AA.

The generation of complex diffraction limited acoustic fields from a simple planar transducer is possible using cheap 3-D printable kinoforms. This approach is extremely promising for several areas of physical acoustics. However, one drawback is that the acoustic field generated from a given kinoform is fixed, limiting flexibility. In this work, multi-frequency acoustic kinoforms are investigated as a means to circumvent that limitation. These are kinoforms designed to generate different distributions of pressure at a target depth when driven at particular design frequencies. An optimisation approach based on direct search for the design of these structures from a set of input frequencies and target distributions is briefly described. The effect of different parameters of the kinoform on the performance are then established. These include the maximum thickness, frequency spacing and target depth. It is found that the maximum thickness has to be limited to avoid significant aberrations, the frequency spacing should be maximised within the usable bandwidth of the transducer, and the optimal thickness is influenced by the choice of target depth. The thin phase approximation is also shown to be increasingly inaccurate for increasing element thicknesses.

Purpose: High intensity focused ultrasound (HIFU) provides a non‐invasive salvage treatment option for patients with recurrence after external beam radiation therapy (EBRT). As part of EBRT the prostate is frequently implanted with permanent fiducial markers. To date, the impact of these markers on subsequent HIFU treatment is unknown. The objective of this work was to systematically investigate, using computational simulations, how these fiducial markers affect the delivery of HIFU treatment. Methods: A series of simulations was performed modelling the propagation of ultrasound pressure waves in the prostate with a single spherical or cylindrical gold marker at different positions and orientations. For each marker configuration, a set of metrics (spatial‐peak temporal‐average intensity, focus shift, focal volume) was evaluated to quantify the distortion introduced at the focus. An analytical model was also developed describing the marker effect on the intensity at the focus. The model was used to examine the marker's impact in a clinical setting through case studies. Results: The simulations show that the presence of the marker in the pre‐focal region causes reflections which induce a decrease in the focal intensity and focal volume, and a shift of the maximum pressure point away from the transducer's focus. These effects depend on the shape and orientation of the marker and become more pronounced as its distance from the transducer's focus decreases, with the distortion introduced by the marker greatly increasing when placed within 5 mm of the focus. The analytical model approximates the marker's effect and can be used as an alternative method to the computationally intensive and time consuming simulations for quickly estimating the intensity at the focus. A retrospective review of a small patient cohort selected for focal HIFU after failed EBRT indicates that the presence of the marker may affect HIFU treatment delivery. Conclusions: The distortion introduced by the marker to the HIFU beam when positioned close to the focus may result in an undertreated region beyond the marker due to less energy arriving at the focus, and an overtreated region due to reflections. Further work is necessary to investigate whether the results presented here justify the revision of the patient selection criteria or the markers’ placement protocol.

Reconstructing images from measured time domain signals is an essential step in tomography-mode photoacoustic imaging. However, in practice, there are many complicating factors that make it difficult to obtain high-resolution images. These include incomplete or undersampled data, filtering effects, acoustic and optical attenuation, and uncertainties in the material parameters. Here, the processing and image reconstruction steps routinely used by the Photoacoustic Imaging Group at University College London are discussed. These include correction for acoustic and optical attenuation, spatial resampling, material parameter selection, image reconstruction, and log compression. The effect of each of these steps is demonstrated using a representative in vivo dataset. All of the algorithms discussed form part of the open-source k-Wave toolbox (available from http://www.k-wave.org).

Photoacoustic tomography (PAT) is an emerging biomedical imaging from coupled physics technique, in which the image contrast is due to optical absorption, but the information is carried to the surface of the tissue as ultrasound pulses. Many algorithms and formulae for PAT image reconstruction have been proposed for the case when a complete data set is available. In many practical imaging scenarios, however, it is not possible to obtain the full data, or the data may be sub-sampled for faster data acquisition. In such cases, image reconstruction algorithms that can incorporate prior knowledge to ameliorate the loss of data are required. Hence, recently there has been an increased interest in using variational image reconstruction. A crucial ingredient for the application of these techniques is the adjoint of the PAT forward operator, which is described in this article from physical, theoretical and numerical perspectives. First, a simple mathematical derivation of the adjoint of the PAT forward operator in the continuous framework is presented. Then, an efficient numerical implementation of the adjoint using a k-space time domain wave propagation model is described and illustrated in the context of variational PAT image reconstruction, on both 2D and 3D examples including inhomogeneous sound speed. The principal advantage of this analytical adjoint over an algebraic adjoint (obtained by taking the direct adjoint of the particular numerical forward scheme used) is that it can be implemented using currently available fast wave propagation solvers.

Purpose or Objective:The purpose of the study was to evaluate the consistency, accuracy and timesaving of a growcut segmentation algorithm for heterogeneous tumor volumes. Material and Methods:We present a new PET segmentation method, which is developed as a combination algorithm of Otsu and the Grow-cut segmentation algorithms and henceforth referred to as Otsu_GC.An initial contour of the tumor was defined using Otsu algorithm, which sets the threshold to minimize the intra-class variance of the tumor and its background.A concentric 3D shell was defined around the initial tumor contour at a distance of twice the slice thickness and extends up to four times the slice thickness.The space between the initial tumor contour and the inner edge of the shell ensured that the background voxels did not include the spill over voxels.The segmentation then employs the Grow-cut algorithm with the initial tumor contour and the 3D shell as the foreground and background seed respectively.The images underwent preprocessing, which included resampling to thinner slices with smaller in-plane voxel sizes that equal the CT slices.Edge preservation and contrast enhancement was achieved by convolution of high boost filter kernel in spatial domain and denoising with Gaussian blur (σ = 1pixel) filter.The implementation of preprocessing was in MATLAB and the segmentation was with SlicerRT and Grow-cut modules from 3D Slicer.The algorithm was tested on 11 heterogeneous NSCLC tumors (coefficient of variance: mean 0.35 ± 0.04) from 9 retrospective patient data.The manual contour of the PET uptake by the treating clinician was used as the ground truth for validation using Dice Similarity coefficient (DSC) and absolute volume difference as the evaluation metrics.The true contours were also compared to adaptive threshold (Tadaptive) and 40% SUVmax threshold (T40) based isocontours.The PET(Otsu-GC) contours were also provided as the initial contour that was edited for final gross tumor volume (GTV) definition, which included composite information from CT and PET.The time taken for manual GTV contouring versus the time to edit the PET(Otsu-GC) contours was assessed as a measure of efficiency in this approach.

A new method for the creation of patterned, focused, optically generated acoustic fields using a single optical pulse is introduced. This utilises multi-layer `holograms' composed of several spatially separate absorbing layers. Each layer is individually patterned so as to focus at a set of targeted points. To create the patterns, a ray-tracing model was implemented to calculate the impulse response of pixels within each absorbing layer to a set of targeted points. An optimisation approach was then used to find the optimal pattern for each layer to create a field evenly focused at each of the target points. The method was validated using both numerical simulations and acoustic field measurements. It was demonstrated that a 3×3 array of acoustic foci could be generated from a 3-layer hologram using a single laser pulse.

Kidney cancer is a severe disease which can be treated non-invasively using high-intensity focused ultrasound (HIFU) therapy. However, tissue in front of the transducer and the deep location of kidney can cause significant losses to the efficiency of the treatment. The effect of attenuation, refraction and reflection due to different tissue types on HIFU therapy of the kidney was studied using a nonlinear ultrasound simulation model. The geometry of the tissue was derived from a computed tomography (CT) dataset of a patient which had been segmented for water, bone, soft tissue, fat and kidney. The combined effect of inhomogeneous attenuation and soundspeed was found to result in an 11.0 dB drop in spatial peak-temporal average (SPTA) intensity in the kidney compared to pure water. The simulation without refraction effects showed a 6.3 dB decrease indicating that both attenuation and refraction contribute to the loss in focal intensity. The losses due to reflections at soft tissue interfaces were less than 0.1 dB. Focal point shifting due to refraction effects resulted in -1.3, 2.6 and 1.3 mm displacements in x-, y- and z-directions respectively. Furthermore, focal point splitting into several smaller subvolumes was observed. The total volume of the secondary focal points was approximately 46% of the largest primary focal point. This could potentially lead to undesired heating outside the target location and longer therapy times.

Measurement of high acoustic pressures is necessary in order to fully characterise clinical high-intensity focused ultrasound (HIFU) fields, and for accurate validation of computational models of ultrasound propagation. However, many existing methods are unable to withstand the extreme pressures generated in these fields, and those that can often have high noise levels. Here, a robust sensor, based on a planar Fabry-Pérot interferometer with hard dielectric spacer and mirrors, was used to measure acoustic pressure in the field of a 3.3 MHz single element spherically focused bowl transducer. In preliminary measurements, peak positive pressures of 27 MPa, and peak negative pressures of 14 MPa were measured. The noise equivalent pressure scaled with the adjustable dynamic range of the system between 50 kPa for pressures up to 8 MPa and 235 kPa for measurements up to 70 MPa. This makes the system suitable for measuring low pressure regions of the field as well as the high focal pressures. The -3 dB bandwidth of the sensor was 600 MHz, and the effective element size was 25 μm, which makes the sensor well suited to the measurement of the highly nonlinear and localised high-pressure focal regions generated in HIFU fields. Waveforms were acquired at a rate of 200 Hz, several orders of magnitude faster than can be achieved with a hydrophone scanning system. This sensor represents a critical improvement in measurement capability for HIFU fields in terms of dynamic range, bandwidth, noise equivalent pressure, and acquisition speed.