Simulating Focused Ultrasound Transducers using Discrete Sources on Regular Cartesian Grids

Accurately representing the behaviour of acoustic sources is an important part of ultrasound simulation. This is particularly challenging in ultrasound therapy where multielement arrays are often used. Typically, sources are defined as a boundary condition over a 2D plane within the computational model. However, this approach can become difficult to apply to arrays with multiple elements distributed over a non-planar surface. In this work, a grid-based discrete source model for single and multi-element bowl-shaped transducers is developed to model the source geometry explicitly within a regular Cartesian grid. For each element, the source model is defined as a symmetric, simply-connected surface with a single grid point thickness. Simulations using the source model with the opensource k-Wave toolbox are validated using the Rayleigh integral, O'Neil's solution, and experimental measurements of a focused bowl transducer under both quasi continuous wave and pulsed excitation. Close agreement is shown between the discrete bowl model and the axial pressure predicted by O'Neil's solution for a uniform curved radiator, even at very low grid resolutions. Excellent agreement is also shown between the discrete bowl model and experimental measurements. To accurately reproduce the near-field pressure measured experimentally, it is necessary to derive the drive signal at each grid point of the bowl model directly using holography. However, good agreement is also obtained in the focal region using uniformly radiating monopole sources distributed over the bowl surface. This allows the response of multi-element transducers to be modelled, even where measurement of an input plane is not possible

Experimental validation of k-Wave: Nonlinear wave propagation in layered, absorbing fluid media

Models of ultrasound propagation in biologically relevant media have applications in planning and verification of ultrasound therapies and computational dosimetry. To be effective, the models must be able to accurately predict both the spatial distribution and amplitude of the acoustic pressure. This requires that the models are validated in absolute terms, which for arbitrarily heterogeneous media should be performed by comparison with measurements of the acoustic field. In this study, simulations performed using the open-source k-Wave acoustics toolbox, with a measurement-based source definition, were quantitatively validated against measurements of acoustic pressure in water and layered absorbing fluid media. In water, the measured and simulated spatial peak pressures agreed to within 3% under linear conditions and 7% under non-linear conditions. After propagation through a planar or wedge shaped glycerol-filled phantom, the difference in spatial peak pressure was 8.5% and 10.7%, respectively. These differences are within or close to the expected uncertainty of the acoustic pressure measurement. The -6 dB width and length of the focus agreed to within 4% in all cases, and the focal positions were within 0.7 mm for the planar phantom and 1.2 mm for the wedge shaped phantom. These results demonstrate that when the acoustic medium properties and geometry are well known, accurate quantitative predictions of the acoustic field can be made using k-Wave

Investigation of the repeatability and reproducibility of hydrophone measurements of medical ultrasound fields

Accurate measurements of acoustic pressure are required for characterisation of ultrasonic transducers and for experimental validation of models of ultrasound propagation. Errors in measured pressure can arise from a variety of sources, including variations in the properties of the source and measurement equipment, calibration uncertainty, and processing of measured data. In this study, the repeatability of measurements made with four probe and membrane hydrophones was examined. The pressures measured by these hydrophones in three different ultrasound fields, with both linear and nonlinear, pulsed and steady state driving conditions, were compared to assess the reproducibility of measurements. The coefficient of variation of the focal peak positive pressure was less than 2% for all hydrophones across five repeated measurements. When comparing hydrophones, pressures measured in a spherically focused 1.1 MHz field were within 7% for all except 1 case, and within 10% for a broadband 5 MHz pulse from a diagnostic linear array. Larger differences of up to 55% were observed between measurements of a tightly focused 3.3 MHz field, which were reduced for some hydrophones by the application of spatial averaging corrections. Overall, the major source of these differences was spatial averaging and uncertainty in the complex frequency response of the hydrophones

Quantifying the effects of standing waves within the skull for ultrasound mediated opening of the blood-brain-barrier

Ultrasound mediated opening of the blood-brain barrier (BBB) has been shown to be effective in enhancing the delivery of therapeutic agents to the brain. However, challenges remain in targeting and specificity of BBB opening due to attenuation, aberration and reverberation of transcranial ultrasound fields. In this study, experimental and numerical assessment was performed of standing waves within an ex vivo human skull when delivering ultrasound pulses of varying lengths at 300 kHz using a large aperture focused ultrasound transducer. Simulations showed minimal distortion of the focal region but low amplitude standing waves were established within the skull with bursts of 50 cycles or more. Under the same conditions, the experimental measurements showed small variations in focal pressure which took 300 to 600 µs to stabilise. The pattern of sidelobes and superimposed standing waves was generally more complex when the focus was placed closer to the side and base of the skull. This data supports the use of large aperture diameter transducers and short pulse lengths for targeted BBB opening

Experimental assessment of skull aberration and transmission loss at 270 kHz for focused ultrasound stimulation of the primary visual cortex

Transcranial focused ultrasound is a rapidly emerging method for non-invasive neuromodulation and stimulation. However, the skull causes a significant acoustic barrier and can reduce the focal intensity and alter the position and shape of the focus compared to free-field. In this study, the insertion loss and focal distortion due to the skull bone were quantified using three ex vivo human skulls and a focused ultrasound transducer operating at 270 kHz targeted on the approximate positions of the left and right primary visual cortex. Compared to free-field, the average insertion loss was -9.8 dB (± 2.2 dB), while the average focal shift was 1.7 mm (± 0.56 mm) in the lateral direction and 2.8 mm (±4.2 mm) in the axial direction. Overall, the acoustic aberrations were small compared to the size of the focal volume, meaning effective stimulation at this frequency can likely be achieved without patient-specific targeting. However, the insertion loss was significant and should be considered when selecting the target focal intensity for human studies

Pseudospectral time-domain (PSTD) methods for the wave equation: Realising boundary conditions with discrete sine and cosine transforms

Pseudospectral time domain (PSTD) methods are widely used in many branches of acoustics for the numerical solution of the wave equation, including biomedical ultrasound and seismology. The use of the Fourier collocation spectral method in particular has many computational advantages. However, the use of a discrete Fourier basis is also inherently restricted to solving problems with periodic boundary conditions. Here, a family of spectral collocation methods based on the use of a sine or cosine basis is described. These retain the computational advantages of the Fourier collocation method but instead allow homogeneous Dirichlet (sound-soft) and Neumann (sound-hard) boundary conditions to be imposed. The basis function weights are computed numerically using the discrete sine and cosine transforms, which can be implemented using O(N log N) operations analogous to the fast Fourier transform. Practical details of how to implement spectral methods using discrete sine and cosine transforms are provided. The technique is then illustrated through the solution of the wave equation in a rectangular domain subject to different combinations of boundary conditions. The extension to boundaries with arbitrary real reflection coefficients or boundaries that are non-reflecting is also demonstrated using the weighted summation of the solutions with Dirichlet and Neumann boundary conditions.Comment: 21 pages, 10 figure

Prostatic calcifications: Quantifying occurrence, radiodensity, and spatial distribution in prostate cancer patients

Background: To evaluate the prevalence, density, and distribution of prostate calcification in patients with prostate cancer. / Methods: Patients who underwent both Gallium-68 PSMA PET/CT and MRI of the prostate over the course of a year were selected for analysis. The CT images with visible calcifications within the prostate were included and calcifications automatically isolated using a threshold of 130 HU. The corresponding multiparametric MRI was assessed and the peripheral zone, transition zone, MRI-visible tumor, and urethra manually contoured. The contoured MRI and CT images were registered using rigid registration, and calcifications mapped automatically to the MRI contours. / Results: A total of 85 men (age range 50–88, mean 69 years, standard deviation 7.2 years) were assessed. The mean serum Prostate Specific Antigen PSA was 16.7, range 0.12 to 94.4. Most patients had intermediate-risk disease (68%; Gleason grade group 2 and 3), 26% had high-risk disease (Gleason grade group 4 and 5), and 6% had low-risk disease (Gleason grade group 1). Forty-six patients out of 85 (54%) had intraprostatic calcification. Calcification occurred more in transition zone than the peripheral zone (65% vs. 35%). The mean density of the calcification was 227 HU (min 133, max 1,966 HU). In 12 patients, the calcification was within an MRI-visible tumor, in 24 patients, there were calcifications within a 9 mm distance of the tumor border, and in 9 patients, there were calcifications located between the urethra and tumor. / Conclusions: Calcifications are common in patients with prostate cancer. Their density and location may make them a significant consideration when planning treatment or retreatment with some types of minimally invasive therapy

Experimental study of beam distortion due to fiducial markers during salvage HIFU in the prostate

BACKGROUND: Prostate cancer is frequently treated using external beam radiation therapy (EBRT). Prior to therapy, the prostate is commonly implanted with a small number of permanent fiducial markers used to monitor the position of the prostate during therapy. In the case of local cancer recurrence, high-intensity focused ultrasound (HIFU) provides a non-invasive salvage treatment option. However, the impact of the fiducial markers on HIFU treatment has not been thoroughly studied to date. The objective of this study was to experimentally investigate the effect of a single EBRT fiducial marker on the efficacy of HIFU treatment delivery using a tissue-mimicking material (TMM). METHODS: A TMM with the acoustic properties of the prostate was developed based on a polyacrylamide hydrogel containing bovine serum albumin. Each phantom was implanted with a cylindrical fiducial marker and then sonicated using a 3.3 MHz focused bowl HIFU transducer. Two sets of experiments were performed. In the first, a single lesion was created at different positions along either the anteroposterior or left-right axes relative to the marker. In the second, a larger ablation volume was created by raster scanning. The size and position of the ablated volume were assessed using a millimetre grid overlaid on the phantom. RESULTS: The impact of the marker on the position and size of the HIFU lesion was significant when the transducer focus was positioned within 7 mm anteriorly, 18 mm posteriorly or within 3 mm laterally of the marker. Beyond this, the generated lesion was not affected. When the focus was anterior to the marker, the lesion increased in size due to reflections. When the focus was posterior, the lesion decreased in size or was not present due to shadowing. CONCLUSIONS: The presence of an EBRT fiducial marker may result in an undertreated region beyond the marker due to reduced energy arriving at the focus, and an overtreated region in front of the marker due to reflections. Depending on the position of the targeted regions and the distribution of the markers, both effects may be undesirable and reduce treatment efficacy. Further work is necessary to investigate whether these results indicate the necessity to reconsider patient selection and treatment planning for prostate salvage HIFU after failed EBRT