Modeling power law absorption and dispersion for acoustic propagation using the fractional Laplacian

Strategies and safety simulations for ultrasonic cervical spinal cord neuromodulation

Objective. Focused ultrasound spinal cord neuromodulation has been demonstrated in small animals. However, most of the tested neuromodulatory exposures are similar in intensity and exposure duration to the reported small animal threshold for possible spinal cord damage. All efforts must be made to minimize the risk and assure the safety of potential human studies, while maximizing potential treatment efficacy. This requires an understanding of ultrasound propagation and heat deposition within the human spine.Approach. Combined acoustic and thermal modelling was used to assess the pressure and heat distributions produced by a 500 kHz source focused to the C5/C6 level via two approaches (a) the posterior acoustic window between vertebral posterior arches, and (b) the lateral intervertebral foramen from which the C6 spinal nerve exits. Pulse trains of fifty 0.1 s pulses (pulse repetition frequency: 0.33 Hz, free-field spatial peak pulse-averaged intensity: 10 W cm-2) were simulated for four subjects and for ±10 mm translational and ±10∘rotational source positioning errors.Main results.Target pressures ranged between 20%-70% of free-field spatial peak pressures with the posterior approach, and 20%-100% with the lateral approach. When the posterior source was optimally positioned, peak spine heating values were below 1 ∘C, but source mispositioning resulted in bone heating up to 4 ∘C. Heating with the lateral approach did not exceed 2 ∘C within the mispositioning range. There were substantial inter-subject differences in target pressures and peak heating values. Target pressure varied three to four-fold between subjects, depending on approach, while peak heating varied approximately two-fold between subjects. This results in a nearly ten-fold range between subjects in the target pressure achieved per degree of maximum heating.Significance. This study highlights the utility of trans-spine ultrasound simulation software and need for precise source-anatomy positioning to assure the subject-specific safety and efficacy of focused ultrasound spinal cord therapies.

On the imaging depth limit of photoacoustic tomography in the visible and first near-infrared windows

It is well known that photoacoustic tomography (PAT) can circumvent the photon scattering problem in optical imaging and achieve high-contrast and high-resolution imaging at centimeter depths. However, after two decades of development, the long-standing question of the imaging depth limit of PAT in biological tissues remains unclear. Here we propose a numerical framework for evaluating the imaging depth limit of PAT in the visible and the first near-infrared windows. The established framework simulates the physical process of PAT and consists of seven modules, including tissue modelling, photon transportation, photon to ultrasound conversion, sound field propagation, signal reception, image reconstruction, and imaging depth evaluation. The framework can simulate the imaging depth limits in general tissues, such as the human breast, the human abdomen-liver tissues, and the rodent whole body and provide accurate evaluation results. The study elucidates the fundamental imaging depth limit of PAT in biological tissues and can provide useful guidance for practical experiments.

An efficient method for transcranial ultrasound focus correction based on the coupling of boundary integrals and finite elements

Transcranial focused ultrasound is a novel technique for the noninvasive treatment of brain diseases. The success of the treatment greatly depends on achieving precise and efficient intraoperative focus. However, compensating for aberrated ultrasound waves caused by the skull through numerical simulation-based phase corrections is a challenging task due to the significant computational burden involved in solving the acoustic wave equation. In this article, we propose a promising strategy using the coupling of the boundary integral equation method (BIEM) and the finite element method (FEM) to overcome the above limitation. Specifically, we adopt the BIEM to obtain the Robin-to-Dirichlet maps on the boundaries of the skull and then couple the maps to the FEM matrices via a dual interpolation technique, resulting in a computational domain including only the skull. Three simulation experiments were conducted to evaluate the effectiveness of the proposed method, including a convergence test and two skull-induced aberration corrections in 2D and 3D ultrasound. The results show that the method's convergence is guaranteed as the element size decreases, leading to a decrease in pressure error. The computation times for simulating a 500 kHz ultrasound field on a regular desktop computer were found to be 0.47 ± 0.01 s in the 2D case and 43.72 ± 1.49 s in the 3D case, provided that lower-upper decomposition (approximately 13 s in 2D and 2.5 h in 3D) was implemented in advance. We also demonstrated that more accurate transcranial focusing can be achieved by phase correction compared to the noncorrected results (with errors of 1.02 mm vs. 6.45 mm in 2D and 0.28 mm vs. 3.07 mm in 3D). The proposed strategy is valuable for enabling online ultrasound simulations during treatment, facilitating real-time adjustments and interventions.

An all-ultrasound cranial imaging method to establish the relationship between cranial FUS incidence angle and transcranial attenuation in non-human primates in 3D

Focused ultrasound (FUS) is a non-invasive and non-ionizing technique which deploys ultrasound waves to induce bio-effects. When paired with acoustically active particles such as microbubbles (MBs), it can open the blood brain barrier (BBB) to facilitate drug delivery otherwise inhibited due to the presence of BBB. One of the parameters that affects the FUS beam propagation is the beam incidence angle on the skull. Prior work by our group has shown that, as incidence angles deviate from 90°, FUS focal pressures attenuate and result in a smaller BBB opening volume. The incidence angles calculated in our prior studies were in 2D and used skull information from CT. The study presented herein develops methods to calculate incidence angle in 3D in non-human primate (NHP) skull fragments using harmonic ultrasound imaging without using ionizing radiation. Our results show that ultrasound harmonic imaging is capable of accurately depicting features such as sutures and eye-sockets of the skull. Furthermore, we were able to reproduce previously reported relationships between the incidence angle and FUS beam attenuation. We also show feasibility of performing ultrasound harmonic imaging in in-vivo non-human primates. The all-ultrasound method presented herein combined with our neuronavigation system stands to increase more widespread adoption of FUS and render it accessible by eliminating the need for CT cranial mapping.

S-Wave Accelerates Optimization-based Photoacoustic Image Reconstruction in vivo

OBJECTIVE

Photoacoustic imaging has undergone rapid development in recent years. To simulate photoacoustic imaging on a computer, the most popular MATLAB toolbox currently used for the forward projection process is k-Wave. However, k-Wave suffers from significant computation time. Here we propose a straightforward simulation approach based on superposed Wave (s-Wave) to accelerate photoacoustic simulation.

METHODS

In this study, we consider the initial pressure distribution as a collection of individual pixels. By obtaining standard sensor data from a single pixel beforehand, we can easily manipulate the phase and amplitude of the sensor data for specific pixels using loop and multiplication operators. The effectiveness of this approach is validated through an optimization-based reconstruction algorithm.

RESULTS

The results reveal significantly reduced computation time compared with k-Wave. Particularly in a sparse 3-D configuration, s-Wave exhibits a speed improvement >2000 times compared with k-Wave. In terms of optimization-based image reconstruction, in vivo imaging results reveal that using the s-Wave method yields images highly similar to those obtained using k-Wave, while reducing the reconstruction time by approximately 50 times.

CONCLUSION

Proposed here is an accelerated optimization-based algorithm for photoacoustic image reconstruction, using the fast s-Wave forward projection simulation. Our method achieves substantial time savings, particularly in sparse system configurations. Future work will focus on further optimizing the algorithm and expanding its applicability to a broader range of photoacoustic imaging scenarios.

Transcranial Ultrasonic Focusing by a Phased Array Based on Micro-CT Images

In this paper, we utilize micro-computed tomography (micro-CT) to obtain micro-CT images with a resolution of 60 μm and establish a micro-CT model based on the k-wave toolbox, which can visualize the microstructures in trabecular bone, including pores and bone layers. The transcranial ultrasound phased array focusing field characteristics in the micro-CT model are investigated. The ultrasonic waves are multiply scattered in skull and time delays calculations from the transducer to the focusing point are difficult. For this reason, we adopt the pulse compression method and the linear frequency modulation Barker code to compute the time delay and implement phased array focusing in the micro-CT model. It is shown by the simulation results that ultrasonic loss is mainly caused by scattering from the microstructures of the trabecular bone. The ratio of main and side lobes of the cross-correlation calculation is improved by 5.53 dB using the pulse compression method. The focusing quality and the calculation accuracy of time delay are improved. Meanwhile, the beamwidth at the focal point and the sound pressure amplitude decrease with the increase in the signal frequency. Focusing at different depths indicates that the beamwidth broadens with the increase in the focusing depth, and beam deflection focusing maintains good consistency in the focusing effect at a distance of 9 mm from the focal point. This indicates that the phased-array method has good focusing results and focus tunability in deep cranial brain. In addition, the sound pressure at the focal point can be increased by 8.2% through amplitude regulation, thereby enhancing focusing efficiency. The preliminary experiment verification is conducted with an ex vivo skull. It is shown by the experimental results that the phased array focusing method using pulse compression to calculate the time delay can significantly improve the sound field focusing effect and is a very effective transcranial ultrasound focusing method.

4D spectral-spatial computational photoacoustic dermoscopy

Photoacoustic dermoscopy (PAD) is an emerging non-invasive imaging technology aids in the diagnosis of dermatological conditions by obtaining optical absorption information of skin tissues. Despite advances in PAD, it remains unclear how to obtain quantitative accuracy of the reconstructed PAD images according to the optical and acoustic properties of multilayered skin, the wavelength and distribution of excitation light, and the detection performance of ultrasound transducers. In this work, a computing method of four-dimensional (4D) spectral-spatial imaging for PAD is developed to enable quantitative analysis and optimization of structural and functional imaging of skin. This method takes the optical and acoustic properties of heterogeneous skin tissues into account, which can be used to correct the optical field of excitation light, detectable ultrasonic field, and provide accurate single-spectrum analysis or multi-spectral imaging solutions of PAD for multilayered skin tissues. A series of experiments were performed, and simulation datasets obtained from the computational model were used to train neural networks to further improve the imaging quality of the PAD system. All the results demonstrated the method could contribute to the development and optimization of clinical PADs by datasets with multiple variable parameters, and provide clinical predictability of photoacoustic (PA) data for human skin.

A Forward Model Incorporating Elevation-Focused Transducer Properties for 3-D Full-Waveform Inversion in Ultrasound Computed Tomography

Ultrasound computed tomography (USCT) is an emerging medical imaging modality that holds great promise for improving human health. Full-waveform inversion (FWI)-based image reconstruction methods account for the relevant wave physics to produce high spatial resolution images of the acoustic properties of the breast tissues. A practical USCT design employs a circular ring-array comprised of elevation-focused ultrasonic transducers, and volumetric imaging is achieved by translating the ring-array orthogonally to the imaging plane. In commonly deployed slice-by-slice (SBS) reconstruction approaches, the 3-D volume is reconstructed by stacking together 2-D images reconstructed for each position of the ring-array. A limitation of the SBS reconstruction approach is that it does not account for 3-D wave propagation physics and the focusing properties of the transducers, which can result in significant image artifacts and inaccuracies. To perform 3-D image reconstruction when elevation-focused transducers are employed, a numerical description of the focusing properties of the transducers should be included in the forward model. To address this, a 3-D computational model of an elevation-focused transducer is developed to enable 3-D FWI-based reconstruction methods to be deployed in ring-array-based USCT. The focusing is achieved by applying a spatially varying temporal delay to the ultrasound pulse (emitter mode) and recorded signal (receiver mode). The proposed numerical transducer model is quantitatively validated and employed in computer simulation studies that demonstrate its use in image reconstruction for ring-array USCT.

A simulation study on the sensitivity of transcranial ray-tracing ultrasound modeling to skull properties

In transcranial focused ultrasound therapies, such as treating essential tremor via thermal ablation in the thalamus, acoustic energy is focused through the skull using a phased-array transducer. Ray tracing is a computationally efficient method that can correct skull-induced phase aberrations via per-element phase delay calculations using patient-specific computed tomography (CT) data. However, recent studies show that variations in CT-derived Hounsfield unit may account for only 50% of the speed of sound variability in human skull specimens, potentially limiting clinical transcranial ultrasound applications. Therefore, understanding the sensitivity of treatment planning methods to material parameter variations is essential. The present work uses a ray-tracing simulation model to explore how imprecision in model inputs, arising from clinically significant uncertainties in skull properties or considerations of acoustic phenomena, affects acoustic focusing quality through the skull. We propose and validate new methods to optimize ray-tracing skull simulations for clinical treatment planning, relevant for predicting intracranial target's thermal rise, using experimental data from ex-vivo human skulls.

The effect of source backing materials and excitation pulse durations on laser-generated ultrasound waveforms

In this article, it is shown experimentally that a planar laser-generated ultrasound source with a hard reflective backing will generate higher acoustic pressures than a comparable source with an acoustically matched backing when the stress confinement condition is not met. Furthermore, while the source with an acoustically matched backing will have a broader bandwidth when the laser pulse is short enough to ensure stress confinement, the bandwidths of both source types will converge as the laser pulse duration increases beyond stress confinement. The explanation of the results is supported by numerical simulations.

Numerical and experimental evaluation of low-intensity transcranial focused ultrasound wave propagation using human skulls for brain neuromodulation

BACKGROUND

Low-intensity transcranial focused ultrasound (tFUS) has gained considerable attention as a promising noninvasive neuromodulatory technique for human brains. However, the complex morphology of the skull hinders scholars from precisely predicting the acoustic energy transmitted and the region of the brain impacted during the sonication. This is due to the fact that different ultrasound frequencies and skull morphology variations greatly affect wave propagation through the skull.

PURPOSE

Although the acoustic properties of human skull have been studied for tFUS applications, such as tumor ablation using a multielement phased array, there is no consensus about how to choose a single-element focused ultrasound (FUS) transducer with a suitable frequency for neuromodulation. There are interests in exploring the magnitude and dimension of tFUS beam through human parietal bone for modulating specific brain lobes. Herein, we aim to investigate the wave propagation of tFUS on human skulls to understand and address the concerns above.

METHODS

Both experimental measurements and numerical modeling were conducted to investigate the transmission efficiency and beam pattern of tFUS on five human skulls (C3 and C4 regions) using single-element FUS transducers with six different frequencies (150-1500 kHz). The degassed skull was placed in a water tank, and a calibrated hydrophone was utilized to measure acoustic pressure past it. The cranial computed tomography scan data of each skull were obtained to derive a high-resolution acoustic model (grid point spacing: 0.25 mm) in simulations. Meanwhile, we modified the power-law exponent of acoustic attenuation coefficient to validate numerical modeling and enabled it to be served as a prediction tool, based on the experimental measurements.

RESULTS

The transmission efficiency and -6 dB beamwidth were evaluated and compared for various frequencies. An exponential decrease in transmission efficiency and a logarithmic decrease of -6 dB beamwidth with an increase in ultrasound frequency were observed. It is found that a >750 kHz ultrasound leads to a relatively lower tFUS transmission efficiency (<5%), whereas a <350 kHz ultrasound contributes to a relatively broader beamwidth (>5 mm). Based on these observations, we further analyzed the dependence of tFUS wave propagation on FUS transducer aperture size.

CONCLUSIONS

We successfully studied tFUS wave propagation through human skulls at different frequencies experimentally and numerically. The findings have important implications to predict tFUS wave propagation for ultrasound neuromodulation in clinical applications, and guide researchers to develop advanced ultrasound transducers as neural interfaces.

A photoacoustic patch for three-dimensional imaging of hemoglobin and core temperature

Electronic patches, based on various mechanisms, allow continuous and noninvasive monitoring of biomolecules on the skin surface. However, to date, such devices are unable to sense biomolecules in deep tissues, which have a stronger and faster correlation with the human physiological status than those on the skin surface. Here, we demonstrate a photoacoustic patch for three-dimensional (3D) mapping of hemoglobin in deep tissues. This photoacoustic patch integrates an array of ultrasonic transducers and vertical-cavity surface-emitting laser (VCSEL) diodes on a common soft substrate. The high-power VCSEL diodes can generate laser pulses that penetrate >2 cm into biological tissues and activate hemoglobin molecules to generate acoustic waves, which can be collected by the transducers for 3D imaging of the hemoglobin with a high spatial resolution. Additionally, the photoacoustic signal amplitude and temperature have a linear relationship, which allows 3D mapping of core temperatures with high accuracy and fast response. With access to biomolecules in deep tissues, this technology adds unprecedented capabilities to wearable electronics and thus holds significant implications for various applications in both basic research and clinical practice.

Transcranial ultrasound stimulation to human middle temporal complex improves visual motion detection and modulates electrophysiological responses

BACKGROUND

Transcranial ultrasound stimulation (TUS) holds promise as a novel technology for non-invasive neuromodulation, with greater spatial precision than other available methods and the ability to target deep brain structures. However, its safety and efficacy for behavioural and electrophysiological modulation remains controversial and it is not yet clear whether it can be used to manipulate the neural mechanisms supporting higher cognitive function in humans. Moreover, concerns have been raised about a potential TUS-induced auditory confound.

OBJECTIVES

We aimed to investigate whether TUS can be used to modulate higher-order visual function in humans in an anatomically-specific way whilst controlling for auditory confounds.

METHODS

We used participant-specific skull maps, functional localisation of brain targets, acoustic modelling and neuronavigation to guide TUS delivery to human visual motion processing cortex (hMT+) whilst participants performed a visual motion detection task. We compared the effects of hMT+ stimulation with sham and control site stimulation and examined EEG data for modulation of task-specific event-related potentials. An auditory mask was applied which prevented participants from distinguishing between stimulation and sham trials.

RESULTS

Compared with sham and control site stimulation, TUS to hMT+ improved accuracy and reduced response times of visual motion detection. TUS also led to modulation of the task-specific event-related EEG potential. The amplitude of this modulation correlated with the performance benefit induced by TUS. No pathological changes were observed comparing structural MRI obtained before and after stimulation.

CONCLUSIONS

The results demonstrate for the first time the precision, efficacy and safety of TUS for stimulation of higher-order cortex and cognitive function in humans whilst controlling for auditory confounds.

Effects of phase aberration on transabdominal focusing for a large aperture, lowf-number histotripsy transducer

Objective. Soft tissue phase aberration may be particularly severe for histotripsy due to large aperture and lowf-number transducer geometries. This study investigated how phase aberration from human abdominal tissue affects focusing of a large, strongly curved histotripsy transducer.Approach.A computational model (k-Wave) was experimentally validated withex vivoporcine abdominal tissue and used to simulate focusing a histotripsy transducer (radius: 14.2 cm,f-number: 0.62, central frequencyfc: 750 kHz) through the human abdomen. Abdominal computed tomography images from 10 human subjects were segmented to create three-dimensional acoustic property maps. Simulations were performed focusing at 3 target locations in the liver of each subject with ideal phase correction, without phase correction, and after separately matching the sound speed of water and fat to non-fat soft tissue.Main results.Experimental validation in porcine abdominal tissue showed that simulated and measured arrival time differences agreed well (average error, ∼0.10 acoustic cycles atfc). In simulations with human tissue, aberration created arrival time differences of 0.65μs (∼0.5 cycles) at the target and shifted the focus from the target by 6.8 mm (6.4 mm pre-focally along depth direction), on average. Ideal phase correction increased maximum pressure amplitude by 95%, on average. Matching the sound speed of water and fat to non-fat soft tissue decreased the average pre-focal shift by 3.6 and 0.5 mm and increased pressure amplitude by 2% and 69%, respectively.Significance.Soft tissue phase aberration of large aperture, lowf-number histotripsy transducers is substantial despite low therapeutic frequencies. Phase correction could potentially recover substantial pressure amplitude for transabdominal histotripsy. Additionally, different heterogeneity sources distinctly affect focusing quality. The water path strongly affects the focal shift, while irregular tissue boundaries (e.g. fat) dominate pressure loss.

Numerical spatial impulse response calculations for a circular piston radiating in a lossy medium

Exact analytical expressions for the spatial impulse response are available for certain transducer geometries. These exact expressions for the spatial impulse response, which are only available for lossless media, analytically evaluate the Rayleigh integral to describe the effect of diffraction in the time domain. To extend the concept of the spatial impulse response by including the effect of power law attenuation in a lossy medium, time-domain Green's functions for the Power Law Wave Equation, which are expressed in terms of stable probability density functions, are computed numerically and superposed. Numerical validations demonstrate that the lossy spatial impulse for a circular piston converges to the analytical lossless spatial impulse response as the value of the attenuation constant grows small. The lossy spatial impulse response is then evaluated in different spatial locations for four specific values of the power law exponent using several different values for the attenuation constant. As the attenuation constant or the distance from the source increases, the amplitude decreases while an increase in temporal broadening is observed. The sharp edges that appear in the time-limited lossless impulse response are replaced by increasingly smooth curves in the lossy impulse response, which decays slowly as a function of time.

Power laws prevail in medical ultrasound

Major topics in medical ultrasound rest on the physics of wave propagation through tissue. These include fundamental treatments of backscatter, speed of sound, attenuation, and speckle formation. Each topic has developed its own rich history, lexicography, and particular treatments. However, there is ample evidence to suggest that power law relations are operating at a fundamental level in all the basic phenomena related to medical ultrasound. This review paper develops, from literature over the past 60 years, the accumulating theoretical basis and experimental evidence that point to power law behaviors underlying the most important tissue-wave interactions in ultrasound and in shear waves which are now employed in elastography. The common framework of power laws can be useful as a coherent overview of topics, and as a means for improved tissue characterization.

Multiphysical numerical study of photothermal therapy of glioblastoma with photoacoustic temperature monitoring in a mouse head

This paper presents a multiphysical numerical study of a photothermal therapy performed on a numerical phantom of a mouse head containing a glioblastoma. The study has been designed to be as realistic as possible. Heat diffusion simulations were performed on the phantom to understand the temperature evolution in the mouse head and therefore in the glioblastoma. The thermal dose has been calculated and lesions caused by heat are shown. The thermal damage on the tumor has also been quantified. To improve the effectiveness of the therapy, the photoabsorber's concentration was increased locally, at the tumor site, to mimic the effect of using absorbing contrast agents such as nanoparticles. Photoacoustic simulations were performed in order to monitor temperature in the phantom: as the Grüneisen parameter changes with the temperature, the photoacoustic signal undergoes changes that can be linked to temperature evolution. These photoacoustic simulations were performed at different instants during the therapy and the evolution of the photoacoustic signal as a function of the spatio-temporal distribution of the temperature in the phantom was observed and quantified. We have developed in this paper a numerical tool that can be used to help defining key parameters of a photothermal therapy.

Evaluation of a pipeline for simulation, reconstruction, and classification in ultrasound-aided diffuse optical tomography of breast tumors

SIGNIFICANCE

Diffuse optical tomography is an ill-posed problem. Combination with ultrasound can improve the results of diffuse optical tomography applied to the diagnosis of breast cancer and allow for classification of lesions.

AIM

To provide a simulation pipeline for the assessment of reconstruction and classification methods for diffuse optical tomography with concurrent ultrasound information.

APPROACH

A set of breast digital phantoms with benign and malignant lesions was simulated building on the software VICTRE. Acoustic and optical properties were assigned to the phantoms for the generation of B-mode images and optical data. A reconstruction algorithm based on a two-region nonlinear fitting and incorporating the ultrasound information was tested. Machine learning classification methods were applied to the reconstructed values to discriminate lesions into benign and malignant after reconstruction.

RESULTS

The approach allowed us to generate realistic US and optical data and to test a two-region reconstruction method for a large number of realistic simulations. When information is extracted from ultrasound images, at least 75% of lesions are correctly classified. With ideal two-region separation, the accuracy is higher than 80%.

CONCLUSIONS

A pipeline for the generation of realistic ultrasound and diffuse optics data was implemented. Machine learning methods applied to a optical reconstruction with a nonlinear optical model and morphological information permit to discriminate malignant lesions from benign ones.

Experimental Demonstration of Trans-Skull Volumetric Passive Acoustic Mapping With the Heterogeneous Angular Spectrum Approach

Real-time, 3-D, passive acoustic mapping (PAM) of microbubble dynamics during transcranial focused ultrasound (FUS) is essential for optimal treatment outcomes. The angular spectrum approach (ASA) potentially offers a very efficient method to perform PAM, as it can reconstruct specific frequency bands pertinent to microbubble dynamics and may be extended to correct aberrations caused by the skull. Here, we experimentally assess the abilities of heterogeneous ASA (HASA) to perform trans-skull PAM. Our experimental investigations demonstrate that the 3-D PAMs of a known 1-MHz source, constructed with HASA through an ex vivo human skull segment, reduced both the localization error (from 4.7 ± 2.3 to 2.3 ± 1.6 mm) and the number, size, and energy of spurious lobes caused by aberration, with the modest additional computational expense. While further improvements in the localization errors are expected with arrays with denser elements and larger aperture, our analysis revealed that experimental constraints associated with the array pitch and aperture (here, 1.8 mm and 2.5 cm, respectively) can be ameliorated by interpolation and peak finding techniques. Beyond the array characteristics, our analysis also indicated that errors in the registration (translation and rotation of ±5 mm and ±5°, respectively) of the skull segment to the array can lead to peak localization errors of the order of a few wavelengths. Interestingly, errors in the spatially dependent speed of sound in the skull (±20%) caused only subwavelength errors in the reconstructions, suggesting that registration is the most important determinant of point source localization accuracy. Collectively, our findings show that HASA can address source localization problems through the skull efficiently and accurately under realistic conditions, thereby creating unique opportunities for imaging and controlling the microbubble dynamics in the brain.

Multitarget Transcranial Ultrasound Therapy in Small Animals Based on Phase-Only Acoustic Holographic Lens

Transcranial ultrasound therapy has become a noninvasive method for treating neurological and psychiatric disorders, and studies have further demonstrated that multitarget transcranial ultrasound therapy is a better solution. At present, multitarget transcranial ultrasound therapy in small animals can only be achieved by the multitransducer or phased array. However, multiple transducers may cause spatial interference, and the phased array system is complicated, expensive, and especially unsuitable for small animals. This study is the first to design and fabricate a miniature acoustic holography lens for multitarget transcranial ultrasound therapy in rats. The acoustic holographic lens, working at a frequency of 1.0 MHz, with a size of 10.08 mm ×10.08 mm and a pixel resolution of 0.72 mm, was designed, optimized, and fabricated. The dual-focus transcranial ultrasound generated based on the lens was measured; the full-width at half-maximum (FWHM) of the focal spots in the y -direction was 2.15 and 2.27 mm and in the z -direction was 2.3 and 2.36 mm. The focal length was 5.4 mm, and the distance between the two focuses was 5.6 mm, close to the desired values of 5.4 and 6.0 mm. Finally, the multiple-target blood-brain barrier opening in rats' bilateral secondary visual cortex (mediolateral area, V2ML) was demonstrated using the transcranial ultrasound therapy system based on the lens. These results demonstrate the good performance of the multitarget transcranial ultrasound therapy system for small animals, including high spatial resolution, small size, and low cost.

3-D Stochastic Numerical Breast Phantoms for Enabling Virtual Imaging Trials of Ultrasound Computed Tomography

Ultrasound computed tomography (USCT) is an emerging imaging modality for breast imaging that can produce quantitative images that depict the acoustic properties of tissues. Computer-simulation studies, also known as virtual imaging trials, provide researchers with an economical and convenient route to systematically explore imaging system designs and image reconstruction methods. When simulating an imaging technology intended for clinical use, it is essential to employ realistic numerical phantoms that can facilitate the objective, or task-based, assessment of image quality (IQ). Moreover, when computing objective IQ measures, an ensemble of such phantoms should be employed, which displays the variability in anatomy and object properties that are representative of the to-be-imaged patient cohort. Such stochastic phantoms for clinically relevant applications of USCT are currently lacking. In this work, a methodology for producing realistic 3-D numerical breast phantoms for enabling clinically relevant computer-simulation studies of USCT breast imaging is presented. By extending and adapting an existing stochastic 3-D breast phantom for use with USCT, methods for creating ensembles of numerical acoustic breast phantoms are established. These breast phantoms will possess clinically relevant variations in breast size, composition, acoustic properties, tumor locations, and tissue textures. To demonstrate the use of the phantoms in virtual USCT studies, two brief case studies are presented, which addresses the development and assessment of image reconstruction procedures. Examples of breast phantoms produced by use of the proposed methods and a collection of 52 sets of simulated USCT measurement data have been made open source for use in image reconstruction development.

Measurement of the ultrasound attenuation and dispersion in 3D-printed photopolymer materials from 1 to 3.5 MHz

Over the past decade, the range of applications in biomedical ultrasound exploiting 3D printing has rapidly expanded. For wavefront shaping specifically, 3D printing has enabled a diverse range of new, low-cost approaches for controlling acoustic fields. These methods rely on accurate knowledge of the bulk acoustic properties of the materials; however, to date, robust knowledge of these parameters is lacking for many materials that are commonly used. In this work, the acoustic properties of eight 3D-printed photopolymer materials were characterised over a frequency range from 1 to 3.5 MHz. The properties measured were the frequency-dependent phase velocity and attenuation, group velocity, signal velocity, and mass density. The materials were fabricated using two separate techniques [PolyJet and stereolithograph (SLA)], and included Agilus30, FLXA9960, FLXA9995, Formlabs Clear, RGDA8625, RGDA8630, VeroClear, and VeroWhite. The range of measured density values across all eight materials was 1120-1180 kg  · m^-3, while the sound speed values were between 2020 to 2630 m  · s^-1, and attenuation values typically in the range 3-9 dB  ·  MHz^-1· cm^-1.

Acoustic holograms for bilateral blood-brain barrier opening in a mouse model

Transcranial focused ultrasound (FUS) in conjunction with circulating microbubbles injection is the sole non-invasive technique that temporally and locally opens the blood-brain barrier (BBB), allowing targeted drug delivery into the central nervous system (CNS). However, single-element FUS technologies do not allow the simultaneous targeting of several brain structures with high-resolution, and multi-element devices are required to compensate the aberrations introduced by the skull. In this work, we present the first preclinical application of acoustic holograms to perform a bilateral BBB opening in two mirrored regions in mice. The system consisted of a single-element focused transducer working at 1.68~MHz, coupled to a 3D-printed acoustic hologram designed to produce two symmetric foci in anesthetized mice \textit{in vivo} and, simultaneously, compensate the aberrations of the wavefront caused by the skull bones. T1-weighed MR images showed gadolinium extravasation at two symmetric quasi-spherical focal spots. By encoding time-reversed fields, holograms are capable of focusing acoustic energy with a resolution near the diffraction limit at multiple spots inside the skull of small preclinical animals. This work demonstrates the feasibility of hologram-assisted BBB opening for low-cost and highly-localized targeted drug delivery in the CNS in symmetric regions of separate hemispheres.

Accelerating frequency-domain numerical methods for weakly nonlinear focused ultrasound using nested meshes

The numerical simulation of weakly nonlinear ultrasound is important in treatment planning for focused ultrasound (FUS) therapies. However, the large domain sizes and generation of higher harmonics at the focus make these problems extremely computationally demanding. Numerical methods typically employ a uniform mesh fine enough to resolve the highest harmonic present in the problem, leading to a very large number of degrees of freedom. This paper proposes a more efficient strategy in which each harmonic is approximated on a separate mesh, the size of which is proportional to the wavelength of the harmonic. The increase in resolution required to resolve a smaller wavelength is balanced by a reduction in the domain size. This nested meshing is feasible owing to the increasingly localised nature of higher harmonics near the focus. Numerical experiments are performed for FUS transducers in homogeneous media to determine the size of the meshes required to accurately represent the harmonics. In particular, a fast volume potential approach is proposed and employed to perform convergence experiments as the computation domain size is modified. This approach allows each harmonic to be computed via the evaluation of an integral over the domain. Discretising this integral using the midpoint rule allows the computations to be performed rapidly with the FFT. It is shown that at least an order of magnitude reduction in memory consumption and computation time can be achieved with nested meshing. Finally, it is demonstrated how to generalise this approach to inhomogeneous propagation domains.

Photoacoustic computed tomography for functional human brain imaging [Invited]

The successes of magnetic resonance imaging and modern optical imaging of human brain function have stimulated the development of complementary modalities that offer molecular specificity, fine spatiotemporal resolution, and sufficient penetration simultaneously. By virtue of its rich optical contrast, acoustic resolution, and imaging depth far beyond the optical transport mean free path (∼1 mm in biological tissues), photoacoustic computed tomography (PACT) offers a promising complementary modality. In this article, PACT for functional human brain imaging is reviewed in its hardware, reconstruction algorithms, in vivo demonstration, and potential roadmap.

Comparison of compressional and elastic wave simulations for patient-specific planning prior to transcranial photoacoustic-guided neurosurgery

SIGNIFICANCE

Simulations have the potential to be a powerful tool when planning the placement of photoacoustic imaging system components for surgical guidance. While elastic simulations (which include both compressional and shear waves) are expected to more accurately represent the physical transcranial acoustic wave propagation process, these simulations are more time-consuming and memory-intensive than the compressional-wave-only simulations that our group previously used to identify optimal acoustic windows for transcranial photoacoustic imaging.

AIM

We present qualitative and quantitative comparisons of compressional and elastic wave simulations to determine which option is more suitable for preoperative surgical planning.

APPROACH

Compressional and elastic photoacoustic k-Wave simulations were performed based on a computed tomography volume of a human cadaver head. Photoacoustic sources were placed in the locations of the internal carotid arteries and likely positions of neurosurgical instrument tips. Transducers received signals from three previously identified optimal acoustic windows (i.e., the ocular, nasal, and temporal regions). Target detectability, image-based target size estimates, and target-to-instrument distances were measured using the generalized contrast-to-noise ratio (gCNR), resolution, and relative source distances, respectively, for each simulation method.

RESULTS

The gCNR was equivalent between compressional and elastic simulations. The areas of the -6  dB contours of point spread functions utilized to measure resolution differed by 0.33 to 3.35  mm2. Target-to-instrument distance measurements were within 1.24 mm of the true distances.

CONCLUSIONS

These results indicate that it is likely sufficient to utilize the less time-consuming, less memory-intensive compressional wave simulations for presurgical planning.

Towards in vivo Dosimetry for Prostate Radiotherapy with a Transperineal Ultrasound Array: A Simulation Study

X-ray-induced acoustic computed tomography (XACT) is a promising imaging modality to monitor the position of the radiation beam and the deposited dose during external beam radiotherapy delivery. The purpose of this study was to investigate the feasibility of using a transperineal ultrasound transducer array for XACT imaging to guide the prostate radiotherapy. A customized two-dimensional (2D) matrix ultrasound transducer array with 10000 (100×100 elements) ultrasonic sensors with a central frequency of 1 MHz was designed on a 5 cm×5 cm plane to optimize three-dimensional (3D) volumetric imaging. The CT scan and dose treatment plan for a prostate patient undergoing intensity modulated radiation therapy (IMRT) were obtained. In-house simulation was developed to model the time varying X-ray induced acoustic (XA) signals detected by the transperineal ultrasound array. A 3D filtered back projection (FBP) algorithm has been used for 3D XACT image reconstruction. Results of this study will greatly enhance the potential of XACT imaging for real time in vivo dosimetry during radiotherapy.

Applications of Distributed-Order Fractional Operators: A Review

Distributed-order fractional calculus (DOFC) is a rapidly emerging branch of the broader area of fractional calculus that has important and far-reaching applications for the modeling of complex systems. DOFC generalizes the intrinsic multiscale nature of constant and variable-order fractional operators opening significant opportunities to model systems whose behavior stems from the complex interplay and superposition of nonlocal and memory effects occurring over a multitude of scales. In recent years, a significant amount of studies focusing on mathematical aspects and real-world applications of DOFC have been produced. However, a systematic review of the available literature and of the state-of-the-art of DOFC as it pertains, specifically, to real-world applications is still lacking. This review article is intended to provide the reader a road map to understand the early development of DOFC and the progressive evolution and application to the modeling of complex real-world problems. The review starts by offering a brief introduction to the mathematics of DOFC, including analytical and numerical methods, and it continues providing an extensive overview of the applications of DOFC to fields like viscoelasticity, transport processes, and control theory that have seen most of the research activity to date.

Imaging With Therapeutic Acoustic Wavelets-Short Pulses Enable Acoustic Localization When Time of Arrival is Combined With Delay and Sum

Passive acoustic mapping (PAM) is an algorithm that reconstructs the location of acoustic sources using an array of receivers. This technique can monitor therapeutic ultrasound procedures to confirm the spatial distribution and amount of microbubble activity induced. Current PAM algorithms have an excellent lateral resolution but have a poor axial resolution, making it difficult to distinguish acoustic sources within the ultrasound beams. With recent studies demonstrating that short-length and low-pressure pulses-acoustic wavelets-have the therapeutic function, we hypothesized that the axial resolution could be improved with a quasi-pulse-echo approach and that the resolution improvement would depend on the wavelet's pulse length. This article describes an algorithm that resolves acoustic sources axially using time of flight and laterally using delay-and-sum beamforming, which we named axial temporal position PAM (ATP-PAM). The algorithm accommodates a rapid short pulse (RaSP) sequence that can safely deliver drugs across the blood-brain barrier. We developed our algorithm with simulations (k-wave) and in vitro experiments for one-, two-, and five-cycle pulses, comparing our resolution against that of two current PAM algorithms. We then tested ATP-PAM in vivo and evaluated whether the reconstructed acoustic sources mapped to drug delivery within the brain. In simulations and in vitro, ATP-PAM had an improved resolution for all pulse lengths tested. In vivo, experiments in mice indicated that ATP-PAM could be used to target and monitor drug delivery into the brain. With acoustic wavelets and time of flight, ATP-PAM can locate acoustic sources with a vastly improved spatial resolution.

Impact of Aperture, Depth, and Acoustic Clutter on the Performance of Coherent Multi-Transducer Ultrasound Imaging

Transducers with a larger aperture size are desirable in ultrasound imaging to improve resolution and image quality. A coherent multi-transducer ultrasound imaging system (CoMTUS) enables an extended effective aperture through the coherent combination of multiple transducers. In this study, the discontinuous extended aperture created by CoMTUS and its performance for deep imaging and through layered media are investigated by both simulations and experiments. Typical image quality metrics—resolution, contrast and contrast-to-noise ratio—are evaluated and compared with a standard single probe imaging system. Results suggest that the image performance of CoMTUS depends on the relative spatial location of the arrays. The resulting effective aperture significantly improves resolution, while the separation between the arrays may degrade contrast. For a limited gap in the effective aperture (less than a few centimetres), CoMTUS provides benefits to image quality compared to the standard single probe imaging system. Overall, CoMTUS shows higher sensitivity and reduced loss of resolution with imaging depth. In general, CoMTUS imaging performance was unaffected when imaging through a layered medium with different speed of sound values and resolution improved up to 80% at large imaging depths.

Skull acoustic aberration correction in photoacoustic microscopy using a vector space similarity model: a proof-of-concept simulation study

Skull bone represents a highly acoustical impedance mismatch and a dispersive barrier for the propagation of acoustic waves. Skull distorts the amplitude and phase information of the received waves at different frequencies in a transcranial brain imaging. We study a novel algorithm based on vector space similarity model for the compensation of the skull-induced distortions in transcranial photoacoustic microscopy. The results of the algorithm tested on a simplified numerical skull phantom, demonstrate a fully recovered vasculature with the recovery rate of 91.9%.

Breaking the resolution limit in photoacoustic imaging using non-negativity and sparsity

The spatial resolution achievable in photoacoustic imaging decreases with the imaging depth, resulting in blurred images for deeper structures. Apart from technical limitations, the ultimate resolution limit results from the second law of thermodynamics. The attenuation of the optically generated acoustic waves on their way from the imaged structure to the sample surface by scattering and dissipation leads to an increase of entropy. The resulting loss of spatial resolution for structures embedded in attenuating media can be compensated by numerical methods that make use of additional available information. In this article, we demonstrate this using experimental data from plane one-dimensional (1D) acoustic waves propagating in fat tissue. The acoustic waves are optically induced by nanosecond laser pulses and measured with piezoelectric transducers. The experimental results of 1D compensation are also relevant for photoacoustic imaging in 2D or 3D in an acoustically attenuating medium by dividing the reconstruction problem into two steps: First, the ideal signal, which is the solution of the un-attenuated wave equation, is determined by the proposed 1D attenuation compensation for each detector signal. In a second step, any ultrasound reconstruction method for un-attenuated data can be used for image reconstruction. For the reconstruction of a small step milled into a silicon wafer surface, which allows the generation of two photoacoustic pulses with a small time offset, we take advantage of non-negativity and sparsity and inverted the measured, frequency dependent acoustic attenuation of the fat tissue. We were able to improve the spatial resolution for imaging through 20 mm of porcine fat tissue compared to the diffraction limit at the cut-off frequency by at least a factor of two.

Investigation of the Effect of the Skull in Transcranial Photoacoustic Imaging: A Preliminary Ex Vivo Study

Although transcranial photoacoustic imaging (TCPAI) has been used in small animal brain imaging, in animals with thicker skull bones or in humans both light illumination and ultrasound propagation paths are affected. Hence, the PA image is largely degraded and in some cases completely distorted. This study aims to investigate and determine the maximum thickness of the skull through which photoacoustic imaging is feasible in terms of retaining the imaging target structure without incorporating any post processing. We identify the effect of the skull on both the illumination path and acoustic propagation path separately and combined. In the experimental phase, the distorting effect of ex vivo sheep skull bones with thicknesses in the range of 0.7~1.3 mm are explored. We believe that the findings in this study facilitate the clinical translation of TCPAI.

Heterogeneous Angular Spectrum Method for Trans-Skull Imaging and Focusing

Ultrasound, alone or in concert with circulating microbubble contrast agents, has emerged as a promising modality for therapy and imaging of brain diseases. While this has become possible due to advancements in aberration correction methods, a range of applications, including adaptive focusing and tracking of the microbubble dynamics through the human skull, may benefit from even more computationally efficient methods to account for skull aberrations. Here, we derive a general method for the angular spectrum approach (ASA) in a heterogeneous medium, based on a numerical marching scheme to approximate the full implicit solution. We then demonstrate its functionality with simulations for (human) skull-related aberration correction and trans-skull passive acoustic mapping. Our simulations show that the general solution provides accurate trans-skull focusing as compared to the uncorrected case (error in focal point location of 1.0 ± 0.4 mm vs 2.2 ± 0.7 mm) for clinically relevant frequencies (0.25-1.5MHz), apertures (50-100 mm), and targets, with peak focal pressures approximately 30 ± 17% of the free field case, with the effects of skull attenuation and amplitude shading included. In the case of source localization, our method leads to an average of 75% error reduction (from 2.9 ± 1.8 mm to 0.7 ± 0.5 mm) and 40-60% increase in peak intensity, evaluated over the range of frequencies (0.4-1.2 MHz), apertures (50-100 mm), and point source locations (40 mm by 50 mm grid) as compared to the homogeneous medium ASA. Overall, total computation times for both focusing and point source localization of the order milliseconds (166 ± 37 ms, compared with 44 ± 4 ms for the homogeneous ASA formulation) can be attained with this approach. Collectively our findings indicate that the proposed phase correction method based on the ASA could provide a computationally efficient and accurate method for trans-skull transmit focusing and imaging of point scatterers, potentially opening new possibilities for treatment and diagnosis of brain diseases.

Generating Bessel beams with broad depth-of-field by using phase-only acoustic holograms

We report zero-th and high-order acoustic Bessel beams with broad depth-of-field generated using acoustic holograms. While the transverse field distribution of Bessel beams generated using traditional passive methods is correctly described by a Bessel function, these methods present a common drawback: the axial distribution of the field is not constant, as required for ideal Bessel beams. In this work, we experimentally, numerically and theoretically report acoustic truncated Bessel beams of flat-intensity along their axis in the ultrasound regime using phase-only holograms. In particular, the beams present a uniform field distribution showing an elongated focal length of about 40 wavelengths, while the transverse width of the beam remains smaller than 0.7 wavelengths. The proposed acoustic holograms were compared with 3D-printed fraxicons, a blazed version of axicons. The performance of both phase-only holograms and fraxicons is studied and we found that both lenses produce Bessel beams in a wide range of frequencies. In addition, high-order Bessel beam were generated. We report first order Bessel beams that show a clear phase dislocation along their axis and a vortex with single topological charge. The proposed method may have potential applications in ultrasonic imaging, biomedical ultrasound and particle manipulation applications using passive lenses.

Exact and approximate analytical time-domain Green's functions for space-fractional wave equations

The Chen-Holm and Treeby-Cox wave equations are space-fractional partial differential equations that describe power law attenuation of the form α(ω)≈α₀|ω|^y. Both of these space-fractional wave equations are causal, but the phase velocities differ, which impacts the shapes of the time-domain Green's functions. Exact and approximate closed-form time-domain Green's functions are derived for these space-fractional wave equations, and the resulting expressions contain symmetric and maximally skewed stable probability distribution functions. Numerical results are evaluated with ultrasound parameters for breast and liver at different times as a function of space and at different distances as a function of time, where the reference calculations are computed with the Pantis method. The results show that the exact and approximate time-domain Green's functions contain both outbound and inbound propagating terms and that the inbound component is negligible a short distance from the origin. Exact and approximate analytical time-domain Green's functions are also evaluated for the Chen-Holm wave equation with power law exponent y = 1. These comparisons demonstrate that single term analytical expressions containing stable probability densities provide excellent approximations to the time-domain Green's functions for the Chen-Holm and Treeby-Cox wave equations.

A survey of computational frameworks for solving the acoustic inverse problem in three-dimensional photoacoustic computed tomography

Photoacoustic computed tomography (PACT), also known as optoacoustic tomography, is an emerging imaging technique that holds great promise for biomedical imaging. PACT is a hybrid imaging method that can exploit the strong endogenous contrast of optical methods along with the high spatial resolution of ultrasound methods. In its canonical form that is addressed in this article, PACT seeks to estimate the photoacoustically-induced initial pressure distribution within the object. Image reconstruction methods are employed to solve the acoustic inverse problem associated with the image formation process. When an idealized imaging scenario is considered, analytic solutions to the PACT inverse problem are available; however, in practice, numerous challenges exist that are more readily addressed within an optimization-based, or iterative, image reconstruction framework. In this article, the PACT image reconstruction problem is reviewed within the context of modern optimization-based image reconstruction methodologies. Imaging models that relate the measured photoacoustic wavefields to the sought-after object function are described in their continuous and discrete forms. The basic principles of optimization-based image reconstruction from discrete PACT measurement data are presented, which includes a review of methods for modeling the PACT measurement system response and other important physical factors. Non-conventional formulations of the PACT image reconstruction problem, in which acoustic parameters of the medium are concurrently estimated along with the PACT image, are also introduced and reviewed.

Simulation studies of time reversal-based protoacoustic reconstruction for range and dose verification in proton therapy

PURPOSE

In vivo range verification in proton therapy is a critical step to help minimize range and dose uncertainty. We propose to employ a time reversal (TR)-based approach using proton-induced acoustics (protoacoustics) to reconstruct pressure/dose distribution in heterogeneous tissues.

METHODS

The dose distribution of mono-energetic proton pencil beam in a CT-based patient phantom was calculated by Monte Carlo simulation. K-wave toolbox was used to investigate protoacoustic pressurization, propagation and reconstruction in 2D. To address the tissue heterogeneity effect, a number of physical parameters, including mass density (ρ), speed of sound (c), volumetric thermal expansion coefficient (α_V ), isobaric specific heat capacity (C_p ) and attenuation power law prefactor (α₀ ), were empirically converted from CT number. The performance was evaluated using two figures of merit: mean square error (MSE) of pressure profiles and Bragg peak localization error (Δ_BP ). The impact of six parameters of the TR inversion was examined, including number of sensors, sampling duration, sampling timestep, spill time, noise level and number of iterations.

RESULTS

The quantitative accuracy of TR reconstruction and its dependency on the selected parameters is presented. Under optimum conditions, the positioning accuracy of the Bragg peak can be controlled below 1 mm. For instance, MSE is 0.0123 and Δ_BP is 0.59 mm under the following conditions (32 sensors, sampling duration: 600 µs, sampling timestep: 40 ns, spill time: 1 µs, no noise).

CONCLUSIONS

The feasibility of TR-based protoacoustic reconstruction in 2D for proton range verification was first demonstrated. The approach is not only applicable to pencil beam, but also has potential to be extended to passive scattering systems.

Skull's Photoacoustic Attenuation and Dispersion Modeling with Deterministic Ray-Tracing: Towards Real-Time Aberration Correction

Although transcranial photoacoustic imaging has been previously investigated by several groups, there are many unknowns about the distorting effects of the skull due to the impedance mismatch between the skull and underlying layers. The current computational methods based on finite-element modeling are slow, especially in the cases where fine grids are defined for a large 3-D volume. We develop a very fast modeling/simulation framework based on deterministic ray-tracing. The framework considers a multilayer model of the medium, taking into account the frequency-dependent attenuation and dispersion effects that occur in wave reflection, refraction, and mode conversion at the skull surface. The speed of the proposed framework is evaluated. We validate the accuracy of the framework using numerical phantoms and compare its results to k-Wave simulation results. Analytical validation is also performed based on the longitudinal and shear wave transmission coefficients. We then simulated, using our method, the major skull-distorting effects including amplitude attenuation, time-domain signal broadening, and time shift, and confirmed the findings by comparing them to several ex vivo experimental results. It is expected that the proposed method speeds up modeling and quantification of skull tissue and allows the development of transcranial photoacoustic brain imaging.

Resolution Limits in Photoacoustic Imaging Caused by Acoustic Attenuation

In conventional photoacoustic tomography, several effects contribute to the loss of resolution, such as the limited bandwidth and the finite size of the transducer, or the space-dependent speed of sound. They can all be compensated (in principle) technically or numerically. Frequency-dependent acoustic attenuation also limits spatial resolution by reducing the bandwidth of the photoacoustic signal, which can be numerically compensated only up to a theoretical limit given by thermodynamics. The entropy production, which is the dissipated energy of the acoustic wave divided by the temperature, turns out to be equal to the information loss, which cannot be compensated for by any reconstruction method. This is demonstrated for the propagation of planar acoustic waves in water, which are induced by short laser pulses and measured by piezoelectric acoustical transducers. It turns out that for water, where the acoustic attenuation is proportional to the squared frequency, the resolution limit is proportional to the square root of the distance and inversely proportional to the square root of the logarithm of the signal-to-noise ratio. The proposed method could be used in future work for media other than water, such as biological tissue, where acoustic attenuation has a different power-law frequency dependence.

Time-domain simulation of ultrasound propagation with fractional Laplacians for lossy-medium biological tissues with complicated geometries

Simulations of ultrasound wave propagation inside biological tissues have a wide range of practical applications. In previous studies, wave propagation equations in lossy biological media are solved either with convolutions, which consume a large amount of memory, or with pseudo-spectral methods, which cannot handle complicated geometries effectively. The approach described in the paper employed a fractional central difference method (FCD), combined with the immersed boundary (IB) method for the finite-difference, time-domain simulation. The FCD method can solve the fractional Laplace terms in Chen and Holm's lossy-medium equations directly in the physical domain without integral transforms. It also works naturally with the IB method, which enables a simple Cartesian-type grid mesh to be used to solve problems with complicated geometries. The numerical results agree very well with the analytical solutions for frequency power-law attenuation lossy media.

Full Modeling of High-Intensity Focused Ultrasound and Thermal Heating in the Kidney Using Realistic Patient Models

OBJECTIVE

High-intensity focused ultrasound (HIFU) therapy can be used for noninvasive treatment of kidney (renal) cancer, but the clinical outcomes have been variable. In this study, the efficacy of renal HIFU therapy was studied using a nonlinear acoustic and thermal simulations in three patients.

METHODS

The acoustic simulations were conducted with and without refraction in order to investigate its effect on the shape, size, and pressure distribution at the focus. The values for the attenuation, sound speed, perfusion, and thermal conductivity of the kidney were varied over the reported ranges to determine the effect of variability on heating. Furthermore, the phase aberration was studied in order to quantify the underlying phase shifts using a second order polynomial function.

RESULTS

The ultrasound field intensity was found to drop on average 11.1 dB with refraction and 6.4 dB without refraction. Reflection at tissue interfaces was found to result in a loss less than 0.1 dB. Focal point splitting due to refraction significantly reduced the heating efficacy. Perfusion did not have a large effect on heating during short sonication durations. Small changes in temperature were seen with varying attenuation and thermal conductivity, but no visible changes were present with sound speed variations. The aberration study revealed an underlying trend in the spatial distribution of the phase shifts.

CONCLUSION

The results show that the efficacy of HIFU therapy in the kidney could be improved with aberration correction.

SIGNIFICANCE

A method is proposed by that patient specific pre-treatment calculations could be used to overcome the aberration and therefore make ultrasound treatment possible.

Laser generated ultrasound sources using carbon-polymer nanocomposites for high frequency metrology

The characterization of ultrasound fields generated by diagnostic and therapeutic equipment is an essential requirement for performance validation and to demonstrate compliance against established safety limits. This requires hydrophones calibrated to a traceable standard. Currently, the upper calibration frequency range available to the user community is limited to 60 MHz. However, high frequencies are increasingly being used for both imaging and therapy necessitating calibration frequencies up to 100 MHz. The precise calibration of hydrophones requires a source of high amplitude, broadband, quasi-planar, and stable ultrasound fields. There are challenges to using conventional piezoelectric sources, and laser generated ultrasound sources offer a promising solution. In this study, various nanocomposites consisting of a bulk polymer matrix and multi-walled carbon nanotubes were fabricated and tested using pulsed laser of a few nanoseconds for their suitability as a source for high frequency calibration of hydrophones. The pressure amplitude and bandwidths were measured using a broadband hydrophone from 27 different nanocomposite sources. The effect of nonlinear propagation of high amplitude laser generated ultrasound on bandwidth and the effect of bandlimited sensitivity response on the deconvolved pressure waveform were numerically investigated. The stability of the nanocomposite sources under sustained laser pulse excitation was also examined.

Time-domain analysis of power law attenuation in space-fractional wave equations

Ultrasound attenuation in soft tissue follows a power law as a function of the ultrasound frequency, and in medical ultrasound, power law attenuation is often described by fractional calculus models that contain one or more time- or space-fractional derivatives. For certain time-fractional models, exact and approximate time-domain Green's functions are known, but similar expressions are not available for the space-fractional models that describe power law attenuation. To address this deficiency, a numerical approach for calculating time-domain Green's functions for the Chen-Holm space-fractional wave equation and Treeby-Cox space-fractional wave equation is introduced, where challenges associated with the numerical evaluation of a highly oscillatory improper integral are addressed with the Filon integration formula combined with the Pantis method. Numerical results are computed for both of these space-fractional wave equations at different distances in breast and liver with power law exponents of 1.5 and 1.139, respectively. The results show that these two space-fractional wave equations are causal and that away from the origin, the time-domain Green's function for the Treeby-Cox space-fractional wave equation is very similar to the time-domain Green's function for the time-fractional power law wave equation.

Numerical Modeling of Ultrasound Propagation in Weakly Heterogeneous Media Using a Mixed-Domain Method

A mixed-domain method (MDM) is presented in this paper for modeling one-way linear/nonlinear wave propagation in biological tissue with arbitrary heterogeneities, in which sound speed, density, attenuation coefficients, and nonlinear coefficients are all spatial varying functions. The present method is based on solving an integral equation derived from a Westervelt-like equation. One-dimensional problems are first studied to verify the MDM and to reveal its limitations. It is shown that this method is accurate for cases with small variation of sound speed. A 2-D case is further studied with focused ultrasound beams to validate the application of the method in the medical field. Results from the MATLAB toolbox k-Wave are used as the benchmark. Normalized root-mean-square (rms) error estimated at the focus of the transducer is 0.0133 when the coarsest mesh (1/3 of the wavelength) is used in the MDM. Fundamental and second-harmonic fields throughout the considered computational domains are compared and good agreement is observed. Overall, this paper demonstrates that the MDM is a computationally efficient and accurate method when used to model wave propagation in biological tissue with relatively weak heterogeneities.

Acoustic-based proton range verification in heterogeneous tissue: simulation studies

Acoustic-based proton range verification (protoacoustics) is a potential in vivo technique for determining the Bragg peak position. Previous measurements and simulations have been restricted to homogeneous water tanks. Here, a CT-based simulation method is proposed and applied to a liver and prostate case to model the effects of tissue heterogeneity on the protoacoustic amplitude and time-of-flight range verification accuracy. For the liver case, posterior irradiation with a single proton pencil beam was simulated for detectors placed on the skin. In the prostate case, a transrectal probe measured the protoacoustic pressure generated by irradiation with five separate anterior proton beams. After calculating the proton beam dose deposition, each CT voxel's material properties were mapped based on Hounsfield Unit values, and thermoacoustically-generated acoustic wave propagation was simulated with the k-Wave MATLAB toolbox. By comparing the simulation results for the original liver CT to homogenized variants, the effects of heterogeneity were assessed. For the liver case, 1.4 cGy of dose at the Bragg peak generated 50 mPa of pressure (13 cm distal), a 2×  lower amplitude than simulated in a homogeneous water tank. Protoacoustic triangulation of the Bragg peak based on multiple detector measurements resulted in 0.4 mm accuracy for a δ-function proton pulse irradiation of the liver. For the prostate case, higher amplitudes are simulated (92-1004 mPa) for closer detectors (<8 cm). For four of the prostate beams, the protoacoustic range triangulation was accurate to  ⩽1.6 mm (δ-function proton pulse). Based on the results, application of protoacoustic range verification to heterogeneous tissue will result in decreased signal amplitudes relative to homogeneous water tank measurements, but accurate range verification is still expected to be possible.