Modeling power law absorption and dispersion in viscoelastic solids using a split-field and the fractional Laplacian

Photoacoustic digital brain and deep-learning-assisted image reconstruction

Photoacoustic tomography (PAT) is a newly developed medical imaging modality, which combines the advantages of pure optical imaging and ultrasound imaging, owning both high optical contrast and deep penetration depth. Very recently, PAT is studied in human brain imaging. Nevertheless, while ultrasound waves are passing through the human skull tissues, the strong acoustic attenuation and aberration will happen, which causes photoacoustic signals' distortion. In this work, we use 180 T1 weighted magnetic resonance imaging (MRI) human brain volumes along with the corresponding magnetic resonance angiography (MRA) brain volumes, and segment them to generate the 2D human brain numerical phantoms for PAT. The numerical phantoms contain six kinds of tissues, which are scalp, skull, white matter, gray matter, blood vessel and cerebrospinal fluid. For every numerical phantom, Monte-Carlo based optical simulation is deployed to obtain the photoacoustic initial pressure based on optical properties of human brain. Then, two different k-wave models are used for the skull-involved acoustic simulation, which are fluid media model and viscoelastic media model. The former one only considers longitudinal wave propagation, and the latter model takes shear wave into consideration. Then, the PA sinograms with skull-induced aberration is taken as the input of U-net, and the skull-stripped ones are regarded as the supervision of U-net to train the network. Experimental result shows that the skull's acoustic aberration can be effectively alleviated after U-net correction, achieving conspicuous improvement in quality of PAT human brain images reconstructed from the corrected PA signals, which can clearly show the cerebral artery distribution inside the human skull.

Physics-informed neural networks for transcranial ultrasound wave propagation

Transcranial ultrasound imaging has been playing an increasingly important role in the non-invasive treatment of brain disorders. However, the conventional mesh-based numerical wave solvers, which are an integral part of imaging algorithms, suffer from limitations such as high computational cost and discretization error in predicting the wavefield passing through the skull. In this paper, we explore the use of physics-informed neural networks (PINNs) for predicting the transcranial ultrasound wave propagation. The wave equation, two sets of time snapshots data and a boundary condition (BC) are embedded as physical constraints in the loss function during training. The proposed approach has been validated by solving the two-dimensional (2D) acoustic wave equation under three increasingly complex spatially varying velocity models. Our cases demonstrate that due to the meshless nature of PINNs, they can be flexibly applied to different wave equations and types of BCs. By adding physics constraints to the loss function, PINNs can predict wavefields far outside the training data, providing ideas for improving the generalization capability of existing deep learning methods. The proposed approach offers exciting perspectives because of the powerful framework and simple implementation. We conclude with a summary of the strengths, limitations and further research directions of this work.

Evaluation of the effects of focused ultrasound stimulation on the central nervous system through a multiscale simulation approach

The lack of sensory feedback represents one of the main drawbacks of commercial upper limb prosthesis. Transcranial Focused Ultrasound Stimulation (tFUS) seems to be a valid non-invasive technique for restoring sensory feedback allowing to deliver acoustic energy to cortical sensory areas with high spatial resolution and depth penetration. This paper aims at studying in simulation the use of tFUS on cortical sensory areas to evaluate its effects in terms of latency ad firing rate of the cells response, for understanding if these parameters influence the safety and the efficacy of the stimulation. In this paper, in order to study the propagation of the ultrasound wave from the transducer to the cortical cells, a multiscale approach was implemented by building a macroscopic model, which estimates the pressure profile in a simplified 2D human head geometry, and coupling it with the SONIC microscale model, that describes the electrical behaviour of a cortical neuron. The influence of the stimulation parameters and of the skull thickness on the latency and the firing rate are evaluated and the obtained behaviour is linked to the sensory response obtained on human subjects. Results have shown that slight changes in the transducer position should not affect the efficacy of the stimulation; however, high skull thickness leads to lower cells activation. These results will be useful for evaluating safety and effectiveness of tFUS for sensory feedback in closed-loop prosthetic systems.

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.

Multiscale approach for tFUS neurocomputational modelling

Among the non-invasive methods employed for brain stimulation, trans cranial Focused Ultrasound Stimulation (tFUS) is the technique with the best penetration into the tissues and spatial resolution. The development of computational models of US propagation in brain tissue can be useful for estimating the behaviour of neural cells subjected to mechanical stimulus due to US. This paper aims at studying the neural cell response of a cortical Regular Spiking point neuron model, for different values of stimulus Duty Cycle (DC). The main goal is to use a multiscale approach to couple the results obtained from a macroscale simulation on wave propagation in tissue, with neuron model described by Hodgkin-Huxley equations to study latency and firing rate of the RS model. The obtained results showed that latency and firing rate have slight variations along the propagation direction of the US beam, in the focal region under the skull model, for different stimulus DC.

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.

Ultrasound stimulation of the motor cortex during tonic muscle contraction

Transcranial ultrasound stimulation (tUS) shows potential as a noninvasive brain stimulation (NIBS) technique, offering increased spatial precision compared to other NIBS techniques. However, its reported effects on primary motor cortex (M1) are limited. We aimed to better understand tUS effects in human M1 by performing tUS of the hand area of M1 (M1hand) during tonic muscle contraction of the index finger. Stimulation during muscle contraction was chosen because of the transcranial magnetic stimulation-induced phenomenon known as cortical silent period (cSP), in which transcranial magnetic stimulation (TMS) of M1hand involuntarily suppresses voluntary motor activity. Since cSP is widely considered an inhibitory phenomenon, it presents an ideal parallel for tUS, which has often been proposed to preferentially influence inhibitory interneurons. Recording electromyography (EMG) of the first dorsal interosseous (FDI) muscle, we investigated effects on muscle activity both during and after tUS. We found no change in FDI EMG activity concurrent with tUS stimulation. Using single-pulse TMS, we found no difference in M1 excitability before versus after sparsely repetitive tUS exposure. Using acoustic simulations in models made from structural MRI of the participants that matched the experimental setups, we estimated in-brain pressures and generated an estimate of cumulative tUS exposure experienced by M1hand for each subject. We were unable to find any correlation between cumulative M1hand exposure and M1 excitability change. We also present data that suggest a TMS-induced MEP always preceded a near-threshold cSP.

Resolution of Initial Value Problems of Ordinary Differential Equations Systems

In this work, we present some techniques applicable to Initial Value Problems when solving a System of Ordinary Differential Equations (ODE). Such techniques should be used when applying adaptive step-size numerical methods. In our case, a Runge-Kutta-Fehlberg algorithm (RKF45) has been employed, but the procedure presented here can also be applied to other adaptive methods, such as N-body problems, as AP3M or similar ones. By doing so, catastrophic cancellations were eliminated. A mathematical optimization was carried out by introducing the objective function in the ODE System (ODES). Resizing of local errors was also utilised in order to adress the problem. This resize implies the use of certain variables to adjust the integration step while the other variables are used as parameters to determine the coefficients of the ODE system. This resize was executed by using the asymptotic solution of this system. The change of variables is necessary to guarantee the stability of the integration. Therefore, the linearization of the ODES is possible and can be used as a powerful control test. All these tools are applied to a physical problem. The example we present here is the effective numerical resolution of Lemaitre-Tolman-Bondi space-time solutions of Einstein Equations.

Numerical Evaluation of the Effects of Transducer Displacement on Transcranial Focused Ultrasound in the Rat Brain

Focused ultrasound is a promising therapeutic technique, as it involves the focusing of an ultrasonic beam with sufficient acoustic energy into a target brain region with high precision. Low-intensity ultrasound transmission by a single-element transducer is mostly established for neuromodulation applications and blood–brain barrier disruption for drug delivery. However, transducer positioning errors can occur without fine control over the sonication, which can affect repeatability and lead to reliability problems. The objective of this study was to determine whether the target brain region would be stable under small displacement (0.5 mm) of the transducer based on numerical simulations. Computed-tomography-derived three-dimensional models of a rat head were constructed to investigate the effects of transducer displacement in the caudate putamen (CP) and thalamus (TH). Using three different frequencies (1.1, 0.69, and 0.25 MHz), the transducer was displaced by 0.5 mm in each of the following six directions: superior, interior, anterior, posterior, left, and right. The maximum value of the intracranial pressure field was calculated, and the targeting errors were determined by the full-width-at-half-maximum (FWHM) overlap between the free water space (FWHM_water) and transcranial transmission (FWHM_base). When the transducer was positioned directly above the target region, a clear distinction between the target regions was observed, resulting in 88.3%, 81.5%, and 84.5% FWHM_water for the CP and 65.6%, 76.3%, and 64.4% FWHM_water for the TH at 1.1, 0.69, and 0.25 MHz, respectively. Small transducer displacements induced both enhancement and reduction of the peak pressure and targeting errors, compared with when the transducer was displaced in water. Small transducer displacement to the left resulted in the lowest stability, with 34.8% and 55.0% targeting accuracy (FWHM_water) at 1.1 and 0.69 MHz in the TH, respectively. In addition, the maximum pressure was reduced by up to 11% by the transducer displacement. This work provides the targeting errors induced by transducer displacements through a preclinical study and recommends that attention be paid to determining the initial sonication foci in the transverse plane in the cases of small animals.

Verification of Blood-Brain Barrier Disruption Based on the Clinical Validation Platform Using a Rat Model with Human Skull

Methods to improve drug delivery efficiency through blood-brain barrier disruption (BBBD) based on microbubbles and focused ultrasound (FUS) are continuously being studied. However, most studies are being conducted in preclinical trial environments using small animals. The use of the human skull shows differences between the clinical and preclinical trials. BBBD results from preclinical trials are difficult to represent in clinical trials because various distortions of ultrasound by the human skull are excluded in the former. Therefore, in our study, a clinical validation platform based on a preclinical trial environment, using a human skull fragment and a rat model, was developed to induce BBBD under conditions similar to clinical trials. For this, a human skull fragment was inserted between the rat head and a 250 kHz FUS transducer, and optimal ultrasound parameters for the free field (without human skull fragment) and human skull (with human skull fragment) were derived by 300 mV_pp and 700 mV_pp, respectively. BBBD was analyzed according to each case using magnetic resonance images, Evans blue dye, cavitation, and histology. Although it was confirmed using magnetic resonance images and Evans blue dye that a BBB opening was induced in each case, multiple BBB openings were observed in the brain tissues. This phenomenon was analyzed by numerical simulation, and it was confirmed to be due to standing waves owing to the small skull size of the rat model. The stable cavitation doses (SCD_h and SCD_u) in the human skull decreased by 13.6- and 5.3-fold, respectively, compared to those in the free field. Additionally, the inertial cavitation dose in the human skull decreased by 1.05-fold compared to that of the free field. For the histological analysis, although some extravasated red blood cells were observed in each case, it was evaluated as recoverable based on our previous study results. Therefore, our proposed platform can help deduct optimal ultrasound parameters and BBBD results for clinical trials in the preclinical trials with small animals because it considers variables relevant to the human skull.

"HIFU Beam:" A Simulator for Predicting Axially Symmetric Nonlinear Acoustic Fields Generated by Focused Transducers in a Layered Medium

"HIFU beam" is a freely available software tool that comprises a MATLAB toolbox combined with a user-friendly interface and binary executable compiled from FORTRAN source code (HIFU beam. (2021). Available: http://limu.msu.ru/node/3555?language=en). It is designed for simulating high-intensity focused ultrasound (HIFU) fields generated by single-element transducers and annular arrays with propagation in flat-layered media that mimic biological tissues. Numerical models incorporated in the simulator include evolution-type equations, either the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation or one-way Westervelt equation, for radially symmetric ultrasound beams in homogeneous and layered media with thermoviscous or power-law acoustic absorption. The software uses shock-capturing methods that allow for simulating strongly nonlinear acoustic fields with high-amplitude shocks. In this article, a general description of the software is given along with three representative simulation cases of ultrasound transducers and focusing conditions typical for therapeutic applications. The examples illustrate major nonlinear wave effects in HIFU fields including shock formation. Two examples simulate propagation in water, involving a single-element source (1-MHz frequency, 100-mm diameter, 90-mm radius of curvature) and a 16-element annular array (3-MHz frequency, 48-mm diameter, and 35-mm radius of curvature). The third example mimics the scenario of a HIFU treatment in a "water-muscle-kidney" layered medium using a source typical for abdominal HIFU applications (1.2-MHz frequency, 120-mm diameter, and radius of curvature). Linear, quasi-linear, and shock-wave exposure protocols are considered. It is intended that "HIFU beam" can be useful in teaching nonlinear acoustics; designing and characterizing high-power transducers; and developing exposure protocols for a wide range of therapeutic applications such as shock-based HIFU, boiling histotripsy, drug delivery, immunotherapy, and others.

Effect of Skull Porous Trabecular Structure on Transcranial Ultrasound Imaging in the Presence of Elastic Wave Mode Conversion at Varying Incidence Angle

With the advancement of aberration correction techniques, transcranial ultrasound imaging has exhibited great potential in applications such as imaging neurological function and guiding therapeutic ultrasound. However, the feasibility of transcranial imaging varies among individuals because of the differences in skull acoustic properties. To better understand the fundamental mechanisms underlying the variation in imaging performance, the effect of the structure of the porous trabecular bone on transcranial imaging performance (i.e., target localization errors and resolution) was investigated for the first time through the use of elastic wave simulations and experiments. Simulation studies using high-resolution computed tomography data from ex vivo skull samples revealed that imaging at large incidence angles reduced the target localization error for skulls having low porosity; however, as skull porosity increased, large angles of incidence resulted in degradation of resolution and increased target localization errors. Experimental results indicate that imaging at normal incidence introduced a localization error of 1.85 ± 0.10 mm, while imaging at a large incidence angle (40°) resulted in an increased localization error of 6.54 ± 1.33 mm and caused a single point target to no longer appear as a single, coherent target in the resulting image, which is consistent with simulation results. This first investigation of the effects of skull microstructure on transcranial ultrasound imaging indicates that imaging performance is highly dependent on the porosity of the skull, particularly at non-normal angles of incidence.

A modified mixed domain method for modeling acoustic wave propagation in strongly heterogeneous media

In this paper, phase correction and amplitude compensation are introduced to a previously developed mixed domain method (MDM), which is only accurate for modeling wave propagation in weakly heterogeneous media. Multiple reflections are also incorporated with the one-way model to improve the accuracy. The resulting model is denoted as the modified mixed domain method (MMDM) and is numerically evaluated for its accuracy and efficiency using four distinct cases. It is found that the MMDM is significantly more accurate than the MDM for strongly heterogeneous media, especially when the phase aberrating layer is approximately perpendicular to the acoustic beam. Additionally, a convergence study suggests that the second-order reflection could be sufficient for cases involving high contrast inhomogeneities and large loss values (e.g., skulls). The method developed in this work could facilitate therapeutic ultrasound for treating brain-related diseases and disorders.

A generalized fractional-order elastodynamic theory for non-local attenuating media

This study presents a generalized elastodynamic theory, based on fractional-order operators, capable of modelling the propagation of elastic waves in non-local attenuating solids and across complex non-local interfaces. Classical elastodynamics cannot capture hybrid field transport processes that are characterized by simultaneous propagation and diffusion. The proposed continuum mechanics formulation, which combines fractional operators in both time and space, offers unparalleled capabilities to predict the most diverse combinations of multiscale, non-local, dissipative and attenuating elastic energy transport mechanisms. Despite the many features of this theory and the broad range of applications, this work focuses on the behaviour and modelling capabilities of the space-fractional term and on its effect on the elastodynamics of solids. We also derive a generalized fractional-order version of Snell's Law of refraction and of the corresponding Fresnel's coefficients. This formulation allows predicting the behaviour of fully coupled elastic waves interacting with non-local interfaces. The theoretical results are validated via direct numerical simulations.

Iterative image reconstruction in transcranial photoacoustic tomography based on the elastic wave equation

Photoacoustic computed tomography (PACT) is an emerging computed imaging modality that exploits optical contrast and ultrasonic detection principles to form images of the photoacoustically induced initial pressure distribution within tissue. The PACT reconstruction problem corresponds to a time-domain inverse source problem, where the initial pressure distribution is recovered from the measurements recorded on an aperture outside the support of the source. A major challenge in transcranial PACT of the brain is to compensate for aberrations and attenuation in the measured data due to the propagation of the photoacoustic wavefields through the skull. To properly account for these effects, a wave equation-based inversion method can be employed that can model the heterogeneous elastic properties of the medium. In this study, an optimization-based image reconstruction method for 3D transcranial PACT is developed based on the elastic wave equation. To accomplish this, a forward-adjoint operator pair based on a finite-difference time-domain discretization of the 3D elastic wave equation is utilized to compute penalized least squares estimates of the initial pressure distribution. Computer-simulation and experimental studies are conducted to investigate the robustness of the reconstruction method to model mismatch and its ability to effectively resolve cortical and superficial brain structures.

Simulation of nonlinear trans-skull focusing and formation of shocks in brain using a fully populated ultrasound array with aberration correction

Multi-element high-intensity focused ultrasound phased arrays in the shape of hemispheres are currently used in clinics for thermal lesioning in deep brain structures. Certain side effects of overheating non-targeted tissues and skull bones have been revealed. Here, an approach is developed to mitigate these effects. A specific design of a fully populated 256-element 1-MHz array shaped as a spherical segment (F-number, F_# = 1) and filled by randomly distributed equal-area polygonal elements is proposed. Capability of the array to generate high-amplitude shock fronts at the focus is tested in simulations by combining three numerical algorithms for linear and nonlinear field modeling and aberration correction. The algorithms are based on the combination of the Rayleigh integral, a linear pseudo-spectral time domain Kelvin-Voigt model, and nonlinear Westervelt model to account for the effects of inhomogeneities, aberrations, reflections, absorption, nonlinearity, and shear waves in the skull. It is shown that the proposed array can generate nonlinear waveforms with shock amplitudes >60 MPa at the focus deep inside the brain without exceeding the existing technical limitation on the intensity of 40 W/cm² at the array elements. Such shock amplitudes are sufficient for mechanical ablation of brain tissues using the boiling histotripsy approach and implementation of other shock-based therapies.

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.

Acoustic manipulation of particles in a cylindrical cavity: Theoretical and experimental study on the effects of boundary conditions

Precise manipulation of microparticles in microchannels is a primary technique for numerous lab-on-a-chip bioengineering research and applications, as it determines the chip's functions and analytical results. Acoustic manipulation, using the acoustic radiation force, is a compact, versatile and contactless manipulation technique, which can be easily integrated with other microfluidic components. It is our main purpose to report the effect of boundary condition of a cylindrical microfluidic cavity on the acoustic particles' manipulation. A device consisting of a cylindrical cavity in a silicon wafer with three kinds of top boundary conditions (rigid, soft, and imperfect rigid boundary) has been built. The corresponding distributions of acoustic radiation force are analyzed analytically and numerically. Experiments are performed with 2.5 μm radius polystyrene microspheres in the cavity covered by three reflective layers (340 μm-thick glass, 400 μm-thick PDMS, and 660 μm-thick glass film), respectively, which specify the three different boundary conditions at the top of the cavity. It is demonstrated that the boundary condition of a cavity influences the acoustic radiation force and the stable positions of particles, and this is in agreement with the theoretical predictions. Thus, the effects of boundary conditions need to be considered for precise acoustic manipulation.

A two-dimensional (2D) systems biology-based discrete liver tissue model: A simulation study with implications for ultrasound elastography of liver fibrosis

Continuum tissue models that were often used to simulate or analyze the mechanical properties of tissues being imaged may not be biologically realistic. Our primary objective was to establish the feasibility of using systems biology to construct biologically relevant tissue models linking tissue structure, composition and architecture to the ultrasound measurements directly. The first application was designated to model fibrotic liver tissues. The proposed liver tissue model leveraged established histopathology knowledge of fibrotic liver tissues. Particularly, rules of systems biology derived from molecular histopathology were first implemented into an agent-based software platform SPARK to reflect progressions of liver fibrosis with/without steatosis. Then, microscopic compositions of tissues (e.g. cellular components) were converted to computing grids (at the 50-100 μm scale) for wave simulations using an open-source K-Wave. To verify the physical soundness of the proposed model, virtual wave speed measurements (i.e. shear wave speed [SWS] and the speed of sound [SOS]) were performed. Our initial results demonstrated that the simulated SWS values increased with the progression of liver fibrosis (from 1.5 m/s [Fibrosis stage 1] to 4 m/s [Fibrosis stage 4]). Similarly, the simulated SOS values were within the range of clinical data (from 1575 m/s [Fibrosis stage 0-3] to 1594 m/s [Fibrosis stage 4]). In summary, we found that those systems biology simulated fibrotic liver tissues with and without steatosis can reflect spatial characteristics of relevant histology. Also, their mechanical characteristics (i.e. shear/compressional wave speed) were in good agreement with data reported in the clinical literature.

The fractal derivative wave equation: Application to clinical amplitude/velocity reconstruction imaging

This paper proposes a dissipative acoustic wave equation in which the fractal derivative is employed to represent dissipation. The proposed model is derived from the viscoelastic constitutive relationship via the fractal derivative. It is noted that the fractal derivative is a local operator and avoids the expensive computational costs of non-local fractional derivative, which is popular in recent decades to describe frequency-dependent dissipation in acoustic wave propagation in soft materials. The proposed model is tested to simulate the clinical amplitude/velocity reconstruction imaging of breast tumors, where the reflecting plate is imaged as an elevated line in correspondence to tumor. Numerical experiments show that the present model is capable of indicating the size, position and quantity of tumors. The comparative study confirms that the fractal derivative acoustic wave equation has an advantage over the fractional derivative model regarding computational costs.

Time domain reconstruction of sound speed and attenuation in ultrasound computed tomography using full wave inversion

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.

Nonthermal ablation of deep brain targets: A simulation study on a large animal model

PURPOSE

Thermal ablation with transcranial MRI-guided focused ultrasound (FUS) is currently limited to central brain targets because of heating and other beam effects caused by the presence of the skull. Recently, it was shown that it is possible to ablate tissues without depositing thermal energy by driving intravenously administered microbubbles to inertial cavitation using low-duty-cycle burst sonications. A recent study demonstrated that this ablation method could ablate tissue volumes near the skull base in nonhuman primates without thermally damaging the nearby bone. However, blood-brain disruption was observed in the prefocal region, and in some cases, this region contained small areas of tissue damage. The objective of this study was to analyze the experimental model with simulations and to interpret the cause of these effects.

METHODS

The authors simulated prior experiments where nonthermal ablation was performed in the brain in anesthetized rhesus macaques using a 220 kHz clinical prototype transcranial MRI-guided FUS system. Low-duty-cycle sonications were applied at deep brain targets with the ultrasound contrast agent Definity. For simulations, a 3D pseudospectral finite difference time domain tool was used. The effects of shear mode conversion, focal steering, skull aberrations, nonlinear propagation, and the presence of skull base on the pressure field were investigated using acoustic and elastic wave propagation models.

RESULTS

The simulation results were in agreement with the experimental findings in the prefocal region. In the postfocal region, however, side lobes were predicted by the simulations, but no effects were evident in the experiments. The main beam was not affected by the different simulated scenarios except for a shift of about 1 mm in peak position due to skull aberrations. However, the authors observed differences in the volume, amplitude, and distribution of the side lobes. In the experiments, a single element passive cavitation detector was used to measure the inertial cavitation threshold and to determine the pressure amplitude to use for ablation. Simulations of the detector's acoustic field suggest that its maximum sensitivity was in the lower part of the main beam, which may have led to excessive exposure levels in the experiments that may have contributed to damage in the prefocal area.

CONCLUSIONS

Overall, these results suggest that case-specific full wave simulations before the procedure can be useful to predict the focal and the prefocal side lobes and the extent of the resulting bioeffects produced by nonthermal ablation. Such simulations can also be used to optimally position passive cavitation detectors. The disagreement between the simulations and the experiments in the postfocal region may have been due to shielding of the ultrasound field due to microbubble activity in the focal region. Future efforts should include the effects of microbubble activity and vascularization on the pressure field.

Preclinical evaluation of a low-frequency transcranial MRI-guided focused ultrasound system in a primate model

This study investigated thermal ablation and skull-induced heating with a 230 kHz transcranial MRI-guided focused ultrasound (TcMRgFUS) system in nonhuman primates. We evaluated real-time acoustic feedback and aimed to understand whether cavitation contributed to the heating and the lesion formation. In four macaques, we sonicated thalamic targets at acoustic powers of 34-560 W (896-7590 J). Tissue effects evaluated with MRI and histology were compared to MRI-based temperature and thermal dose measurements, acoustic emissions recorded during the experiments, and acoustic and thermal simulations. Peak temperatures ranged from 46 to 57 °C, and lesions were produced in 5/8 sonicated targets. A linear relationship was observed between the applied acoustic energy and both the focal and brain surface heating. Thermal dose thresholds were 15-50 cumulative equivalent minutes at 43 °C, similar to prior studies at higher frequencies. Histology was also consistent with earlier studies of thermal effects in the brain. The system successfully controlled the power level and maintained a low level of cavitation activity. Increased acoustic emissions observed in 3/4 animals occurred when the focal temperature rise exceeded approximately 16 °C. Thresholds for thermally-significant subharmonic and wideband emissions were 129 and 140 W, respectively, corresponding to estimated pressure amplitudes of 2.1 and 2.2 MPa. Simulated focal heating was consistent with the measurements for sonications without thermally-significant acoustic emissions; otherwise it was consistently lower than the measurements. Overall, these results suggest that the lesions were produced by thermal mechanisms. The detected acoustic emissions, however, and their association with heating suggest that cavitation might have contributed to the focal heating. Compared to earlier work with a 670 kHz TcMRgFUS system, the brain surface heating was substantially reduced and the focal heating was higher with this 230 kHz system, suggesting that a reduced frequency can increase the treatment envelope for TcMRgFUS and potentially reduce the risk of skull heating.