Simulation of ultrasonic pulse propagation through the abdominal wall

Toward widespread use of virtual trials in medical imaging innovation and regulatory science

The rapid advancement in the field of medical imaging presents a challenge in keeping up to date with the necessary objective evaluations and optimizations for safe and effective use in clinical settings. These evaluations are traditionally done using clinical imaging trials, which while effective, pose several limitations including high costs, ethical considerations for repetitive experiments, time constraints, and lack of ground truth. To tackle these issues, virtual trials (aka in silico trials) have emerged as a promising alternative, using computational models of human subjects and imaging devices, and observer models/analysis to carry out experiments. To facilitate the widespread use of virtual trials within the medical imaging research community, a major need is to establish a common consensus framework that all can use. Based on the ongoing efforts of an AAPM Task Group (TG387), this article provides a comprehensive overview of the requirements for establishing virtual imaging trial frameworks, paving the way toward their widespread use within the medical imaging research community. These requirements include credibility, reproducibility, and accessibility. Credibility assessment involves verification, validation, uncertainty quantification, and sensitivity analysis, ensuring the accuracy and realism of computational models. A proper credibility assessment requires a clear context of use and the questions that the study is intended to objectively answer. For reproducibility and accessibility, this article highlights the need for detailed documentation, user-friendly software packages, and standard input/output formats. Challenges in data and software sharing, including proprietary data and inconsistent file formats, are discussed. Recommended solutions to enhance accessibility include containerized environments and data-sharing hubs, along with following standards such as CDISC (Clinical Data Interchange Standards Consortium). By addressing challenges associated with credibility, reproducibility, and accessibility, virtual imaging trials can be positioned as a powerful and inclusive resource, advancing medical imaging innovation and regulatory science.

The Biomechanics of Musculoskeletal Tissues during Activities of Daily Living: Dynamic Assessment Using Quantitative Transmission-Mode Ultrasound Techniques

The measurement of musculoskeletal tissue properties and loading patterns during physical activity is important for understanding the adaptation mechanisms of tissues such as bone, tendon, and muscle tissues, particularly with injury and repair. Although the properties and loading of these connective tissues have been quantified using direct measurement techniques, these methods are highly invasive and often prevent or interfere with normal activity patterns. Indirect biomechanical methods, such as estimates based on electromyography, ultrasound, and inverse dynamics, are used more widely but are known to yield different parameter values than direct measurements. Through a series of literature searches of electronic databases, including Pubmed, Embase, Web of Science, and IEEE Explore, this paper reviews current methods used for the in vivo measurement of human musculoskeletal tissue and describes the operating principals, application, and emerging research findings gained from the use of quantitative transmission-mode ultrasound measurement techniques to non-invasively characterize human bone, tendon, and muscle properties at rest and during activities of daily living. In contrast to standard ultrasound imaging approaches, these techniques assess the interaction between ultrasound compression waves and connective tissues to provide quantifiable parameters associated with the structure, instantaneous elastic modulus, and density of tissues. By taking advantage of the physical relationship between the axial velocity of ultrasound compression waves and the instantaneous modulus of the propagation material, these techniques can also be used to estimate the in vivo loading environment of relatively superficial soft connective tissues during sports and activities of daily living. This paper highlights key findings from clinical studies in which quantitative transmission-mode ultrasound has been used to measure the properties and loading of bone, tendon, and muscle tissue during common physical activities in healthy and pathological populations.

Aberration correction in abdominal histotripsy

In transabdominal histotripsy, ultrasound pulses are focused on the body to noninvasively destroy soft tissues via cavitation. However, the ability to focus is limited by phase aberration, or decorrelation of the ultrasound pulses due to spatial variation in the speed of sound throughout heterogeneous tissue. Phase aberration shifts, broadens, and weakens the focus, thereby reducing the safety and efficacy of histotripsy therapy. This paper reviews and discusses aberration effects in histotripsy and in related therapeutic ultrasound techniques (e.g., high intensity focused ultrasound), with an emphasis on aberration by soft tissues. Methods for aberration correction are reviewed and can be classified into two groups: model-based methods, which use segmented images of the tissue as input to an acoustic propagation model to predict and compensate phase differences, and signal-based methods, which use a receive-capable therapy array to detect phase differences by sensing acoustic signals backpropagating from the focus. The relative advantages and disadvantages of both groups of methods are discussed. Importantly, model-based methods can correct focal shift, while signal-based methods can restore substantial focal pressure, suggesting that both methods should be combined in a 2-step approach. Aberration correction will be critical to improving histotripsy treatments and expanding the histotripsy treatment envelope to enable non-invasive, non-thermal histotripsy therapy for more patients.

Aberration correction in diagnostic ultrasound: A review of the prior field and current directions

Medical ultrasound images are reconstructed with simplifying assumptions on wave propagation, with one of the most prominent assumptions being that the imaging medium is composed of a constant sound speed. When the assumption of a constant sound speed are violated, which is true in most in vivoor clinical imaging scenarios, distortion of the transmitted and received ultrasound wavefronts appear and degrade the image quality. This distortion is known as aberration, and the techniques used to correct for the distortion are known as aberration correction techniques. Several models have been proposed to understand and correct for aberration. In this review paper, aberration and aberration correction are explored from the early models and correction techniques, including the near-field phase screen model and its associated correction techniques such as nearest-neighbor cross-correlation, to more recent models and correction techniques that incorporate spatially varying aberration and diffractive effects, such as models and techniques that rely on the estimation of the sound speed distribution in the imaging medium. In addition to historical models, future directions of ultrasound aberration correction are proposed.

Sound Speed Estimation for Distributed Aberration Correction in Laterally Varying Media

Spatial variation in sound speed causes aberration in medical ultrasound imaging. Although our previous work has examined aberration correction in the presence of a spatially varying sound speed, practical implementations were limited to layered media due to the sound speed estimation process involved. Unfortunately, most models of layered media do not capture the lateral variations in sound speed that have the greatest aberrative effect on the image. Building upon a Fourier split-step migration technique from geophysics, this work introduces an iterative sound speed estimation and distributed aberration correction technique that can model and correct for aberrations resulting from laterally varying media. We first characterize our approach in simulations where the scattering in the media is known a-priori. Phantom and in-vivo experiments further demonstrate the capabilities of the iterative correction technique. As a result of the iterative correction scheme, point target resolution improves by up to a factor of 4 and lesion contrast improves by up to 10.0 dB in the phantom experiments presented.

Deep learning for hetero-homo conversion in channel-domain for phase aberration correction in ultrasound imaging

Echo imaging in ultrasound computed tomography (USCT) using the synthetic aperture technique is performed with the assumption that the speed of sound is constant in the system. However, tissue heterogeneity causes a mismatch between the predicted arrival time and the actual arrival time of the echo signal, which will result in phase aberration, leading to the quality degradation of the reconstructed B-mode image. The conventional correction methods that use the correlation of each different channel require the presence of strong point scatterers and involve the problem of local solutions due to excessive correction. In this study, we propose a novel approach to correcting the signal distortion due to sound speed heterogeneity using a deep neural network (DNN). The DNN was trained to convert the distorted radio frequency (RF) inputs for the heterogeneous medium to the distortion-free RF outputs for the homogeneous medium. The network with U-net architecture using ResNet-34 as a backbone was trained using the hetero-homo corresponding channel-domain RF data generated via numerical simulations. The trained network performed phase aberration correction in the channel-domain RF, with the B-mode images reconstructed with the corrected RF demonstrating a higher contrast and an improved resolution compared with uncorrected cases. It was also demonstrated that the DNN model is robust to both varied reflection intensities and varied sound speed heterogeneities. The successful results demonstrated that the proposed DNN-based method is effective for phase aberration correction in US imaging.

Ultrasound Matrix Imaging-Part II: The Distortion Matrix for Aberration Correction Over Multiple Isoplanatic Patches

This is the second article in a series of two which report on a matrix approach for ultrasound imaging in heterogeneous media. This article describes the quantification and correction of aberration, i.e. the distortion of an image caused by spatial variations in the medium speed-of-sound. Adaptive focusing can compensate for aberration, but is only effective over a restricted area called the isoplanatic patch. Here, we use an experimentally-recorded matrix of reflected acoustic signals to synthesize a set of virtual transducers. We then examine wave propagation between these virtual transducers and an arbitrary correction plane. Such wave-fronts consist of two components: (i) An ideal geometric wave-front linked to diffraction and the input focusing point, and; (ii) Phase distortions induced by the speed-of-sound variations. These distortions are stored in a so-called distortion matrix, the singular value decomposition of which gives access to an optimized focusing law at any point. We show that, by decoupling the aberrations undergone by the outgoing and incoming waves and applying an iterative strategy, compensation for even high-order and spatially-distributed aberrations can be achieved. After a numerical validation of the process, ultrasound matrix imaging (UMI) is applied to the in-vivo imaging of a gallbladder. A map of isoplanatic modes is retrieved and is shown to be strongly correlated with the arrangement of tissues constituting the medium. The corresponding focusing laws yield an ultrasound image with drastically improved contrast and transverse resolution. UMI thus provides a flexible and powerful route towards computational ultrasound.

Ultrasound Matrix Imaging-Part I: The Focused Reflection Matrix, the F-Factor and the Role of Multiple Scattering

This is the first article in a series of two dealing with a matrix approach for aberration quantification and correction in ultrasound imaging. Advanced synthetic beamforming relies on a double focusing operation at transmission and reception on each point of the medium. Ultrasound matrix imaging (UMI) consists in decoupling the location of these transmitted and received focal spots. The response between those virtual transducers form the so-called focused reflection matrix that actually contains much more information than a confocal ultrasound image. In this paper, a time-frequency analysis of this matrix is performed, which highlights the single and multiple scattering contributions as well as the impact of aberrations in the monochromatic and broadband regimes. Interestingly, this analysis enables the measurement of the incoherent input-output point spread function at any pixel of this image. A fitting process enables the quantification of the single scattering, multiple scattering and noise components in the image. From the single scattering contribution, a focusing criterion is defined, and its evolution used to quantify the amount of aberration throughout the ultrasound image. In contrast to the state-of-the-art coherence factor, this new indicator is robust to multiple scattering and electronic noise, thereby providing a contrasted map of the focusing quality at a much better transverse resolution. After a validation of the proof-of-concept based on time-domain simulations, UMI is applied to the in-vivo study of a human calf. Beyond this specific example, UMI opens a new route for speed-of-sound and scattering quantification in ultrasound imaging.

Transport and distribution of biotherapeutics in different tissue layers after subcutaneous injection

The subcutaneous injection is the main route of administration for monoclonal antibodies (mAbs) and several other biotherapeutics due to the patient comfort and cost-effectiveness. However, their transport and distribution after subcutaneous injection is poorly understood. Here, we exploit a three-dimensional poroelastic model to find the biomechanical response of the tissue, including interstitial pressure and tissue deformation during the injection. We quantify the drug concentration inside the tissue. We start with a single-layer model of the tissue. We show that during injection, the difference between the permeability of the solvent and solute will result in a higher drug concentration proportional to the inverse permeability ratio. Then we study the role of tissue layered properties with primary layers, including epidermis, dermis, subcutaneous (SQ), and muscle layers, on tissue biomechanical response to injection and drug transport. We show that the drug will distribute mainly in the SQ layer due to its lower elastic moduli. Finally, we study the effect of secondary tissue elements like the deep fascia layer and the network of septa fibers inside the SQ tissue. We use the Voronoi algorithm to create random geometry of the septa network. We show how drugs accumulate around these tissue components as observed in experimental SQ injection. Next, we study the effect of injection rate on drug concentration. We show how higher injection rates will slightly increase the drug concentration around septa fibers. Finally we demonstrate how the concentration dependent viscosity will increase the concentration of biotherapeutics in the direction of septa fibers. .

Spatial Coherence in Medical Ultrasound: A Review

Traditional pulse-echo ultrasound imaging heavily relies on the discernment of signals based on their relative magnitudes but is limited in its ability to mitigate sources of image degradation, the most prevalent of which is acoustic clutter. Advances in computing power and data storage have made it possible for echo data to be alternatively analyzed through the lens of spatial coherence, a measure of the similarity of these signals received across an array. Spatial coherence is not currently explicitly calculated on diagnostic ultrasound scanners but a large number of studies indicate that it can be employed to describe image quality, to adaptively select system parameters and to improve imaging and target detection. With the additional insights provided by spatial coherence, it is poised to play a significant role in the future of medical ultrasound. This review details the theory of spatial coherence in pulse-echo ultrasound and key advances made over the last few decades since its introduction in the 1980s.

Robust and durable aberrative and absorptive phantom for therapeutic ultrasound applications

Phase aberration induced by soft tissue inhomogeneities often complicates high-intensity focused ultrasound (HIFU) therapies by distorting the field and, previously, we designed and fabricated a bilayer gel phantom to reproducibly mimic that effect. A surface pattern containing size scales relevant to inhomogeneities of a porcine body wall was introduced between gel materials with fat- and muscle-like acoustic properties-ballistic and polyvinyl alcohol gels. Here, the phantom design was refined to achieve relevant values of ultrasound absorption and scattering and make it more robust, facilitating frequent handling and use in various experimental arrangements. The fidelity of the interfacial surface of the fabricated phantom to the design was confirmed by three-dimensional ultrasound imaging. The HIFU field distortions-displacement of the focus, enlargement of the focal region, and reduction of focal pressure-produced by the phantom were characterized using hydrophone measurements with a 1.5 MHz 256-element HIFU array and found to be similar to those induced by an ex vivo porcine body wall. A phase correction approach was used to mitigate the aberration effect on nonlinear focal waveforms and enable boiling histotripsy treatments through the phantom or body wall. The refined phantom represents a practical tool to explore HIFU therapy systems capabilities.

Distributed Aberration Correction Techniques Based on Tomographic Sound Speed Estimates

Phase aberration is widely considered a major source of image degradation in medical pulse-echo ultrasound. Traditionally, near-field phase aberration correction techniques are unable to account for distributed aberrations due to a spatially varying speed of sound in the medium, while most distributed aberration correction techniques require the use of point-like sources and are impractical for clinical applications where diffuse scattering is dominant. Here, we present two distributed aberration correction techniques that utilize sound speed estimates from a tomographic sound speed estimator that builds on our previous work with diffuse scattering in layered media. We first characterize the performance of our sound speed estimator and distributed aberration correction techniques in simulations where the scattering in the media is known a priori. Phantom and in vivo experiments further demonstrate the capabilities of the sound speed estimator and the aberration correction techniques. In phantom experiments, point target resolution improves from 0.58 to 0.26 and 0.27 mm, and lesion contrast improves from 17.7 to 23.5 and 25.9 dB, as a result of distributed aberration correction using the eikonal and wavefield correlation techniques, respectively.

Occult Regions of Suppressed Coherence in Liver B-Mode Images

Ultrasound is an essential tool for diagnosing and monitoring diseases, but it can be limited by poor image quality. Lag-one coherence (LOC) is an image quality metric that can be related to signal-to-noise ratio and contrast-to-noise ratio. In this study, we examine matched LOC and B-mode images of the liver to discern patterns of low image quality, as indicated by lower LOC values, occurring beneath the abdominal wall, near out-of-plane vessels and adjacent to hyperechoic targets such the liver capsule. These regions of suppressed coherence are often occult; they present as temporally stable uniform speckle on B-mode images, but the LOC measurements in these regions suggest substantially degraded image quality. Quantitative characterization of the coherence suppression beneath the abdominal wall reveals a consistent pattern both in simulations and in vivo; sharp drops in coherence occurring beneath the abdominal wall asymptotically recover to a stable coherence at depth. Simulation studies suggest that abdominal wall reverberation clutter contributes to the initial drop in coherence but does not influence the asymptotic LOC value. Clinical implications are considered for contrast loss in B-mode imaging and estimation errors for elastography and Doppler imaging.

Ultrasonic Attenuation of an Agar, Silicon Dioxide, and Evaporated Milk Gel Phantom

Background:

It has been demonstrated that agar-based gel phantoms can emulate the acoustic parameters of real tissues and are the most commonly used tissue-mimicking materials for high-intensity focused ultrasound applications. The following study presents ultrasonic attenuation measurements of agar-based phantoms with different concentrations of additives (percent of agar, silicon dioxide and evaporated milk) in an effort of matching the material's acoustic property as close as possible to human tissues.

Methods:

Nine different agar-based phantoms with various amounts of agar, silicon dioxide, and evaporated milk were prepared. Attenuation measurements of the samples were conducted using the through-transmission immersion techniques.

Results:

The ultrasonic attenuation coefficient of the agar-based phantoms varied in the range of 0.30–1.49 dB/cm-MHz. The attenuation was found to increase in proportion to the concentration of agar and evaporated milk. Silicon dioxide was found to significantly contribute to the attenuation coefficient up to 4% weight to volume (w/v) concentration.

Conclusion:

The acoustic attenuation coefficient of agar-based phantoms can be adjusted according to the tissue of interest in the range of animal and human tissues by the proper selection of agar, silicon dioxide, and evaporated milk.

Discrete Approximations of Acoustic Source Distributions

The modeling of source a distributions of finite spatial extent in ultrasound and medical imaging applications is a problem of longstanding interest. In time-domain methods, such as the finite-difference time-domain or pseudospectral approaches, one requirement is the representation of such distributions over a grid, normally Cartesian. Various artifacts, including staircasing errors, can arise. In this short contribution, the problem of the representation of distribution over a grid is framed as an optimization problem in the Fourier domain over a preselected set of grid points, thus maintaining control over computational cost and allowing the fine-tuning of the optimization to the wavenumber range of interest for a particular numerical method. Numerical results are presented in the important special case of the spherical cap or bowl source.

Reverberation Noise Suppression in Ultrasound Channel Signals Using a 3D Fully Convolutional Neural Network

Diffuse reverberation is ultrasound image noise caused by multiple reflections of the transmitted pulse before returning to the transducer, which degrades image quality and impedes the estimation of displacement or flow in techniques such as elastography and Doppler imaging. Diffuse reverberation appears as spatially incoherent noise in the channel signals, where it also degrades the performance of adaptive beamforming methods, sound speed estimation, and methods that require measurements from channel signals. In this paper, we propose a custom 3D fully convolutional neural network (3DCNN) to reduce diffuse reverberation noise in the channel signals. The 3DCNN was trained with channel signals from simulations of random targets that include models of reverberation and thermal noise. It was then evaluated both on phantom and in-vivo experimental data. The 3DCNN showed improvements in image quality metrics such as generalized contrast to noise ratio (GCNR), lag one coherence (LOC) contrast-to-noise ratio (CNR) and contrast for anechoic regions in both phantom and in-vivo experiments. Visually, the contrast of anechoic regions was greatly improved. The CNR was improved in some cases, however the 3DCNN appears to strongly remove uncorrelated and low amplitude signal. In images of in-vivo carotid artery and thyroid, the 3DCNN was compared to short-lag spatial coherence (SLSC) imaging and spatial prediction filtering (FXPF) and demonstrated improved contrast, GCNR, and LOC, while FXPF only improved contrast and SLSC only improved CNR.

Modeling Ultrasound Propagation in the Moving Brain: Applications to Shear Shock Waves and Traumatic Brain Injury

Traumatic brain injury (TBI) studies on the living human brain are experimentally infeasible due to ethical reasons and the elastic properties of the brain degrade rapidly postmortem. We present a simulation approach that models ultrasound propagation in the human brain, while it is moving due to the complex shear shock wave deformation from a traumatic impact. Finite difference simulations can model ultrasound propagation in complex media such as human tissue. Recently, we have shown that the fullwave finite difference approach can also be used to represent displacements that are much smaller than the grid size, such as the motion encountered in shear wave propagation from ultrasound elastography. However, this subresolution displacement model, called impedance flow, was only implemented and validated for acoustical media composed of randomly distributed scatterers. Herein, we propose a generalization of the impedance flow method that describes the continuous subresolution motion of structured acoustical maps, and in particular of acoustical maps of the human brain. It is shown that the average error in simulating subresolution displacements using impedance flow is small when compared to the acoustical wavelength ( λ /1702). The method is then applied to acoustical maps of the human brain with a motion that is imposed by the propagation of a shear shock wave. This motion is determined numerically with a custom piecewise parabolic method that is calibrated to ex vivo observations of shear shocks in the porcine brain. Then the fullwave simulation tool is used to model transmit-receive imaging sequences based on an L7-4 imaging transducer. The simulated radio frequency data are beamformed using a conventional delay-and-sum method and a normalized cross-correlation method designed for shock wave tracking is used to determine the tissue motion. This overall process is an in silico reproduction of the experiments that were previously performed to observe shear shock waves in fresh porcine brain. It is shown that the proposed generalized impedance flow method accurately captures the shear wave motion in terms of the wave profile, shock front characteristics, odd harmonic spectrum generation, and acceleration at the shear shock front. We expect that this approach will lead to improvements in image sequence design that takes into account the aberration and multiple reflections from the brain and in the design of tracking algorithms that can more accurately capture the complex brain motion that occurs during a traumatic impact. These methods of modeling ultrasound propagation in moving media can also be applied to other displacements, such as those generated by shear wave elastography or blood flow.

Bilayer aberration-inducing gel phantom for high intensity focused ultrasound applications

Aberrations induced by soft tissue inhomogeneities often complicate high-intensity focused ultrasound (HIFU) therapies. In this work, a bilayer phantom made from polyvinyl alcohol hydrogel and ballistic gel was built to mimic alternating layers of water-based and lipid tissues characteristic of an abdominal body wall and to reproducibly distort HIFU fields. The density, sound speed, and attenuation coefficient of each material were measured using a homogeneous gel layer. A surface with random topographical features was designed as an interface between gel layers using a 2D Fourier spectrum approach and replicating different spatial scales of tissue inhomogeneities. Distortion of the field of a 256-element 1.5 MHz HIFU array by the phantom was characterized through hydrophone measurements for linear and nonlinear beam focusing and compared to the corresponding distortion induced by an ex vivo porcine body wall of the same thickness. Both spatial shift and widening of the focal lobe were observed, as well as dramatic reduction in focal pressures caused by aberrations. The results suggest that the phantom produced levels of aberration that are similar to a real body wall and can serve as a research tool for studying HIFU effects as well as for developing algorithms for aberration correction.

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.

Virtual clinical trials in medical imaging: a review

The accelerating complexity and variety of medical imaging devices and methods have outpaced the ability to evaluate and optimize their design and clinical use. This is a significant and increasing challenge for both scientific investigations and clinical applications. Evaluations would ideally be done using clinical imaging trials. These experiments, however, are often not practical due to ethical limitations, expense, time requirements, or lack of ground truth. Virtual clinical trials (VCTs) (also known as in silico imaging trials or virtual imaging trials) offer an alternative means to efficiently evaluate medical imaging technologies virtually. They do so by simulating the patients, imaging systems, and interpreters. The field of VCTs has been constantly advanced over the past decades in multiple areas. We summarize the major developments and current status of the field of VCTs in medical imaging. We review the core components of a VCT: computational phantoms, simulators of different imaging modalities, and interpretation models. We also highlight some of the applications of VCTs across various imaging modalities.

Measurement of the shear modulus in thin-layered tissues using numerical simulations and shear wave elastography

Measurement of mechanical properties of thin-layered tissues has broad applications in the diagnosis of several pathologies. Ultrasound shear wave elastography (SWE) measures the shear wave speed as a means of estimating the mechanical properties of tissues. However, the wave speed in thin-layered tissues is affected by their thickness and the properties of surrounding tissues. The objective of this study is to introduce a method that combines numerical simulations and SWE measurements to provide a more accurate calculation of shear modulus in layered tissues. In the proposed method, the spatial distribution of the acoustic radiation force (ARF) emitted by the transducer was first computed. The ARF was then used as input for simulating the guided wave propagation in the thin layer with its surroundings. The simulations were repeated for several values of the shear modulus of the layer to obtain the corresponding simulated wave speed. By comparing the measured and simulated wave speeds, a more accurate (corrected) shear modulus can be obtained. The proposed method was validated using experiments in agarose gels. In-vivo SWE measurements were also performed for the fascia of the tibialis anterior (TA) muscle and the aponeurosis of musculotendinous junction (MTJ) in medial gastrocnemius (MG) head in a group of healthy individuals. The simulated and measured wave speed in gel constructs were in good agreement with a maximum error of 7.22%. The average of measured wave speed of fascia and aponeurosis was 3.90 ± 0.16 m/s and 2.33 ± 0.60 m/s, while the corresponding corrected shear modulus was 95.63 ± 17.89 kPa and 6.36 ± 8.98 kPa, respectively. Thickness had a substantial effect on the wave speed in thin-layered tissues with decreasing speed for thinner tissues. The SWE-based simulation method presented in this study has the potential of enhancing clinical assessment for several musculoskeletal conditions involving thin-layered tissues.

Unsupervised clustering method to convert high-resolution magnetic resonance volumes to three-dimensional acoustic models for full-wave ultrasound simulations

Simulations of acoustic wave propagation, including both the forward and the backward propagations of the wave (also known as full-wave simulations), are increasingly utilized in ultrasound imaging due to their ability to more accurately model important acoustic phenomena. Realistic anatomic models, particularly those of the abdominal wall, are needed to take full advantage of the capabilities of these simulation tools. We describe a method for converting fat-water-separated magnetic resonance imaging (MRI) volumes to anatomical models for ultrasound simulations. These acoustic models are used to map acoustic imaging parameters, such as speed of sound and density, to grid points in an ultrasound simulation. The tissues of these models are segmented from the MRI volumes into five primary classes of tissue in the human abdominal wall (skin, fat, muscle, connective tissue, and nontissue). This segmentation is achieved using an unsupervised machine learning algorithm, fuzzy c-means clustering (FCM), on a multiscale feature representation of the MRI volumes. We describe an automated method for utilizing FCM weights to produce a model that achieves ∼ 90 % agreement with manual segmentation. Two-dimensional (2-D) and three-dimensional (3-D) full-wave nonlinear ultrasound simulations are conducted, demonstrating the utility of realistic 3-D abdominal wall models over previously available 2-D abdominal wall models.

Spatiotemporally-controlled transgene expression in hydroxyapatite-fibrin composite scaffolds using high intensity focused ultrasound

Conventional tissue engineering approaches rely on scaffold-based delivery of exogenous proteins, genes, and/or cells to stimulate regeneration via growth factor signaling. However, scaffold-based approaches do not allow active control of dose, timing, or spatial localization of a delivered growth factor once the scaffold is implanted, yet these are all crucial parameters in promoting tissue regeneration. To address this limitation, we developed a stable cell line containing a heat-activated and rapamycin-dependent gene expression system. In this study, we investigate how high intensity focused ultrasound (HIFU) can spatiotemporally control firefly luciferase (fLuc) transgene activity both in vitro and in vivo by the tightly controlled generation of hyperthermia. Cells were incorporated into composite scaffolds containing fibrin and hydroxyapatite particles, which yielded significant increases in acoustic attenuation and heating in response to HIFU compared to fibrin alone. Using 2.5 MHz HIFU, transgene activation was observed at acoustic intensities of 201 W/cm2 and higher. Transgene activation was spatially patterned in the scaffolds by rastering HIFU at speeds up to 0.15 mm/s. In an in vivo study, a 67-fold increase in fLuc activity was observed in scaffolds exposed to HIFU and rapamycin versus rapamycin only at 2 days post implantation. Repeated activation of transgene expression was also demonstrated 8 days after implantation. No differences in in vivo scaffold degradation or compaction were observed between +HIFU and -HIFU groups. These results highlight the potential utility of using this heat-activated and rapamycin-dependent gene expression system in combination with HIFU for the controlled stimulation of tissue regeneration.

Equivalent-Source Acoustic Holography for Projecting Measured Ultrasound Fields Through Complex Media

Holographic projections of experimental ultrasound measurements generally use the angular spectrum method or Rayleigh integral, where the measured data are imposed as a Dirichlet boundary condition. In contrast, full-wave models, which can account for more complex wave behavior, often use interior mass or velocity sources to introduce acoustic energy into the simulation. Here, a method to generate an equivalent interior source that reproduces the measurement data is proposed based on gradient-based optimization. The equivalent-source can then be used with full-wave models (for example, the open-source k-Wave toolbox) to compute holographic projections through complex media including nonlinearity and heterogeneous material properties. Numerical and experimental results using both time-domain and continuous-wave sources are used to demonstrate the accuracy of the approach.

An iterative fullwave simulation approach to multiple scattering in media with randomly distributed microbubbles

Ultrasound contrast agents (UCA), such as microbubbles, enhance the scattering properties of blood, which is otherwise hypoechoic. The multiple scattering interactions of the acoustic field with UCA are poorly understood due to the complexity of the multiple scattering theories and the nonlinear microbubble response. The majority of bubble models describe the behavior of UCA as single, isolated microbubbles suspended in infinite medium. Multiple scattering models such as the independent scattering approximation can approximate phase velocity and attenuation for low scatterer volume fractions. However, all current models and simulation approaches only describe multiple scattering and nonlinear bubble dynamics separately. Here we present an approach that combines two existing models: (1) a full-wave model that describes nonlinear propagation and scattering interactions in a heterogeneous attenuating medium and (2) a Paul-Sarkar model that describes the nonlinear interactions between an acoustic field and microbubbles. These two models were solved numerically and combined with an iterative approach. The convergence of this combined model was explored in silico for 0.5 × 10⁶ microbubbles ml^-1, 1% and 2% bubble concentration by volume. The backscattering predicted by our modeling approach was verified experimentally with water tank measurements performed with a 128-element linear array transducer. An excellent agreement in terms of the fundamental and harmonic acoustic fields is shown. Additionally, our model correctly predicts the phase velocity and attenuation measured using through transmission and predicted by the independent scattering approximation.

Subresolution Displacements in Finite Difference Simulations of Ultrasound Propagation and Imaging

Time domain finite difference simulations are used extensively to simulate wave propagation. They approximate the wave field on a discrete domain with a grid spacing that is typically on the order of a tenth of a wavelength. The smallest displacements that can be modeled by this type of simulation are thus limited to discrete values that are integer multiples of the grid spacing. This paper presents a method to represent continuous and subresolution displacements by varying the impedance of individual elements in a multielement scatterer. It is demonstrated that this method removes the limitations imposed by the discrete grid spacing by generating a continuum of displacements as measured by the backscattered signal. The method is first validated on an ideal perfect correlation case with a single scatterer. It is subsequently applied to a more complex case with a field of scatterers that model an acoustic radiation force-induced displacement used in ultrasound elasticity imaging. A custom finite difference simulation tool is used to simulate propagation from ultrasound imaging pulses in the scatterer field. These simulated transmit-receive events are then beamformed into images, which are tracked with a correlation-based algorithm to determine the displacement. A linear predictive model is developed to analytically describe the relationship between element impedance and backscattered phase shift. The error between model and simulation is λ/ 1364 , where λ is the acoustical wavelength. An iterative method is also presented that reduces the simulation error to λ/ 5556 over one iteration. The proposed technique therefore offers a computationally efficient method to model continuous subresolution displacements of a scattering medium in ultrasound imaging. This method has applications that include ultrasound elastography, blood flow, and motion tracking. This method also extends generally to finite difference simulations of wave propagation, such as electromagnetic or seismic waves.

Visualization of Small-Diameter Vessels by Reduction of Incoherent Reverberation With Coherent Flow Power Doppler

Power Doppler (PD) imaging is a widely used technique for flow detection. Despite the wide use of Doppler ultrasound, limitations exist in the ability of Doppler ultrasound to assess slow flow in the small-diameter vasculature, such as the maternal spiral arteries and fetal villous arteries of the placenta and focal liver lesions. The sensitivity of PD in small vessel detection is limited by the low signal produced by slow flow and the noise associated with small vessels. The noise sources include electronic noise, stationary or slowly moving tissue clutter, reverberation clutter, and off-axis scattering from tissue, among others. In order to provide more sensitive detection of slow flow in small diameter vessels, a coherent flow imaging technique, termed coherent flow PD (CFPD), is characterized and evaluated with simulation, flow phantom experiment studies, and an in vivo animal small vessel detection study. CFPD imaging was introduced as a technique to detect slow blood flow. It has been demonstrated to detect slow flow below the detection threshold of conventional PD imaging using identical pulse sequences and filter parameters. In this paper, we compare CFPD with PD in the detection of blood flow in small-diameter vessels. The results from the study suggest that CFPD is able to provide a 7.5-12.5-dB increase in the signal-to-noise ratio (SNR) over PD images for the same physiological conditions and is less susceptible to reverberation clutter and thermal noise. Due to the increase in SNR, CFPD is able to detect small vessels in high channel noise cases, for which PD was unable to generate enough contrast to observe the vessel.

Superharmonic Imaging for Medical Ultrasound: a Review

Ultrasound with harmonics has emerged as an exceptional alternative to competitively low resolution fundamental ultrasound imaging. The use of second harmonic is already a trend now but higher harmonics are also being seen as even better option due to its improved resolution. The resolution improved with frequency but achieves penetration of reduced energy. The cumulative addition of higher harmonics during propagation yields higher harmonics giving better resolution with adequate penetration. This paper summarizes the progress of such similar decade old harmonic ultrasound imaging technique i.e., superharmonic imaging (SHI) geared towards medical field. It comprises of harmonics higher than second harmonic preferably up to 5th harmonic. We conclude that SHI can be an advanced ultrasound imaging with comprehensive high resolution and adequate penetration depth on sole and coded modes.

On System-Dependent Sources of Uncertainty and Bias in Ultrasonic Quantitative Shear-Wave Imaging

Ultrasonic quantitative shear-wave imaging methods have been developed over the last decade to estimate tissue elasticity by measuring the speed of propagating shear waves following acoustic radiation force excitation. This work discusses eight sources of uncertainty and bias arising from ultrasound system-dependent parameters in ultrasound shear-wave speed (SWS) measurements. Each of the eight sources of error is discussed in the context of a linear, isotropic, elastic, homogeneous medium, combining previously reported analyses with Field II simulations, full-wave 2-D acoustic propagation simulations, and experimental studies. Errors arising from both spatial and temporal sources lead to errors in SWS measurements. Arrival time estimation noise, speckle bias, hardware fluctuations, and phase aberration cause uncertainties (variance) in SWS measurements, while pulse repetition frequency (PRF) and beamforming errors, as well as coupling medium sound speed mismatch, cause biases in SWS measurements (accuracy errors). Calibration of the sources of bias is an important step in the development of shear-wave imaging systems. In a well-calibrated system, where the sources of bias are minimized, and averaging over a region of interest (ROI) is employed to reduce the sources of uncertainty, an SWS error can be expected.

Modeling of wave propagation for medical ultrasound: a review

Numerical modeling of medical ultrasound has advanced tremendously in the past two decades. This opens up a great number of opportunities for medical ultrasound and associated technologies. Numerous new governing equations and algorithms have emerged and been applied to studying various medical ultrasound applications, including ultrasound imaging, photo-acoustic imaging, and therapeutic ultrasound. In addition, thanks to the rapid development of computers, modeling acoustic wave propagation in three-dimensional, large-scale domains has become a reality. This article will provide an indepth literature and technical review of recent progress on numerical modeling of medical ultrasound. Future challenges will also be discussed.

Ultrasound in Radiology: From Anatomic, Functional, Molecular Imaging to Drug Delivery and Image-Guided Therapy

During the past decade, ultrasound has expanded medical imaging well beyond the "traditional" radiology setting: a combination of portability, low cost, and ease of use makes ultrasound imaging an indispensable tool for radiologists as well as for other medical professionals who need to obtain imaging diagnosis or guide a therapeutic intervention quickly and efficiently. Ultrasound combines excellent ability for deep penetration into soft tissues with very good spatial resolution, with only a few exceptions (ie, those involving overlying bone or gas). Real-time imaging (up to hundreds and thousands of frames per second) enables guidance of therapeutic procedures and biopsies; characterization of the mechanical properties of the tissues greatly aids with the accuracy of the procedures. The ability of ultrasound to deposit energy locally brings about the potential for localized intervention encompassing the following: tissue ablation, enhancing penetration through the natural barriers to drug delivery in the body and triggering drug release from carrier microparticles and nanoparticles. The use of microbubble contrast agents brings the ability to monitor and quantify tissue perfusion, and microbubble targeting with ligand-decorated microbubbles brings the ability to obtain molecular biomarker information, that is, ultrasound molecular imaging. Overall, ultrasound has become the most widely used imaging modality in modern medicine; it will continue to grow and expand.

Scattering by single physically large and weak scatterers in the beam of a single-element transducer

Quantitative ultrasound techniques are generally applied to characterize media whose scattering sites are considered to be small compared to a wavelength. In this study, the backscattered response of single weakly scattering spheres and cylinders with diameters comparable to the beam width of a 2.25 MHz single-element transducer were simulated and measured in the transducer focal plane to investigate the impact of physically large scatterers. The responses from large single spherical scatterers at the focus were found to closely match the plane-wave response. The responses from large cylindrical scatterers at the focus were found to differ from the plane-wave response by a factor of f(-1). Normalized spectra from simulations and measurements were in close agreement: the fall-off of the responses as a function of lateral position agreed to within 2 dB for spherical scatterers and to within 3.5 dB for cylindrical scatterers. In both measurement and simulation, single scatterer diameter estimates were biased by less than 3% for a more highly focused transducer compared to estimates for a more weakly focused transducer. The results suggest that quantitative ultrasound techniques may produce physically meaningful size estimates for media whose response is dominated by scatterers comparable in size to the transducer beam.

Spatial coherence in human tissue: implications for imaging and measurement

The spatial coherence properties of the signal backscattered by human tissue and measured by an ultrasound transducer array are investigated. Fourier acoustics are used to describe the propagation of ultrasound through a model of tissue that includes reverberation and random scattering in the imaging plane. The theoretical development describes how the near-field tissue layer, transducer aperture properties, and reflectivity function at the focus reduce the spatial coherence of the imaging wave measured at the transducer surface. Simulations are used to propagate the acoustic field through a histologically characterized sample of the human abdomen and to validate the theoretical predictions. In vivo measurements performed with a diagnostic ultrasound scanner demonstrate that simulations and theory closely match the measured spatial coherence characteristics in the human body across the transducer array's entire spatial extent. The theoretical framework and simulations are then used to describe the physics of spatial coherence imaging, a type of ultrasound imaging that measures coherence properties instead of echo brightness. The same echo data from an F/2 transducer was used to generate B-mode and short lag spatial coherence images. For an anechoic lesion at the focus, the contrast-to-noise ratio is 1.21 for conventional B-mode imaging and 1.95 for spatial coherence imaging. It is shown that the contrast in spatial coherence imaging depends on the properties of the near-field tissue layer and the backscattering function in the focal plane.

Reverberation clutter from subcutaneous tissue layers: simulation and in vivo demonstrations

The degradation of ultrasonic image quality is typically attributed to aberration and reverberation. Although the sources and impact of aberration are well understood, very little is known about the source and impact of image degradation caused by reverberation. Reverberation is typically associated with multiple reflections at two interfaces along the same propagation path, as with the arterial wall or a metal sphere. However, the reverberation that results in image degradation includes more complex interaction between the propagating wave and the tissue. Simulations of wave propagation in realistic and simplified models of the abdominal wall are used to illustrate the characteristics of coherent and diffuse clutter generated by reverberation. In the realistic models, diffuse reverberation clutter is divided into that originating from the tissue interfaces and that originating from sub-resolution diffuse scatterers. In the simplified models, the magnitude of the reverberation clutter is observed as angle and density of the connective tissue are altered. The results suggest that multi-path scattering from the connective tissue/fat interfaces is a dominant component of reverberation clutter. Diffuse reverberation clutter is maximal when the connective tissue is near normal to the beam direction and increases with the density of connective tissue layers at these large angles. The presence of a thick fascial or fibrous layer at the distal boundary of the abdominal wall magnifies the amount of reverberation clutter. The simulations also illustrate that compression of the abdominal layer, a technique often used to mitigate clutter in overweight and obese patients, increases the decay of reverberation clutter with depth. In addition, rotation of the transducer or steering of the beam with respect to highly reflecting boundaries can reduce coherent clutter and transform it to diffuse clutter, which can be further reduced using coherence-based beamforming techniques. In vivo images of the human bladder illustrate some of the reverberation effects observed in simulation.

Simulation techniques in hyperthermia treatment planning

Abstract Clinical trials have shown that hyperthermia (HT), i.e. an increase of tissue temperature to 39-44 °C, significantly enhance radiotherapy and chemotherapy effectiveness [1]. Driven by the developments in computational techniques and computing power, personalised hyperthermia treatment planning (HTP) has matured and has become a powerful tool for optimising treatment quality. Electromagnetic, ultrasound, and thermal simulations using realistic clinical set-ups are now being performed to achieve patient-specific treatment optimisation. In addition, extensive studies aimed to properly implement novel HT tools and techniques, and to assess the quality of HT, are becoming more common. In this paper, we review the simulation tools and techniques developed for clinical hyperthermia, and evaluate their current status on the path from 'model' to 'clinic'. In addition, we illustrate the major techniques employed for validation and optimisation. HTP has become an essential tool for improvement, control, and assessment of HT treatment quality. As such, it plays a pivotal role in the quest to establish HT as an efficacious addition to multi-modality treatment of cancer.

Harmonic spatial coherence imaging: an ultrasonic imaging method based on backscatter coherence

We introduce a harmonic version of the short-lag spatial coherence (SLSC) imaging technique, called harmonic spatial coherence imaging (HSCI). The method is based on the coherence of the second-harmonic backscatter. Because the same signals that are used to construct harmonic B-mode images are also used to construct HSCI images, the benefits obtained with harmonic imaging are also obtained with HSCI. Harmonic imaging has been the primary tool for suppressing clutter in diagnostic ultrasound imaging, however secondharmonic echoes are not necessarily immune to the effects of clutter. HSCI and SLSC imaging are less sensitive to clutter because clutter has low spatial coherence. HSCI shows favorable imaging characteristics such as improved contrast-to-noise ratio (CNR), improved speckle SNR, and better delineation of borders and other structures compared with fundamental and harmonic B-mode imaging. CNRs of up to 1.9 were obtained from in vivo imaging of human cardiac tissue with HSCI, compared with 0.6, 0.9, and 1.5 in fundamental B-mode, harmonic B-mode, and SLSC imaging, respectively. In vivo experiments in human liver tissue demonstrated SNRs of up to 3.4 for HSCI compared with 1.9 for harmonic B-mode. Nonlinear simulations of a heart chamber model were consistent with the in vivo experiments.

Three-dimensional in silico breast phantoms for multimodal image simulations

Anatomic simulators have provided researchers with the realistic objects needed to develop and evaluate medical imaging approaches. Today we have new insights into the cellular biology of breast tissues that is driving many new targeted diagnostic and therapeutic approaches, including molecular imaging. We report on our initial efforts to build a scalable framework for the construction of realistic 3-D in silico breast phantoms (ISBP) capable of leveraging existing knowledge and yet adaptable to fully integrate future discoveries. The ISBP frames are developed with scalable anatomical shapes and morphologic features as adapted from a rich literature on this topic. Frames are populated with tissue subtypes essential for imaging and object contrast functions are assigned. These data can be resampled to match the intrinsics scales of various imaging modalities; we explore mammography, sonography and computed tomography. Initial comparisons between simulated and clinical images demonstrate reasonable agreement and provides guidance for future development of a more realistic ISBP. An end-to-end simulation of breast images is described to demonstrate techniques for including stochastic variability and deterministic physical principles on which image formation is based.

Sources of image degradation in fundamental and harmonic ultrasound imaging: a nonlinear, full-wave, simulation study

A full-wave equation that describes nonlinear propagation in a heterogeneous attenuating medium is solved numerically with finite differences in the time domain. This numerical method is used to simulate propagation of a diagnostic ultrasound pulse through a measured representation of the human abdomen with heterogeneities in speed of sound, attenuation, density, and nonlinearity. Conventional delay-and-sum beamforming is used to generate point spread functions (PSFs) that display the effects of these heterogeneities. For the particular imaging configuration that is modeled, these PSFs reveal that the primary source of degradation in fundamental imaging is due to reverberation from near-field structures. Compared with fundamental imaging, reverberation clutter in harmonic imaging is 27.1 dB lower. Simulated tissue with uniform velocity but unchanged impedance characteristics indicates that for harmonic imaging, the primary source of degradation is phase aberration.

Sources of image degradation in fundamental and harmonic ultrasound imaging using nonlinear, full-wave simulations

A full-wave equation that describes nonlinear propagation in a heterogeneous attenuating medium is solved numerically with finite differences in the time domain (FDTD). This numerical method is used to simulate propagation of a diagnostic ultrasound pulse through a measured representation of the human abdomen with heterogeneities in speed of sound, attenuation, density, and nonlinearity. Conventional delay-andsum beamforming is used to generate point spread functions (PSF) that display the effects of these heterogeneities. For the particular imaging configuration that is modeled, these PSFs reveal that the primary source of degradation in fundamental imaging is reverberation from near-field structures. Reverberation clutter in the harmonic PSF is 26 dB higher than the fundamental PSF. An artificial medium with uniform velocity but unchanged impedance characteristics indicates that for the fundamental PSF, the primary source of degradation is phase aberration. An ultrasound image is created in silico using the same physical and algorithmic process used in an ultrasound scanner: a series of pulses are transmitted through heterogeneous scattering tissue and the received echoes are used in a delay-and-sum beamforming algorithm to generate images. These beamformed images are compared with images obtained from convolution of the PSF with a scatterer field to demonstrate that a very large portion of the PSF must be used to accurately represent the clutter observed in conventional imaging.

Statistical model of clutter suppression in tissue harmonic imaging

A statistical model is developed for the suppression of clutter in tissue harmonic imaging (THI). Tissue heterogeneity is modeled as a random phase screen that is characterized by its correlation length and variance. With the autocorrelation function taken to be Gaussian and for small variance, statistical solutions are derived for the mean intensities at the fundamental and second-harmonic frequencies in the field of a focused sound beam that propagates through the phase screen. The statistical solutions are verified by comparison with ensemble averaging of direct numerical simulations. The model demonstrates that THI reduces the aberration clutter appearing in the focal region regardless of the depth of the aberrating layer, with suppression of the clutter most effective when the layer is close to the source. The model is also applied to the reverberation clutter that is transmitted forward along the axis of the beam. As with aberration clutter, suppression of such reverberation clutter by THI is most pronounced when the tissue heterogeneity is located close to the source.

Computational models of distributed aberration in ultrasound breast imaging

Two methods for simulation of ultrasound wavefront distortion are introduced and compared with aberration produced in simulations using digitized breast tissue specimens and a conventional multiple time-shift screen model. In the first method, aberrators are generated using a computational model of breast anatomy. In the second method, 10 to 12 irregularly shaped, strongly scattering inclusions are superimposed on the multiple-screen model to create a screen-inclusion model. Linear 2-D propagation of a 7.5-MHz planar, pulsed wavefront through each aberrator is computed using a first-order k-space method. The anatomical and screen-inclusion models reproduce two characteristics of arrival-time fluctuations observed in simulations using the digitized specimens that are not represented in simulations using the multiple-screen model: non-Gaussian first-order statistics and sharp changes in the rms arrival-time fluctuation as a function of propagation distance. The anatomical and screen-inclusion models both produce energy- level fluctuations similar to the digitized specimens, but the anatomical model more closely matches the pulse-shape distortion produced by the specimens. Both aberration models can readily be extended to 3-D, and the screen-inclusion model has the advantage of simplicity of implementation. Both models should enable more rigorous evaluation of adaptive focusing algorithms than is possible using conventional time-shift screen models.

Large-scale propagation of ultrasound in a 3-D breast model based on high-resolution MRI data

A 40 x 35 x 25-mm(3) specimen of human breast consisting mostly of fat and connective tissue was imaged using a 3-T magnetic resonance scanner. The resolutions in the image plane and in the orthogonal direction were 130 microm and 150 microm, respectively. Initial processing to prepare the data for segmentation consisted of contrast inversion, interpolation, and noise reduction. Noise reduction used a multilevel bidirectional median filter to preserve edges. The volume of data was segmented into regions of fat and connective tissue by using a combination of local and global thresholding. Local thresholding was performed to preserve fine detail, while global thresholding was performed to minimize the interclass variance between voxels classified as background and voxels classified as object. After smoothing the data to avoid aliasing artifacts, the segmented data volume was visualized using isosurfaces. The isosurfaces were enhanced using transparency, lighting, shading, reflectance, and animation. Computations of pulse propagation through the model illustrate its utility for the study of ultrasound aberration. The results show the feasibility of using the described combination of methods to demonstrate tissue morphology in a form that provides insight about the way ultrasound beams are aberrated in three dimensions by tissue.

Shock-induced heating and millisecond boiling in gels and tissue due to high intensity focused ultrasound

Nonlinear propagation causes high-intensity ultrasound waves to distort and generate higher harmonics, which are more readily absorbed and converted to heat than the fundamental frequency. Although such nonlinear effects have been investigated previously and found to not significantly alter high-intensity focused ultrasound (HIFU) treatments, two results reported here change this paradigm. One is that at clinically relevant intensity levels, HIFU waves not only become distorted but form shock waves in tissue. The other is that the generated shock waves heat the tissue to boiling in much less time than predicted for undistorted or weakly distorted waves. In this study, a 2-MHz HIFU source operating at peak intensities up to 25,000 W/cm(2) was used to heat transparent tissue-mimicking phantoms and ex vivo bovine liver samples. Initiation of boiling was detected using high-speed photography, a 20-MHz passive cavitation detector and fluctuation of the drive voltage at the HIFU source. The time to boil obtained experimentally was used to quantify heating rates and was compared with calculations using weak shock theory and the shock amplitudes obtained from nonlinear modeling and measurements with a fiber optic hydrophone. As observed experimentally and predicted by calculations, shocked focal waveforms produced boiling in as little as 3 ms and the time to initiate boiling was sensitive to small changes in HIFU output. Nonlinear heating as a result of shock waves is therefore important to HIFU, and clinicians should be aware of the potential for very rapid boiling because it alters treatments.

Distributed three-dimensional simulation of B-mode ultrasound imaging using a first-order k-space method

Computational modeling is an important tool in ultrasound imaging research, but realistic three-dimensional (3D) simulations can exceed the capabilities of serial computers. This paper uses a 3D simulator based on a k-space method that incorporates relaxation absorption and nonreflecting boundary conditions. The simulator, which runs on computer clusters, computes the propagation of a single wavefront. In this paper, an allocation algorithm is introduced to assign each scan line to a group of nodes and use multiple groups to compute independent lines concurrently. The computational complexity required for realistic simulations is analyzed using example calculations of ultrasonic propagation and attenuation in the 30-50 MHz band. Parallel efficiency for B-mode imaging simulations is evaluated for various numbers of scan lines and cluster nodes. An aperture-projection technique is introduced to simulate imaging with a focused transducer using reduced computation grids. This technique is employed to synthesize B-mode images that show realistic 3D refraction artifacts. Parallel computing using 20 nodes to compute groups of ten scan lines concurrently reduced the execution time for each image to 18.6 h, compared to a serial execution time of 357.5 h. The results demonstrate that fully 3D imaging simulations are practical using contemporary computing technology.

A heterogeneous nonlinear attenuating full-wave model of ultrasound

A full-wave equation that describes nonlinear propagation in a heterogeneous attenuating medium is solved numerically with finite differences in the time domain (FDTD). Three-dimensional solutions of the equation are verified with water tank measurements of a commercial diagnostic ultrasound transducer and are shown to be in excellent agreement in terms of the fundamental and harmonic acoustic fields and the power spectrum at the focus. The linear and nonlinear components of the algorithm are also verified independently. In the linear nonattenuating regime solutions match results from Field II, a well established software package used in transducer modeling, to within 0.3 dB. Nonlinear plane wave propagation is shown to closely match results from the Galerkin method up to 4 times the fundamental frequency. In addition to thermoviscous attenuation we present a numerical solution of the relaxation attenuation laws that allows modeling of arbitrary frequency dependent attenuation, such as that observed in tissue. A perfectly matched layer (PML) is implemented at the boundaries with a numerical implementation that allows the PML to be used with high-order discretizations. A -78 dB reduction in the reflected amplitude is demonstrated. The numerical algorithm is used to simulate a diagnostic ultrasound pulse propagating through a histologically measured representation of human abdominal wall with spatial variation in the speed of sound, attenuation, nonlinearity, and density. An ultrasound image is created in silico using the same physical and algorithmic process used in an ultrasound scanner: a series of pulses are transmitted through heterogeneous scattering tissue and the received echoes are used in a delay-and-sum beam-forming algorithm to generate a images. The resulting harmonic image exhibits characteristic improvement in lesion boundary definition and contrast when compared with the fundamental image. We demonstrate a mechanism of harmonic image quality improvement by showing that the harmonic point spread function is less sensitive to reverberation clutter.

The acoustic field in biomedical tissue with midscale inhomogeneities

Biomedical ultrasound is often used for investigations within and close to tissue inhomogeneities, such as lesions and plaques, that are midsized compared with the ultrasound wavelength. The scaled wavenumber is typically in the range 1 to 100. Even with small (less than 10%) sound speed variations, such objects are associated with very complicated diffractive field magnitude modulations. The corresponding phase modulations are much more regular, and this observation is the basis for the method described in this paper. The acoustic field can be expressed in terms of a scattering integral. For biomedical parameters, calculations with the widely used Born approximation give accurate results in only very limited circumstances. In this paper we demonstrate the importance of the initial phase estimate, and introduce the Phase Corrected Scattering Integral (PCSI) method. We show that remarkably accurate results for the acoustic field can be obtained from a single evaluation of the scattering integral if this incorporates an initial estimate of the phase modulation imposed by the inhomogeneity. A simple ray model can be used to find the phase correction. The PCSI method deals very effectively with scattering due to small changes in sound speed and irregular geometry, both characteristic of biomedical problems.

The cross algorithm for phase-aberration correction in medical ultrasound images formed with two-dimensional arrays

Common-midpoint signals in the near-field signal-redundancy (NFSR) algorithm for one-dimensional arrays are acquired using three consecutive transducer elements. An all-row-plus-two-column algorithm has been proposed to implement the one-dimensional NFSR algorithm on two dimensional arrays. The disadvantage of this method is that its ambiguity profile is not linear and a timeconsuming iterative method has to be used to linearize the ambiguity profile. An all-row-plus-two-column-and-a-diagonal algorithm has also been proposed. Its ambiguity profile is linear, but it is very sensitive to noise and cannot be used. In this paper, a novel cross algorithm is proposed to implement the NFSR algorithm on two-dimensional arrays. In this algorithm, common-midpoint signals are acquired using four adjacent transducer elements, which is not available in one-dimensional arrays. Its advantage includes a linear ambiguity profile and a higher measurement signal-to-noise ratio. The performance of the cross algorithm is evaluated theoretically. The region of redundancy is analyzed. The procedure for deriving the phaseaberration profile from peak positions of cross-correlation functions between common-midpoint signals is discussed. This algorithm is tested with a simulated data set acquired with a two-dimensional array, and the result shows that the cross algorithm performs better than the all-row plus-twocolumn NFSR algorithm.

A comparison of time-domain solutions for the full-wave equation and the parabolic wave equation for a diagnostic ultrasound transducer

A study of numerical solutions to the linear wave equation and the parabolic wave equation is presented. Finite-difference, time-domain methods are used to calculate the acoustic field emitted from a phased diagnostic ultrasound transducer in a non-attenuating medium. Results are compared to Field II, a simulation package that has been used extensively to linearly model transducers in ultrasound. The simulation of the parabolic equation can accurately predict the lateral beamplot for large f/#s, but, it exhibits 2-3 dB errors for small f/#s. It also overestimates the depth at which the focus occurs. For the considered array, it is shown that the finite-difference solution of the wave equation is accurate for a small and large f/#. The lateral beamplots and axial intensities are in excellent agreement with the Field II simulations.

Ultrasound beam propagation using the hybrid angular spectrum method

We introduce a fast and accurate numerical method for simulating the propagation of an ultrasound beam inside inhomogeneous tissue for mapping beam absorption, refraction and diffraction in the body. The technique, called the hybrid angular spectrum method, is an extension of the angular spectrum method to inhomogeneous tissue. Inhomogeneous tissue is modeled using voxels, each with its own speed of sound, density and absorption coefficient. The proposed technique produces very fast simulations, with total calculation times of about one minute for a 201x201x101 model.

Modeling the effects of treating diabetic wounds with engineered skin substitutes

In this paper, a novel mathematical model of wound healing in both normal and diabetic cases is presented, focusing upon the effects of adding two currently available commercial engineered skin substitute therapies to the wound (Apligraf) and Dermagraft). Our work extends a previously developed model, which considers inflammatory and repair macrophage dynamics in normal and diabetic wound healing. Here, we extend the model to include equations for platelet-derived growth factor concentration, fibroblast density, collagen density, and hyaluronan concentration. This enables us to examine the variation of these components in both normal and diabetic wound healing cases, and to model the treatment protocols of these therapies. Within the context of our model, we find that the key component to successful healing in diabetic wounds is hyaluronan and that the therapies work by increasing the amount of hyaluronan available in the wound environment. The time-to-healing results correlate with those observed in clinical trials and the model goes some way to establishing an understanding of why diabetic wounds do not heal, and how these treatments affect the diabetic wound environment to promote wound closure.