Real-time ultrasound simulation using the GPU

Ultrasound simulators can be used for training ultrasound image acquisition and interpretation. In such simulators, synthetic ultrasound images must be generated in real time. Anatomy can be modeled by computed tomography (CT). Shadows can be calculated by combining reflection coefficients and depth dependent, exponential attenuation. To include speckle, a pre-calculated texture map is typically added. Dynamic objects must be simulated separately. We propose to increase the speckle realism and allow for dynamic objects by using a physical model of the underlying scattering process. The model is based on convolution of the point spread function (PSF) of the ultrasound scanner with a scatterer distribution. The challenge is that the typical field-of-view contains millions of scatterers which must be selected by a virtual probe from an even larger body of scatterers. The main idea of this paper is to select and sample scatterers in parallel on the graphic processing unit (GPU). The method was used to image a cyst phantom and a movable needle. Speckle images were produced in real time (more than 10 frames per second) on a standard GPU. The ultrasound images were visually similar to images calculated by a reference method.     

Quantitative modeling of the anisotropy of ultrasonic backscatterfrom canine myocardium

Reports extensions and new results of the First Time Domain Born approximation model used by Mottley and Miller (1982) to describe the anisotropy of ultrasonic backscatter measured in canine myocardium. The interaction of an ultrasonic plane wave impulse with a single cylindrical scatterer using time and frequency domain approaches is reviewed. Myocardial tissue is modeled as a suspension of aligned cylindrically shaped scatterers uniformly distributed in a homogeneous medium. The authors propose extensions to this model to deal with nonideal scatterer orientation, by introducing axial distribution functions and scatterer size distributions based on histology, modeled as a uniform distribution. The backscatter coefficient in the range 2.0-8.0 MHz is calculated. An algorithm to compute the average differential scattering cross section is presented. Ultrasonic elastic properties of myocardial tissue are discussed. Results of the anisotropy of the numerically computed backscatter parameters for model media having nominal mechanical and acoustic properties of canine myocardial tissue are presented and compared to available experimental data along with discussion of possible conclusions     

Modeling and analysis of ultrasound backscattering by spherical aggregates and rouleaux of red blood cells

The present study concerns the modeling and analysis of ultrasound backscattering by red blood cell (RBC) aggregates, which under pathological conditions play a significant role in the rheology of blood within human vessels. A theoretical model based on the convolution between a tissue matrix and a point spread function, representing, respectively, the RBC aggregates and the characteristics of the ultrasound system, was used to examine the influence of the scatterer shape and size on the backscattered power. Both scatterers in the form of clumps of RBC aggregates and rouleaux were modeled. For all simulations, the hematocrit was kept constant at 10%, the ultrasound frequency was 10 MHz, the insonification angle was varied from 0 to 90 degrees , and the scatterer size (diameter for clumps and length for rouleaux) ranged from 4 mum to 120 mum. Under Rayleigh scattering by assuming a Poisson distribution of scatterers in space, the ultrasound backscattered power increased linearly with the particle volume. For non-Rayleigh scatterers, the intensity of the echoes diminished as the scatterer volume increased, with the exception of rouleaux at an angle of 90 degrees . As expected, the backscattered power was angularly dependent for anisotropic particles (rouleaux). The ultrasound backscattered power did not always increase with the size of the aggregates, especially when they were no longer Rayleigh scatterers. In the case of rouleaux, the anisotropy of the backscattered power is emphasized in the non-Rayleigh region.     

Ultrasonic detection of the anisotropy of protein cross linking in myocardium at diagnostic frequencies

Increased myocardial stiffness in aging and diabetes that may result in pathologies such as diastolic dysfunction has been attributed, in part, to an increase in cross linking of extracellular matrix proteins such as collagen. With the development of new approaches to cardiovascular therapy, it becomes increasingly important to develop noninvasive approaches for monitoring changes in myocardial cross linking. The objective of this study was to use ultrasound at frequencies used in clinical echocardiography to measure changes in myocardial attenuation resulting from increased cross linking as a function of angle of insonification over a complete rotation. Through-transmission radiofrequency-based measurements were performed on 36 specimens from 12 freshly excised ovine hearts at room temperature, which were then fixed in formalin to induce protein cross linking prior to repeated measurements. For angles near perpendicular to the myofiber direction, the measured slope of attenuation increased from 0.52 +/- 0.07 dB/(cm MHz) (mean +/- one standard deviation) for freshly excised to 0.85 +/- 0.08 dB/(cm MHz) for formalin-fixed myocardium. In contrast, results for parallel insonification exhibit considerable overlap (1.88 +/- 0.17 for freshly excised and 1.75 +/- 0.19 dB/(cm MHz) for formalin-fixed myocardium). Results of this study suggest that the response of the extracellular collagenous matrix to changes in cross linking is directionally dependent. The anisotropy of ultrasonic attenuation thus may provide an approach for noninvasive monitoring of the extent and progression of myocardial disease associated with changes in protein cross linking. Accounting for effects due to anisotropy may be essential for the future detection of such changes using ultrasonic attenuation in vivo.     

Ultrasound speckle reduction using harmonic oscillator models

A speckle reduction algorithm called the harmonic imaging (HI) algorithm is presented. It is based on a multicomponent scattering model for medical ultrasonics. The backscattered ultrasound quadrature signal is modeled as the sum of three components after demodulation. The first component represents nonresolvable diffuse scatterers, while the second component represents subresolvable quasi-periodic scatterers. The third component represents resolvable quasi-periodic scatterers and mirroring surfaces. Since the second component gives rise to the most long range destructive interference effects it is eliminated in the HI algorithm to reduce speckle. Due to its slow spatial variation, it can be almost completely eliminated simply by differentiating the backscattered demodulated quadrature signal. Lissajous-like figures are observed in complex plots of the signals from ultrasound beams going through tissues with quasi-periodic components and sometimes in areas with only diffuse scatterers. Therefore the sum of the complex signals from the resolvable and nonresolvable scatterers within a resolution cell is modeled by two orthogonal and independent harmonic oscillators. The estimated, total energy of these two oscillators determines the gray level value of the HI image within the resolution cell. The HI images produced using radio frequency data from a phantom and from tissues in vivo are more blurred than ordinary envelope images, but the signal to noise ratio and tissue contrast were higher for the HI images     

Creation of various skin sensations using pulsed focused ultrasound: Evidence for functional neuromodulation

Ultrasound application to neural tissues modifies their activity, and it is increasingly considered as a new mode of functional neuromodulation in both central and peripheral nervous system. We investigate that ultrasound focused to skin surface can induce differential peripheral sensations by modulating the activity of sensory receptors. Pulsed focused ultrasound was applied to the last digit of human hands for 10 s using combinations of acoustic frequencies (350 and 650 kHz), tone‐burst‐durations (0.1 and 1.0 ms), pulse repetition frequencies (10 and 100 Hz) with 1% duty cycle, and acoustic intensities (3–100 mW/cm²), divided into two ambient temperatures (20 and 40°C). On insonification, volunteers reported cooling, warming, vibrotactile sensations, and mild nociception, while there was no actual increase to the skin temperature. Continuous insonification, in contrast to pulsed insonification, failed to elicit these sensations. Our results suggest that pulsed ultrasound temporarily modifies the activity of the sensory receptors on the skin, and casts future utility in dermatological applications as well as in the field of haptic device interfaces. © 2014 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 24, 167–174, 2014     

Statistical characterization of diffuse scattering in ultrasound images

The marginal statistics for the diffused ultrasound speckle echo has been postulated as exhibiting circularly symmetric Gaussian behavior similar to the laser speckle for monochromatic illumination under the assumption of a large number of unresolvable scatterers per resolution cell. This is known in the literature as the Rayleigh scattering condition. This paper presents a formal statistical test, the Kolmogorov-Smirnov nonparametric goodness of fit statistical test, to test the hypothesis that the unresolvable part (diffuse part) of the backscatter echo follows a Rayleigh scattering condition, and obtain numerical values for the scatterer concentration required for the Rayleigh condition to be valid. In addition, it presents a formal statistical test, the Kolmogorov-Smirnov nonparametric homogeneity statistical test, to compare two regions of interest with different scattering concentrations without prior knowledge of the nature of the scattering conditions (Rayleigh or non-Rayleigh scattering). Unlike all previous parametric testing methods that treat the A-scan or B-scan echo as a random sample, the authors' method presents formal tests based on the colored nature of the diffuse backscattered echo which is a more realistic model of the diffuse scattering component. The tests are demonstrated on simulations of RF scans with different scatterer concentrations per resolution cell as well as on phantom data which mimic tissue.     

Effect of red cell clustering and anisotropy on ultrasound blood backscatter: a Monte Carlo study

When flowing at a low shear rate, blood appears hyperechogenic on ultrasound B-scans. The formation of red blood cell (RBC) aggregates that also alters blood viscosity is the microscopic mechanism explaining this acoustical phenomenon. In this study, Monte Carlo simulations were performed to predict how RBC clustering increases ultrasound scattering by blood. A bidimensional Gibbs-Markov random point process parameterized by the adhesion energy epsilon and an anisotropy index nu was used to describe RBC positions for a hematocrit H = 40%. The frequency dependence of the backscattering coefficient chi(f) was computed using Born approximation. The backscattering coefficient chi0 at 5 MHz and the spectral slopes n(x) and n(y) (chi alpha f(nx) or f(ny)) measured, respectively, when the insonification is parallel and perpendicular with the RBC cluster axis were then extracted. Under isotropic conditions, chi0 increased up to 7 dB with epsilon and n(x) = n(y) decreased from 4.2 to 3.4. Under anisotropic conditions, the backscattering was stronger perpendicularly to aggregate axis, resulting in n(x) < n(y). The anisotropy in scattering appeared more pronounced when epsilon or nu increased. These two dimensional results generally predict that low-frequency blood backscatter is related to cluster dimension, and higher-frequency properties are affected by finer morphological features as anisotropy. This numerically establishes that ultrasound backscatter spectroscopy on a large frequency range is pertinent to characterize in situ hemorheology.     

Toward a real-time simulation of ultrasound image sequences based on a 3-D set of moving scatterers

Data simulation is an important research tool to evaluate algorithms. Two types of methods are currently used to simulate medical ultrasound data: those based on acoustic models and those based on convolution models. The simulation of ultrasound data sequences is very time-consuming. In addition, many applications require accounting for the out-ofplane motion induced by the 3-D displacement of scatterers. The purpose of this paper is to propose a model adapted to a fast simulation of ultrasonic data sequences with 3-D moving scatterers. Our approach is based on the convolution model. The scatterers are moved in a 3-D continuous medium between each pair of images and then projected onto the imaging plane before being convolved. This paper discusses the practical implementation of the convolution that can be performed directly or after a grid approximation. The grid approximation convolution is obviously faster than the direct convolution but generates errors resulting from the approximation to the grid?s nodes. We provide the analytical expression of these errors and then define 2 intensity-based criteria to quantify them as a function of the spatial sampling. The simulation of an image requires less than 2 s with oversampling, thus reducing these errors. The simulation model is validated with first- and second-order statistics. The positions of the scatterers at each imaging time can be provided by a displacement model. An example applied to flow imaging is proposed. Several cases are used to show that this displacement model provides realistic data. It is validated with speckle tracking, a well-known motion estimator in ultrasound imaging.     

Ultrafast compound imaging for 2-D motion vector estimation: application to transient elastography

This paper describes a new technique for two-dimensional (2-D) imaging of the motion vector at a very high frame rate with ultrasound. Its potential is experimentally demonstrated for transient elastography. But, beyond this application, it also could be promising for color flow and reflectivity imaging. To date, only axial displacements induced in human tissues by low-frequency vibrators were measured during transient elastography. The proposed technique allows us to follow both axial and lateral displacements during the shear wave propagation and thus should improve Young's modulus image reconstruction. The process is a combination of several ideas well-known in ultrasonic imaging: ultra-fast imaging, multisynthetic aperture beamforming, 1-D speckle tracking, and compound imaging. Classical beamforming in the transmit mode is replaced here by a single plane wave insonification increasing the frame rate by at least a factor of 128. The beamforming is achieved only in the receive mode on two independent subapertures. Comparison of successive frames by a classical 1-D speckle tracking algorithm allows estimation of displacements along two different directions linked to the subapertures beams. The variance of the estimates is finally improved by tilting the emitting plane wave at each insonification, thus allowing reception of successive decorrelated speckle patterns.     

Tissue stiffness imaging method using temporal variation of ultrasound speckle pattern

Applying vibration to a medium makes it vibrate. The resulting change in scatterer distribution inside the medium due to applied vibration changes the speckle pattern of ultrasound images. In this case, scatterers in a hard medium experience small displacements, and those in a soft medium experience large displacements. As a result, the amount of speckle pattern brightness change in ultrasound images is related to the tissue stiffness. Using this dependency, a two-dimensional profile of relative tissue stiffness can be constructed qualitatively at the display pixel resolution by determining at each pixel the standard deviation and/or the difference between minimum and maximum values over a certain number of consecutive B-mode images. Experiments with phantoms show that the softer the tissue, the larger the standard deviation. The proposed imaging modality is a simple yet practical method of resolving hard cysts surrounded by soft background in a phantom using B-mode frame data only.     

Speckle motion artifact under tissue rotation

Speckle patterns in ultrasound images may move in a way which bears no simple relationship to the motion of the corresponding tissues. In some instances the speckle motion replicates the underlying tissue motion, in others it does not. The authors name “speckle motion artifact” the difference between the speckle and the underlying tissue motion. An echographic image formation model is used to study the motion artifact produced by a rotating phantom and observed by a linear scan imaging system with a Gaussian beam. The authors propose that when the tissue is modeled as a random array of small and numerous scatterers, such motion aberration be accounted for by the 2D phase characteristics of the imaging system. An analytic prediction of this motion artifact in relation to the imaging system characteristics (beam width, transducer frequency, pulse duration) is presented. It is shown that the artifact results from the curvature of the system point spread function, which in turn determines the curvature of the 2D phase characteristics. To the authors' knowledge, it is the first time a comprehensive model of ultrasonic speckle motion artifact is presented. The model has been developed to study rotation-induced artifact; the method is however quite general and can be extended to study the effects of other tissue motion, in particular deformation and shear     

Ultrasound speckle reduction using modified Gabor filters

B-mode ultrasound images are characterized by speckle artifact, which may make the interpretation of images difficult. One widely used method for ultrasound speckle reduction is the split spectrum processing (SSP), but the use of one-dimensional (1-D), narrow-band filters makes the resultant image experience a significant resolution loss. In order to overcome this critical drawback, we propose a novel method for speckle reduction in ultrasound medical imaging, which uses a bank of wideband 2-D directive filters, based on modified Gabor functions. Each filter is applied to the 2-D radio-frequency (RF) data, resulting in a B-mode image filtered in a given direction. The compounding of the filters outputs give rise to a final image in which speckle is reduced and the structure is enhanced. We have denoted this method as directive filtering (DF). Because the proposed filters have effectively the same bandwidth as the original image, it is possible to avoid the resolution loss caused by the use of narrow-band filters, as with SSP. The tests were carried out with both simulated and real clinical data. Using the signal-to-noise ratio (SNR) to quantify the amount of speckle of the ultrasound images, we have achieved an average SNR enhancement of 2.26 times with simulated data and 1.18 times with real clinical data.     

Aberration correction by time reversal of moving speckle noise

Focusing a wave through heterogeneous media is an important problem in medical ultrasound imaging. In such aberrating media, in the presence of a small number of point reflectors, iterative time reversal is a well-known method able to focus on the strongest reflector. However, in presence of speckle noise generated by many non-resolved scatterers, iterative time reversal alone does not work. In this paper, we propose the use of the echoes coming from moving particles in a flow, such as red blood cells, to generate a virtual point reflector by iterative time reversal. The construction of the virtual point reflector is performed by a coherent addition of independent realizations of speckle coming from moving particles. After focusing on a virtual point reflector, ultrasound images can be locally corrected inside an isoplanatic patch. An application for the correction of power Doppler images is presented. A theoretical analysis shows that this iterative method allows focusing on the point of maximal insonification of the uncorrected beam.     

Tissue characterization using the continuous wavelet transform. Part I: Decomposition method

In this paper, a novel decomposition of the RF ultrasound signal into its coherent and diffused components is proposed. This decomposition is based on thresholding the energy of the continuous wavelet transform of the RF signal using appropriate wavelets. The two components are modeled separately, and the model parameters are estimated. Previous work (Cohen et al. 1997) required assumptions about the periodicity of the coherent scatterers in the tissue. These assumptions are not necessary in this work. The decomposition algorithm is tested on simulated RF images. The accuracy of the estimated parameters is presented as well as the performance of the algorithm in low coherent-to-diffuse components' energy ratios (SNR)     

Speckle decorrelation due to two-dimensional flow gradients

The performance of ultrasonic velocity estimation methods is degraded by speckle decorrelation, the change in received echoes over time. Because ultrasonic speckle is formed by the complex sum of echoes from subresolution scatterers, it is sensitive to the relative motion of those scatterers. Velocity gradients in flowing blood result in relative scatterer motion and can be a significant source of speckle decorrelation. Computer simulations were performed to evaluate speckle decorrelation due to two-dimensional flow gradients. Results indicate that decorrelation due to flow gradients is sensitive to the angle of flow and has a maximum at a beam-vessel angle of 0 degrees , i.e., purely axial flow. A quantitative summary of the major factors causing speckle decorrelation indicates that flow gradients are the most significant contributors under the conditions modeled.     

Ultrasonic backscatter imaging by shear-wave-induced echo phase encoding of target locations

We present a novel method for ultrasound backscatter image formation wherein lateral resolution of the target is obtained by using traveling shear waves to encode the lateral position of targets in the phase of the received echo. We demonstrate that the phase modulation as a function of shear wavenumber can be expressed in terms of a Fourier transform of the lateral component of the target echogenicity. The inverse transform, obtained by measurements of the phase modulation over a range of shear wave spatial frequencies, yields the lateral scatterer distribution. Range data are recovered from time of flight as in conventional ultrasound, yielding a B-mode-like image. In contrast to conventional ultrasound imaging, where mechanical or electronic focusing is used and lateral resolution is determined by aperture size and wavelength, we demonstrate that lateral resolution using the proposed method is independent of the properties of the aperture. Lateral resolution of the target is achieved using a stationary, unfocused, single-element transducer. We present simulated images of targets of uniform and non-uniform shear modulus. Compounding for speckle reduction is demonstrated. Finally, we demonstrate image formation with an unfocused transducer in gelatin phantoms of uniform shear modulus.     

Fast ultrasound imaging simulation in K-space

Most available ultrasound imaging simulation methods are based on the spatial impulse response approach. The execution speed of such a simulation is of the order of days for one heart-sized frame using desktop computers. For some applications, the accuracy of such rigorous simulation approaches is not necessary. This work outlines a much faster 3-D ultrasound imaging simulation approach that can be applied to tasks like simulating 3-D ultrasound images for speckle-tracking. The increased speed of the proposed simulation method is based primarily on the approximation that the point spread function is set to be spatially invariant, which is a reasonably good approximation when using polar coordinates for simulating images from phased arrays with constant aperture. Ultrasound images are found as the convolution of the PSF and an object of sparsely distributed scatterers. The scatterers are passed through an anti-aliasing filter before insertion into a regular beam-space grid to reduce the bandwidth and significantly reduce the amount of data. A comparison with the well-established simulation software package field II has been made. A simulation of a cyst image using the same input object was found to be in the order of 7000 times slower than the presented method. Following these considerations, the proposed simulation method can be a rapid and valuable tool for working with 3-D ultrasound imaging and in particular 3-D speckle-tracking.