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In medical imaging, quantitative measurements have shown promise in identifying diseases by classifying normal vs. pathological parameters from tissues. The support vector machine (SVM) has shown promise as a supervised classification algorithm and has been widely used. However, the classification results typically identify a category of abnormal tissues, but do not necessarily differentiate progressive stages of a disease. Moreover, the classification result is typically provided independently as a supplement to medical images, which contributes to an overload of information sources in the clinic. Hence, we propose a new imaging method utilizing the SVM to integrate classification results into medical images. This framework is called disease-specific imaging (DSI) which produces a color overlaid highlight on B-mode ultrasound images indicating the type, location, and severity of pathology from different conditions. In this paper, the SVM training was performed to construct hyperplanes that can differentiate normal, fibrosis, steatosis, and pancreatic ductal adenocarcinoma (PDAC) metastases in livers based on ultrasound echoes. Also, cluster centroids for specific diseases define unique disease axes, and the inner product between measured features and any disease axis selected by the SVM quantifies the disease progression. The features were measured from 2794 ultrasound frames using the H-scan analysis, attenuation estimation, and B-mode image analysis. The performance of our proposed DSI method was evaluated for a pre-clinical model of steatosis (n = 400 frames). The contribution of each feature was assessed, and the results were compared with ground truth from histology. Moreover, the images generated by our DSI were compared with earlier imaging methods of B-mode, H-scan, and histology. The comparisons demonstrate that DSI images yield higher sensitivity to monitor progressive steatosis than B-mode and H-scan and provide a comparable performance with the histology. For the parameter comparison, DSI and H-scan resulted in similar correlation with histology (r(s)=0.83), but higher than attenuation (r(s)=0.73) and B-mode (r(s)=0.47). Therefore, we conclude that DSI utilizing the SVM applied to steatosis can visually represent the classification results with color highlighting, which can simplify the interpretation of classification compared to the traditional SVM result. We expect the proposed DSI can be used for any medical imaging modality that can estimate multiple quantitative parameters at high resolution.

The study of ultrasound tissue interactions in fatty livers has a long history with strong clinical potential for assessing steatosis. Recently we proposed alternative measures of first- and second-order statistics of echoes from soft tissues, namely, the H-scan, which is based on a matched filter approach, to quantify scattering transfer functions and the Burr distribution to model speckle patterns. Taken together, these approaches produce a multiparameter set that is directly related to the fundamentals of ultrasound propagation in tissue. To apply this approach to the problem of assessing steatotic livers, these analyses were applied to in vivo rat livers ( N = 21 ) under normal feeding conditions or after receiving a methionine- and choline-deficient diet that produces steatosis within a few weeks. Ultrasound data were acquired at baseline and again at weeks 2 and 6 before applying the H-scan and Burr analyses. Furthermore, a classification technique known as the support vector machine was then used to find clusters of the five parameters that are characteristic of the different steatotic liver conditions as confirmed by histologic processing of excised liver tissue samples. With the in vivo multiparametric ultrasound measurement approach and determination of clusters, steatotic can be discriminated from normal livers with 100% accuracy in a rat animal model.

We report shear wave phase and group velocity, dispersion and attenuation in oil-in-gelatin viscoelastic phantoms and in vivo liver data. Moreover, we measured the power law coefficient from each dispersion curve and used it, together with the shear wave velocity, to calculate an approximate value for attenuation that agrees with independent attenuation measurements. Results in phantoms exhibit good agreement for all parameters with respect to independent mechanical measurements. For in vivo data, the livers of 20 patients were scanned. Results were compared with pathology scores obtained from liver biopsies. Across these cases, increases in shear wave dispersion and attenuation were related to increased steatosis score. It was found that shear wave dispersion and attenuation are experimentally linked, consistent with simple predictions based on the rheology of tissues, and can be used individually or jointly to assess tissue viscosity. Thus, this study indicates the possible utility of using shear wave dispersion and attenuation to non-invasively and quantitatively assess steatosis.

Fifty years of research on the nature of backscatter from tissues has resulted in a number of promising diagnostic parameters. We recently introduced two analyses tied directly to the biophysics of ultrasound scattering: the H-scan, based on a matched filter approach to distinguishing scattering transfer functions, and the Burr distribution for quantification of speckle patterns. Together, these analyses can produce at least five parameters that are directly linked to the mathematics of ultrasound in tissue. These have been measured in vivo in 35 rat livers under normal conditions and after exposure to compounds that induce inflammation, fibrosis, and steatosis in varying combinations. A classification technique, the support vector machine, is employed to determine clusters of the five parameters that are signatures of the different liver conditions. With the multiparametric measurement approach and determination of clusters, the different types of liver pathology can be discriminated with 94.6% accuracy.

There are a growing set of ultrasound and viscoelastic measures that can be correlated with fat or fibrosis in the liver. We find that fat and fibrosis jointly influence important properties of the liver and can be considered as confounding cofactors within most simple measures. For example, shear wave attenuation is sensitive to the accumulation of viscous fat, but is also influenced by the degree of fibrosis, so attenuation by itself is insufficient for accurate estimation of liver fat. However, using some robust elastography techniques to assess both the shear wave phase velocity and the shear wave attenuation in a region of the liver, these measured values are found to be sufficient information for solving for both the unknown fat percent volume and the liver stiffness related to fibrosis score. A classical theory of composite viscoelastic materials is used to solve for the unknowns. Examples from human clinical studies are shown to correspond to biopsy proven grades of steatosis and fibrosis.

Shear wave propagation in the liver has been a robust subject of research, with shear wave speed receiving the most attention. The correlation between increased shear wave speed and increased fibrosis in the liver has been established as a useful diagnostic tool. In comparison, the precise mechanisms of shear wave attenuation, and its relation to diseased states of the liver, are less well-established. This study focused on the hypothesis that steatosis adds a viscous (lossy) component to the liver, which increases shear wave attenuation. Twenty patients' livers were scanned with ultrasound and with induced shear wave propagation, and the resulting displacement profiles were analyzed using recently developed estimators to derive both the speed and attenuation of the shear waves within 6-cm2 regions of interest. The results were compared with pathology scores obtained from liver biopsies taken under ultrasound guidance. Across these cases, increases in shear wave attenuation were linked to increased steatosis score. This preliminary study supports the hypothesis and indicates the possible utility of the measurements for non-invasive and quantitative assessment of steatosis.

The non-invasive quantification of tumor burden and the response to therapies remain an important objective for imaging modalities. To characterize the performance of two newly optimized ultrasound-based analyses, we applied shear wave and H-scan scattering analyses to repeated trans-abdominal ultrasound scans of a murine model of metastatic pancreatic cancer. In addition, bioluminescence measurements were obtained as an alternative reference. The tumor metastases grow aggressively and result in death at approximately 4 wk if untreated, but longer for those treated with chemotherapy. We found that our three imaging methods (shear wave speed, H-scan, bioluminescence) trended toward increasing output measures with time during tumor growth, and these measures were delayed for the group receiving chemotherapy. The relative sensitivity of H-scan tracked closely with bioluminescence measurements, particularly in the early to mid-stages of tumor growth. The correlation between H-scan and bioluminescence was found to be strong, with a Spearman's rank correlation coefficient greater than 0.7 across the entire series. These preliminary results suggest that non-invasive ultrasound imaging analyses are capable of tracking the response of tumor models to therapeutic agents.

Recent work has established an analytical formulation of broadband fields which extend in the axial direction and converge to a narrow concentrated line. Those unique (needle) fields have their origins in an angular spectrum configuration in which the forward propagating wavenumber of the field ( k z) is constant across any z plane for all of the propagated frequencies. A 3 MHz-based, finite amplitude distorted simulation of such a field is considered here in a water path scenario relevant to medical imaging. That nonlinear simulation had its focal features compared to those of a comparable Gaussian beam. The results suggest that the unique convergence of the needle pulse to a narrow but extended axial line in linear propagation is also inherited by higher harmonics in nonlinear propagation. Furthermore, the linear needle field's relatively short duration focal pulses, and the asymptotic declines of its radial profiles, also hold for the associated higher harmonics. Comparisons with the Gaussian field highlight some unique and potentially productive features of needle fields.Recent work has established an analytical formulation of broadband fields which extend in the axial direction and converge to a narrow concentrated line. Those unique (needle) fields have their origins in an angular spectrum configuration in which the forward propagating wavenumber of the field ( k z) is constant across any z plane for all of the propagated frequencies. A 3 MHz-based, finite amplitude distorted simulation of such a field is considered here in a water path scenario relevant to medical imaging. That nonlinear simulation had its focal features compared to those of a comparable Gaussian beam. The results suggest that the unique convergence of the needle pulse to a narrow but extended axial line in linear propagation is also inherited by higher harmonics in nonlinear propagation. Furthermore, the linear needle field's relatively short duration focal pulses, and the asymptotic declines of its radial profiles, also hold for the associated higher harmonics. Comparisons with the Gaussian fi...

The propagation of shear waves from impulsive forces is an important topic in elastography. Observations of shear wave propagation can be obtained with numerous clinical imaging systems. Parameter estimations of the shear wave speed in tissues, and more generally the viscoelastic parameters of tissues, are based on some underlying models of shear wave propagation. The models typically include specific choices of the spatial and temporal shape of the impulsive force and the elastic or viscoelastic properties of the medium. In this work, we extend the analytical treatment of 2-D shear wave propagation in a biomaterial. The approach applies integral theorems relevant to the solution of the generalized Helmholtz equation, and does not depend on a specific rheological model of the tissue's viscoelastic properties. Estimators of attenuation and shear wave speed are derived from the analytical solutions, and these are applied to an elastic phantom, a viscoelastic phantom and in vivo liver using a clinical ultrasound scanner. In these samples, estimated shear wave group velocities ranged from 1.7 m/s in the liver to 2.5 m/s in the viscoelastic phantom, and these are lower-bounded by independent measurements of phase velocity.

Recent theoretical developments have defined the conditions for forming a broadband beam that is narrow in axial extent but extended in range. The formulation is based on the classical angular spectrum decomposition and the requirement for arranging all spatial and temporal frequencies such that all components have constant phase propagation between planes. Analytic formulations are given for a 1-D source and a 2-D axisymmetric source, and comparisons are made against conventional focused Gaussian beams under similar conditions relevant to medical imaging systems.

A recent series of theoretical and experimental results support the hypothesis that ultrasound speckle statistics and backscatter are deeply rooted in power law behaviors. The implications for the tissue characterization are direct and lead to Burr distributions for speckle analysis and the H-scan analysis for the tissue characterization.

The H-scan analysis provides a matched filter approach to quantifying the scattering transfer function of tissue, at high resolution, in medical ultrasound. The approach yields quantitative estimates and high resolution images where color encodes the scattering information, and the results on normal and diseased tissues will be presented.

Elastography provides tissue stiffness information that attempts to characterize the elastic properties of tissue. However, there is still limited literature comparing elastographic modalities for tissue characterization. This study focuses on two quantitative techniques using different vibration sources that have not been compared to date: crawling wave sonoelastography (CWS) and single tracking location shear wave elasticity imaging (STL-SWEI). To understand each technique’s performance, shear wave speed (SWS) was measured in homogeneous phantoms and ex vivo beef liver tissue. Then, the contrast, contrast-to-noise ratio (CNR), and lateral resolution were measured in an inclusion and two-layer phantoms. The SWS values obtained with both modalities were validated with mechanical measurements (MM) which serve as ground truth. The SWS results for the three different homogeneous phantoms (10%, 13%, and 16% gelatin concentrations) and ex vivo beef liver tissue showed good agreement between CWS, STL-SWEI, and MM as a function of frequency. For all gelatin phantoms, the maximum accuracy errors were 2.52% and 2.35% using CWS and STL-SWEI, respectively. For the ex vivo beef liver, the maximum accuracy errors were 9.40% and 7.93% using CWS and STL-SWEI, respectively. For lateral resolution, contrast, and CNR, both techniques obtained comparable measurements for vibration frequencies less than 300 Hz (CWS) and distances between the push beams ( $\Delta x$ ) between 3 mm and 5.31 mm (STL-SWEI). The results obtained in this study agree over an SWS range of 1–6 m/s. They are expected to agree in perfectly linear, homogeneous, and isotropic materials, but the SWS overlap is not guaranteed in all materials because each of the three methods have unique features.

The placenta is the critical interface between the mother and the developing fetus and is essential for survival and growth. Despite the widespread use of ultrasound imaging and Doppler in obstetrics and gynecology and the recent growth of elastographic technologies, little is known about the biomechanical (elastic shear wave) properties of the placenta and the range of normal and pathologic parameters that are present. This study uses a well-developed protocol for perfusing whole placentas, post-delivery, to maintain tissue integrity and function for hours. In this model, the placenta is living, whole and maintained within normal physiologic parameters such as flow, arterial pressure and oxygen, throughout examination by ultrasound, Doppler and shear wave elastography. The preliminary results indicate that normal placental tissue on the fetal side has shear wave speeds on the order of 2 m/s, in a range similar to those of animal livers. Some abnormalities are found outside this range, and thus, elastographic measures of the placenta may provide useful assessments related to the state of the tissue.

The issue of speckle statistics from ultrasound images of soft tissues such as the liver has a long and rich history. A number of theoretical distributions, some related to random scatterers or fades in optics and radar, have been formulated for pulse-echo interference patterns. This work proposes an alternative framework in which the dominant echoes are presumed to result from Born scattering from fluid filled vessels that permeate the tissue parenchyma. These are modeled as a branching, fractal, self-similar, multi scale collection of cylindrical scatterers governed by a power law distribution relating the number of branches at each radius. A deterministic accounting of the echo envelopes across the scales from small to large is undertaken, leading to a closed form theoretical formula for the histogram of the envelope of the echoes. The normalized histogram is found to be related to the classical Burr distribution, with the key power law parameter directly related to that of the number density of vessels vs. diameter, frequently reported in the range of 2 to 4. Examples are given from liver scans to demonstrate the applicability of the theory., Comment: 26 pages, 14 figures. This article has been submitted to The Journal of the Acoustical Society of America. After it is published, it will be found at http://asa.scitation.org/journal/jas

H-scan ultrasound (US) is a new imaging technique that relies on matching a model that describes US image formation to the mathematics of a class of Gaussian-weighted Hermite polynomials (GH). In short, H-scan US (where the ‘H’ denotes Hermite or hue) is a tissue classification technique that images the relative size of acoustic scatterers. Herein, we detail development of a real-time H-scan US imaging technology that was implemented on a programmable US research scanner (Vantage 256, Verasonics Inc, Kirkland, WA). This custom US imaging system has a dual display for real-time visualization of both the H-scan and B-scan US images. This MATLAB-based (Mathworks Inc, Natick, MA) system includes a graphical user interface (GUI) for controlling the entire US scan sequence including the raw radio frequency (RF) data acquisition parameters, image processing, variable control of a parallel set of convolution filters used to derive the H-scan US signal, and data (cine loop) save. The system-level structure used for software-based image reconstruction and display is detailed. Imaging studies were conducted using a series of homogeneous and heterogeneous tissue-mimicking phantom materials embedded with monodisperse spherical US scatterers of size 15–40 µm in diameter. Relative to H-scan US image measurements from a phantom with 15 µm-sized scatterers, data from phantoms with the 30 and 40 µm-sized scatterers exhibited mean intensity increases of 5.2% and 11.6%, respectively. Overall, real-time H-scan US imaging is a promising approach for visualizing the relative size and distribution of acoustic scattering objects.

Biological effects of megahertz-frequency diagnostic ultrasound are thoroughly monitored by professional societies throughout the world. A corresponding, thorough, quantitative evaluation of the archival literature on the biological effects of low-frequency vibration is needed. Biological effects, of course, are related directly to what those exposures do physically to the tissue-specifically, to the shear strains that those sources produce in the tissues. Instead of the simple compressional strains produced by diagnostic ultrasound, realistic sources of low-frequency vibration produce both fast (∼1,500 m/s) and slow (1-10 m/s) waves, each of which may have longitudinal and transverse shear components. Part 1 of this series illustrates the resulting strains, starting with those produced by longitudinally and transversely oscillating planes, through monopole and dipole sources of fast waves and, finally, to the case of a sphere moving in translation-the simplest model of the fields produced by realistic sources.

For nearly 100 y in the study of cyclical motion in materials, a particular phenomenon called “linear hysteresis” or “ideal hysteretic damping” has been widely observed. More recently in the field of shear wave elastography, the basic mechanisms underlying shear wave losses in soft tissues are in question. Could linear hysteresis play a role? An underlying theoretical question must be answered: Is there a real and causal physical model that is capable of producing linear hysteresis over a band of shear wave frequencies used in diagnostic imaging schemes? One model that can approximately produce classic linear hysteresis behavior, by examining a generalized Maxwell model with a specific power law relaxation spectrum, is described here. This provides a theoretical plausibility for the phenomenon as a candidate for models of tissue behavior.

H-Scan is a new ultrasound imaging technique that relies on matching a model of pulse-echo formation to the mathematics of a class of Gaussian-weighted Hermite polynomials. This technique may be beneficial in the measurement of relative scatterer sizes and in cancer therapy, particularly for early response to drug treatment. Because current H-scan techniques use focused ultrasound data acquisitions, spatial resolution degrades away from the focal region and inherently affects relative scatterer size estimation. Although the resolution of ultrasound plane wave imaging can be inferior to that of traditional focused ultrasound approaches, the former exhibits a homogeneous spatial resolution throughout the image plane. The purpose of this study was to implement H-scan using plane wave imaging and investigate the impact of spatial angular compounding on H-scan image quality. Parallel convolution filters using two different Gaussian-weighted Hermite polynomials that describe ultrasound scattering events are applied to the radiofrequency data. The H-scan processing is done on each radiofrequency image plane before averaging to get the angular compounded image. The relative strength from each convolution is color-coded to represent relative scatterer size. Given results from a series of phantom materials, H-scan imaging with spatial angular compounding more accurately reflects the true scatterer size caused by reductions in the system point spread function and improved signal-to-noise ratio. Preliminary in vivo H-scan imaging of tumor-bearing animals suggests this modality may be useful for monitoring early response to chemotherapeutic treatment. Overall, H-scan imaging using ultrasound plane waves and spatial angular compounding is a promising approach for visualizing the relative size and distribution of acoustic scattering sources.

Elastography is a modality that estimates tissue stiffness and, thus, provides useful information for clinical diagnosis. Attention has focused on the measurement of shear wave propagation; however, many methods assume shear wave propagation is unidirectional and aligned with the lateral imaging direction. Any deviations from the assumed propagation result in biased estimates of shear wave speed. To address these challenges, directional filters have been applied to isolate shear waves with different propagation directions. Recently, a new method was proposed for tissue stiffness estimation involving creation of a reverberant shear wave field propagating in all directions within the medium. These reverberant conditions lead to simple solutions, facile implementation and rapid viscoelasticity estimation of local tissue. In this work, this new approach based on reverberant shear waves was evaluated and compared with another well-known elastography technique using two calibrated elastic and viscoelastic phantoms. Additionally, the clinical feasibility of this technique was analyzed by assessing shear wave speed in human liver and breast tissues, in vivo. The results indicate that it is possible to estimate the viscoelastic properties in each scanned medium. Moreover, a better approach to estimation of shear wave speed was obtained when only the phase information was taken from the reverberant waves, which is equivalent to setting all magnitudes within the bandpass equal to unity: an idealization of a perfectly isotropic reverberant shear wave field.

Across a range of spectral estimation problems and beam focusing problems, it is necessary to constrain the properties of a function and its Fourier transform. In many cases, compact functions in both domains are desired, within the theoretical bounds of the uncertainty principle. Recently, a hyperbolic sine function of modified argument and power was found to be an approximate eigenfunction of the Fourier transform operation, and demonstrated useful properties of compactness with low side lobes. The empirical finding of the eigenfunction relationship is explained by comparison with the prolate spheroidal wave functions, which have exact eigenfunction properties, and their usefulness is demonstrated by examples.

We describe a surface-based approach to the generation of shear wave interference patterns, called crawling waves (CrW), within a medium and derive local estimates of biomechanical properties of tissue. In previous experiments, elongated bars operating as vibration sources were used to generate CrW propagation in samples. In the present study, however, a pair of miniature circular vibration sources was applied to the overlying skin to generate the CrW within the medium. The shape and position of the miniature sources make this configuration more applicable for in vivo implementation. A modified ultrasound imaging system is used to display the CrW propagation. A shear speed mapping algorithm is developed using a detailed analysis of the CrW. The proposed setup is applied to several biomaterials including a homogeneous phantom, an inhomogeneous phantom and an ex vivo human liver. The data are analyzed using the mapping algorithm to reveal the biomechanical properties of the biomaterials.

In ''imaging the biomechanical properties of tissues,'' a number of approaches analyze shear wave propagation initiated by a short radiation force push. Unfortunately, it has been experimentally observed that the displacement-versus-time curves for lossy tissues are rapidly damped and distorted in ways that can confound simple tracking approaches. This article addresses the propagation, decay and distortion of pulses in lossy and dispersive media, to derive closed-form analytic expressions for the propagating pulses. The theory identifies key terms that drive the distortion and broadening of the pulse. Furthermore, the approach taken is not dependent on any particular viscoelastic model of tissue, but instead takes a general first-order approach to dispersion. Examples with a Gaussian beam pattern and realistic dispersion parameters are given along with general guide- lines for identifying the features of the distorting wave that are the most compact. (E-mail: kevin.parker@ rochester.edu) 2014 World Federation for Ultrasound in Medicine & Biology.

This review considers three general classes of physical as opposed to phenomenological models of the shear elasticity of tissues. The first is simple viscoelasticity. This model has a special role in elastography because it is the language in which experimental and clinical data are communicated. The second class of models involves acoustic relaxation, in which the medium contains inner time-dependent systems that are driven through the external bulk medium. Hysteresis, the phenomenon characterizing the third class of models, involves losses that are related to strain rather than time rate of change of strain. In contrast to the vast efforts given to tissue characterization through their bulk moduli over the last half-century, similar research using low-frequency shear data is in its infancy. Rather than a neat summary of existing facts, this essay is a framework for hypothesis generation—guessing what physical mechanisms give tissues their shear properties.

In beamforming, a critical design issue is the choice of the window or apodization function. Because the transverse beam pattern at focal depth is related to the Fourier transform of the apodization function, designers must evaluate the properties of the function and its transform, jointly, to optimize the system. This paper illustrates systematic approaches to designing useful functions.

A number of imaging systems exhibit speckle, which is caused by the interaction of a coherent pulse reflecting off of random reflectors. The limitations of these systems are quite serious because the speckle phenomenon creates a pattern of nulls and peaks from subresolvable scatterers or targets that are difficult to interpret. Another limitation of these pulse-echo imaging systems is that their resolution is dependent on the full spatial extent of the propagating pulse, usually several wavelengths in the axial or propagating dimension and typically longer in the transverse direction. This limits the spatial resolution to many multiples of the wavelength. This paper focuses on the particular case of ultrasound B-scan imaging and develops an inverse filter solution that eliminates both the speckle phenomenon and the poor resolution dependency on the pulse length and width to produce super-resolution ultrasound (SURUS) images. The key to the inverse filter is the creation of pulse shapes that have stable inverses. This is derived by use of the standard Z-transform and related properties. Although the focus of this paper is on examples from ultrasound imaging systems, the results are applicable to other pulse-echo imaging systems that also can exhibit speckle statistics.

An ultrasound system (GE Logiq 9) was modified to produce a synthetic crawling wave using shear wave displacements generated by the radiation force of focused beams formed at the left and the right edge of the region of interest (ROI). Two types of focusing, normal and axicon, were implemented. Baseband (IQ) data was collected to determine the left and right displacements, which were then used to calculate an interference pattern. By imposing a variable delay between the two pushes, the interference pattern moves across the ROI to produce crawling waves. Also temperature and pressure measurements were made to assess the safety issues. The temperature profiles measured in a veal liver along the focal line showed the maximum temperature rise less than 0.8 °C, and the pressure measurements obtained in degassed water and derated by 0.3 dB/cm/MHz demonstrate that the system can operate within FDA safety guidelines.

Crawling waves, which are interfering shear wave patterns, can be generated in liver tissue over a range of frequencies. Some important biomechanical properties of the liver can be determined by imaging the crawling waves using Doppler techniques and analyzing the patterns. We report that the dispersion of shear wave velocity and attenuation, that is, the frequency dependence of these parameters, are strongly correlated with the degree of steatosis in a mouse liver model, ex vivo. The results demonstrate the possibility of assessing liver steatosis using noninvasive imaging methods that are compatible with color Doppler scanners and, furthermore, suggest that liver steatosis can be separated from fibrosis by assessing the dispersion or frequency dependence of shear wave propagations.

Normal liver tissue is soft and pliable. With inflammation, however, many of the cells die and are replaced by collagenous fibrils and the tissue gets stiffer. The progress is often slow-extending over decades in many cases. When liver stiffness increases by a factor of about five, the condition is called cirrhosis, a disease with serious medical implications. After the onset of cirrhosis, the probability of developing hepatic cancer increases at the rate of about 5% per year. Precise, noninvasive measurement of liver stiffness, a simple application of elastography, promises to be a safe, inexpensive method to monitor the progress of liver patients, improve outcome, save many lives and much suffering and reduce the cost of medical care.

We introduce a novel 2-D sonoelastographic technique for estimating local shear velocities from propagating shear wave interference patterns (termed crawling waves) in this paper. A relationship between the local crawling wave spatial phase derivatives and local shear wave velocity is derived, with phase derivatives estimated using a 2-D autocorrelation technique. Comparisons were made between the 2-D sonoelastographic shear velocity estimation technique and its computationally simpler 1-D precursor. In general, the 2-D sonoelastographic shear velocity estimator outperformed the 1-D-based technique in terms of accuracy and estimator noise minimization. For both approaches, increasing the estimator kernel size reduces noise levels but lowers spatial resolution. Homogeneous elastic phantom results demonstrate the ability of sonoelastographic shear velocity imaging to quantify the true underlying shear velocity distributions as verified using time-of-flight measurements. Results also indicate that increasing the estimator kernel size increases the transition zone length about boundaries in heterogeneous elastic mediums and may complicate accurate quantification of smaller elastically contrasting lesions. Furthermore, analysis of contrast-to-noise ratio (CNR) values for sonoelastograms obtained in heterogeneous elastic phantoms reveal that the 2-D sonoelastographic shear velocity estimation technique outperforms the 1-D version for a given kernel size in terms of image noise minimization and contrast enhancement. Experimental results from an embedded porcine liver specimen with a radiofrequency ablation (RFA) lesion demonstrates that the 2-D sonoelastographic shear velocity estimation technique minimizes image noise artifacts and yields a consistent lesion boundary when compared with gross pathology. Volume measurements of the RFA lesion obtained from shear velocity sonoelastograms was comparable to that obtained by fluid displacement of the dissected lesion as illustrated by 3-D volume reconstructions. Overall, 2-D sonoelastographic shear velocity imaging was shown to be a promising new approach to characterizing the shear velocity distribution of elastic materials.

Biomechanical properties of soft tissues are important for a wide range of medical applications, such as surgical simulation and planning and detection of lesions by elasticity imaging modalities. Currently, the data in the literature is limited and conflicting. Furthermore, to assess the biomechanical properties of living tissue in vivo, reliable imaging-based estimators must be developed and verified. For these reasons we developed and compared two independent quantitative methods – crawling wave estimator (CRE) and mechanical measurement (MM) for soft tissue characterization. The CRE method images shear wave interference patterns from which the shear wave velocity can be determined and hence the Young’s modulus can be obtained. The MM method provides the complex Young’s modulus of the soft tissue from which both elastic and viscous behavior can be extracted. This article presents the systematic comparison between these two techniques on the measurement of gelatin phantom, veal liver, thermal-treated veal liver, and human prostate. It was observed that the Young’s moduli of liver and prostate tissues slightly increase with frequency. The experimental results of the two methods are highly congruent, suggesting CRE and MM methods can be reliably used to investigate viscoelastic properties of other soft tissues, with CRE having the advantages of operating in nearly real time and in situ.

In this paper, a novel sonoelastographic technique for estimating local shear velocities from propa- gating shear wave interference patterns (termed crawling waves) is introduced. A relationship between the local crawling wave spatial phase derivatives and local shear wave velocity is derived with phase derivatives estimated using an autocorrelation technique. Results from homogeneous phantoms demonstrate the ability of sonoelas- tographic shear velocity imaging to quantify the true underlying shear velocity distributions as verified using time-of-flight measurements. Heterogeneous phantom results reveal the capacity for lesion detection and shear velocity quantification as validated from mechanical measurements on phantom samples. Experimental results obtained from a prostate specimen illustrated feasibility for shear velocity imaging in tissue. More importantly, high-contrast visualization of focal carcinomas was demonstrated introducing the clinical potential of this novel sonoelastographic imaging technique. (E-mail: hoyt@ece.rochester.edu) © 2007 Published by Elsevier Inc. on behalf of the World Federation for Ultrasound in Medicine & Biology.

A sphere moving back and forth in tissue generates the kinds of complex displacement fields that are used in elastography. The analytical solution of Hans Oestreicher for this phenomenon [(1951). J. Acoust. Soc. Am. 23, 704–714] gives an understanding of the transverse and longitudinal, fast and slow waves that are generated. The results suggest several ways to determine the absorption coefficients of tissues, which together with phase velocity permit the computation of both the real shear modulus and the shear viscosity as functions of frequency.

The authors have recently demonstrated the shear wave interference patterns created by two coherent vibration sources imaged with the vibration sonoelastography technique. If the two sources vibrate at slightly different frequencies omega and omega+deltaomega, respectively, the interference patterns move at an apparent velocity of (deltaomega/2omega)upsilon(shear), where upsilon(shear) is the shear wave speed. We name the moving interference patterns "crawling waves." In this paper, we extend the techniques to inspect biomaterials with nonuniform stiffness distributions. A relationship between the local crawling wave speed and the local shear wave velocity is derived. In addition, a modified technique is proposed whereby only one shear wave source propagates shear waves into the medium at the frequency omega. The ultrasound probe is externally vibrated at the frequency omega-deltaomega. The resulting field estimated by the ultrasound (US) scanner is proven to be an exact representation of the propagating shear wave field. The authors name the apparent wave motion "holography waves." Real-time video sequences of both types of waves are acquired on various inhomogeneous elastic media. The distribution of the crawling/holographic wave speeds are estimated. The estimated wave speeds correlate with the stiffness distributions.

The H-scan is based on a simplified framework for characterizing scattering behavior, and visualizing the results as color coding of the B-scan image. The methodology begins with a standard convolution model of pulse-echo formation from typical situations, and then matches those results to the mathematics of Gaussian Weighted Hermite Functions. The nth successive differentiation of the Gaussian pulse G = exp(-t 2) generates the nth order Hermite polynomial (Poularikas 2010). The function H 4(t)G resembles a broadband pulse. Assuming a pulse-echo system has a round trip impulse response of A 0 H 4(t)G, then we expect that a reflection from a step function of acoustic impedance will produce a corresponding received echo proportional to GH4(t). However, a thin layer of higher impedance, or a small scatterer or incoherent cloud of small scatterers would produce higher order Hermite functions as echoes. In this framework, the identification task is simply to classify echoes by similarity to either GH 4(t), or ...

Some of Edwin Carstensen's final papers considered elastographic shear waves, which had opened up a new set of questions regarding stress and strain in tissues. Carstensen, from his commanding perspective overlooking nearly 70 years of fields and waves in tissues, could uniquely make the following statement: “At present, no consensus group has undertaken a systematic evaluation of the biological effects of low-frequency strains…Thanks to developments in the field of elastography over the last two decades, we now have the tools needed to measure low-frequency strains in tissues directly…Despite the fundamental importance of strain in bioeffects, no bioeffects investigators to our knowledge have taken advantage of these techniques. In fact, strain is rarely mentioned in the bioeffects literature” (Carstensen et al., “Biological effects of low-frequency shear strain: physical descriptors,” Ultrasound Med Biol 42(1)1-15, 2016). Indeed, with this topic, his “voyage of exploration and illumination” had truly co...

A number of new approaches to measure the viscoelastic properties of the liver are now available to clinicians, many involving shear waves. However, we are at an early stage in understanding the physical processes that govern shear wave propagation in normal liver, with more unknowns added when pathologies such as steatosis are present. This technical note focuses on what is known about the characterization of normal and steatotic (or fatty) livers, with a particular focus on dispersion. Some studies in phantoms and mouse livers support the hypothesis that, starting with a normal liver, increasing accumulations of micro- and macrosteatosis will increase the lossy viscoelastic properties of shear waves in a medium. This results in an increased dispersion (or slope) of shear wave speed and attenuation in the steatotic livers. Theoretical and empirical findings across a number of studies are summarized.

Hysteresis is a phenomenon that has been observed across many different materials and situations. Under small-amplitude cyclical motion, classical hysteresis designates a constant loss per cycle over a wide range of frequencies. This is also consistent with an increase in losses or attenuation with frequency that is strictly proportional to the first power of frequency. Unfortunately, the classical (and simple) frequency domain description of hysteresis does not result in a real and causal impulse response, and therefore is not useful for predicting laboratory results. This problem has led to many errors as well as other more fruitful approaches over the years. The frequency domain requirements for hysteresis are re-examined and it is demonstrated that there is a family of solutions that provide real and causal impulse responses over some extended frequency range. The family is conveniently divided into highpass, lowpass, and bandpass causal systems. These are populated by closed form analytical solutions which can be applied to the prediction of motion and waves in hysteretic materials and systems.

The thin film phantom is a new type of ultrasound resolution test object. It consists of a thin planar substrate that is acoustically matched to the surrounding media. Precisely located scatterers on the surface of the substrate generate echo signals. The patterning of scatterers on the substrate allows echogenicity to be controlled as a function of position, which enables the production of a test object with highly reproducible and controllable scattering characteristics. We show that by vibrating the substrate in a suitable manner, an echo signal may be generated that simulates bidirectional flow. We demonstrate that a vibration of low amplitude at frequency f/sub 0/ produces a Doppler spectral signal at f/sub 0/ and -f/sub 0/, within the limits of aliasing. Furthermore, by driving the film with a bandlimited noise signal, we illustrate how a velocity distribution may be simulated. A time-varying flow velocity may be simulated by varying the noise bandwidth with time. Finally, using this technique, we demonstrate a system that simulates an arterial flow pattern, including its characteristic velocity distribution in forward and reverse directions simultaneously.

Fully developed speckle patterns observed in coherent imagery are characterized by a Rayleigh-distributed envelope amplitude. Non-Rayleigh distributions are observed in many cases, such as when the number of scatterers in a resolution cell is small or scatterers are organized with some periodicity. Distributions resulting from the assumption of random scatterer phase (random walk models) have been used to describe the speckle amplitude in these cases, leading to K, Rician, and homodyned-K amplitude distributions. An alternative is to incorporate nonrandom phase implicitly by adopting models that directly describe the spatial placement of point scatterers. We examine the consequences of assuming that scattering is described in one dimension by a stationary renewal process in which the arrival times are the locations of ideal point scatterers, the interscatterer distances are drawn from a gamma distribution, and the scatterer amplitudes are allowed to be correlated in space. This model has been called the marked regularity model because variations of the model parameters can generate spatial distributions ranging from clustered to random to nearly periodic. We will demonstrate that all of the non-Rayleigh distributions generated by the previous random phase models can also be generated by the marked regularity model, and we show under what conditions the different distributions will result. We also demonstrate that the regularity model is inherently capable of describing certain sparse scattering conditions. Therefore, the model can represent many cases and provide an intuitively pleasing description of the spatial placement of the scatterers.

A multilevel motion model-based approach to ultrasonic speckle tracking has been developed that addresses the inherent trade-offs associated with traditional single-level block matching (SLBM) methods. The multilevel block matching (MLBM) algorithm uses variable matching block and search window sizes in a coarse-to-fine scheme, preserving the relative immunity to noise associated with the use of a large matching block while preserving the motion field detail associated with the use of a small matching block. To decrease further the sensitivity of the multilevel approach to noise, speckle decorrelation and false matches, a smooth motion model-based block matching (SMBM) algorithm has been implemented that takes into account the spatial inertia of soft tissue elements. The new algorithms were compared to SLBM through a series of experiments involving manual translation of soft tissue phantoms, motion field computer simulations of rotation, compression and shear deformation, and an experiment involving contraction of human forearm muscles. Measures of tracking accuracy included mean squared tracking error, peak signal-to-noise ratio (PSNR) and blinded observations of optical flow. Measures of tracking efficiency included the number of sum squared difference calculations and the computation time. In the phantom translation experiments, the SMBM algorithm successfully matched the accuracy of SLBM using both large and small matching blocks while significantly reducing the number of computations and computation time when a large matching block was used. For the computer simulations, SMBM yielded better tracking accuracies and spatial resolution when compared with SLBM using a large matching block. For the muscle experiment, SMBM outperformed SLBM both in terms of PSNR and observations of optical flow. We believe that the smooth motion model-based MLBM approach represents a meaningful development in ultrasonic soft tissue motion measurement.

The accumulation of fat droplets within the liver is an important marker of liver disease. This study assesses gradations of steatosis in mouse livers using crawling waves, which are interfering patterns of shear waves introduced into the liver by external sources. The crawling waves are detected by Doppler ultrasound imaging techniques, and these are analyzed to estimate the shear wave speed as a function of frequency between 200 and 360 Hz. In a study of 70 mice with progressive increases in steatosis from 0% to >60%, increases in steatosis are found to increase the dispersion, or frequency dependence, of shear wave speed. This finding confirms an earlier, smaller study and points to the potential of a scoring system for steatosis based on shear wave dispersion.

Recently, a number of methods have been developed that make it possible to image the elastic properties of soft tissues. Because certain types of tissues such as malignant lesions, for example, have elastic properties that are markedly different from surrounding tissues, elasticity imaging could provide a significant adjunct to current diagnostic ultrasonic methods. Further, elasticity imaging techniques could be used to augment the study of tissues that change their elastic properties, such as skeletal and cardiac muscle. In this paper, we survey some of the previous work done in the related field of biomechanics, and we review measurement techniques from the 1950s to the 1980s. Different approaches to elastic imaging and signal processing are then discussed and a lexicography for elastic imaging is introduced. It is hoped that this nomenclature will provide a meaningful categorization of various approaches and will make evident the inherent parameters displayed and conditions applied in deriving the resulting images. Key assumptions and signal processing approaches are also reviewed. Finally, directions for future work are suggested.

Earlier studies, in which murine kidneys were exposed to spherically diverging, spark-generated shock waves, demonstrated extensive hemorrhage in the interior of the organ at peak positive pressures somewhat less than 10 MPa. With comparable pulse numbers, this investigation, using the focal fields of a piezoelectric lithotripter, found no damage to murine kidneys at peak positive pressures as high as 40 MPa. Comparison of these cases and earlier bioeffects studies using pulsed, focused ultrasound leads to the conclusion that damage to murine kidneys is not simply correlated with peak positive pressure or peak negative pressure, nor is spectral content of the wave able to explain the striking differences in damage from these sources. With 200 individual shock waves from the piezoelectric lithotripter applied ventrally, 20–30% of the animals suffered superficial kidney damage (bleeding into the capsule), but the same exposure conditions produced severe intestinal hemorrhage in more than 80% of the animals.