Task-oriented comparison of power spectral density estimation methods for quantifying acoustic attenuation in diagnostic ultrasound using a reference phantom method

Inter- and Intra-Operator Variability of Regularized Backscatter Quantitative Ultrasound for the Characterization of Breast Masses

OBJECTIVES

Here we report on the intra- and inter-operator variability of the backscatter coefficient (BSC) estimated with a new low-variance quantitative ultrasound (QUS) approach applied to breast lesions in vivo.

METHODS

Radiofrequency (RF) echo signals were acquired from 29 BIRADS 4 and 5 breast lesions in 2 sequential cohorts following 2 imaging protocols: cohort 1) radial and antiradial views, and cohort 2) short- and long-axis views. Protocol 2 was implemented after retraining and discussion on how to improve reproducibility. Each patient was scanned by at least 2 of 3 radiologists; each performed 3 acquisitions with transducer and patient repositioning in between acquisitions. BSC was estimated using a low-variance QUS approach based on regularization. Intra- and inter-operator variability of the intra-lesion median BSC was evaluated with a multifactorial ANOVA test (P-values) and the intraclass correlation coefficient (ICC).

RESULTS

Inter-operator variability was only significant in the first protocol (P < .007); ICCinter  = .77 (95% CI .71-.82), indicating good inter-operator agreement. In the second protocol, the inter-operator variability was not significant (P > .05) and agreement was excellent (ICCinter  = .92 [.89-.94]). In both protocols, the intra-operator variability was not significant.

CONCLUSIONS

Our findings demonstrate the need for standardizing image acquisition protocols for backscatter-based QUS to reduce inter-operator variability and ensure its successful translation to the characterization of suspicious breast masses.

A Geometric Model of Ultrasound Backscatter to Describe Microstructural Anisotropy of Tissue

Methods to assess ultrasound backscatter anisotropy from clinical array transducers have recently been developed. However, they do not provide information about the anisotropy of microstructural features of the specimens. This work develops a simple geometric model, referred to as the secant model, of backscatter coefficient anisotropy. Specifically, we evaluate anisotropy of the frequency dependence of the backscatter coefficient parameterized in terms of effective scatterer size. We assess the model in phantoms with known scattering sources and in a skeletal muscle, a well-known anisotropic tissue. We demonstrate that the secant model can determine the orientation of the anisotropic scatterers, as well as accurately determining effective scatterer sizes, and it may classify isotropic versus anisotropic scatterers. The secant model may find utility in monitoring disease progression as well as characterizing normal tissue architectures.

Recent Advances in Attenuation Estimation

This chapter reviews some of the recent advances in the estimation of the local and the total attenuation, with an emphasis on reducing the bias and variance of the estimates. A special focus is put on describing the effect of power spectrum estimation on bias and variance, the introduction of regularization strategies, as well as on eliminating the need to use reference phantoms for compensating for system dependent effects.

Regularized Ultrasound Phantom-Free Local Attenuation Coefficient Slope (ACS) Imaging in Homogeneous and Heterogeneous Tissues

Attenuation maps or measurements based on the local attenuation coefficient slope (ACS) in quantitative ultrasound (QUS) have shown potential for the diagnosis of liver steatosis. In liver cancers, tissue abnormalities and tumors detected using ACS are also of interest to provide new image contrast to clinicians. Current phantom-based approaches have the limitation of assuming a comparable speed of sound between the reference phantom and insonified tissues. Moreover, these methods present the inconvenience for operators to acquire data on phantoms and patients. The main goal was to alleviate these drawbacks by proposing a methodology for constructing phantom-free regularized (PF-R) local ACS maps and investigate the performance in both homogeneous and heterogeneous media. The proposed method was tested on two tissue-mimicking media with different ACS constructed as homogeneous phantoms, side-by-side and top-to-bottom phantoms, and inclusion phantoms with different attenuations. Moreover, an in vivo proof-of-concept was performed on healthy, steatotic, and cancerous human liver datasets. Modifications brought to previous works include: 1) a linear interpolation of the power spectrum in the log scale; 2) the relaxation of the underlying hypothesis on the diffraction factor; 3) a generalization to nonhomogeneous local ACS; and 4) an adaptive restriction of frequencies to a more reliable range than the usable frequency range. Regularization was formulated as a generalized least absolute shrinkage and selection operator (LASSO), and a variant of the Bayesian information criterion (BIC) was applied to estimate the Lagrangian multiplier on the LASSO constraint. In addition, we evaluated the proposed algorithm when applying median filtering before and after regularization. Tests conducted showed that the PF-R yielded robust results in all tested conditions, suggesting potential for additional validation as a diagnosis method.

A multiparametric volumetric quantitative ultrasound imaging technique for soft tissue characterization

Quantitative ultrasound (QUS) offers a non-invasive and objective way to quantify tissue health. We recently presented a spatially adaptive regularization method for reconstruction of a single QUS parameter, limited to a two dimensional region. That proof-of-concept study showed that regularization using homogeneity prior improves the fundamental precision-resolution trade-off in QUS estimation. Based on the weighted regularization scheme, we now present a multiparametric 3D weighted QUS (3D QUS) method, involving the reconstruction of three QUS parameters: attenuation coefficient estimate (ACE), integrated backscatter coefficient (IBC) and effective scatterer diameter (ESD). With the phantom studies, we demonstrate that our proposed method accurately reconstructs QUS parameters, resulting in high reconstruction contrast and therefore improved diagnostic utility. Additionally, the proposed method offers the ability to analyze the spatial distribution of QUS parameters in 3D, which allows for superior tissue characterization. We apply a three-dimensional total variation regularization method for the volumetric QUS reconstruction. The 3D regularization involving N planes results in a high QUS estimation precision, with an improvement of standard deviation over the theoretical 1/N rate achievable by compounding N independent realizations. In the in vivo liver study, we demonstrate the advantage of adopting a multiparametric approach over the single parametric counterpart, where a simple quadratic discriminant classifier using feature combination of three QUS parameters was able to attain a perfect classification performance to distinguish between normal and fatty liver cases.

Quantitative ultrasound imaging of soft biological tissues: a primer for radiologists and medical physicists

Quantitative ultrasound (QUS) aims at quantifying interactions between ultrasound and biological tissues. QUS techniques extract fundamental physical properties of tissues based on interactions between ultrasound waves and tissue microstructure. These techniques provide quantitative information on sub-resolution properties that are not visible on grayscale (B-mode) imaging. Quantitative data may be represented either as a global measurement or as parametric maps overlaid on B-mode images. Recently, major ultrasound manufacturers have released speed of sound, attenuation, and backscatter packages for tissue characterization and imaging. Established and emerging clinical applications are currently limited and include liver fibrosis staging, liver steatosis grading, and breast cancer characterization. On the other hand, most biological tissues have been studied using experimental QUS methods, and quantitative datasets are available in the literature. This educational review addresses the general topic of biological soft tissue characterization using QUS, with a focus on disseminating technical concepts for clinicians and specialized QUS materials for medical physicists. Advanced but simplified technical descriptions are also provided in separate subsections identified as such. To understand QUS methods, this article reviews types of ultrasound waves, basic concepts of ultrasound wave propagation, ultrasound image formation, point spread function, constructive and destructive wave interferences, radiofrequency data processing, and a summary of different imaging modes. For each major QUS technique, topics include: concept, illustrations, clinical examples, pitfalls, and future directions.

Analytic Global Regularized Backscatter Quantitative Ultrasound

Although a variety of techniques have been developed to reduce the appearance of B-mode speckle, quantitative ultrasound (QUS) aims at extracting the hidden properties of the tissue. Herein, we propose two novel techniques to accurately and precisely estimate two important QUS parameters, namely, the average attenuation coefficient and the backscatter coefficient. Both the techniques optimize a cost function that incorporates data and continuity constraint terms, which we call AnaLytical Global rEgularized BackscatteR quAntitative ultrasound (ALGEBRA). We propose two versions of ALGEBRA, namely, 1-D- and 2-D-ALGEBRA. In 1-D-ALGEBRA, the regularized cost function is formulated in the axial direction, and the QUS parameters are calculated for one line of radio frequency (RF) echo data. In 2-D-ALGEBRA, the regularized cost function is formulated for the entire image, and the QUS parameters throughout the image are estimated simultaneously. This simultaneous optimization allows 2-D-ALGEBRA to "see" all the data before estimating the QUS parameters. In both the methods, we efficiently optimize the cost functions by casting it as a sparse linear system of equations. As a result of this efficient optimization, 1-D-ALGEBRA and 2-D-ALGEBRA are, respectively, 600 and 300 times faster than optimization using the dynamic programming (DP) method previously proposed by our group. In addition, the proposed technique has fewer input parameters that require manual tuning. Our results demonstrate that the proposed ALGEBRA methods substantially outperform least-square and DP methods in estimating the QUS parameters in phantom experiments.

Correlation length ratio as a parameter for determination of fiber-like structures in soft tissues

Quantitative ultrasound methods can provide valuable information about the microstructure of a material or tissue. This works well when the common assumptions of homogeneity, isotropy, and diffuse scattering conditions are valid. In biological tissues, however, these assumptions are often violated because the microstructure of biological tissues is often heterogeneous and anisotropic. The microstructure of biological tissues can change with disease, and therefore accurate identification and description of a tissue's microstructure can offer important clinical insight. To address the challenge of evaluating the microstructure of biological tissues, here we introduce a novel parameter called the correlation length ratio (CLR), a ratio of lateral to axial correlation lengths for backscattered echo signals. We developed it to determine the presence of fiber-like structures in soft tissues by comparing this value in tissue to a threshold determined from a reference material that is homogeneous, isotropic, and provides diffuse scattering. We tested this novel parameter in phantoms with spherical scattering sources, in an anisotropic phantom (containing elongated fibers), and in human biceps muscle. We found that the CLR accurately detected the presence of elongated structures in both the anisotropic phantom and muscle. These results encourage further exploration of this novel parameter in microstructurally complex tissues.

Challenges of conducting quantitative ultrasound with a multimodal optical imaging system

High-frequency quantitative ultrasound is a potential non-invasive source of imaging cell-tissue scale biomarkers for major diseases such as heart disease, cancer, and preterm birth. However, one of the barriers to developing such biomarkers is that it is labor-intensive to compare quantitative ultrasound images to optical images of the tissue structure. We have previously developed a multiscale imaging system that can obtain registered qualitative ultrasound and optical images, but there are further technical challenges to obtaining quantitative data: System-specific details of obtaining and processing data with Verasonics high-frequency transducers; the need for high-frequency reference phantoms; and off-axis clutter from imaging above a glass coverslip. This paper provides a characterization of the Verasonics ultrasound system with the 18.5 MHz L22-14v and 28.5 MHz L38-22v transducers, describes the construction of high-frequency reference phantoms, and details methods for reducing off-axis clutter. The paper features a demonstration multiscale image of a wild type mouse mammary gland that incorporates quantitative ultrasound with both transducers and second harmonic generation microscopy. These advances demonstrate a way to obtain, on a single system with a cohesive and integrated pipeline, quantitative ultrasound data that is correlated with optical imaging without the need for extensive sample preparation.

Attenuation Coefficient Parameter Computations for Tissue Composition Assessment of Carotid Atherosclerotic Plaque in Vivo

Quantitative ultrasound has been used to assess carotid plaque tissue composition. Here, we compute the attenuation coefficient (AC) in vivo with the optimum power spectral shift estimator (OPSSE) and reference phantom method (RPM), extract AC parameters and form parametric maps. Differences between OPSSE and RPM AC parameters are computed. Relationships between AC parameters, surgical scores and histopathology assessments are examined. Kendall's τ correlations between OPSSE AC and surgical scores are significant, including those between cholesterol and Standard Deviation (adjusted p = 0.038); thrombus and Minimum (adjusted p = 0.002), Maximum (adjusted p = 0.021) and Standard Deviation (adjusted p = 0.001); ulceration and Average (adjusted p = 0.033), Median (unadjusted p = 0.013), Maximum (unadjusted p = 0.039) and Mode (adjusted p = 0.009). The strongest correlations with histopathology are percentage cholesterol and Median OPSSE (unadjusted p = 0.007); percentage hemorrhage and Minimum OPSSE (adjusted p < 0.001); hemosiderin score and Median OPSSE (adjusted p = 0.010); and percentage calcium and Percentage Non-physical RPM Pixels (unadjusted p = 0.014). Kruskal-Wallis H and Dunn's post hoc tests have the ability to distinguish between groups (p < 0.05). Results suggest AC parameters may assist in vivo evaluation of carotid plaque vulnerability.

Quantitative Ultrasound Detects Smooth Muscle Activity at the Cervical Internal Os in Vitro

The cervix has two biomechanical functions: to remain closed while the fetus develops throughout pregnancy, and to open for delivery of the fetus at full term. This dual function is principally attributed to collagen within the extracellular matrix (ECM). However, recent evidence suggests that other ECM, and non-ECM, components play a role as well. One component is smooth muscle cells arranged circumferentially near the internal os. In this study, we investigate correlations between cervical smooth muscle cell force generation and the effective scatterer diameter (ESD), a quantitative ultrasound parameter directly related to the acoustic impedance distribution and, therefore, a potential biomarker of muscle contractility. Using whole cervical slices (N = 5), we determined significant positive correlations (quantified with Pearson's r) between muscle force generation and ESD immediately after administration of oxytocin (median r = 0.90). In summary, the ESD may prove a useful biomarker for studying structure and function of cervical smooth muscle in vivo.

Modeling ultrasound attenuation in porous structures with mono-disperse random pore distributions using the independent scattering approximation: a 2D simulation study

The validity of the independent scattering approximation (ISA) to predict the frequency dependent attenuation in 2D models of simplified structures of cortical bone is studied. Attenuation of plane waves at central frequencies ranging from 1 to 8 MHz propagating in structures with mono-disperse random pore distributions with pore diameter and pore density in the range of those of cortical bone are evaluated by finite difference time domain numerical simulations. An approach to assess the multiple scattering of waves in random media is discussed to determine the pore diameter ranges at which the ISA is applicable. A modified version of the ISA is proposed to more accurately predict the attenuation in porosity ranges where it would traditionally fail. The results show that the modified ISA can model the frequency-dependent attenuation of ultrasonic wave with pore diameter and density ranges comparable to those of cortical bone.

A Quantitative Ultrasound-Based Multi-Parameter Classifier for Breast Masses

This manuscript reports preliminary results obtained by combining estimates of two or three (among seven) quantitative ultrasound (QUS) parameters in a model-free, multi-parameter classifier to differentiate breast carcinomas from fibroadenomas (the most common benign solid tumor). Forty-three patients scheduled for core biopsy of a suspicious breast mass were recruited. Radiofrequency echo signal data were acquired using clinical breast ultrasound systems equipped with linear array transducers. The reference phantom method was used to obtain system-independent estimates of the specific attenuation (ATT), the average backscatter coefficients, the effective scatterer diameter (ESD) and an effective scatterer diameter heterogeneity index (ESDHI) over regions of interest within each mass. In addition, the envelope amplitude signal-to-noise ratio (SNR), the Nakagami shape parameter, m, and the maximum collapsed average (maxCA) of the generalized spectrum were also computed. Classification was performed using the minimum Mahalanobis distance to the centroids of the training classes and tested against biopsy results. Classification performance was evaluated with the area under the receiver operating characteristic (ROC) curve. The best performance with a two-parameter classifier used the ESD and ESDHI and resulted in an area under the ROC curve of 0.98 (95% confidence interval [CI]: 0.95-1.00). Classification performance improved with three parameters (ATT, ESD and ESDHI) yielding an area under the ROC curve of 0.999 (0.995-1.000). These results suggest that system-independent QUS parameters, when combined in a model-free classifier, are a promising tool to characterize breast tumors. A larger study is needed to further test this idea.

Quantitative Ultrasound Parameters Based on the Backscattered Echo Power Signal as Biomarkers of Cervical Remodeling: A Longitudinal Study in the Pregnant Rhesus Macaque

Clinical prediction and especially prevention of abnormal birth timing, particularly pre-term, is poor. The cervix plays a key role in birth timing; it first serves as a rigid barrier to protect the developing fetus, then becomes the pathway to delivery of that fetus. Imaging biomarkers to define this remodeling process could provide insights to improve prediction of birth timing and elucidate novel targets for preventive therapies. Quantitative ultrasound (QUS) approaches that appear promising for this purpose include shear wave speed (SWS) estimation to quantify softness, as well as parameters based on backscattered power, such as the mean backscattered power difference (mBSPD) and specific attenuation coefficient (SAC), to quantify the organization of tissue microstructure. Invasive studies in rodents demonstrated that as pregnancy advances, cervical microstructure disorganizes as tissue softness and compliance increase. Our non-invasive studies in pregnant women and rhesus macaques suggested that QUS can detect these microstructural changes in vivo. Our previous study in the same cohort showed a progressive decline in SWS during pregnancy, consistent with increasing tissue softness, and we hypothesized that backscatter parameters would also decrease, consistent with increasing microstructural disorganization. In this study, we analyzed the mBSPD and SAC in the cervices of rhesus macaques (n = 18). We found that both mBSPD and SAC decreased throughout pregnancy (p < 0.001 for both parameters) and that the former appears to be a more reliable biomarker. In summary, biomarkers that can characterize tissue microstructural organization are promising for comprehensive characterization of cervical remodeling in pregnancy.

Attenuation Coefficient Estimation of Normal Placentas

Attenuation coefficient estimation has the potential to be a useful tool for placental tissue characterization. A current challenge is the presence of inhomogeneities in biological tissue that result in a large variance in the attenuation coefficient estimate (ACE), restricting its clinical utility. In this work, we propose a new Attenuation Estimation Region Of Interest (AEROI) selection method for computing the ACE based on the (i) envelope signal-to-noise ratio deviation and (ii) coefficient of variation of the transmit pulse bandwidth. The method was first validated on a tissue-mimicking phantom, for which an 18%-21% reduction in the standard deviation of ACE and a 14%-24% reduction in the ACE error, expressed as a percentage of reported ACE, were obtained. A study on 59 post-delivery clinically normal placentas was then performed. The proposed AEROI selection method reduced the intra-subject standard deviation of ACE from 0.72 to 0.39 dB/cm/MHz. The measured ACE of 59 placentas was 0.77 ± 0.37 dB/cm/MHz, which establishes a baseline for future studies on placental tissue characterization.

Quantitative ultrasound and apoptotic death in the neonatal primate brain

Apoptosis is triggered in the developing mammalian brain by sedative, anesthetic or antiepileptic drugs during late gestation and early life. Whether human children are vulnerable to this toxicity mechanism remains unknown, as there are no imaging techniques to capture it. Apoptosis is characterized by distinct structural features, which affect the way damaged tissue scatters ultrasound compared to healthy tissue. We evaluated whether apoptosis, triggered by the anesthetic sevoflurane in the brains of neonatal rhesus macaques, can be detected using quantitative ultrasound (QUS). Neonatal (n = 15) rhesus macaques underwent 5 h of sevoflurane anesthesia. QUS images were obtained through the sagittal suture at 0.5 and 6 h. Brains were collected at 8 h and examined immunohistochemically to analyze apoptotic neuronal and oligodendroglial death. Significant apoptosis was detected in white and gray matter throughout the brain, including the thalamus. We measured a change in the effective scatterer size (ESS), a QUS biomarker derived from ultrasound echo signals obtained with clinical scanners, after sevoflurane-anesthesia in the thalamus. Although initial inclusion of all measurements did not reveal a significant correlation, when outliers were excluded, the change in the ESS between the pre- and post-anesthesia measurements correlated strongly and proportionally with the severity of apoptotic death. We report for the first time in vivo changes in QUS parameters, which may reflect severity of apoptosis in the brains of infant nonhuman primates. These findings suggest that QUS may enable in vivo studies of apoptosis in the brains of human infants following exposure to anesthetics, antiepileptics and other brain injury mechanisms.

Quantitative Ultrasound Biomarkers Based on Backscattered Acoustic Power: Potential for Quantifying Remodeling of the Human Cervix during Pregnancy

As pregnancy progresses, the cervix remodels from a rigid structure to one pliable enough to allow delivery of a fetus, a process that involves progressive disorganization of cervical microstructure. Quantitative ultrasound biomarkers that may detect this process include those derived from the backscattered echo signal, namely, acoustic attenuation and backscattered power loss. We recently reported that attenuation and backscattered power loss are affected by tissue anisotropy and heterogeneity in the ex vivo cervix. In this study, we compared attenuation and backscattered power difference in a group of women in early pregnancy (first trimester) with those in a group in late pregnancy (third trimester). We observed a significant decrease in the backscattered power difference in late as compared with early pregnancy, suggesting decreased microstructural organization in late pregnancy, a finding that is consistent with animal models of cervical remodeling. In contrast, we found no difference in attenuation between the time points. These results suggest that the backscattered power difference, but perhaps not attenuation, may be a useful clinical biomarker of cervical remodeling.

Multiparametric QUS Analysis for Placental Tissue Characterization

Multiparametric Quantitative Ultrasound (QUS) holds promise for characterizing placental tissue and detecting placental disorders. In this study, we simultaneously extract two qualitatively different QUS parameters, namely attenuation coefficient estimate (ACE) and shear wave speed from ultrasound radio frequency data acquired using a shear wave vibro elastography (SWAVE) method. The study comprised data from 59 post-delivery clinically normal placentas. The shear wave speed was found to be equal to 1.74 ± 0.13 m/s whereas the attenuation coefficient estimate was 0.57 ± 0.48 dB/cm-MHz. This provides a baseline for future studies of placental disorders.

Power Spectrum Consistency among Systems and Transducers

Use of the reference phantom method for computing acoustic attenuation and backscatter is widespread. However, clinical application of these methods has been limited by the need to acquire reference phantom data. We determined that the data acquired from 11 transducers of the same model and five clinical ultrasound systems of the same model produce equivalent estimates of reference phantom power spectra. We describe that the contribution to power spectral density variance among systems and transducers equals that from speckle variance with 59 uncorrelated echo signals. Thus, when the number of uncorrelated lines of data is small, speckle variance will dominate the power spectral density estimate variance introduced by different systems and transducers. These results suggest that, at least for this particular transducer and imaging system combination, one set of reference phantom calibration data is highly representative of the average among equivalent transducers and systems that are in good working order.

Low Variance Estimation of Backscatter Quantitative Ultrasound Parameters Using Dynamic Programming

One of the main limitations of ultrasound imaging is that image quality and interpretation depend on the skill of the user and the experience of the clinician. Quantitative ultrasound (QUS) methods provide objective, system-independent estimates of tissue properties, such as acoustic attenuation and backscattering properties of tissue, which are valuable as objective tools for both diagnosis and intervention. Accurate and precise estimation of these properties requires correct compensation for intervening tissue attenuation. Prior attempts to estimate intervening-tissue attenuation based on minimizing cost functions that compared backscattered echo data to models have resulted in limited precision and accuracy. To overcome these limitations, in this paper, we incorporate the prior information of piecewise continuity of QUS parameters as a regularization term into our cost function. We further propose to calculate this cost function using dynamic programming (DP), a computationally efficient optimization algorithm that finds the global optimum. Our results on tissue-mimicking phantoms show that DP substantially outperforms a published least squares method in terms of both estimation bias and variance.

Anisotropy and Spatial Heterogeneity in Quantitative Ultrasound Parameters: Relevance to the Study of the Human Cervix

Imaging biomarkers based on quantitative ultrasound can offer valuable information about properties that inform tissue function and behavior such as microstructural organization (e.g., collagen alignment) and viscoelasticity (i.e., compliance). For example, the cervix feels softer as its microstructure remodels during pregnancy, an increase in compliance that can be objectively quantified with shear wave speed and therefore shear wave speed estimation is a potential biomarker of cervical remodeling. Other proposed biomarkers include parameters derived from the backscattered echo signal, such as attenuation and backscattered power loss, because such parameters can provide insight into tissue microstructural alignment and organization. Of these, attenuation values for the pregnant cervix have been reported, but large estimate variance reduces their clinical value. That said, parameter estimates based on the backscattered echo signal may be incorrect if assumptions they rely on, such as tissue isotropy and homogeneity, are violated. For that reason, we explored backscatter and attenuation parameters as potential biomarkers of cervical remodeling via careful investigation of the assumptions of isotropy and homogeneity in cervical tissue. Specifically, we estimated the angle- and spatial-dependence of parameters of backscattered power and acoustic attenuation in the ex vivo human cervix, using the reference phantom method and electronic steering of the ultrasound beam. We found that estimates are anisotropic and spatially heterogeneous, presumably because the tissue itself is anisotropic and heterogeneous. We conclude that appropriate interpretation of imaging biomarkers of cervical remodeling must account for tissue anisotropy and heterogeneity.

Quantifying Backscatter Anisotropy Using the Reference Phantom Method

Acoustic properties can be exploited to infer and evaluate tissue microstructure. However, common assumptions are that the medium of interest is homogeneous and isotropic, and that its underlying physical properties cause diffuse scattering. In this paper, we describe how we developed and tested novel parameters designed to address isotropy/anisotropy in backscattered echo signal power in complex biological tissues. Specifically, we explored isotropy/anisotropy in backscattered power in isotropic phantoms (spherical glass beads), an anisotropic phantom (dialysis phantom with rodlike fibers), and an in vivo human tissue with well-described anisotropy (bicep muscle). Our approach uses the reference phantom method to compensate for system transfer and diffraction losses when electronically beamsteering a linear array transducer. We define three parameters to quantify the presence and orientation of anisotropic scatterers, as well as address magnitude of anisotropy. We found that these parameters can detect and sense the degree of anisotropy in backscatter in both phantoms and bicep muscle. Bias of the summary anisotropy parameters, induced through a speed of sound mismatch of sample media and reference phantom, was less than 0.2 dB if the speed of sound was within ±20 m/s of the sample media. In summary, these new parameters may be useful for testing the assumption of isotropy as well as providing more detailed information about the underlying microstructural sources of backscatter in complex biological tissues.

Analysis of Coherent and Diffuse Scattering Using a Reference Phantom

The estimation of many spectral-based quantitative ultrasound parameters assumes that backscattered echo signals are from a stationary, incoherent scattering process. The accuracy of these assumptions in real tissue can limit the diagnostic value of these parameters and the physical insight about tissue microstructure they can convey. This work presents an empirical decision test to determine the presence of significant coherent contributions to echo signals and whether they are caused by low scatterer number densities or the presence of specular reflectors or scatterers with periodic spacing. This is achieved by computing parameters from echo signals that quantify stationary or nonstationary features related to coherent scattering, and then comparing their values to thresholds determined from a reference material providing diffuse scattering. The paper first presents a number of parameters with demonstrated sensitivity to coherent scattering and describes criteria to select those with the highest sensitivity using simulated and phantom-based echo data. Results showed that the echo amplitude signal-to-noise ratio and the multitaper-generalized spectrum were the parameters with the highest sensitivity to coherent scattering with stationary and nonstationary features, respectively. These parameters were incorporated into the reference-based decision test, which successfully identified regions in simulated and tissue-mimicking phantoms with different incoherent and coherent scattering conditions. When scatterers with periodic organization were detected, the combination of stationary and nonstationary analysis permitted the estimation of the mean spacing below and above the resolution limit imposed by the pulse size. Preliminary applications of this algorithm to human cervical tissue ex vivo showed correspondence between regions of B-mode images showing bright reflectors, tissue interfaces, and hypoechoic regions with regions classified as specular reflectors and low scatterer number density. These results encourage further application of the algorithm to more structurally complex phantoms and tissue.

Optimum Diffraction-Corrected Frequency-Shift Estimator of the Ultrasonic Attenuation Coefficient

The ultrasonic attenuation coefficient is an important parameter that has been studied extensively in Quantitative Ultrasound and Tissue Characterization. There are various methods described in the literature that estimate this parameter by measuring either spectral difference (i.e., decay) or spectral shift of the backscattered echo signal. Under ideal conditions, i.e., in the absence of abrupt changes in tissue backscattering, Spectral Difference methods can produce estimates with high accuracy and precision. On the other hand, diffraction-corrected Spectral Shift methods (e.g., the Hybrid method) are better suited for application in practical settings using clinical ultrasound scanners. However, current Spectral Shift methods use inefficient frequency shift estimators that ultimately degrade the quality of attenuation coefficient estimates. In this paper, a probabilistic model of the backscattered radiofrequency (RF) echo is used to derive the Cramér-Rao lower bound (CRLB) on estimation variance of the spectral centroid. Next, an efficient correlation-based shift estimator is presented that achieves the CRLB. Used in conjunction with a well-characterized reference phantom to correct for diffraction and other system-related effects, this estimator greatly improves the accuracy and precision of Spectral- Shift attenuation estimation. A theoretical analysis of this method is provided, and its performance is quantitatively compared with that of the Hybrid method using simulated and experimental phantom studies. A minimum of 3-fold reduction in the standard deviation of attenuation coefficient estimates is observed using the new method.

Review of Quantitative Ultrasound: Envelope Statistics and Backscatter Coefficient Imaging and Contributions to Diagnostic Ultrasound

Conventional medical imaging technologies, including ultrasound, have continued to improve over the years. For example, in oncology, medical imaging is characterized by high sensitivity, i.e., the ability to detect anomalous tissue features, but the ability to classify these tissue features from images often lacks specificity. As a result, a large number of biopsies of tissues with suspicious image findings are performed each year with a vast majority of these biopsies resulting in a negative finding. To improve specificity of cancer imaging, quantitative imaging techniques can play an important role. Conventional ultrasound B-mode imaging is mainly qualitative in nature. However, quantitative ultrasound (QUS) imaging can provide specific numbers related to tissue features that can increase the specificity of image findings leading to improvements in diagnostic ultrasound. QUS imaging can encompass a wide variety of techniques including spectral-based parameterization, elastography, shear wave imaging, flow estimation, and envelope statistics. Currently, spectral-based parameterization and envelope statistics are not available on most conventional clinical ultrasound machines. However, in recent years, QUS techniques involving spectral-based parameterization and envelope statistics have demonstrated success in many applications, providing additional diagnostic capabilities. Spectral-based techniques include the estimation of the backscatter coefficient (BSC), estimation of attenuation, and estimation of scatterer properties such as the correlation length associated with an effective scatterer diameter (ESD) and the effective acoustic concentration (EAC) of scatterers. Envelope statistics include the estimation of the number density of scatterers and quantification of coherent to incoherent signals produced from the tissue. Challenges for clinical application include correctly accounting for attenuation effects and transmission losses and implementation of QUS on clinical devices. Successful clinical and preclinical applications demonstrating the ability of QUS to improve medical diagnostics include characterization of the myocardium during the cardiac cycle, cancer detection, classification of solid tumors and lymph nodes, detection and quantification of fatty liver disease, and monitoring and assessment of therapy.

Acoustic Properties of Breast Fat

OBJECTIVES

The American College of Radiology Breast Imaging Reporting and Data System (BI-RADS) atlas for ultrasound (US) qualitatively describes the echogenicity and attenuation of a mass, where fat lobules serve as a standard for comparison. This study aimed to estimate acoustic properties of breast fat under clinical imaging conditions to determine the degree to which properties vary among patients.

METHODS

Twenty-four women with solid breast masses scheduled for biopsy were scanned with a Siemens S2000 scanner and 18L6 linear array transducer (Siemens Medical Solutions, Malvern, PA). Offline analysis estimated the attenuation coefficient and backscatter coefficients (BSCs) from breast fat using the reference phantom method. The average BSC was calculated over 6 to 12 MHz to objectively quantify the BI-RADS US echo pattern descriptor, and effective scatterer diameters were also estimated.

RESULTS

A power law fit to the attenuation coefficient versus frequency yielded an attenuation coefficient of 1.28 dB·cm(-1) MHz(-0.73). The mean attenuation coefficient versus frequency slope ± SD at 7 MHz was 0.73 ± 0.23 dB·cm(-1) MHz(-1), in agreement with previously reported values. The BSC versus frequency showed close agreement among all patients, both in magnitude and frequency dependence, with a power law fit of (0.6 ± 0.25) ×10(-4) sr(-1) cm(-1) MHz(-2.49). The average backscatter in the 6-12-MHz range was 0.004 ± 0.002 sr(-1) cm(-1). The mean effective scatterer diameter for fat was 60.2 ± 9.5 μm.

CONCLUSIONS

The agreement in parameter estimates for breast fat among these patients supports the use of fat as a standard for comparison with tumors. Results also suggest that objective quantification of these BI-RADS US descriptors may reduce subjectivity when interpreting B-mode image data.

Effective scatterer diameter estimates for broad scatterer size distributions

Acoustic form factors have been used to model the frequency dependence of acoustic scattering in phantoms and tissues. This work demonstrates that a broad range of scatterer sizes, individually well represented by Faran theory or a Gaussian form factor, is not accurately described by a single effective scatterer from either of these models. Contributions from a distribution of discrete scatterer sizes for two different form factor functions (Gaussian form factors and scattering functions from Faran's theory) were calculated and linearly combined. Composite form factors created from Gaussian distributions of scatterer sizes centered at 50 µm with standard deviations of up to σ = 40 µm were fit to each scattering model between 2 and 12 MHz. Scatterer distributions were generated using one of two assumptions: the number density of the scatterer diameter distribution was Gaussian distributed, or the volume fraction of each scatterer diameter in the distribution was Gaussian distributed. Each simulated form factor was fit to a single-diameter form factor model for Gaussian and exponential form factors. The mean-squared error (MSE) between the composite simulated data and the best-fit single-diameter model was smaller with an exponential form factor model, compared with a Gaussian model, for distributions with standard deviations larger than 30% of the centroid value. In addition, exponential models were shown to have better ability to distinguish between Faran scattering model-based distributions with varying center diameters than the Gaussian form factor model. The evidence suggests that when little is known about the scattering medium, an exponential scattering model provides a better first approximation to the scattering correlation function for a broad distribution of spherically symmetric scatterers than when a Gaussian form factor model is assumed.

Scatterer number density considerations in reference phantom-based attenuation estimation

Attenuation estimation and imaging have the potential to be a valuable tool for tissue characterization, particularly for indicating the extent of thermal ablation therapy in the liver. Often the performance of attenuation estimation algorithms is characterized with numerical simulations or tissue-mimicking phantoms containing a high scatterer number density (SND). This ensures an ultrasound signal with a Rayleigh distributed envelope and a signal-to-noise ratio (SNR) approaching 1.91. However, biological tissue often fails to exhibit Rayleigh scattering statistics. For example, across 1647 regions of interest in five ex vivo bovine livers, we obtained an envelope SNR of 1.10 ± 0.12 when the tissue was imaged with the VFX 9L4 linear array transducer at a center frequency of 6.0 MHz on a Siemens S2000 scanner. In this article, we examine attenuation estimation in numerical phantoms, tissue-mimicking phantoms with variable SNDs and ex vivo bovine liver before and after thermal coagulation. We find that reference phantom-based attenuation estimation is robust to small deviations from Rayleigh statistics. However, in tissue with low SNDs, large deviations in envelope SNR from 1.91 lead to subsequently large increases in attenuation estimation variance. At the same time, low SND is not found to be a significant source of bias in the attenuation estimate. For example, we find that the standard deviation of attenuation slope estimates increases from 0.07 to 0.25 dB/cm-MHz as the envelope SNR decreases from 1.78 to 1.01 when estimating attenuation slope in tissue-mimicking phantoms with a large estimation kernel size (16 mm axially × 15 mm laterally). Meanwhile, the bias in the attenuation slope estimates is found to be negligible (<0.01 dB/cm-MHz). We also compare results obtained with reference phantom-based attenuation estimates in ex vivo bovine liver and thermally coagulated bovine liver.