Mean Scatterer Spacing Estimation Research Articles

Scatterer spacing based on Gabor atoms matched from harmonic ultrasound echoes to improve assessment of microwave‐induced thermal lesions

AbstractBackgroundMicrowave ablation (MWA) is a minimally invasive alternative for the treatment of unresectable liver tumors. To verify the effectiveness and safety of MWA, it is critical to measure the temperature variation and assess the regions of the microwave‐induced thermal lesions.PurposeRecent studies have indicated that the locations of optimally matched Gabor atoms (LOMGA) from ultrasound radiofrequency (RF) echo signals allow accurate and stable scatterer spacing estimation. Herein, a harmonic‐based LOMGA method is proposed to estimate the scatterer spacing for improving the assessment of microwave‐induced thermal lesions.MethodsThe mean scatterer spacing (MSS) is estimated via the LOMGA method incorporating the selection of concise atoms from separated second‐harmonic RF echo signals with the pulse‐inversion algorithm for thermal lesion evaluation. In vitro experiments, 10 fresh porcine liver samples were ablated at different time nodes during the ablation period, and 200 sets of second‐harmonic and fundamental RF echo signals were randomly selected from the regions of interest in the coagulated liver samples for MSS estimation. The means and standard deviations of the MSSs, as well as the linear regression for the mean MSSs, were calculated from fundamental and second‐harmonic signals for comparison and evaluation, the receiver operating characteristic (ROC) curves for the 200 sets of fundamental‐based and harmonic‐based MSS estimates from the 10 liver samples at five pairs of adjacent time nodes were calculated, and one‐way analysis of variance (ANOVA) tests were performed for the five pairs of adjacent time nodes. The fundamental and harmonic‐based p‐values in the ANOVA tests and the areas under the ROC curves (AUCs) were calculated to statistically analyze the differences in the MSSs between adjacent time nodes.ResultsThe harmonic‐based increments in the intensity variation and coherent components were larger than the fundamental‐based increments with the increasing ablation time. The harmonic‐based MSSs from the 10 liver samples at five pairs of adjacent time nodes were found to be highly statistically significant (p < 0.01). Thus, the harmonic‐based MSSs had greater variations. Compared with the fundamental‐based results, for the five preset ST values, the average increment in the harmonic‐based mean slopes was 69.22% and the average decrement in the mean standard deviations was 11.67% for the linear‐fitting MSS results, and the results were statistically significant (p < 0.05).ConclusionHarmonic‐based MSSs are more sensitive and robust to variations in coagulated tissues, which is advantageous for the assessment of microwave‐induced thermal lesions.

The mean scatterer spacing estimation with the Gabor atoms selected based on the Nakagami distribution

Abstract Mean scatterer spacing (MSS) is a quantitative signature for disease diagnosis and tissue characterization. However, it is difficult to objectively extract the coherent components from the ultrasound RF echo signals to improve the accuracy performance of the MSS estimation. In the present study, a novel MSS estimation method with the matched Gabor atoms selected based on Nakagami parameters is proposed. Firstly, the ultrasound signals are decomposed into a series of Gabor atoms, and the envelopes of the residual signals are fitted with the Nakagami distribution. Then, the second order difference (SOD) of the shape parameters in Nakagami distribution is calculated to select the optimal atoms to match the coherent components. Finally, the locations of the selected Gabor atoms are used to estimate the MSS. In order to evaluate the performance of the proposed method, the simulated RF echo signals are modelled based on four regular degrees of the scatterer distributions, and then the optimally matched atoms are selected to estimate MSSs. The results based on simulated signals demonstrate that the propose method can provide accurate MSS estimation, which are advantageous for improving quantitative diagnosis of diseases and tissue characterization

Classification of breast lesions using quantitative ultrasound biomarkers

Quantitative ultrasound (QUS) parameters are gaining attention recently as non-invasive biomarkers for soft tissue characterization. In this work, we use two QUS parameters, namely effective scatterer diameter (ESD) and mean scatterer spacing (MSS), for binary classification of breast lesions. To produce improved classification results, we propose a modified frequency-domain technique for ESD estimation of breast tissues from the diffuse component of backscattered radio-frequency (RF) data. Ensemble empirical mode decomposition (EEMD) is performed to separate the diffuse component from the coherent component of the backscattered RF data. A non-parametric Kolmogorov–Smirnov (K-S) test is employed for automatic selection of the intrinsic mode functions (IMFs). A novel multi-step system effect minimization process is also used. The ESD is estimated using a novel nearest neighborhood average regression line fitting (NNARLF) algorithm. Furthermore, we use an ameliorated EEMD domain autoregressive (AR) spectral estimation technique for MSS estimation. On using the ESD for binary classification of 139 lesions, we obtain high sensitivity, specificity, accuracy values of 95.45%, 95.79%, and 95.68%, respectively. The area under the receiver operating characteristics (ROC) curve is 0.95. On combining ESD with MSS we obtain even more improved sensitivity, specificity, and accuracy values of 97.73%, 95.79%, and 96.40%, respectively. The area under the ROC also increases to 0.97. This high classification performance demonstrates the potential of the use of these QUS parameters as non-invasive biomarkers for breast cancer detection.

EEMD Domain AR Spectral Method for Mean Scatterer Spacing Estimation of Breast Tumors From Ultrasound Backscattered RF Data

We present a novel method for estimating the mean scatterer spacing (MSS) of breast tumors using ensemble empirical mode decomposition (EEMD) domain analysis of deconvolved backscattered radio frequency (RF) data. The autoregressive (AR) spectrum from which the MSS is estimated is obtained from the intrinsic mode functions (IMFs) due to regular scatterers embedded in RF data corrupted by the diffuse scatterers. The IMFs are chosen by giving priority to the presence of an enhanced fundamental harmonic and the presence of a greater number of higher harmonics in the AR spectrum estimated from the IMFs. The AR model order is chosen by minimizing the mean absolute percentage error (MAPE) criterion. In order to ensure that the backscattered data is indeed from a source of coherent scattering, we begin by performing a non-parametric Kolmogorov-Smirnov (K-S) classification test on the backscattered RF data. Deconvolution of the backscattered RF data, which have been classified by the K-S test as sources of significant coherent scattering, is done to reduce the system effect. EEMD domain analysis is then performed on the deconvolved data. The proposed method is able to recover the harmonics associated with the regular scatterers and overcomes many problems encountered while estimating the MSS from the AR spectrum of raw RF data. Using our technique, a mean absolute percentage error (MAPE) of 5.78% is obtained while estimating the MSS from simulated data, which is lower than that of the existing techniques. Our proposed method is shown to outperform the state of the art techniques, namely, singular spectrum analysis, generalized spectrum (GS), spectral autocorrelation (SAC), and modified SAC for different simulation conditions. The MSS for in vivo normal breast tissue is found to be 0.69 ± 0.04 mm; for benign and malignant tumors it is found to be 0.73 ± 0.03 and 0.79 ± 0.04 mm, respectively. The separation between the MSS values of normal and benign tissues for our proposed method is similar to the separations obtained for the conventional methods, but the separation between the MSS values for benign and malignant tissues for our proposed method is slightly higher than that for the conventional methods. When the MSS is used to classify breast tumors into benign and malignant, for a threshold-based classifier, the increase in specificity, accuracy, and area under curve are 18%, 19%, and 22%, respectively, and that for statistical classifiers are 9%, 13%, and 19%, respectively, from that of the next best existing technique.

A Review of Ultrasound Tissue Characterization with Mean Scatterer Spacing.

Tissues exhibiting quasi-periodic structures can be modeled as a collection of diffuse scatterers and coherent scatterers. The mean scatterer spacing (MSS) of coherent and quasi-periodic components is directly related to tissue microstructure and has become an important quantitative ultrasound (QUS) parameter in the characterization of quasi-periodic tissues. In this paper, a review of the literature on the development of MSS as a QUS parameter was conducted. First, a unified theoretical background of MSS estimates was provided. Then, the application of MSS estimates was summarized with respect to liver, spleen, breast, bone, muscle, and other tissues. MSS estimation techniques were applied to (a) the diagnosis of hepatitis, liver fibrosis and cirrhosis, and lesions in tissues such as liver, breast, and spleen; (b) the differentiation between benign and malignant breast tumors, and the grading of breast cancer; (c) the detection of cancellous bone; and (d) the monitoring of the efficacy of treatments such as thermal ablation, with various levels of success. Future developments were also discussed in terms of real-time implementation of MSS estimates, local MSS estimation, relationship of MSS to other QUS parameters, combination of MSS with other QUS parameters, in vivo validation of MSS estimates, MSS parametric imaging, and three-dimensional ultrasound tissue characterization.

Alterations in Ultrasound Scattering Following Thermal Ablation in ex vivo Bovine Liver.

Thermal ablation is a minimally invasive cancer treatment which has been rapidly gaining clinical acceptance. It is well known that thermal ablation increases the acoustic attenuation and shear modulus of tissue. In this work, we examine changes to the spatial distribution of scatterers in liver tissue following thermal ablation. Acoustic scatterers within liver tissue have frequently been modeled as pseudo-periodic. The positions of pseudo-periodic scatterers have been Gamma distributed along the beam dimension, and these scatterers are characterized by their mean scatterer spacing (MSS). Prior work have demonstrated significant changes in MSS due to diffuse liver disease, such as steatosis progressing to cirrhosis. However, relatively few results have been reported regarding changes in MSS following thermal ablation. In this study, we estimated MSS in ex vivo bovine liver by detecting local maxima in spectral coherence functions calculated using Thomson's multi-taper method. We examined a large number of uncorrelated regions of interest recorded from five normal bovine livers (~300 images from each animal). We also examined a large number of ROI's from five bovine livers following thermal coagulation. All bovine livers were obtained from a commercial meat production facility immediately following animal sacrifice and imaged within 12 hours. Thermal coagulation was induced by heating liver in saline water baths at 80° C for 45 minutes. For normal, unheated liver an MSS of approximately 1.5 mm was estimated. Following thermal ablation, an MSS of approximately 0.5 mm in thermally coagulated tissue was obtained. Frequently, studies estimating MSS in liver tissue provide an MSS estimate regardless of the state of tissue. Authors rarely present what their MSS estimation algorithm would produce if it were applied to tissue which is better modeled as a collection of uniformly, randomly distributed scatterers lacking periodicity. In this study, we found that thermal coagulation results in a loss of periodicity. The MSS of 0.5 mm corresponds to the value that a spectral coherence-based MSS algorithm would produce if presented with a signal that was generated from uniform, randomly distributed scatterers.

Mean scatterer spacing estimation in normal and thermally coagulated ex vivo bovine liver.

The liver has been hypothesized to have a unique arrangement of microvasculature that presents as an arrangement of quasiperiodic scatterers to an interrogating ultrasound pulse. The mean scatterer spacing (MSS) of these quasiperiodic scatterers has been proposed as a useful quantitative ultrasound biomarker for characterizing liver tissue. Thermal ablation is an increasingly popular method for treating hepatic tumors, and ultrasonic imaging approaches for delineating the extent of thermal ablation are in high demand. In this work, we examine the distribution of estimated MSS in thermally coagulated bovine liver and normal untreated bovine liver ex vivo. We estimate MSS by detecting local maxima in the spectral coherence function of radio frequency echoes from a clinical transducer, the Siemens VFX 9L4 transducer operating on an S2000 scanner. We find that normal untreated bovine liver was characterized by an MSS of approximately 1.3 mm. We examined regions of interest 12 mm wide laterally, and ranging from 12 mm to 18 mm axially, in 2 mm increments. Over these parameters, the mode of the MSS estimates was between 1.25 and 1.37 mm. On the other hand, estimation of MSS in thermally coagulated liver tissue yields a distribution of MSS estimates whose mode varied between 0.45 and 1.0 mm when examining regions of interest over the same sizes. We demonstrate that the estimated MSS in thermally coagulated liver favors small spacings because the randomly positioned scatterers in this tissue are better modeled as aperiodic scatterers. The submillimeter spacings result from the fact that this was the most probable spacing to be estimated if the discretely sampled spectral coherence function was a uniformly random two-dimensional function.

High-order statistic for mean scatterer spacing estimation for human tissues characterization

The mean scatterer spacing (MSS) has been identified as an important parameter for characterizing human tissues presenting a semi-regular lattice texture. Most of the work in this area involves the uses of an estimated power spectrum density (PSD) of an autoregressive (AR) model to deduce the MSS from backscattered ultrasonic signals. In this paper, we propose a new method of MSS estimation using the third and fourth-order cumulants, named here TFOCs, of the AR parametric model. The results obtained by this new method is compared with those obtained using PSD.

Singular Spectrum Analysis Applied to Backscattered Ultrasound Signals from In Vitro Human Cancellous Bone Specimens

Mean scatterer spacing (MSS) holds particular promise for the detection of changes in quasiperiodic tissue microstructures such as may occur during development of disease in the liver, spleen, or bones. Many techniques that may be applied for MSS estimation (temporal and spectral autocorrelation, power spectrum and cepstrum, higher order statistics, and quadratic transformation) characterize signals that contain a mixture of periodic and nonperiodic contributions. In contrast, singular spectrum analysis (SSA), a method usually applied in nonlinear dynamics, first identifies components of signals corresponding to periodic structures and, second, identifies dominant periodicity. Thus, SSA may better separate periodic structures from nonperiodic structures and noise. Using an ultrasound echo simulation model, we previously demonstrated SSA's potential to identify MSS of structures in quasiperiodic scattering media. The current work aims to observe the behavior of MSS estimation by SSA using ultrasound measurements in phantom materials (two parallel, nylon-line phantoms and four foam phantoms of different densities). The SSA was able to estimate not only the nylon-line distances but also nylon-line thickness. The method also was sensitive to the average pore-size differences of the four sponges. The algorithms then were applied to characterize human cancellous bone microarchitectures. Using 1-MHz center-frequency, radio-frequency ultrasound signals, MSS was measured in 24 in vitro bone samples and ranged front 1.0 to 1.7 mm. The SSA MSS estimates correlate significantly to MSS measured independently front synchrotron microtomography, r/sup 2/=0.68. Thus, application of SSA to backscattered ultrasound signals seems to be useful for providing information linked to tissue microarchitecture that is riot evident from clinical images.

Singular spectrum analysis applied to backscattered ultrasound signals from in vitro human cancellous bone specimens

Mean scatterer spacing (MSS) holds particular promise for the detection of changes in quasiperiodic tissue microstructures such as may occur during development of disease in the liver, spleen, or bones. Many techniques that may be applied for MSS estimation (temporal and spectral autocorrelation, power spectrum and cepstrum, higher order statistics, and quadratic transformation) characterize signals that contain a mixture of periodic and nonperiodic contributions. In contrast, singular spectrum analysis (SSA), a method usually applied in nonlinear dynamics, first identifies components of signals corresponding to periodic structures and, second, identifies dominant periodicity. Thus, SSA may better separate periodic structures from nonperiodic structures and noise. Using an ultrasound echo simulation model, we previously demonstrated SSA's potential to identify MSS of structures in quasiperiodic scattering media. The current work aims to observe the behavior of MSS estimation by SSA using ultrasound measurements in phantom materials (two parallel, nylon-line phantoms and four foam phantoms of different densities). The SSA was able to estimate not only the nylon-line distances but also nylon-line thickness. The method also was sensitive to the average pore-size differences of the four sponges. The algorithms then were applied to characterize human cancellous bone microarchitectures. Using 1-MHz center-frequency, radio-frequency ultrasound signals, MSS was measured in 24 in vitro bone samples and ranged from 1.0 to 1.7 mm. The SSA MSS estimates correlate significantly to MSS measured independently from synchrotron microtomography, r2 = 0.68. Thus, application of SSA to backscattered ultrasound signals seems to be useful for providing information linked to tissue microarchitecture that is not evident from clinical images.

A robust and computationally efficient algorithm for mean scatterer spacing estimation

Mean scatterer spacing (MSS) has been recognized to be a useful tool for tissue characterization. Most of the work in this area either uses the amplitude or the phase information of the spectrum of the backscattered ultrasound echo to estimate the MSS. Simulations have shown that the latter approach is more robust in the presence of irregularities in the scatterer distribution. However, most of the algorithms based on the phase information of the spectrum are computationally demanding and cannot be used in real-time. We present a computationally efficient and robust algorithm which uses the magnitude and phase information of the spectrum to estimate the MSS. This algorithm exploits the spectral redundancy present in the backscattered echo signal by generating spectral lines through a nonlinear (quadratic) transformation of the RF echo signal. Results of simulations comparing the performance of the proposed algorithm and previous approaches from the literature are presented to demonstrate the robustness of the proposed algorithm. Experiments involving phantoms and in vitro tissue samples are also presented. The feasibility of implementing a real-time MSS imaging system based on the proposed method is discussed.

Estimating mean scatterer spacing with the frequency-smoothed spectral autocorrelation function

The quasiperiodicity of regularly spaced scatterers results in characteristic patterns in the spectra of backscattered ultrasonic signals from which the mean scatterer spacing can be estimated. The mean spacing has been considered for classifying certain biological tissue. This paper addresses the problem of estimating the mean scatterer spacing from backscattered ultrasound signals using the frequency-smoothed spectral autocorrelation (SAC) function. The SAC function exploits characteristic differences between the phase spectrum of the resolvable quasiperiodic scatterers and the unresolvable uniformly distributed (diffuse) scatterers to improve estimator performance over other estimators that operate directly on the magnitude spectrum. Mean scatterer spacing estimates are compared for the frequency-smoothed SAC function and a cepstral technique using an AR model. Simulation results indicate that SAC-based estimates converge more reliably over smaller amounts of data than cepstrum-based estimates. An example of computing an estimate from liver tissue scans is also presented for the SAC function and the AR cepstrum.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Mean-scatterer spacing estimates with spectral correlation.

An ultrasonic backscattered signal from material comprised of quasiperiodic scatterers exhibit redundancy over both its phase and magnitude spectra. This paper addresses the problem of estimating mean-scatterer spacing from the backscattered ultrasound signal using spectral redundancy characterized by the spectral autocorrelation (SAC) function. Mean-scatterer spacing estimates are compared for techniques that use the cepstrum and the SAC function. A -scan models consist of a collection of regular scatterers with Gamma distributed spacings embedded in diffuse scatterers with uniform distributed spacings. The model accounts for attenuation by convolving the frequency dependent scattering centers with a time-varying system response. Simulation results indicate that SAC-based estimates converge more reliably over smaller amounts of data than cepstrum-based estimates. A major reason for the performance advantage is the use of phase information by the SAC function, while the cepstrum uses a phaseless power spectral density that is directly affected by the system response and the presence of diffuse scattering (speckle). An example of estimating the mean-scatterer spacing in liver tissue also is presented.