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

Ultrasound normalized cumulative residual entropy imaging: Theory, methodology, and application

BACKGROUND AND OBJECTIVE

Ultrasound information entropy imaging is an emerging quantitative ultrasound technique for characterizing local tissue scatterer concentrations and arrangements. However, the commonly used ultrasound Shannon entropy imaging based on histogram-derived discrete probability estimation suffers from the drawbacks of histogram settings dependence and unknown estimator performance. In this paper, we introduced the information-theoretic cumulative residual entropy (CRE) defined in a continuous distribution of cumulative distribution functions as a new entropy measure of ultrasound backscatter envelope uncertainty or complexity, and proposed ultrasound CRE imaging for tissue characterization.

METHODS

We theoretically analyzed the CRE for Rayleigh and Nakagami distributions and proposed a normalized CRE for characterizing scatterer distribution patterns. We proposed a method based on an empirical cumulative distribution function estimator and a trapezoidal numerical integration for estimating the normalized CRE from ultrasound backscatter envelope signals. We presented an ultrasound normalized CRE imaging scheme based on the normalized CRE estimator and the parallel computation technique. We also conducted theoretical analysis of the differential entropy which is an extension of the Shannon entropy to a continuous distribution, and introduced a method for ultrasound differential entropy estimation and imaging. Monte-Carlo simulation experiments were performed to evaluate the estimation accuracy of the normalized CRE and differential entropy estimators. Phantom simulation and clinical experiments were conducted to evaluate the performance of the proposed normalized CRE imaging in characterizing scatterer concentrations and hepatic steatosis (n = 204), respectively.

RESULTS

The theoretical normalized CRE for the Rayleigh distribution was π/4, corresponding to the case where there were ≥10 randomly distributed scatterers within the resolution cell of an ultrasound transducer. The theoretical normalized CRE for the Nakagami distribution decreased as the Nakagami parameter m increased, corresponding to that the ultrasound backscattered statistics varied from pre-Rayleigh to Rayleigh and to post-Rayleigh distributions. Monte-Carlo simulation experiments showed that the proposed normalized CRE and differential entropy estimators can produce a satisfying estimation accuracy even when the size of the test samples is small. Phantom simulation experiments showed that the proposed normalized CRE and differential entropy imaging can characterize scatterer concentrations. Clinical experiments showed that the proposed ultrasound normalized CRE imaging is capable to quantitatively characterize hepatic steatosis, outperforming ultrasound differential entropy imaging and being comparable to ultrasound Shannon entropy and Nakagami imaging.

CONCLUSION

This study sheds light on the theory and methodology of ultrasound normalized CRE. The proposed ultrasound normalized CRE can serve as a new, flexible quantitative ultrasound envelope statistics parameter. The proposed ultrasound normalized CRE imaging may find applications in quantified characterization of biological tissues. Our code will be made available publicly at https://github.com/zhouzhuhuang.

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

BACKGROUND

Microwave 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.

PURPOSE

Recent 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.

METHODS

The 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.

RESULTS

The 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).

CONCLUSION

Harmonic-based MSSs are more sensitive and robust to variations in coagulated tissues, which is advantageous for the assessment of microwave-induced thermal lesions.

Multimodality quantitative ultrasound envelope statistics imaging based support vector machines for characterizing tissue scatterer distribution patterns: Methods and application in detecting microwave-induced thermal lesions

Ultrasound envelope statistics imaging, including ultrasound Nakagami imaging, homodyned-K imaging, and information entropy imaging, is an important group of quantitative ultrasound techniques for characterizing tissue scatterer distribution patterns, such as scatterer concentrations and arrangements. In this study, we proposed a machine learning approach to integrate the strength of multimodality quantitative ultrasound envelope statistics imaging techniques and applied it to detecting microwave ablation induced thermal lesions in porcine liver ex vivo. The quantitative ultrasound parameters included were homodyned-K α which is a scatterer clustering parameter related to the effective scatterer number per resolution cell, Nakagami m which is a shape parameter of the envelope probability density function, and Shannon entropy which is a measure of signal uncertainty or complexity. Specifically, the homodyned-K log10(α), Nakagami-m, and horizontally normalized Shannon entropy parameters were combined as input features to train a support vector machine (SVM) model to classify thermal lesions with higher scatterer concentrations from normal tissues with lower scatterer concentrations. Through heterogeneous phantom simulations based on Field II, the proposed SVM model showed a classification accuracy above 0.90; the area accuracy and Dice score of higher-scatterer-concentration zone identification exceeded 83% and 0.86, respectively, with the Hausdorff distance <26. Microwave ablation experiments of porcine liver ex vivo at 60-80 W, 1-3 min showed that the SVM model achieved a classification accuracy of 0.85; compared with single log10(α),m, or hNSE parametric imaging, the SVM model achieved the highest area accuracy (89.1%) and Dice score (0.77) as well as the smallest Hausdorff distance (46.38) of coagulation zone identification. We concluded that the proposed multimodality quantitative ultrasound envelope statistics imaging based SVM approach can enhance the capability to characterize tissue scatterer distribution patterns and has the potential to detect the thermal lesions induced by microwave ablation.

Locations of optimally matched Gabor atoms from ultrasound RF echoes for inter-scatterer spacing estimation

BACKGROUND AND OBJECTIVE

The resolvable scatterer spacing related to biological tissue microstructures is a quantitative signature used for the disease diagnosis and tissue classification. In the present study, a method by locating optimally matched Gabor atoms (LOMGA) from ultrasound RF echo signals is proposed to improve the inter-scatterer spacing (ISS) estimation.

METHOD

A series of Gabor atoms are obtained from the signals with a matching pursuit algorithm. Then, the optimum atoms highly correlated with the coherent components are automatically selected according to the second-order difference of the reconstructed signal-to-residue ratio. The distances between the locations of adjacent atoms are applied to estimate the ISSs. In the simulation experiments, four regular degrees of the scatterer distributions are modeled with the Gamma distribution. One hundred sets of ultrasound RF echo signals are simulated based on the regular and diffuse scatterer distributions, and then combined to generate signals with preset coherent-to-diffuse ratios (CDRs). The accuracy performance of the LOMGA method is compared with that based on wavelet transform (WT) algorithm. In the microwave ablation experiments, the ultrasound RF echo signals of the region of interest (ROI) are collected from the normal and coagulated porcine liver tissues. The means and standard deviations of the LOMGA-based ISSs are compared with the WT-based results.

RESULTS

The results based on simulated signals with CDRs from 10 dB to -10 dB demonstrate that the proposed method improves the estimation accuracies of the mean ISSs by 5.10%, 9.00%, 19.80%, and 23.82%, and reduces the mean standard deviations by 27.20%, 22.50%, 11.50%, and 4.49% more than the WT method for the four regularities, respectively. The performance of the LOMGA method is also verified with the ultrasound RF echo signals from ex vivo porcine liver tissues in microwave ablation experiments.

CONCLUSIONS

It is concluded that the LOMGA method can provide more accurate and stable ISS estimation, which improves the performance of the tissue characterization with ISS-based quantitative ultrasound.