Analysis of correlation coefficient filtering in elasticity imaging

Dedicated Ultrasound Speckle Tracking for Quantitative Analysis of Uterine Motion Outside Pregnancy

Fertility problems are nowadays being paralleled by important advances in assisted reproductive technologies. Yet the success rate of these technologies remains low. There is evidence that fertilization outcome is affected by uterine motion, but solutions for quantitative analysis of uterine motion are lacking. This work proposes a dedicated method for uterine-motion quantification by B-mode transvaginal ultrasound. Motion analysis is implemented by speckle tracking based on block matching after speckle-size regularization. Sum of absolute differences is the adopted matching metrics. Prior to the analysis, dedicated singular value decomposition (SVD) filtering is implemented to enhance the uterine motion over noise, clutter, and uncorrelated motion induced by neighboring organs and probe movements. SVD and block matching are first optimized by a dedicated ex vivo setup. Robustness to noise and speckle decorrelation is improved by median filtering of the tracking coordinates from surrounding blocks. Speckle tracking is further accelerated by a diamond search. The method feasibility was tested in vivo with a longitudinal study on nine women, aimed at discriminating between four selected phases of the menstrual cycle known to show different uterine behavior. Each woman was scanned in each phase for 4 min; four sites on the uterine fundus were tracked over time to extract strain and distance signals along the longitudinal and transversal directions of the uterus. Several features were extracted from these signals. Among these features, median frequency and contraction frequency showed significant differences between active and quiet phases. These promising results motivate toward an extended validation in the context of fertilization procedures.

Efficient Two-Pass 3-D Speckle Tracking for Ultrasound Imaging

Speckle tracking based on block matching is the most common method for multi-dimensional motion estimation in ultrasound elasticity imaging. Extension of two-dimensional (2-D) methods to three dimensions (3-D) has been problematic because of the large computational load of 3-D tracking, as well as performance issues related to the low frame (volume) rates of 3-D images. To address both of these problems, we have developed an efficient two-pass tracking method suited to cardiac elasticity imaging. PatchMatch, originally developed for image editing, has been adapted for ultrasound to provide first-pass displacement estimates. Second-pass estimation uses conventional block matching within a much smaller search region. 3-D displacements are then obtained using correlation filtering previously shown to be effective against speckle decorrelation. Both simulated and in vivo canine cardiac results demonstrate that the proposed two-pass method reduces computational cost compared to conventional 3-D exhaustive search by a factor of 10. Moreover, it outperforms one-pass tracking by a factor of about 3 in terms of root-mean-square error relative to available ground-truth displacements.

Ultrasound elasticity imaging for determining the mechanical properties of human posterior tibial tendon: a cadaveric study

Posterior tibial tendon dysfunction (PTTD) is a common degenerative condition leading to a severe impairment of gait. There is currently no effective method to determine whether a patient with advanced PTTD would benefit from several months of bracing and physical therapy or ultimately require surgery. Tendon degeneration is closely associated with irreversible degradation of its collagen structure, leading to changes to its mechanical properties. If these properties could be monitored in vivo, they could be used to quantify the severity of tendonosis and help determine the appropriate treatment. The goal of this cadaveric study was, therefore, to develop and validate ultrasound elasticity imaging (UEI) as a potentially noninvasive technique for quantifying tendon mechanical properties. Five human cadaver feet were mounted in a materials testing system (MTS), while the posterior tibial tendon (PTT) was attached to a force actuator. A portable ultrasound scanner collected 2-D data during loading cycles. Young's modulus was calculated from the strain, loading force, and cross-sectional area of the PTT. Average Young's modulus for the five tendons was (0.45 ± 0.16 GPa) using UEI, which was consistent with simultaneous measurements made by the MTS across the whole tendon (0.52 ± 0.18 GPa). We also calculated the scaling factor (0.12 ± 0.01) between the load on the PTT and the inversion force at the forefoot, a measurable quantity in vivo. This study suggests that UEI could be a reliable in vivo technique for estimating the mechanical properties of the PTT, and as a clinical tool, help guide treatment decisions for advanced PTTD and other tendinopathies.

Radial basis functions for combining shape and speckle tracking in 4D echocardiography

Quantitative analysis of left ventricular deformation can provide valuable information about the extent of disease as well as the efficacy of treatment. In this work, we develop an adaptive multi-level compactly supported radial basis approach for deformation analysis in 3D+time echocardiography. Our method combines displacement information from shape tracking of myocardial boundaries (derived from B-mode data) with mid-wall displacements from radio-frequency-based ultrasound speckle tracking. We evaluate our methods on open-chest canines (N=8) and show that our combined approach is better correlated to magnetic resonance tagging-derived strains than either individual method. We also are able to identify regions of myocardial infarction (confirmed by postmortem analysis) using radial strain values obtained with our approach.

Complex principal components for robust motion estimation

Bias and variance errors in motion estimation result from electronic noise, decorrelation, aliasing, and inherent algorithm limitations. Unlike most error sources, decorrelation is coherent over time and has the same power spectrum as the signal. Thus, reducing decorrelation is impossible through frequency domain filtering or simple averaging and must be achieved through other methods. In this paper, we present a novel motion estimator, termed the principal component displacement estimator (PCDE), which takes advantage of the signal separation capabilities of principal component analysis (PCA) to reject decorrelation and noise. Furthermore, PCDE only requires the computation of a single principal component, enabling computational speed that is on the same order of magnitude or faster than the commonly used Loupas algorithm. Unlike prior PCA strategies, PCDE uses complex data to generate motion estimates using only a single principal component. The use of complex echo data is critical because it allows for separation of signal components based on motion, which is revealed through phase changes of the complex principal components. PCDE operates on the assumption that the signal component of interest is also the most energetic component in an ensemble of echo data. This assumption holds in most clinical ultrasound environments. However, in environments where electronic noise SNR is less than 0 dB or in blood flow data for which the wall signal dominates the signal from blood flow, the calculation of more than one PC is required to obtain the signal of interest. We simulated synthetic ultrasound data to assess the performance of PCDE over a wide range of imaging conditions and in the presence of decorrelation and additive noise. Under typical ultrasonic elasticity imaging conditions (0.98 signal correlation, 25 dB SNR, 1 sample shift), PCDE decreased estimation bias by more than 10% and standard deviation by more than 30% compared with the Loupas method and normalized cross-correlation with cosine fitting (NC CF). More modest gains were observed relative to spline-based time delay estimation (sTDE). PCDE was also tested on experimental elastography data. Compressions of approximately 1.5% were applied to a CIRS elastography phantom with embedded 10.4-mm-diameter lesions that had moduli contrasts of -9.2, -5.9, and 12.0 dB. The standard deviation of displacement estimates was reduced by at least 67% in homogeneous regions at 35 to 40 mm in depth with respect to estimates produced by Loupas, NC CF, and sTDE. Greater improvements in CNR and displacement standard deviation were observed at larger depths where speckle decorrelation and other noise sources were more significant.

Comparison of 2-D speckle tracking and tissue Doppler imaging in an isolated rabbit heart model

Ultrasound strain imaging has been proposed to quantitatively assess myocardial contractility. Cross-correlation-based 2-D speckle tracking (ST) and auto-correlation-based tissue Doppler imaging (TDI) [often called Doppler tissue imaging (DTI)] are competitive ultrasound techniques for this application. Compared with 2-D ST, TDI, as a 1-D method, is sensitive to beam angle and suffers from low strain signal-to-noise ratio because a high pulse repetition frequency is required to avoid aliasing in velocity estimation. In addition, ST and TDI are fundamentally different in the way that physical parameters such as the mechanical strain are derived, resulting in different estimation accuracy and interpretation. In this study, we directly compared the accuracy of TDI and 2-D ST estimates of instantaneous axial normal strain and accumulated axial normal strain using a simulated heart. We then used an isolated rabbit heart model of acute ischemia produced by left descending anterior artery ligation to evaluate the performance of the two methods in detecting abnormal motion. Results showed that instantaneous axial normal strains derived using TDI (0.36% error) were less accurate with larger variance than those derived from 2-D ST (0.08% error) given the same spatial resolution. In addition to poorer accuracy, accumulated axial normal strain estimates derived using TDI suffered from bias, because the accumulation method for TDI cannot trace along the actual tissue displacement path. Finally, we demonstrated the advantage 2-D ST has over TDI to reduce dependency on beam angle for lesion detection by estimating strains based on the principal stretches and their corresponding principal axes.

Phase rotation methods in filtering correlation coefficients for ultrasound speckle tracking

In speckle-tracking-based myocardial strain imaging, large interframe/volume peak-systolic strains cause peak hopping artifacts separating the highest correlation coefficient peak from the true peak. A correlation coefficient filter was previously designed to minimize peak hopping artifacts. For large strains, however, the correlation coefficient filter must follow the strain distribution to remove peak hopping effectively. This processing usually means interpolation and high computational load. To reduce the computational burden, a narrow band approximation using phase rotation is developed in this paper to facilitate correlation coefficient filtering. Correlation coefficients are first phase rotated to increase coherence, then filtered. Rotated phase angles are determined by the local strain and spatial position. This form of correlation coefficient filtering enhances true correlation coefficient peaks in large strain applications if decorrelation due to deformation does not completely destroy the coherence among neighboring correlation coefficients. The assumed strain used in the filter can also deviate from the true strain and still be effective. Further improvement in displacement estimation can be expected by combining correlation coefficient filtering with a new Viterbi-based displacement estimator.