Temporally diffeomorphic cardiac motion estimation from three-dimensional echocardiography by minimization of intensity consistency error

Robust cardiac motion estimation using ultrafast ultrasound data: a low-rank topology-preserving approach

Cardiac motion estimation is an important diagnostic tool for detecting heart diseases and it has been explored with modalities such as MRI and conventional ultrasound (US) sequences. US cardiac motion estimation still presents challenges because of complex motion patterns and the presence of noise. In this work, we propose a novel approach to estimate cardiac motion using ultrafast ultrasound data. Our solution is based on a variational formulation characterized by the L ²-regularized class. Displacement is represented by a lattice of b-splines and we ensure robustness, in the sense of eliminating outliers, by applying a maximum likelihood type estimator. While this is an important part of our solution, the main object of this work is to combine low-rank data representation with topology preservation. Low-rank data representation (achieved by finding the k-dominant singular values of a Casorati matrix arranged from the data sequence) speeds up the global solution and achieves noise reduction. On the other hand, topology preservation (achieved by monitoring the Jacobian determinant) allows one to radically rule out distortions while carefully controlling the size of allowed expansions and contractions. Our variational approach is carried out on a realistic dataset as well as on a simulated one. We demonstrate how our proposed variational solution deals with complex deformations through careful numerical experiments. The low-rank constraint speeds up the convergence of the optimization problem while topology preservation ensures a more accurate displacement. Beyond cardiac motion estimation, our approach is promising for the analysis of other organs that exhibit motion.

Diffeomorphic Multi-Frame Non-Rigid Registration of Cell Nuclei in 2D and 3D Live Cell Images

To gain a better understanding of cellular and molecular processes, it is important to quantitatively analyze the motion of subcellular particles in live cell microscopy image sequences. Since, generally, the subcellular particles move and cell nuclei move as well as deform, it is important to decouple the movement of particles from that of the cell nuclei using non-rigid registration methods. We have developed a diffeomorphic multi-frame approach for non-rigid registration of cell nuclei in 2D and 3D live cell fluorescence microscopy images. Our non-rigid registration approach is based on local optic flow estimation, exploits information from multiple consecutive image frames, and determines diffeomorphic transformations in the log-domain, which allows efficient computation of the inverse transformations. To register single images of an image sequence to a reference image, we use a temporally weighted mean image, which is constructed based on inverse transformations and multiple consecutive frames. Using multiple consecutive frames improves the registration accuracy compared to pairwise registration, and using a temporally weighted mean image significantly reduces the computation time compared with previous work. In addition, we use a flow boundary preserving method for regularization of computed deformation vector fields, which prevents from over-smoothing compared to standard Gaussian filtering. Our approach has been successfully applied to 2D and 3D synthetic as well as real live cell microscopy image sequences, and an experimental comparison with non-rigid pairwise, multi-frame, and temporal groupwise registration has been carried out.

Towards estimating cardiac motion using low-rank representation and topology preservation for ultrafast ultrasound data

Estimation of the cardiac motion is very important in order to detect heart diseases. This work presents a cardiac motion estimation approach using ultrafast ultrasound data. We optimize a variational framework which has the benefits of combining low-rank data representation with topology preservation. We show through the analysis of experimental results that this combination offers a radical reduction in computational time and noise while ensuring preservation of the anatomical structure of the heart under complex deformations. Although in this work we use the heart as a study case, our solution is promising to analyze other organs experiencing motion.

Real Time Three-Dimensional Echocardiographic Evaluations of Fetal Left Ventricular Stroke Volume, Mass, and Myocardial Strain: In Vitro and In Vivo Experimental Study

BACKGROUND

Left ventricular stroke volume, mass, and myocardial strain are valuable indicators of fetal heart function. This study investigated the feasibility of nongated real time three-dimensional echocardiography (RT3DE) to determine fetal stroke volume (SV), left ventricular mass (LVM), and myocardial strain under different conditions.

METHODS

To evaluate fetal hearts, fetal-sized rabbit hearts were used in this study. The in vitro portion of this study was carried out using a balloon inserted into the LV of eight fresh rabbit hearts and driven by a calibrated pulsatile pump. RT3DE volumes were obtained at various pump-set SVs. The in vivo experiments in this study were performed on open-chest rabbits. RT3DE volumes were acquired at the following conditions: baseline, simulated hypervolemia, inferior vena cava (IVC) ligation, and ascending aorta (AAO) ligation. Displacement values and sonomicrometry data were used as references for RT3DE-derived SV, LVM, longitudinal strain (LS), and circumferential strain (CS).

RESULTS

Excellent correlations between RT3DE-derived values and reference values were demonstrated and accompanied by high coefficients of determination (R(2) ) for both in vitro and in vivo studies for SV, LVM, LS, and CS (in vitro: SV: R(2)  = 0.98; LVM: R(2)  = 0.97; LS: R(2)  = 0.87, CS: R(2)  = 0.80; in vivo: SV: R(2)  = 0.92; LVM: R(2)  = 0.98; LS: in vivo: R(2)  = 0.84; CS: in vivo: R(2)  = 0.76; all P < 0.05).

CONCLUSIONS

RT3DE is capable of quantifying the SV, LVM, and myocardial strain of fetal-sized hearts under different conditions. This nongated RT3DE may aid the evaluation of fetal cardiac function, providing a superior understanding of the progress of fetal heart disorders.

Right ventricular strain analysis from three-dimensional echocardiography by using temporally diffeomorphic motion estimation

PURPOSE

Quantitative analysis of right ventricle (RV) motion is important for study of the mechanism of congenital and acquired diseases. Unlike left ventricle (LV), motion estimation of RV is more difficult because of its complex shape and thin myocardium. Although attempts of finite element models on MR images and speckle tracking on echocardiography have shown promising results on RV strain analysis, these methods can be improved since the temporal smoothness of the motion is not considered.

METHODS

The authors have proposed a temporally diffeomorphic motion estimation method in which a spatiotemporal transformation is estimated by optimization of a registration energy functional of the velocity field in their earlier work. The proposed motion estimation method is a fully automatic process for general image sequences. The authors apply the method by combining with a semiautomatic myocardium segmentation method to the RV strain analysis of three-dimensional (3D) echocardiographic sequences of five open-chest pigs under different steady states.

RESULTS

The authors compare the peak two-point strains derived by their method with those estimated from the sonomicrometry, the results show that they have high correlation. The motion of the right ventricular free wall is studied by using segmental strains. The baseline sequence results show that the segmental strains in their methods are consistent with results obtained by other image modalities such as MRI. The image sequences of pacing steady states show that segments with the largest strain variation coincide with the pacing sites.

CONCLUSIONS

The high correlation of the peak two-point strains of their method and sonomicrometry under different steady states demonstrates that their RV motion estimation has high accuracy. The closeness of the segmental strain of their method to those from MRI shows the feasibility of their method in the study of RV function by using 3D echocardiography. The strain analysis of the pacing steady states shows the potential utility of their method in study on RV diseases.