Robust Cardiac Motion Estimation using Ultrafast Ultrasound Data: A Low-Rank-Topology-Preserving Approach

Cardiac motion estimation is an important diagnostic tool to detect 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 the complex motion patterns and the presence of noise. In this work, we propose a novel approach to estimate the cardiac motion using ultrafast ultrasound data. -- Our solution is based on a variational formulation characterized by the L2-regularized class. The displacement is represented by a lattice of b-splines and we ensure robustness by applying a maximum likelihood type estimator. While this is an important part of our solution, the main highlight of this paper is to combine a 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 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. While maintaining the accuracy of the solution, the low-rank preprocessing is shown to speed up the convergence of the variational problem. Beyond cardiac motion estimation, our approach is promising for the analysis of other organs that experience motion.Comment: 15 pages, 10 figures, Physics in Medicine and Biology, 201

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

Three-dimensional ultrasound strain imaging of skeletal muscles

Muscle contraction is characterized by large deformation and translation, which requires a multi-dimensional imaging modality to reveal its behavior. Previous work on ultrasound strain imaging of the muscle contraction was limited to 2D and bi-plane techniques. In this study, a three-dimensional (3D) ultrasound strain imaging technique was tested against 2D strain imaging and used for quantifying deformation of skeletal muscles. A phantom compression study was conducted for an experimental validation of both 2D and 3D methods. The phantom was compressed 3% vertically and pre- and post-compression full volume radio frequency (RF) ultrasound data were acquired using a matrix array transducer. A cross-correlation-based algorithm using either 2D or 3D kernels was applied to obtain the displacement estimates. These estimates were converted to Cartesian space and subsequently, strain was derived using a least-squares strain estimator (LSQSE). The 3D results were compared with the 2D results and the theoretically predicted displacement and strain. Comparison between 2D and 3D kernels was performed on data from a plane with a large tilt angle to study the influence of out-of-plane motion on the two techniques. To demonstrate the in vivo feasibility, 3D strain was calculated from live 3D data, acquired during a 2 second isometric contraction and relaxation of the quadriceps muscle in a healthy volunteer. The phantom study showed good correlation between estimated displacements and the theoretically predicted displacements. Root-mean-squared errors (RMSE) were 0.16, 0.17 and 0.13 mm in the x-, y- and z-direction respectively. The absolute RMSE for the 3D strain values were 0.94, 1.2 and 0.41% in the x-, y- and z-direction respectively. The 2D method performed worse, with 3 (x-direction) to 6 (z-direction) times higher RMSE values. The larger errors in lateral and elevational direction with respect to the axial RMSE are potentially caused by the large angle between the ultrasound beams. Initial in vivo results revealed 3D strain curves which clearly visualized the contraction and relaxation of the quadriceps muscles. Muscle deformation estimation using real-time 3D ultrasound RF-data seems feasible and the use of 3D kernels improves displacement estimation in comparison to 2D techniques. Future work will focus on improving lateral and elevational displacement estimation, and investigating local differences of strain in skeletal muscles and its clinical relevance

Simultaneous vascular strain and blood vector velocity imaging using high frequency versus conventional frequency plane wave ultrasound: a phantom study

Plaque strain and blood vector velocity imaging of stenosed arteries are expected to aid in diagnosis and prevention of cerebrovascular disease. Ultrafast plane wave imaging enables simultaneous strain and velocity estimation. Multiple ultrasound vendors are introducing high frequency ultrasound probes and systems. This study investigates whether the use of high frequency ultrafast ultrasound is beneficial for assessing blood velocities and strain in arteries. The performance of strain and blood flow velocity estimation was compared between a high frequency transducer (MS250, fc =21 MHz) and a clinically utilized transducer (L12-5, fc =9 MHz). Quantitative analysis based on straight tube phantom experiments revealed that the MS250 outperformed the L12-5 in the superficial region: low velocities near the wall were more accurately estimated and wall strains were better resolved. At greater than 2 cm echo depth, the L12-5 performed better, due to the high attenuation of the MS250 probe. Qualitative comparison using a perfused patient-specific carotid bifurcation phantom confirmed these findings. Thus, in conclusion, for strain and blood velocity estimation for depths up to ~2 cm a high frequency probe is recommended

2D versus 3D cross-correlation-based radial and circumferential strain imaging in a 3D atherosclerotic carotid artery model using ultrafast plane wave ultrasound

Three-dimensional vascular strain estimation is crucial for assessment of the location of high strain regions in the carotid artery (CA) and the identification of vulnerable plaque features. This study compares 2D vs. 3D displacement estimation in terms of radial and circumferential strain using simulated ultrasound images of a 3D atherosclerotic CA model at the bifurcation embedded in surrounding tissue. The 3D finite element model (FEM) of a patient-specific, pulsating atherosclerotic CA (pulse pressure 60 mmHg) was generated with ABAQUS FEM software. Global longitudinal motion was superimposed to the model. Radiofrequency (RF) ultrasound data were simulated in Field II by moving point scatterers (vessel wall) according to the deformation patterns of the model. A linear array transducer (f(c) = 9 MHz, pitch = 198 mu m, 192 elements) was used which transmitted plane waves at 3 alternating angles (+19.5 degrees, 0 degrees, -19.5 degrees) at a pulse repetition rate of 10 kHz. Simulations with 20 ms (systole) and 100 ms (diastole) inter-frame (IF) time were performed for 191 equally spaced (0.1 mm) longitudinal positions of the internal CA containing fatty and calcified areas. After delay-and-sum beamforming, IF axial displacements were estimated using a coarse-to-fine normalized cross-correlation method. The axial displacement at 0 degrees was used as the vertical displacement component. Projection of the -19.5 degrees and +19.5 degrees axial displacements yielded the horizontal displacement component. A polar grid and the lumen center were determined in the end-diastolic frame of each longitudinal position and used to convert the tracked vertical and horizontal displacements into radial and circumferential displacements. Least squares strain estimation was performed to determine accumulated radial and circumferential strain. The performance of the 2D and 3D method was compared by calculating the root-mean-squared error (RMSE) of the estimated strains with respect to the reference strains obtained from the model. More accurate strain images were obtained using the 3D displacement estimation for the entire cardiac cycle. The 3D technique clearly outperforms the 2D technique in phases with high IF longitudinal motion

In vivo 3D cardiac and skeletal muscle strain estimation

In this study, BiPlane imaging was adapted for measuring strain in actively deforming tissue in three orthogonal directions. BiPlane imaging assures a sufficient frame rate (75-120 Hz) for accurate strain estimation. A coarse-to-fine iterative 2D strain algorithm using spatial correction and local stretching was implemented. Considering the huge amount of generated data, a fast interpolation scheme was implemented for measuring sub-sample and sub-line displacements. Assuming a 2D parabolic shape of the cross-correlation function, a straightforward and direct calculation of the displacements is possible. The strain estimation method was validated by means of a simulation study and phantom experiments. Rf-data were acquired with a 3D X4 matrix array transducer (Philips Sonos 7500) in BiPlane mode. In vivo verification in human skeletal muscle was performed. Furthermore, cardiac strain imaging was conducted using cardiac BiPlane data of dogs. In a pilot animal study, beagles with an induced valvular aortic stenosis were monitored. The Field II simulation was used for determining the accuracy and detectibility of the algorithm and revealed excellent correlation between applied and measured axial strain (SNR = 43 dB) for a window of 0.60 mm. Obviously, a lower SNR was found in lateral and elevational direction. The in vivo verification experiment in the skeletal muscles revealed similar cumulative axial strain curves (up to 8%) in both the azimuth and elevational direction. The shape of the strain curve matched perfectly with the curve of the measured force. The lateral strain values parallel to the direction of the muscle fibers matched the axial strain curves, whereas the shape of the lateral strain in the perpendicular plane differed due to anisotropy. Finally, strain images of the beagles were calculated. The beagle with the most excessive pressure gradient revealed a decrease of the radial strain. Furthermore, an elongated plateau in the radial strain indicated hypertrophy. In conclusion, 3D cardiac and strain estimation is feasible using a real-time 3D scanner. Additional validation studies of full 3D imaging modes are required to fully validate the technique

2-D versus 3-D cross-correlation-based radial and circumferential strain estimation using multiplane 2-D ultrafast ultrasound in a 3-D atherosclerotic carotid artery model

Three-dimensional (3-D) strain estimation might improve the detection and localization of high strain regions in the carotid artery (CA) for identification of vulnerable plaques. This paper compares 2-D versus 3-D displacement estimation in terms of radial and circumferential strain using simulated ultrasound (US) images of a patient-specific 3-D atherosclerotic CA model at the bifurcation embedded in surrounding tissue generated with ABAQUS software. Global longitudinal motion was superimposed to the model based on the literature data. A Philips L11-3 linear array transducer was simulated, which transmitted plane waves at three alternating angles at a pulse repetition rate of 10 kHz. Interframe (IF) radio-frequency US data were simulated in Field II for 191 equally spaced longitudinal positions of the internal CA. Accumulated radial and circumferential displacements were estimated using tracking of the IF displacements estimated by a two-step normalized cross-correlation method and displacement compounding. Least-squares strain estimation was performed to determine accumulated radial and circumferential strain. The performance of the 2-D and 3-D methods was compared by calculating the root-mean-squared error of the estimated strains with respect to the reference strains obtained from the model. More accurate strain images were obtained using the 3-D displacement estimation for the entire cardiac cycle. The 3-D technique clearly outperformed the 2-D technique in phases with high IF longitudinal motion. In fact, the large IF longitudinal motion rendered it impossible to accurately track the tissue and cumulate strains over the entire cardiac cycle with the 2-D technique

Letter to the editor. Quantitative ultrasound imaging of healthy and reconstructed cleft lip: a feasibility study.

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