Shape-based tracking of left ventricular wall motion

An approach for tracking and quantifying the nonrigid, nonuniform motion of the left ventricular (LV) endocardial wall from two-dimensional (2-D) cardiac image sequences, on a point-by-point basis over the entire cardiac cycle, is presented. Given a set of boundaries, motion computation involves first matching local segments on one contour to segments on the next contour in the sequence using a shape-based strategy. Results from the match process are incorporated with a smoothness term into an optimization functional. The global minimum of this functional is found, resulting in a smooth flow field that is consistent with the match data. The computation is performed for all pairs of frames in the temporal sequence and equally sampled points on one contour are tracked throughout the sequence, resulting in a composite flow field over the entire sequence. Two perspectives on characterizing the optimization functional are presented which result in a tradeoff resolved by the confidence in the initial boundary segmentation. Experimental results for contours derived from diagnostic image sequences of three different imaging modalities are presented. A comparison of trajectory estimates with trajectories of gold-standard markers implanted in the LV wall are presented for validation. The results of this comparison confirm that although cardiac motion is a three-dimensional (3-D) problem, two-dimensional (2-D) analysis provides a rich testing ground for algorithm development     

Sampled-data filtering framework for cardiac motion recovery: optimal estimation of continuous dynamics from discrete measurements

Quantitative and noninvasive estimation of cardiac kinematics has significant physiological and clinical implications. In this paper, a sampled-data filtering framework is presented for the recovery of cardiac motion and deformation functions from periodic medical image sequences. Cardiac dynamics is a continuously evolving physical/physiological process, whereas the imaging data can provide only sampled measurements at discrete time instants. Given such a hybrid paradigm, stochastic multiframe filtering frameworks are constructed to couple the continuous dynamics with the discrete measurements, and to coordinately deal with the parameter uncertainty of the biomechanical constraining model and the noisy nature of the imaging data. The state estimates are predicted according to the continuous-time biomechanically constructed state equation between observation time points, and then updated with the new imaging-derived measurements at discrete time instants, yielding physically more meaningful and more accurate estimation results. Both continuous-discrete Kalman filter and sampled-data Hinfinity filter are applied for motion recovery. While Kalman filter is the optimal estimator under Gaussian noises, the Hinfinity scheme can give robust estimation results when the types and levels of model uncertainties and data disturbances are not available a priori. The strategies are validated through synthetic data experiments to illustrate their advantages and on canine MR phase contrast images and human MR tagging data to show their clinical potential.     

Sequential cardiac segmentation by seed contour tracking

A sequential cardiac segmentation method based on an active contour model, initial seed contour tracking (SCT) scheme, and phase contrast magnetic resonance imaging (MRI) has been developed to improve the accuracy of automatic sequential segmentation of the myocardial boundaries, especially the endocardial boundary. The performance of the proposed method was assessed by experiments performed on phase contrast MRI data sets from three normal human volunteers. Experimental results showed that the propagation of errors caused by improper positioning of initial seed contours in sequential cardiac segmentation was reduced significantly by the use of the SCT scheme.     

LV shape and motion: B-spline-based deformable model and sequential motion decomposition.

In this paper, we extend a previous work by J. Park and propose a uniform framework to reconstruct left ventricle (LV) geometry/motion from tagged MR images. In our work, the LV is modeled as a generalized prolate spheroid, and its motion is decomposed into four components-global translation, polar radial/z-axis compression, twisting, and bending. By formulating model parameters as tensor products of B-splines, we develop efficient algorithms to quickly reconstruct LV geometry/motion from extracted boundary contours and tracked planar tags. Experiments on both synthesized and in vivo data are also reported.     

Automatic contour definition on left ventriculograms by image evidence and a multiple template-based model

An algorithm which utilizes digital image processing and pattern recognition methods for automated definition of left ventricular (LV) contours is presented. Digital image processing and pattern recognition techniques are applied to digitally acquired radiographic images of the heart to extract the LV contours required for quantitative analysis of cardiac function. Knowledge of the image domain is invoked at each step of the algorithm to orient the data search and thereby the complexity of the solution. A knowledge-based image transformation, directional gradient search, expectations of object versus background location, least-cost path searches by dynamic programming, and a digital representation of possible versus impossible ventricular shape are exploited. The digital representation, composed of a set of characteristic templates, was created using contours obtained by manual tracing. The algorithm was tested by application of three sets of 25 images each. Test set one and two were used as training sets for creation of the model for contour correction. Model-based correction proved to be an effective technique, producing significant reduction of error in the final contours.     

磁共振心肌标记图像左心室壁边缘检测

磁共振标记（MR Tagging）技术于90年代初提出，作为一种有效的无创性检测手段，得到不断的研究和改进。它针对人体软组织（如心脏）的形变进行测量，定量分析其运动轨迹，从而判断其功能状况的好坏，具有较高的实用价值。论文提出一种结合形态学、增强的启发式图搜索和区域生长法进行磁共振心肌标记图像左心室壁分割的方法，实验证明这种方法可以很好地分割出磁共振心肌标记图像左心室心肌的内外边缘，并可以进一步用于提取心肌标记，分析心肌运动轨迹。     

Semiautomated segmentation of myocardial contours for fast strain analysis in cine displacement-encoded MRI

The purposes of this study were to develop a semiautomated cardiac contour segmentation method for use with cine displacement-encoded MRI and evaluate its accuracy against manual segmentation. This segmentation model was designed with two distinct phases: preparation and evolution. During the model preparation phase, after manual image cropping and then image intensity standardization, the myocardium is separated from the background based on the difference in their intensity distributions, and the endo- and epi-cardial contours are initialized automatically as zeros of an underlying level set function. During the model evolution phase, the model deformation is driven by the minimization of an energy function consisting of five terms: model intensity, edge attraction, shape prior, contours interaction, and contour smoothness. The energy function is minimized iteratively by adaptively weighting the five terms in the energy function using an annealing algorithm. The validation experiments were performed on a pool of cine data sets of five volunteers. The difference between the semiautomated segmentation and manual segmentation was sufficiently small as to be considered clinically irrelevant. This relatively accurate semiautomated segmentation method can be used to significantly increase the throughput of strain analysis of cine displacement-encoded MR images for clinical applications.      

Parameter distribution models for estimation of population based left ventricular deformation using sparse fiducial markers

We present a method to estimate left ventricular (LV) motion based on three-dimensional (3-D) images that can be derived from any anatomical tomographic or 3-D modality, such as echocardiography, computed tomography, or magnetic resonance imaging. A finite element mesh of the LV was constructed to fit the geometry of the wall. The mesh was deformed by optimizing the nodal parameters to the motion of a sparse number of fiducial markers that were manually tracked in the images through the cardiac cycle. A parameter distribution model (PDM) of LV deformations was obtained from a database of MR tagging studies. This was used to filter the calculated deformation and incorporate a priori information on likely motions. The estimated deformation obtained from 13 normal untagged studies was compared with the deformation obtained from MR tagging. The end systolic (ES) circumferential and longitudinal strain values matched well with a mean difference of 0.1 +/- 3.2% and 0.3 +/- 3.0%, respectively. The calculated apex-base twist angle at ES had a mean difference of 1.0 +/- 2.3 degrees. We conclude that fiducial marker fitting in conjunction with a PDM provides accurate reconstruction of LV deformation in normal subjects.     

Automatic tracking of SPAMM grid and the estimation of deformation parameters from cardiac MR images

Presents a new approach for the automatic tracking of SPAMM (Spatial Modulation of Magnetization) grid in cardiac MR images and consequent estimation of deformation parameters. The tracking is utilized to extract grid points from MR images and to establish correspondences between grid points in images taken at consecutive frames. These correspondences are used with a thin plate spline model to establish a mapping from one image to the next. This mapping is then used for motion and deformation estimation. Spatio-temporal tracking of SPAMM grid is achieved by using snakes-active contour models with an associated energy functional. The authors present a minimizing strategy which is suitable for tracking the SPAMM grid. By continuously minimizing their energy functionals, the snakes lock on to and follow the in-slice motion and deformation of the SPAMM grid. The proposed algorithm was tested with excellent results on 123 images (three data sets each a multiple slice 2D, 16 phase Cine study, three data sets each a multiple slice 2D, 13 phase Cine study and three data sets each a multiple slice 2D, 12 phase Cine study).     

Estimation of deformation gradient and strain from cine-PC velocitydata [cardiac magnetic resonance imaging]

Phase contrast magnetic resonance imaging (MRI) can provide in vivo myocardial velocity field measurements. These data allow densely spaced material points to be tracked throughout the whole heart cycle using, for example, the Fourier tracking algorithm. To process the tracking results for myocardial deformation and strain quantification, the authors developed a method that is based on fitting the tracking results to an appropriate local deformation model. They further analyzed the accuracy and precision of the method and provided performance predictions for several local models. In order to validate the method and the theoretical performance analysis, the authors conducted controlled computer simulations and a phantom study. The results agreed well with expectations. Human heart data were also acquired and analyzed, and provided encouraging results. At the signal-to-noise ratio (SNR) level and spatial resolution expected in clinical settings, the study predicts strain quantification accuracy and precision that may allow the technique to become a practical and powerful noninvasive approach for the study of cardiac function, although clinically acceptable data acquisition strategies for three-dimensional (3-D) data are still a challenge     

A comprehensive cardiac motion estimation framework using both untagged and 3-D tagged MR images based on nonrigid registration

In this paper, we present a novel technique based on nonrigid image registration for myocardial motion estimation using both untagged and 3-D tagged MR images. The novel aspect of our technique is its simultaneous usage of complementary information from both untagged and 3-D tagged MR images. To estimate the motion within the myocardium, we register a sequence of tagged and untagged MR images during the cardiac cycle to a set of reference tagged and untagged MR images at end-diastole. The similarity measure is spatially weighted to maximize the utility of information from both images. In addition, the proposed approach integrates a valve plane tracker and adaptive incompressibility into the framework. We have evaluated the proposed approach on 12 subjects. Our results show a clear improvement in terms of accuracy compared to approaches that use either 3-D tagged or untagged MR image information alone. The relative error compared to manually tracked landmarks is less than 15% throughout the cardiac cycle. Finally, we demonstrate the automatic analysis of cardiac function from the myocardial deformation fields.     

Tracking and finite element analysis of stripe deformation in magnetic resonance tagging

Magnetic resonance tissue tagging allows noninvasive in vivo measurement of soft tissue deformation. Planes of magnetic saturation are created, orthogonal to the imaging plane, which form dark lines (stripes) in the image. The authors describe a method for tracking stripe motion in the image plane, and show how this information can be incorporated into a finite element model of the underlying deformation. Human heart data were acquired from several imaging planes in different orientations and were combined using a deformable model of the left ventricle wall. Each tracked stripe point provided information on displacement orthogonal to the original tagging plane, i.e., a one-dimensional (1-D) constraint on the motion. Three-dimensional (3-D) motion and deformation was then reconstructed by fitting the model to the data constraints by linear least squares. The average root mean squared (rms) error between tracked stripe points and predicted model locations was 0.47 mm (n=3,100 points). In order to validate this method and quantify the errors involved, the authors applied it to images of a silicone gel phantom subjected to a known, well-controlled, 3-D deformation. The finite element strains obtained were compared to an analytic model of the deformation known to be accurate in the central axial plane of the phantom. The average rms errors were 6% in both the reconstructed shear strains and 16% in the reconstructed radial normal strain.     

Tracking the left ventricle in echocardiographic images by learningheart dynamics

In this paper a temporal learning-filtering procedure is applied to refine the left ventricle (LV) boundary detected by an active-contour model. Instead of making prior assumptions about the LV shape or its motion, this information is incrementally gathered directly from the images and is exploited to achieve more coherent segmentation. A Hough transform technique is used to find an initial approximation of the object boundary at the first frame of the sequence. Then, an active-contour model is used in a coarse-to-fine framework, for the estimation of a noisy LV boundary. The PCA transform is applied to form a reduced ordered orthonormal basis of the LV deformations based on a sequence of noisy boundary observations. Then this basis is used to constrain the motion of the active contour in subsequent frames, and thus provide more coherent identification. Results of epicardial boundary identification in B-mode images are presented.     

Segmentation and tracking in echocardiographic sequences: activecontours guided by optical flow estimates

This paper presents a method for segmentation and tracking of cardiac structures in ultrasound image sequences. The developed algorithm is based on the active contour framework. This approach requires initial placement of the contour close to the desired position in the image, usually an object outline. Best contour shape and position are then calculated, assuming that at this configuration a global energy function, associated with a contour, attains its minimum. Active contours can be used for tracking by selecting a solution from a previous frame as an initial position in a present frame. Such an approach, however, fails for large displacements of the object of interest. This paper presents a technique that incorporates the information on pixel velocities (optical flow) into the estimate of initial contour to enable tracking of fast-moving objects. The algorithm was tested on several ultrasound image sequences, each covering one complete cardiac cycle. The contour successfully tracked boundaries of mitral valve leaflets, aortic root and endocardial borders of the left ventricle. The algorithm-generated outlines were compared against manual tracings by expert physicians. The automated method resulted in contours that were within the boundaries of intraobserver variability     

Fast tracking of cardiac motion using 3D-HARP

Magnetic resonance (MR) tagging is capable of accurate, noninvasive quantification of regional myocardial function. Routine clinical use, however, is hindered by cumbersome and time-consuming postprocessing procedures. We propose a fast, semiautomatic method for tracking three-dimensional (3-D) cardiac motion from a temporal sequence of short- and long-axis tagged MR images. The new method, called 3-D-HARmonic Phase (3D-HARP), extends the HARP approach, previously described for two-dimensional (2-D) tag analysis, to 3-D. A 3-D material mesh model is built to represent a collection of material points inside the left ventricle (LV) wall at a reference time. Harmonic phase, a material property that is time-invariant, is used to track the motion of the mesh through a cardiac cycle. Various motion-related functional properties of the myocardium, such as circumferential strain and left ventricular twist, are computed from the tracked mesh. The correlation analysis of 3D-HARP and FINDTAGS + Tag Strain(E) Analysis (TEA), which are well-established tag analysis techniques, shows that the regression coefficients of circumferential strain (E(CC)) and twist angle are r2 = 0.8605 and r2 = 0.8645, respectively. The total time required for tracking 3-D cardiac motion is approximately 10 min in a 9 timeframe tagged MRI dataset and has the potential to be much faster.     

Spline-based cardiac motion tracking using velocity-encoded magnetic resonance imaging

This paper deals with the problem of tracking cardiac motion and deformation using velocity-encoded magnetic resonance imaging. We expand upon an earlier described method and fit a spatiotemporal motion model to measured velocity data. We investigate several different spatial elements both qualitatively and quantitatively using phantom measurements and data from human subjects. In addition, we also use optical flow estimation by the Horn–Schunk method as complementary data in regions where the velocity measurements are noisy. Our results show that it is possible to obtain good motion tracking accuracy in phantoms with relatively few spatial elements, if the type of element is properly chosen. The use of optical flow can correct some measurement artifacts but may give an underestimation of the magnitude of the deformation. In human subjects the different spatial elements perform quantitatively in a similar way but qualitative differences exists, as shown by a semiquantitative visual scoring of the different methods.      

Maximum a Posteriori Strategy for the Simultaneous Motion and Material Property Estimation of the Heart

In addition to its technical merits as a challenging nonrigid motion and structural integrity analysis problem, quantitative estimation of cardiac regional functions and material characteristics has significant physiological and clinical value. We developed a stochastic finite-element framework for the simultaneous recovery of myocardial motion and material parameters from medical image sequences with an extended Kalman filter approach, and we have shown that this simultaneous estimation strategy achieves more accurate and robust results than separated motion and material estimation efforts. In this paper, we present a new computational strategy for the framework based upon the maximum a posteriori estimation principles, realized through the extended Kalman smoother, that produces a sequence of kinematics state and material parameter estimation of the entire myocardium, including the endocardial, epicardial, and midwall tissues. The system dynamics equations of the heart are constructed using a biomechanical model with stochastic parameters, and the tissue material and deformation parameters are jointly estimated from the periodic imaging data. Noise-corrupted synthetic image sequences with known kinematics and material parameters are used to assess the accuracy and robustness of the framework. Experiments with canine magnetic resonance tagging and phase-contrast image sequences have been conducted with very promising results, as validated through comparison to the histological staining of postmortem myocardium.     

Tag and contour detection in tagged MR images of the left ventricle

Tracking magnetic resonance tags in myocardial tissue promises to be an effective tool for the assessment of myocardial motion. The authors describe a hierarchy of image processing steps which rapidly detects both the contours of the myocardial boundaries of the left ventricle and the tags within the myocardium. The method works on both short axis and long axis images containing radial and parallel tag patterns, respectively. Left ventricular boundaries are detected by first removing the tags using morphological closing and then selecting candidate edge points. The best inner and outer boundaries are found using a dynamic program that minimizes a nonlinear combination of several local cost functions. Tags are tracked by matching a template of their expected profile using a least squares estimate. Since blood pooling, contiguous and adjacent tissue, and motion artifacts sometimes cause detection errors, a graphical user interface was developed to allow user correction of anomalous points. The authors present results on several tagged images of a human. A fully automated run generally finds the endocardial boundary and the tag lines extremely well, requiring very little manual correction. The epicardial boundary sometimes requires more intervention to obtain an acceptable result. These methods are currently being used in the analysis of cardiac strain and as a basis for the analysis of alternate tag geometries.     

Contour extraction from cardiac MRI studies using snakes

The author investigated automatic extraction of left ventricular contours from cardiac magnetic resonance imaging (MRI) studies. The contour extraction algorithms were based on active contour models, or snakes. Based on cardiac MR image characteristics, the author suggested algorithms for extracting contours from these large data sets. The author specifically considered contour propagation methods to make the contours reliable enough despite noise, artifacts, and poor temporal resolution. The emphasis was on reliable contour extraction with a minimum of user interaction. Both spin echo and gradient echo studies were considered. The extracted contours were used for determining quantitative measures for the heart and could also be used for obtaining graphically rendered cardiac surfaces.     

FEM analysis of predicting electrode-myocardium contact from RF cardiac catheter ablation system impedance

We used the finite-element method (FEM) to model and analyze the resistance between the catheter tip electrode and the dispersive electrode during radio-frequency cardiac catheter ablation for the prediction of myocardium-electrode contact. We included deformation of the myocardial surface to achieve accurate modeling. For perpendicular catheter contact, we measured the side view of myocardial deformation using X-ray projection imaging. We averaged the deformation contour from nine samples, and then incorporated the contour information into our FEM model. We measured the resistivity of the bovine myocardium using the four-electrode method, and then calculated the resistance change as the catheter penetrated into the myocardium. The FEM result of resistance versus catheter penetration depth matches well with our experimental data.