Denoising human cardiac diffusion tensor magnetic resonance images using sparse representation combined with segmentation.

Cardiac diffusion tensor magnetic resonance imaging (DT-MRI) is noise sensitive, and the noise can induce numerous systematic errors in subsequent parameter calculations. This paper proposes a sparse representation-based method for denoising cardiac DT-MRI images. The method first generates a dictionary of multiple bases according to the features of the observed image. A segmentation algorithm based on nonstationary degree detector is then introduced to make the selection of atoms in the dictionary adapted to the image's features. The denoising is achieved by gradually approximating the underlying image using the atoms selected from the generated dictionary. The results on both simulated image and real cardiac DT-MRI images from ex vivo human hearts show that the proposed denoising method performs better than conventional denoising techniques by preserving image contrast and fine structures.

A new fully-digital anthropomorphic and dynamic thorax/heart model.

A numerical anthropomorphic model of the breathing thorax and the beating heart is presented. It includes the main thoracic/cardiac anatomical structures, the main vessel junctions as well as the structures' motion. Its main feature is that it is based on a Magnetic Resonance Imaging (MRI) examination performed on the same human subject within the same session from which both structural and motion information are retrieved. This confers to the model a very good consistency. This numerical model is virtually imaged by two simulators: a MRI simulator and a Positron Emission Tomography (PET) simulator. The overall resulting model (structure geometry & dynamics, images) is useful for the evaluation of cardiac image processing algorithms such as heart structure segmentation or multi-modality cardiac image registration.

Modeling the 3D coronary tree for labeling purposes.

Coronary artery diseases are usually revealed using X-ray angiographies. Such images are complex to analyze because they provide a 2D projection of a 3D object. Medical diagnosis suffers from inter- and intra-clinician variability. Therefore, reliable software for the 3D reconstruction and labeling of the coronary tree is strongly desired. It requires the matching of the vessels in the different available angiograms, and an approach which identifies the arteries by their anatomical names is a way to solve this difficult problem. This paper focuses on the automatic labeling of the left coronary tree in X-ray angiography. Our approach is based on a 3D topological model, built from the 3D anthropomorphic phantom, Coronix. The phantom is projected under different angles of view to provide a data base of 2D topological models. On the other hand, the vessel skeleton is extracted from the patient's angiogram. The algorithm compares the skeleton with the 2D topological model which has the most similar vascular net shape. The method performs in a hierarchical manner, first labeling the main artery, then the sub-branches. It handles inter-individual anatomical variations, segmentation errors and image ambiguities. We tested the method on standard angiograms of Coronix and on clinical examinations of nine patients. We demonstrated successful scores of 90% correct labeling for the main arteries and 60% for the sub-branches. The method appears to be particularly efficient for the arteries in focus. It is therefore a very promising tool for the automatic 3D reconstruction of the coronary tree from monoplane temporal angiographic clinical sequences.

The effect of geometric and topologic differences in boundary element models on magnetocardiographic localization accuracy.

This study was performed to evaluate the changes in magnetocardiographic (MCG) source localization results when the geometry and the topology of the volume conductor model were altered. Boundary element volume conductor models of three patients were first constructed. These so-called reference torso models were then manipulated to mimic various sources of error in the measurement and analysis procedures. Next, equivalent current dipole localizations were calculated from simulated and measured multichannel MCG data. The localizations obtained with the reference models were regarded as the "gold standard." The effect of each modification was investigated by calculating three-dimensional distances from the gold standard localizations to the locations obtained with the modified model. The results show that the effect of the lungs and the intra-ventricular blood masses is significant for deep source locations and, therefore, the torso model should preferably contain internal inhomogeneities. However, superficial sources could be localized within a few millimeters even with nonindividual, so called standard torso models. In addition, the torso model should extend long enough in the pelvic region, and the positions of the lungs and the ventricles inside the model should be known in order to obtain accurate localizations.

Two-dimensional spatial and temporal displacement and deformation field fitting from cardiac magnetic resonance tagging.

Tagged magnetic resonance imaging is a specially developed technique to noninvasively assess contractile function of the heart. Several methods have been developed to estimate myocardial deformation from tagged image data. Most of these methods do not explicitly impose a continuity constraint through time although myocardial motion is a continuous physical phenomenon. In this paper, we propose to model the spatio-temporal myocardial displacement field by a cosine series model fitted to the entire tagged dataset. The method has been implemented in two dimensions (2D)+time. Its accuracy was successively evaluated on actual tagged data and on a simulated two-dimensional (2D) moving heart model. The simulations show that an overall theoretical mean accuracy of 0.1 mm can be attained with adequate model orders. The influence of the tagging pattern was evaluated and computing time is provided as a function of the model complexity and data size. This method provides an analytical and hierarchical model of the 2D+time deformation inside the myocardium. It was applied to actual tagged data from a healthy subject and from a patient with ischemia. The results demonstrate the adequacy of the proposed model for this evaluation.

Model extraction from magnetic resonance volume data using the deformable pyramid.

A general framework for automatic model extraction from magnetic resonance (MR) images is described. The framework is based on a two-stage algorithm. In the first stage, a geometrical and topological multiresolution prior model is constructed. It is based on a pyramid of graphs. In the second stage, a matching algorithm is described. This algorithm is used to deform the prior pyramid in a constrained manner. The topological and the main geometrical properties of the model are preserved, and at the same time, the model adapts itself to the input data. We show that it performs a fast and robust model extraction from image data containing unstructured information and noise. The efficiency of the deformable pyramid is illustrated on a synthetic image. Several examples of the method applied to MR volumes are also represented.

Reconstruction of 3-D geometry using 2-D profiles and a geometric prior model.

A method has been developed to reconstruct three-dimensional (3-D) surfaces from two-dimensional (2-D) projection data. It is used to produce individualized boundary element models, consisting of thorax and lung surfaces, for electro- and magnetocardiographic inverse problems. Two orthogonal projections are utilized. A geometrical prior model, built using segmented magnetic resonance images, is deformed according to profiles segmented from projection images. In our method, virtual X-ray images of the prior model are first constructed by simulating real X-ray imaging. The 2-D profiles of the model are segmented from the projections and elastically matched with the profiles segmented from patient data. The displacement vectors produced by the elastic 2-D matching are back projected onto the 3-D surface of the prior model. Finally, the model is deformed, using the back-projected vectors. Two different deformation methods are proposed. The accuracy of the method is validated by a simulation. The average reconstruction error of a thorax and lungs was 1.22 voxels, corresponding to about 5 mm.

Simulated annealing, acceleration techniques, and image restoration.

Typically, the linear image restoration problem is an ill-conditioned, underdetermined inverse problem. Here, stabilization is achieved via the introduction of a first-order smoothness constraint which allows the preservation of edges and leads to the minimization of a nonconvex functional. In order to carry through this optimization task, we use stochastic relaxation with annealing. We prefer the Metropolis dynamics to the popular, but computationally much more expensive, Gibbs sampler. Still, Metropolis-type annealing algorithms are also widely reported to exhibit a low convergence rate. Their finite-time behavior is outlined and we investigate some inexpensive acceleration techniques that do not alter their theoretical convergence properties; namely, restriction of the state space to a locally bounded image space and increasing concave transform of the cost functional. Successful experiments about space-variant restoration of simulated synthetic aperture imaging data illustrate the performance of the resulting class of algorithms and show significant benefits in terms of convergence speed.

Stereoscopic visualization of three-dimensional ultrasonic data applied to breast tumours.

OBJECTIVE: This paper presents a technique for stereoscopic visualization applied to three-dimensional (3D) ultrasonic breast data. METHODS: A motorized acquisition system has been designed to translate regularly a linear-phased array transducer, in order to provide a series of parallel echographic slices of the breast. During acquisition, the breast is compressed between a plane support and a plexiglass plate to avoid breast motion. A window in this plate provides access for ultrasonic exploration. From the series of cross-sectional scans, a 3D volume is formed by interpolation between the successive ultrasonic images. A stereoscopic computer-graphic method has been developed to visualize these 3D ultrasonic data. Two conical transparent projections of the volume are computed from two slightly different viewpoints. These two projections make up the stereoscopic pair. This pair is displayed on a stereoscopic monitor for the visualization of the 3D data with the depth dimension. RESULTS: The acquisition system and the method for computing the stereo-echograms were validated using an agar gel phantom. In vivo breast experiments were also performed. CONCLUSION: Visualization of stereo-echographic projections improves the perception of depth and shape of breast tumours.

Tracking geometrical descriptors on 3-D deformable surfaces: application to the left-ventricular surface of the heart.

Motion and deformation analysis of the myocardium are of utmost interest in cardiac imaging. Part of the, research is devoted to the estimation of the heart function by analysis of the shape changes of the left-ventricular endocardial surface. However, most clinically used shape-based approaches are often two-dimensional (2-D) and based on the analysis of the shape at only two cardiac instants. Three-dimensional (3-D) approaches generally make restrictive hypothesis about the actual endocardium motion to be able to recover a point-to-point correspondence between two surfaces. The present work is a first step toward the automatic spatio-temporal analysis and recognition of deformable surfaces. A curvature-based and easily interpretable description of the surfaces is derived. Based on this description, shape dynamics is first globally estimated through the temporal shape spectra. Second, a regional curvature-based tracking approach is proposed assuming a smooth deformation. It combines geometrical and spatial information in order to analyze a specific endocardial region. These methods are applied both on true 3-D X-ray data and on simulated normal and abnormal left ventricles. The results are coherent and easily interpretable. Shape dynamics estimations and comparisons between deformable object sequences are now possible through these techniques. This promising framework is a suitable tool for a complete regional description of deformable surfaces.

Improved vessel visualization in MR angiography by nonlinear anisotropic filtering.

This paper deals with a preprocessing technique of magnetic resonance angiography (MRA) images, applied before maximum-intensity-projection (MIP). The purpose was to recover small low-intensity vessels, visible in individual slices, but lost in MIP images that usually have higher background level than the individual slices. The authors have developed a nonlinear three-dimensional spatial filtering technique (called HD filter) based on anisotropic smoothing. The filter first searches for the local orientation of the vessel. It then performs a nonlinear smoothing in the vessel's local direction so as to avoid blurring its boundaries. Noise level reduction, contrast enhancement, and improved small vessel visibility achieved by this filter are illustrated on dynamic contrast-enhanced subtraction MRA images of the lower limbs.

Estimation of three-dimensional cardiac velocity fields: assessment of a differential method and application to three-dimensional CT data.

We have investigated an optical flow method for the estimation of the three-dimensional endocardial wall motion from high-resolution X-ray CT data. This method was originally proposed by Song and Leahy. It is based on the optical flow, the divergence-free and the smoothness constraints. Due to the characteristics of the imaging modality, we studied the restriction of this approach to the boundary of the left ventricular (LV) cavity. The behaviour of the method is quantified through simulations approximating the overall motion of the LV cavity through an affine transform involving a dilation and a rotation. The method implies the choice of three parameters weighting the constraints. The results show a weak dependence of the velocity field on the weighting of the optical flow constraint. The accuracy of the method relies more heavily on the relative weighting of the smoothness and divergence-free constraints. In our experiments, the best results were obtained for a largely predominant divergence-free constraint. The results also show that the accuracy of the method is reasonable for low values of the rotation angle (minimum mean error of 1.1 voxel for 5 degrees). This is compatible with values reported in other studies for the overall rotation of the LV. We provide a qualitative description of the results obtained in vivo on a canine heart by visualizing the distribution of the estimated velocity vector magnitudes over the endocardial surface. These results (evolution of the field over time, maximum velocities) are in agreement with the known physiological behaviour of the heart.

Automated myocardial edge detection from breath-hold cine-MR images: evaluation of left ventricular volumes and mass.

This paper describes an automated edge detection method for the delineation of the endo- and epicardial borders of the left ventricle from magnetic resonance (MR) images. The feasibility of this technique was demonstrated by processing temporal series of cardiac MR images obtained in 12 healthy subjects and acquired from the apex to the base of the heart in multiple anatomic short axis planes with a breath-hold cine-MR acquisition sequence. This procedure allows the entire heart to be imaged in less than 5 min. The automatic program correctly identified the edges in most cases. In poor contrasted images, a fast and user-friendly interactive procedure was used to correct the border delineation. The proposed method for the contour tracing requires a limited degree of control by the user and thus considerably reduces the tedious and long operator time inherent in the usual manual contour tracing tool. The left ventricular volumes were directly measured from these sets of contours by using the Simpson rule, allowing the end-diastolic volumes (EDV), the end-systolic volumes (ESV), the ejection fraction (EF) and the myocardial mass to be determined. The values measured in this study with the dedicated software were similar to the literature values (EDV = 78.3 ml/m2; ESV = 21.1 ml/m2; EF = 73%). Associated with the ultrafast breath-hold cine-MR imaging, the described edge detection method provides an efficient clinical tool for the direct assessment of cardiac function.

Assessment and visualization of the curvature of the left ventricle from 3D medical images.

We address the problem of using curvature features to assess the three-dimensional (3D) motion of the left ventricle. The adequacy of this approach depends on the actual characteristics of the curvature of the left ventricle and particularly on the spatial and temporal stability of these features. From experimental data, we compute the distribution of the Gaussian curvature over the surface of the left ventricle by using an iterative procedure. The results are visualized in 3D through a voxel-based surface rendering technique. We show that the Gaussian curvature remains stable along the cardiac cycle. This curvature feature could thus provide a reliable basis for further 3D motion analysis of the left ventricle.

Image quality study in 3D X-ray angiography: a first approach using the experimental design strategy.

The visual detection of fine structures and the accuracy of the quantitation of geometric and densitometric features, are closely related to the quality of the images available in two-dimensional (2D) and three-dimensional (3D) X-ray angiography. In this context, we propose to analyze all the parameters influencing this accuracy using an experimental design strategy. Preliminary tests of this procedure, applied to 2D and 3D angiographic data obtained from a dedicated phantom, yield encouraging results. We show that the detection of small arteries in a 3D angiogram is more sensitive to the number of projections than to the X-ray dose.

Assessment of a model for overall left ventricular three-dimensional motion from MRI data.

In this paper we present a complete methodology to evaluate a model for overall three-dimensional (3D) motion of the human left ventricle (LV) from MRI data. The left ventricular motion is approximated by a linear model associated with an affine transformation to determine parameters for non-rigid motion of the LV. The proposed method has been applied to a normal patient and to a patient with cardiac disease. Results obtained show that the linear model provides a fairly good approximation of normal left ventricular motion, whereas serious cardiac disease produces abnormal motion, yielding altered model performances.