Reconstructing the cross sections of coronary arteries from biplane angiograms

An algorithm that reconstructs the cross sections of the lumens of coronary arteries from two mutually orthogonal X-ray projections is described. The algorithm accommodates the possibility of elliptical, crescent, or star shapes. It represents each biplane projection of a transverse slice of the arterial lumen as a binary-valued image. The single-coordinate moments of these two projection images are equal to those of the slice. Since the cross-coordinate moments of the slice are not available from the projections, an algorithm to estimate these moments based on assumptions of smoothness and connectivity is developed. Once all the missing moments are estimated, the image of the slice can be estimated by inverting these moments, using the uniqueness theorem governing the relation between an image and its moments. Preliminary tests of the algorithm on synthetic data, on hardware phantoms and on a segment of a barium-enhanced in vitro coronary artery are reported.     

Estimating the 3D skeletons and transverse areas of coronary arteries from biplane angiograms

A method for estimating the three-dimensional (3D) skeletons and transverse areas of the lumens of coronary arteries from digital X-ray angiograms is described. The method is based on the use of a 3D generalized cylinder (GC) consisting of a series of 3D elliptical disks transverse to and centered on a 3D skeleton (medial axis) of the coronary arteries. The estimates of the transverse areas are based on a nonlinear least-squares-error estimation technique described by D.W. Marquardt (1963). This method exploits densitometric profiles, boundary estimates, and the orientation of the arterial skeleton in 3-space and includes an automatic artery tracking procedure. It applies an adaptive window to the densitometric profile data that are used in the parameter estimation. Preliminary experimental tests of the procedure on angiograms of in vivo human coronaries and on synthetic images yield encouraging results.     

Assessment of diffuse coronary artery disease by quantitative analysis of coronary morphology based upon 3-D reconstruction from biplane angiograms

Quantitative evaluations on coronary vessel systems are of increasing importance in cardiovascular diagnosis, therapy planning, and surgical verification. Whereas local evaluations, such as stenosis analysis, are already available with sufficient accuracy, global evaluations of vessel segments or vessel subsystems are not yet common. Especially for the diagnosis of diffuse coronary artery diseases, the authors combined a 3D reconstruction system operating on biplane angiograms with a length/volume calculation. The 3D reconstruction results in a 3D model of the coronary vessel system, consisting of the vessel skeleton and a discrete number of contours. To obtain an utmost accurate model, the authors focussed on exact geometry determination. Several algorithms for calculating missing geometric parameters and correcting remaining geometry errors were implemented and verified. The length/volume evaluation can be performed either on single vessel segments, on a set of segments, or on subtrees. A volume model based on generalized elliptical conic sections is created for the selected segments. Volumes and lengths (measured along the vessel course) of those elements are summed up. In this way, the morphological parameters of a vessel subsystem can be set in relation to the parameters of the proximal segment supplying it. These relations allow objective assessments of diffuse coronary artery diseases.     

A comparison framework for breathing motion estimation methods from 4-D imaging

Motion estimation is an important issue in radiation therapy of moving organs. In particular, motion estimates from 4-D imaging can be used to compute the distribution of an absorbed dose during the therapeutic irradiation. We propose a strategy and criteria incorporating spatiotemporal information to evaluate the accuracy of model-based methods capturing breathing motion from 4-D CT images. This evaluation relies on the identification and tracking of landmarks on the 4-D CT images by medical experts. Three different experts selected more than 500 landmarks within 4-D CT images of lungs for three patients. Landmark tracking was performed at four instants of the expiration phase. Two metrics are proposed to evaluate the tracking performance of motion-estimation models. The first metric cumulates over the four instants the errors on landmark location. The second metric integrates the error over a time interval according to an a priori breathing model for the landmark spatiotemporal trajectory. This latter metric better takes into account the dynamics of the motion. A second aim of this paper is to estimate the impact of considering several phases of the respiratory cycle as compared to using only the extreme phases (end-inspiration and end-expiration). The accuracy of three motion estimation models (two image registration-based methods and a biomechanical method) is compared through the proposed metrics and statistical tools. This paper points out the interest of taking into account more frames for reliably tracking the respiratory motion.     

Video compression of coronary angiograms based on discrete wavelet transform with block classification

A new method of video compression for angiographic images has been developed to achieve high compression ratio (~20:1) while eliminating block artifacts which leads to loss of diagnostic accuracy. This method adopts motion picture experts group's (MPEGs) motion compensated prediction to takes advantage of frame to frame correlation. However, in contrast to MPEG, the error images arising from mismatches in the motion estimation are encoded by discrete wavelet transform (DWT) rather than block discrete cosine transform (DCT). Furthermore, the authors developed a classification scheme which label each block in an image as intra, error, or background type and encode it accordingly. This hybrid coding can significantly improve the compression efficiency in certain eases. This method can be generalized for any dynamic image sequences applications sensitive to block artifacts.     

Object-based 3-D reconstruction of arterial trees from magnetic resonance angiograms

By exploiting a priori knowledge of arterial shape and smoothness, subpixel accuracy reconstructions are achieved from only four noisy projection images. The method incorporates a priori knowledge of the structure of branching arteries into a natural optimality criterion that encompasses the entire arterial tree. An efficient optimization algorithm for object estimation is presented, and its performance on simulated, phantom, and in vivo magnetic resonance angiograms is demonstrated. It is shown that accurate reconstruction of bifurcations is achievable with parametric models.     

Prospective motion correction of X-ray images for coronary interventions

A method for prospective motion correction of X-ray imaging of the heart is presented. A 3D + t coronary model is reconstructed from a biplane coronary angiogram obtained during free breathing. The deformation field is parameterized by cardiac and respiratory phase, which enables the estimation of the state of the arteries at any phase of the cardiac-respiratory cycle. The motion of the three-dimensional (3-D) coronary model is projected onto the image planes and used to compute a dewarping function for motion correcting the images. The use of a 3-D coronary model facilitates motion correction of images acquired with the X-ray system at arbitrary orientations. The performance of the algorithm was measured by tracking the motion of selected left coronary landmarks using a template matching cross-correlation. In three patients, we motion corrected the same images used to construct their 3D + t coronary model. In this best case scenario, the algorithm reduced the motion of the landmarks by 84%-85%, from mean RMS displacements of 12.8-14.6 pixels to 2.1-2.2 pixels. Prospective motion correction was tested in five patients by building the coronary model from one dataset, and correcting a second dataset. The patient's cardiac and respiratory phase are monitored and used to calculate the appropriate correction parameters. The results showed a 48%-63% reduction in the motion of the landmarks, from a mean RMS displacement of 11.5-13.6 pixels to 4.4-7.1 pixels.     

Three-dimensional motion tracking of coronary arteries in biplane cineangiograms

A three-dimensional (3-D) method for tracking the coronary arteries through a temporal sequence of biplane X-ray angiography images is presented. A 3-D centerline model of the coronary vasculature is reconstructed from a biplane image pair at one time frame, and its motion is tracked using a coarse-to-fine hierarchy of motion models. Three-dimensional constraints on the length of the arteries and on the spatial regularity of the motion field are used to overcome limitations of classical two-dimensional vessel tracking methods, such as tracking vessels through projective occlusions. This algorithm was clinically validated in five patients by tracking the motion of the left coronary tree over one cardiac cycle. The root mean square reprojection errors were found to be submillimeter in 93% (54/58) of the image pairs. The performance of the tracking algorithm was quantified in three dimensions using a deforming vascular phantom. RMS 3-D distance errors were computed between centerline models tracked in the X-ray images and gold-standard centerline models of the phantom generated from a gated 3-D magnetic resonance image acquisition. The mean error was 0.69 (+/- 0.06) mm over eight temporal phases and four different biplane orientations.     

Displacement and velocity of the coronary arteries: cardiac and respiratory motion

This paper presents measurements of three-dimensional (3-D) displacements and velocities of the coronary arteries due to the myocardial beating motion and due to breathing. Data were acquired by reconstructing the coronary arteries and their motion from biplane angiograms in 10 patients. A parametric motion model was used to separate the cardiac and breathing motion fields. The arteries move consistently toward the left, inferior, and anterior during a cardiac contraction. The displacement and velocity of the right coronary artery during a cardiac contraction was larger than measured for the left coronary tree. Cardiac motion dominates the respiratory motion of the coronary arteries during spontaneous breathing. On inspiration, the arteries move caudally, but the motion in the left-right and anterior-posterior axes was variable. Spatial variation in respiratory displacement and velocity of the coronary arteries indicates that the breathing motion of the heart is more complex than a 3-D translation.     

Evaluation of JPEG 2000 encoder options: human and model observer detection of variable signals in X-ray coronary angiograms

Previous studies have evaluated the effect of the new still image compression standard JPEG 2000 using nontask based image quality metrics, i.e., peak-signal-to-noise-ratio (PSNR) for nonmedical images. In this paper, the effect of JPEG 2000 encoder options was investigated using the performance of human and model observers (nonprewhitening matched filter with an eye filter, square-window Hotelling, Laguerre-Gauss Hotelling and channelized Hotelling model observer) for clinically relevant visual tasks. Two tasks were investigated: the signal known exactly but variable task (SKEV) and the signal known statistically task (SKS). Test images consisted of real X-ray coronary angiograms with simulated filling defects (signals) inserted in one of the four simulated arteries. The signals varied in size and shape. Experimental results indicated that the dependence of task performance on the JPEG 2000 encoder options was similar for all model and human observers. Model observer performance in the more tractable and computationally economic SKEV task can be used to reliably estimate performance in the complex but clinically more realistic SKS task. JPEG 2000 encoder settings different from the default ones resulted in greatly improved model and human observer performance in the studied clinically relevant visual tasks using real angiography backgrounds.     

A study of the motion and deformation of the heart due to respiration

This paper describes a quantitative assessment of respiratory motion of the heart and the construction of a model of respiratory motion. Three-dimensional magnetic resonance scans were acquired on eight normal volunteers and ten patients. The volunteers were imaged at multiple positions in the breathing cycle between full exhalation and full inhalation while holding their breath. The exhalation volume was segmented and used as a template to which the other volumes were registered using an intensity-based rigid registration algorithm followed by nonrigid registration. The patients were imaged at inhale and exhale only. The registration results were validated by visual assessment and consistency measurements indicating subvoxel registration accuracy. For all subjects, we assessed the nonrigid motion of the heart at the right coronary artery, right atrium, and left ventricle. We show that the rigid-body motion of the heart is primarily in the craniocaudal direction with smaller displacements in the right-left and anterior-posterior directions; this is in agreement with previous studies. Deformation was greatest for the free wall of the right atrium and the left ventricle; typical deformations were 3-4 mm with deformations of up to 7 mm observed in some subjects. Using the registration results, landmarks on the template surface were mapped to their correct positions through the breathing cycle. Principal component analysis produced a statistical model of the motion and deformation of the heart. We discuss how this model could be used to assist motion correction.     

On the optimality of magnetic resonance tag patterns for heart wall motion estimation

Tracking of cardiac motion using magnetic resonance tagging has attracted increasing attention in recent years. Several methods for tagging the cardiac tissue and tracking the motion of the tags have been developed. However, the choice of tag pattern that minimizes tracking error has received less attention. In this paper, we are concerned with the optimal tagging and acquisition of MR tagged images for cardiac motion analysis. We formulate the measurement of tissue deformation as a multidimensional parametric estimation problem which can be solved using the nonlinear least squares estimator. Along with this, we derive the Cramer-Rao lower bound (CRLB) on the average estimation error variance. We then show that under certain conditions a complex sinusoidal tag shape minimizes the CRLB. We validate our results with computer simulations. Finally, based on the previous findings, we make recommendations concerning the most desirable imaging strategy for images tagged with a complex sinusoidal tag pattern.     

A nonsmoothing approach to the estimation of vessel contours in angiograms

Accurate and fully automatic assessment of vessel (stenoses) dimensions in angiographic images has been sought as a diagnostic tool, in particular for coronary heart disease. Here, the authors propose a new technique to estimate vessel borders in angiographic images, a necessary first step of any automatic analysis system. Unlike in previous approaches, the obtained edge estimates are not artificially smoothed; this is extremely important since quantitative analysis is the goal. Another important feature of the proposed technique is that no constant background is assumed, this making it well suited for nonsubtracted angiograms. The key aspect of the authors' approach is that continuity/smoothness constraints are not used to modify the estimates directly derived from the image (which would introduce distortion) but rather to elect (without modifying) candidate estimates. Robustness against unknown background is provided by the use a morphological edge operator, instead of some linear operator (such as a matched filter) which has to assume known background and known vessel shape.     

Comparison of impedance and inductance ventilation sensors onadults during breathing, motion, and simulated airway obstruction

The goal of this study was to compare the relative performance of two noninvasive ventilation sensing technologies on adults during artifacts. The authors recorded changes in transthoracic impedance and cross-sectional area of the abdomen (abd) and ribcage (rc) using impedance pneumography (IP) and respiratory inductance plethysmography (RIP) on ten adult subjects during natural breathing, motion artifact, simulated airway obstruction, yawning, snoring, apnea, and coughing. The authors used a pneumotachometer to measure air flow and tidal volume as the standard. They calibrated all sensors during natural breathing, and performed measurements during all maneuvers without changing the calibration parameters. No sensor provided the most-accurate measure of tidal volume for all maneuvers. Overall, the combination of inductance sensors [RIP(sum)] calibrated during an isovolume maneuver had a bias (weighted mean difference) as low or lower than all individual sensors and all combinations of sensors. The IP(rc) sensor had a bias as low or lower than any individual sensor. The cross-correlation coefficient between sensors was high during natural breathing, but decreased during artifacts. The cross correlation between sensor pairs was lower during artifacts without breathing than it was during maneuvers with breathing for four different sensor combinations. The authors tested a simple breath-detection algorithm on all sensors and found that RIP(sum) resulted in the fewest number of false breath detections, with sensitivity of 90.8% and positive predictivity of 93.6%     

Recursive tracking of vascular networks in angiograms based on the detection-deletion scheme

A computer algorithm was developed for automated identification of 2-D vascular networks in X-ray angiograms. This was accomplished by using an adaptive tracking algorithm in a three-stage recursive procedure. First, given a starting position and direction, a segment in the vascular network was identified. Second, by filling it with the surrounding background pixel values, the detected segment was deleted from the angiogram. The detection-deletion scheme was employed to prevent the problem of tracking-path reentry in those areas where vessels overlap. Third, all branch points were detected by use of matched filtering along both edges of the vessel. The detected branch points were used as the starting points in the next recursion. The recursive procedure terminated when no new branch point was found. The algorithm showed a good performance when it was applied to angiograms of coronary and radial arteries. To provide a quantitative evaluation, vascular networks identified by the algorithm were compared to those identified by a human. The algorithm made some false-negative errors, but very few false-positive errors.     

On the computation of motion from sequences of images-A review

Recent developments are reviewed in the computation of motion and structure of objects in a scene from a sequence of images. Two distinct paradigms are highlighted: (i) the feature-based approach and (ii) the optical-flow-based approach. The comparative merits/demerits of these approaches are discussed. The current status of research in these areas is reviewed and future research directions are indicated     

Estimating the motion direction from brightness gradient on lines

In previous work we combined feature-based techniques and optical flow methods to obtain depth or motion. The expressions relating the brightness constraint to the three-dimensional (3D) localization and motion of a line and its projection were established. In this paper, those expressions have been used to obtain the motion direction of a camera when the rotation velocity is bounded without assumptions about the depth of lines. Our approach exploits the visibility constraint and it allows us to make use of a priori information about the scene or the motion. With the proposed technique, the topology (easily extracted in the image) that relates adjacent edge elements into line segments is exploited to better compute camera motion. Besides the motion direction, our method allows also to compute the rotation velocity when lines in prominent 3D directions are available     

A 3D reconstruction of vascular structures from two X-ray angiograms using an adapted simulated annealing algorithm

A three-dimensional (3D) reconstruction of the vessel lumen from two angiographic views, based on the reconstruction of a series of cross-sections, is proposed. Assuming uniform mixing of contrast medium and background subtraction, the cross-section of each vessel is reconstructed through a binary representation. A priori information about both the slice to be reconstructed and the relationships between adjacent slices are incorporated to lessen ambiguities on the reconstruction. Taking into account the knowledge of normal vessel geometry, an initial solution of each slice is created using an elliptic model-based method. This initial solution is then deformed to be made consistent with projection data while being constrained into a connected realistic shape. For that purpose, properties on the expected optimal solution are described through a Markov random field. To find an optimal solution, a specific optimization algorithm based on simulated annealing is used. The method performs well both on single vessels and on branching vessels possessing an additional inherent ambiguity when viewed at oblique angles. Results on 2D slice independent reconstruction and 3D reconstruction of a stack of spatially continuous 2D slices are presented for single vessels and bifurcations.