Novel Approach for 3-D Reconstruction of Coronary Arteries From Two Uncalibrated Angiographic Images

Three-dimensional reconstruction of vessels from digital X-ray angiographic images is a powerful technique that compensates for limitations in angiography. It can provide physicians with the ability to accurately inspect the complex arterial network and to quantitatively assess disease induced vascular alterations in three dimensions. In this paper, both the projection principle of single view angiography and mathematical modeling of two view angiographies are studied in detail. The movement of the table, which commonly occurs during clinical practice, complicates the reconstruction process. On the basis of the pinhole camera model and existing optimization methods, an algorithm is developed for 3-D reconstruction of coronary arteries from two uncalibrated monoplane angiographic images. A simple and effective perspective projection model is proposed for the 3-D reconstruction of coronary arteries. A nonlinear optimization method is employed for refinement of the 3-D structure of the vessel skeletons, which takes the influence of table movement into consideration. An accurate model is suggested for the calculation of contour points of the vascular surface, which fully utilizes the information in the two projections. In our experiments with phantom and patient angiograms, the vessel centerlines are reconstructed in 3-D space with a mean positional accuracy of 0.665 mm and with a mean back projection error of 0.259 mm. This shows that the algorithm put forward in this paper is very effective and robust.     

Three-dimensional guide-wire reconstruction from biplane image sequences for integrated display in 3-D vasculature

Using three-dimensional rotational X-ray angiography (3DRA), three-dimensional (3-D) information of the vasculature can be obtained prior to endovascular interventions. However, during interventions, the radiologist has to rely on fluoroscopy images to manipulate the guide wire. In order to take full advantage of the 3-D information from 3DRA data during endovascular interventions, a method is presented that yields an integrated display of the position of the guide wire and vasculature in 3-D. The method relies on an automated method that tracks the guide wire simultaneously in biplane fluoroscopy images. Based on the calibrated geometry of the C-arm, the 3-D guide-wire position is determined and visualized in the 3-D coordinate system of the vasculature. The method is evaluated in an intracranial anthropomorphic vascular phantom. The influence of the angle between projections, distortion correction of the projection images, and accuracy of geometry knowledge on the accuracy of 3-D guide-wire reconstruction from biplane images is determined. If the calibrated geometry information is used and the images are corrected for distortion, a mean distance to the reference standard of 0.42 mm and a tip distance of 0.65 mm is found, which means that accurate guide-wire reconstruction from biplane images can be performed.     

Evaluation of iterative sparse object reconstruction from few projections for 3-D rotational coronary angiography

A 3-D reconstruction of the coronary arteries offers great advantages in the diagnosis and treatment of cardiovascular disease, compared to 2-D X-ray angiograms. Besides improved roadmapping, quantitative vessel analysis is possible. Due to the heart's motion, rotational coronary angiography typically provides only 5–10 projections for the reconstruction of each cardiac phase, which leads to a strongly undersampled reconstruction problem. Such an ill-posed problem can be approached with regularized iterative methods. The coronary arteries cover only a small fraction of the reconstruction volume. Therefore, the minimization of the ${mbi L}_1$ norm of the reconstructed image, favoring spatially sparse images, is a suitable regularization. Additional problems are overlaid background structures and projection truncation, which can be alleviated by background reduction using a morphological top-hat filter. This paper quantitatively evaluates image reconstruction based on these ideas on software phantom data, in terms of reconstructed absorption coefficients and vessel radii. Results for different algorithms and different input data sets are compared. First results for electrocardiogram-gated reconstruction from clinical catheter-based rotational X-ray coronary angiography are presented. Excellent 3-D image quality can be achieved.      

Reconstruction of coronary arteries from a single rotational X-ray projection sequence

Cardiovascular diseases remain the primary cause of death in developed countries. In most cases, exploration of possibly underlying coronary artery pathologies is performed using X-ray coronary angiography. Current clinical routine in coronary angiography is directly conducted in two-dimensional projection images from several static viewing angles. However, for diagnosis and treatment purposes, coronary artery reconstruction is highly suitable. The purpose of this study is to provide physicians with a three-dimensional (3-D) model of coronary arteries, e.g., for absolute 3-D measures for lesion assessment, instead of direct projective measures deduced from the images, which are highly dependent on the viewing angle. In this paper, we propose a novel method to reconstruct coronary arteries from one single rotational X-ray projection sequence. As a side result, we also obtain an estimation of the coronary artery motion. Our method consists of three main consecutive steps: 1) 3-D reconstruction of coronary artery centerlines, including respiratory motion compensation; 2) coronary artery four-dimensional motion computation; 3) 3-D tomographic reconstruction of coronary arteries, involving compensation for respiratory and cardiac motions. We present some experiments on clinical datasets, and the feasibility of a true 3-D Quantitative Coronary Analysis is demonstrated.     

Geometrically correct 3-D reconstruction of intravascularultrasound images by fusion with biplane angiography-methods andvalidation

In the rapidly evolving field of intravascular ultrasound (IVUS), the assessment of vessel morphology still lacks a geometrically correct three-dimensional (3-D) reconstruction. The IVUS frames are usually stacked up to form a straight vessel, neglecting curvature and the axial twisting of the catheter during the pullback. Our method combines the information about vessel cross-sections obtained from IVUS with the information about the vessel geometry derived from biplane angiography. First, the catheter path is reconstructed from its biplane projections, resulting in a spatial model. The locations of the IVUS frames are determined and their orientations relative to each other are calculated using a discrete approximation of the Frenet-Serret formulas known from differential geometry. The absolute orientation of the frame set is established, utilizing the imaging catheter itself as an artificial landmark. The IVUS images are segmented, using our previously developed algorithm. The fusion approach has been extensively validated in computer simulations, phantoms, and cadaveric pig hearts.     

Modeling and optimization of rotational C-arm stereoscopic X-rayangiography

Stereoscopy can be an effective method for obtaining three-dimensional (3-D) spatial information from two-dimensional (2-D) projection X-ray images, without the need for tomographic reconstruction. This much-needed information is missed in many X-ray diagnostic and interventional procedures, such as the treatment of vascular aneurysms. Fast C-arm X-ray systems can obtain multiple angle sequences of stereoscopic image pairs from a single contrast injection and a single breath hold. To advance this solution, we developed a model of stereo angiography, performed perception experiments and related results to optimal acquisition. The model described horizontal disparity for the C-arm geometry that agreed very well with measurements from a geometric phantom. The perceptual accommodation-convergence conflict and geometry limited the effective stereoscopic field of view (SFOV). For a typical large image intensifier system, it was 28 cm x 31 cm at the center of rotation (COR). In the model, blurring from finite focal-spot size and C-arm motion reduced depth resolution on the digital display. Near the COR, the predicted depth resolution was 3-11 mm for a viewing angle of 7 degrees , which agreed favorably with results from recently published studies. The model also described how acquisition parameters affected spatial warping of curves of equal apparent depth. Pincushioning and the difference between the acquisition and display geometry were found to introduce additional distortions to stereo displays. Preference studies on X-ray angiograms indicated that the ideal viewing angle should be small (1-2 degrees), which agreed with some previously published work. Perceptual studies indicated that stereo angiograms should have high artery contrast and that digital processing to increase contrast improved stereopsis. Digital subtraction angiograms, with different motion errors between the left and right-eye views, gave artifacts that confused stereopsis. The addition of background to subtracted images reduced this effect and provided other features for improved depth perception. Using the modeling results and typical clinical angiography requirements, we recommend acquisition protocols and engineering specifications that are achievable on current high-end systems.     

Estimation of dynamically evolving ellipsoids with applications to medical imaging

The estimation of dynamically evolving ellipsoids from noisy lower-dimensional projections is examined. In particular, this work describes a model-based approach using geometric reconstruction and recursive estimation techniques to obtain a dynamic estimate of left-ventricular ejection fraction from a gated set of planar myocardial perfusion images. The proposed approach differs from current ejection fraction estimation techniques both in the imaging modality used and in the subsequent processing which yields a dynamic ejection fraction estimate. For this work, the left ventricle is modeled as a dynamically evolving three-dimensional (3-D) ellipsoid. The left-ventricular outline observed in the myocardial perfusion images is then modeled as a dynamic, two-dimensional (2-D) ellipsoid, obtained as the projection of the former 3-D ellipsoid. This data is processed in two ways: first, as a 3-D dynamic ellipsoid reconstruction problem; second, each view is considered as a 2-D dynamic ellipse estimation problem and then the 3-D ejection fraction is obtained by combining the effective 2-D ejection fractions of each view. The approximating ellipsoids are reconstructed using a Rauch-Tung-Striebel smoothing filter, which produces an ejection fraction estimate that is more robust to noise since it is based on the entire data set; in contrast, traditional ejection fraction estimates are based only on true frames of data. Further, numerical studies of the sensitivity of this approach to unknown dynamics and projection geometry are presented, providing a rational basis for specifying system parameters. This investigation includes estimation of ejection fraction from both simulated and real data.     

Motion correction for coronary stent reconstruction from rotational X-ray projection sequences

This paper presents a new method for 3-D tomographic reconstruction of stent in X-ray cardiac rotational angiography. The method relies on 2-D motion correction from two radiopaque markerballs located on each side of the stent. The two markerballs are on a guidewire and linked to the balloon, which is introduced into the artery. Once the balloon has been inflated, deflated, and the stent deployed, a rotational sequence around the patient is acquired. Under the assumption that the guidewire and the stent have the same 3-D motion during rotational acquisition, we developed an algorithm to correct cardiac stent motion on the 2-D X-ray projection images. The 3-D image of the deployed stent is then reconstructed with the Feldkamp algorithm using all the available projections. Although the correction is an approximation, we show that the intrinsic geometrical error of our method has no visual impact on the reconstruction when the 2-D markerball centers are exactly detected and the markerballs have the same 3-D motion as the stent. Qualitative and quantitative results on simulated sequences under different realistic conditions demonstrate the robustness of the method. Finally, results from animal data acquired on a rotational angiography device are presented.     

Performance analysis of maximum intensity projection algorithm for display of MRA images

The maximum intensity projection (MIP) is a popularly used algorithm for display of MRA images, but its performance has not been rigorously analyzed before. In this paper, four measures are proposed for the performance of the MIP algorithm and the quality of images projected from three-dimensional (3-D) data, which are vessel voxel projection probability, vessel detection probability, false vessel probability, and vessel-tissue contrast-to-noise ratio (CNR). As side products, vessel-missing probability, vessel receiver operating characteristics (ROC's), and mean number of false vessels are also studied. Based on the assumptions that the intensities of vessel, tissue, and noise along a projection path are independent Gaussian, these measures are derived and obtained all in closed forms. All the measures are functions of explicit parameters: vessel-to-tissue noise ratio (VTNR) and CNR of 3-D data prior to the MIP, vessel diameter, and projection length. It is shown that the MIP algorithm increases the CNR of large vessels whose CNR prior to the MIP is high and whose diameters are large. The increase in CNR increases with projection path length. On the other hand, all the proposed measures indicate that the small vessels that have low CNR prior to the MIP and small diameters suffer from the MIP. The performance gets worse as projection path length increases. All measures demonstrate a better performance when the vessel diameter is larger. Other properties and possible applications of the derived measures are also discussed.     

Tomographic reconstruction using an adaptive tetrahedral mesh defined by a point cloud

Medical images in nuclear medicine are commonly represented in three dimensions as a stack of two-dimensional images that are reconstructed from tomographic projections. Although natural and straightforward, this may not be an optimal visual representation for performing various diagnostic tasks. A method for three-dimensional (3-D) tomographic reconstruction is developed using a point cloud image representation. A point cloud is a set of points (nodes) in space, where each node of the point cloud is characterized by its position and intensity. The density of the nodes determines the local resolution allowing for the modeling of different parts of the image with different resolution. The reconstructed volume, which in general could be of any resolution, size, shape, and topology, is represented by a set of nonoverlapping tetrahedra defined by the nodes. The intensity at any point within the volume is defined by linearly interpolating inside a tetrahedron from the values at the four nodes that define the tetrahedron. This approach creates a continuous piecewise linear intensity over the reconstruction domain. The reconstruction provides a distinct multiresolution representation, which is designed to accurately and efficiently represent the 3-D image. The method is applicable to the acquisition of any tomographic geometry, such as parallel-, fan-, and cone-beam; and the reconstruction procedure can also model the physics of the image detection process. An efficient method for evaluating the system projection matrix is presented. The system matrix is used in an iterative algorithm to reconstruct both the intensity and location of the distribution of points in the point cloud. Examples of the reconstruction of projection data generated by computer simulations and projection data experimentally acquired using a Jaszczak cardiac torso phantom are presented. This work creates a framework for voxel-less multiresolution representation of images in nuclear medicine.     

基于造影图像的冠状动脉三维定量分析的研究

由于X射线造影成像把血管三维空间结构投影到二维图像上,基于二维造影图像的传统诊治方法存在很大局限性.本文在冠状动脉树三维重建的基础上,研究了冠状动脉的三维定量分析方法,提出血管直径、分支夹角和血管段长度的三维测量方法.并利用冠状动脉树实物模型进行实验,对二维和三维定量分析结果进行了比较.实验结果表明,三维定量分析能够有效地提高临床医学参数的测量精度.因此,在冠心病的临床诊断和介入治疗中,该方法能够可靠地诊断血管狭窄及选择和放置支架.     

A comparison of deconvolution and windowed subtraction techniques for scatter compensation in SPECT

Three procedures for the removal of Compton-scattered data in SPECT by constrained deconvolution are presented. The first is a deconvolution of a 2-D measured PSRF containing scatter from a single reconstructed transaxial image; the second is a deconvolution of a 2-D measured point-source response function (PSRF) from each frame of projection data prior to reconstruction; the third involves deconvolution of a 3-D measured PSRF from a stack of reconstructed slices. Results of applying these procedures to data obtained from a phantom containing cold cylinders and to data from a cold spot-resolution phantom are presented and are shown to be superior to the results of correcting for scatter by scatter-window substraction. Both 3-D deconvolution from reconstructed images and 2-D deconvolution from projection data show major improvements in image contrast, resolution, and quantitation. Improvements are especially marked for small (1.0-3.0 cm) cold sources.     

Registration and tracking to integrate X-ray and MR images in an XMR facility

We describe a registration and tracking technique to integrate cardiac X-ray images and cardiac magnetic resonance (MR) images acquired from a combined X-ray and MR interventional suite (XMR). Optical tracking is used to determine the transformation matrices relating MR image coordinates and X-ray image coordinates. Calibration of X-ray projection geometry and tracking of the X-ray C-arm and table enable three-dimensional (3-D) reconstruction of vessel centerlines and catheters from bi-plane X-ray views. We can, therefore, combine single X-ray projection images with registered projection MR images from a volume acquisition, and we can also display 3-D reconstructions of catheters within a 3-D or multi-slice MR volume. Registration errors were assessed using phantom experiments. Errors in the combined projection images (two-dimensional target registration error--TRE) were found to be 2.4 to 4.2 mm, and the errors in the integrated volume representation (3-D TRE) were found to be 4.6 to 5.1 mm. These errors are clinically acceptable for alignment of images of the great vessels and the chambers of the heart. Results are shown for two patients. The first involves overlay of a catheter used for invasive pressure measurements on an MR volume that provides anatomical context. The second involves overlay of invasive electrode catheters (including a basket catheter) on a tagged MR volume in order to relate electrophysiology to myocardial motion in a patient with an arrhythmia. Visual assessment of these results suggests the errors were of a similar magnitude to those obtained in the phantom measurements.     

Optimal CT scanning plan for long-bone 3-D reconstruction

Digital computed tomographic (CT) data are widely used in three-dimensional (3-D) construction of bone geometry and density features for 3-D modelling purposes. During in vivo CT data acquisition the number of scans must be limited in order to protect patients from the risks related to X-ray absorption. The aim of this work is to automatically define, given a finite number of CT slices, the scanning plan which returns the optimal 3-D reconstruction of a bone segment from in vivo acquired CT images. An optimization algorithm based on a Discard-Insert-Exchange technique has been developed. In the proposed method the optimal scanning sequence is searched by minimizing the overall reconstruction error of a two-dimensional (2-D) prescanning image: an anterior-posterior (AP) X-ray projection of the bone segment. This approach has been validated in vitro on 3 different femurs. The 3-D reconstruction errors obtained through the optimization of the scanning plan on the 3-D prescanning images and on the corresponding 3-D data sets have been compared. 2-D and 3-D data sets have been reconstructed by linear interpolation along the longitudinal axis. Results show that direct 3-D optimization yields root mean square reconstruction errors which are only 4%-7% lower than the 2-D-optimized plan, thus proving that 2-D-optimization provides a good suboptimal scanning plan for 3-D reconstruction. Further on, 3-D reconstruction errors given by the optimized scanning plan and a standard radiological protocol for long bones have been compared. Results show that the optimized plan yields 20%-50% lower 3-D reconstruction errors     

An X-ray-based method for the determination of the contrast agent propagation in 3-D vessel structures

A method for the determination of the contrast-agent propagation in vessel trees is presented. A standard three-dimensional (3-D) rotational angiography procedure is performed to reconstruct the morphology of the contrast-filled vessel tree in a 3-D volume. An additional fluoroscopy projection series acquired with a fixed projection angle delivers the temporal information of the bolus propagating. The mapping of the propagation information from the two-dimensional projections to the 3-D image data set is the topic of this paper. A symbolic tree structure is built up that represents the vessel tree including bifurcations. Neighborhood relations between vessel pieces are given in three dimensions. This facilitates filtering procedures and plausibility controls of the resulting time dependent 3-D data set. The presented method proved to be accurate with phantom data and gives novel insight in the feeding structure of arterio-venous malformations and aneurysms.     

基于刚体几何不变性的雷达目标运动路径拟合和三维优化重建方法

对于飞机、船舰等刚体雷达目标,其在运动过程中具有空间几何不变性。利用这一约束条件,可以通过雷达回波中提取出的目标散射点的一维距离史重建出目标的三维形状和运动路径。鉴于现有的基于几何不变性的雷达目标三维重建算法存在鲁棒性差的问题,本文利用雷达目标的运动惰性,对初步重建后得到的目标运动路径进行了拟合,并利用拟合后的运动路径对目标散射点的三维坐标进行了优化重建。文中对重建的误差进行了分析,提出了仿射扰动和欧式重建误差的误差模型。仿真实验证明,经仿射匹配校正后的拟合路径与真实路径基本吻合,从而可以有效获得目标的运动特征;同时,利用本文提出的优化重建方法能够有效抑制目标的欧式重建误差,提高了重建算法的准确性。      

Parallelized Bayesian inversion for three-dimensional dental X-ray imaging

Diagnostic and operational tasks based on dental radiology often require three-dimensional (3-D) information that is not available in a single X-ray projection image. Comprehensive 3-D information about tissues can be obtained by computerized tomography (CT) imaging. However, in dental imaging a conventional CT scan may not be available or practical because of high radiation dose, low-resolution or the cost of the CT scanner equipment. In this paper, we consider a novel type of 3-D imaging modality for dental radiology. We consider situations in which projection images of the teeth are taken from a few sparsely distributed projection directions using the dentist's regular (digital) X-ray equipment and the 3-D X-ray attenuation function is reconstructed. A complication in these experiments is that the reconstruction of the 3-D structure based on a few projection images becomes an ill-posed inverse problem. Bayesian inversion is a well suited framework for reconstruction from such incomplete data. In Bayesian inversion, the ill-posed reconstruction problem is formulated in a well-posed probabilistic form in which a priori information is used to compensate for the incomplete information of the projection data. In this paper we propose a Bayesian method for 3-D reconstruction in dental radiology. The method is partially based on Kolehmainen et al. 2003. The prior model for dental structures consist of a weighted /spl lscr//sup 1/ and total variation (TV)-prior together with the positivity prior. The inverse problem is stated as finding the maximum a posteriori (MAP) estimate. To make the 3-D reconstruction computationally feasible, a parallelized version of an optimization algorithm is implemented for a Beowulf cluster computer. The method is tested with projection data from dental specimens and patient data. Tomosynthetic reconstructions are given as reference for the proposed method.     

Nondestructive measurement for arbitrary RIP distribution of optical fiber preforms

A nondestructive method is presented to determine simultaneously the refractive index profile and the cross section geometry of optical fiber preforms. An improved formula for calculating the optical path length from the deflection function is derived. The preform is rotated through 180/spl deg/ and the deflection angle data collected, then the back projection technique and linear interpolation algorithm are used in the computed tomographic two-dimensional (2-D) profile reconstruction for preforms of nonuniform cross section. To minimize the computing time, the spatial Nyquist frequency is analytically used to estimate the angle sampling number of views and the numbers of points per scan in advance. Numerical simulations and experimental results show that using 180/spl deg/ angle of view deflection data, accurate preform index distribution reconstructions are obtained.     

VOIR: a volumetric image reconstruction algorithm based on Fouriertechniques for inversion of the 3-D Radon transform

A novel volumetric image reconstruction algorithm known as VOIR is presented for inversion of the 3-D Radon transform or its radial derivative. The algorithm is a direct implementation of the projection slice theorem for plane integrals. It generalizes one of the most successful methods in 2-D Fourier image reconstruction involving concentric-square rasters to 3-D; in VOIR, the spectral data, which is calculated by fast Fourier techniques, lie on concentric cubes and are interpolated by a bilinear method on the sides of these concentric cubes. The algorithm has great computational advantages over filtered-backprojection algorithms; for images of side dimension N, the numerical complexity of VOIR is O(N(3) log N) instead of O(N (4)) for backprojection techniques. An evaluation of the image processing performance is reported by comparison of reconstructed images from simulated cone-beam scans of a contrast and resolution test object. The image processing performance is also characterized by an analysis of the edge response from the reconstructed images.     

Quantitative analysis of reconstructed 3-D coronary arterial tree and intracoronary devices

Traditional quantitative coronary angiography is performed on two-dimensional (2-D) projection views. These views are chosen by the angiographer to minimize vessel overlap and foreshortening. With 2-D projection views that are acquired in this nonstandardized fashion, however, there is no way to know or estimate how much error occurs in the QCA process. Furthermore, coronary arteries possess a curvilinear shape and undergo a cyclical deformation due to their attachment to the myocardium. Therefore, it is necessary to obtain three-dimensional (3-D) information to best describe and quantify the dynamic curvilinear nature of the human coronary artery. Using a patient-specific 3-D coronary reconstruction algorithm and routine angiographic images, a new technique is proposed to describe: 1) the curvilinear nature of 3-D coronary arteries and intracoronary devices; 2) the magnitude of the arterial deformation caused by intracoronary devices and due to heart motion; and 3) optimal view(s) with respect to the desired "pathway" for delivering intracoronary devices.