Digital subtraction angiographic image sequences of a calibration phantom are acquired at 30 frames per second from a C-arm gantry covering an angular arc of more than 180 degrees rotating at 40 degrees/s. For each frame, after XRII distortion correction, the relation between the source and its image plane orientation in 3D space is estimated from fiducial markers in the calibration phantom. This gives a mapping between the three-dimensional calibration object and its two- dimensional projection at each gantry angle. We derive eleven mapping coefficients as a function of gantry angle. We use the coefficients to backproject the contribution to any physical voxel. Thus the wobble correction is incorporated directly into cone-beam backprojection. In the absence of gantry wobble, this method is equivalent to the short-scan Feldkamp algorithm, any deviation of the coefficients from those perfect values can be taken as a measure of the gantry wobble. The mapping method requires no special knowledge of the system geometry and any wobble, twisting of the C-arm or XRII during rotation is automatically included. A phantom with tungsten- carbide beads is reconstructed. Accuracy is obtained by comparing reprojections of the center of the tungsten beads with their known values.
Small pellets are often used as fiducial markers in a calibration phantom to estimate the geometrical parameters in 3D (three-dimensional) reconstruction. But calibration accuracy depends on the accuracy of locating the pellet centers. Here we describe a technique for fast and accurate detection of these centers. The phantom consists of tungsten carbide pellets arranged in a helical trajectory. The plastic holder mounting the pellets may cause unequal distribution of attenuation around edge pellets compared to the center ones. After log subtraction with flood frames the grayscale gradient in the background is derived within the mask for every point for a reliable background correction. The pellets are identified from the amplitude projections of each frame and a mask is used to refine its position. The grayscale gradient of the background is suitably estimated at each point by the equation of a plane. The center obtained after gradient filter correction is compared with manual measurement, and to measurement using a single background value for each mask. Gradient correction gives centers within 0.3 +/- 0.1 pixel of the manual measurements for the edge pellets, while a single value for background correction yields results within 0.6 +/- 0.3 pixel.
We have developed methods for determining 3D vessel centerlines from biplane image sequences. For dynamic quantities, e.g., vessel motion or flow, the correspondence between points along calculated centerlines must be established. We have developed and compared two techniques for determination of correspondence and of vessel motion during the heart cycle. Clinical biplane image sequences of coronary vascular trees were acquired. After manual indication of vessel points in each image, vessels were tracked, bifurcation points were calculated, and vascular hierarchy was established automatically. The imaging geometry and the 3D vessel centerlines were calculated for each pair of biplane images from the image data alone. The motion vectors for all centerline points were calculated using corresponding points determined by two methods, either as points of nearest approach of the two centerlines or as having the same cumulative arclength from the vessel origin. Corresponding points calculated using the two methods agreed to within 0.3 cm on average. Calculated motion of vessels appeared to agree with motion visible in the images. Relative 3D positions and motion vectors can be calculated reliably with minimal user interaction.
Quantitative vascular analysis is useful for treatment planning and evaluation of atherosclerosis, but it requires accurate and reliable determination of the 3D vascular structures from biplane images. To facilitate vascular analysis, we have developed technique for reliable estimation of the biplane imaging geometry as well as 3D vascular structures without using a calibration phantom. The centerlines of the vessels were tracked, and bifurcation points and their hierarchy were then determined automatically. The corresponding bifurcation points in biplane images were used to obtain an estimate of the imaging geometry with the enhanced Metz-Fencil technique, starting with an initial estimate based on gantry information. This initial estimate was iteratively refined by means of non-linear optimization techniques that aligned the projections of the reconstructed 3D bifurcation points with their respective image points. Methods have also been developed for assessing the accuracy and reliability of the calculated 3D vascular centerlines. Accuracy was evaluated by comparison of distances within a physical phantom with those in the reconstructed phantom. The reliability of the calculated geometries and 3D positions were evaluated using data from multiple projections and observers.
The use of a C-arm radiographic system for 3D reconstruction of opacified vasculature presents several computational and engineering challenges. Factors that may lead to inconsistency at the projection data set and subsequent reconstruction errors include image noise, variations in vessel opacification during the acquisition, and inaccurate determination of the imaging geometry. We have utilized simulations to study the effect of these factors on 3D reconstruction with algebraic reconstruction technique (ART) in order to identify possible artifacts and loss of image quality in the 3D image. Corrective measures designed to counter artifacts such as smoothing, averaging, and use of constraints with ART have been developed and validated. These studies have made it possible to identify the causes of artifacts in preliminary in vivo applications, and to estimate the tolerance for imperfections in data acquisition. Moreover, these works have established modifications to the reconstruction procedure for reducing image artifacts and improving image quality.
A method for 3D cone beam reconstruction of cerebral vasculature (both morphology and grayscale) from a limited number (less than 10) of digital subtraction angiographic (DSA) projections obtained with a standard biplane C-arm x-ray system is described. The reconstruction method includes geometric calibration of the source and detector orientation, spatial image distortion correction, and algebraic reconstruction technique (ART) with non- negativity constraint. Accuracy of voxel gray scale values estimated by ART is enhanced by determination of weights based on the intersection volume between a pyramidal ray and cubic voxel. The reconstruction is accelerated by retaining only the vessel containing voxels and distributed computing. Reconstruction of a phantom containing fiducial markers at known 3D locations demonstrated that the reconstructed geometry is accurate to less than a pixel width. Reconstruction is also obtained from an anatomic skull phantom with an embedded cerebral vasculature reproduction that includes an aneurysm. Three dimensional reconstruction exhibited the necessary details, both structural and grayscale.
Typical digital subtraction angiography (DSA) acquisition rates are often inadequate for visualizing and analyzing fast-moving flow patterns. Therefore, an interpolation method that captures the angiographic flow pattern was developed. The temporal change of gray value in each pixel along a blood vessel records the flow movement at that location. Thus, temporal interpolation was performed on a pixel-by-pixel basis. To generate each interpolated image, a polynomial interpolation was applied to six sequential images. To validate the interpolation technique, a flow phantom was imaged with a high acquisition frame rate, and interpolation was done in a lower frame rate and compared to the acquired data. The interpolated images were also compared to results from linear interpolation and cubic spline interpolation. Clinical utility was illustrated on DSA images of cerebral vasculature with aneurysms. Image sequences of 60 frame/s were generated from DSA images acquired at 7.5 frame/s. The results show improved flow pattern visualization, especially flow head locations in blood vessels. This interpolation method has also been applied to dynamic 3D reconstruction from biplane DSA projections. In this application, the method was used to offset temporal discrepancies between biplane projection pairs and contrast injections, making dynamic 3D reconstruction possible.
The exact weighting function in 3D image reconstruction from 2D projections with cone beam geometry is obtained as the volume of intersection of a pyramidal ray with a cubic voxel. This intersection yields a convex polyhedron whose faces are formed by either the side of the pyramid or the voxel face. For each face of a voxel, we maintain a vertex link map. When one of the four pyramidal ray planes clips the voxel, we obtain a new face and a set of new vertices, while updating existing faces and their vertex link maps. Progressively clipping the voxel by the necessary ray planes yields the intersection polyhedron, whose faces and vertices are provided by the face list and its associated vertex link maps. To generate the weight, the volume of the polyhedron is calculated by dividing the polyhedron into tetrahedrons, whose volumes are summed. The exact calculated weights were used to reconstruct 3D vascular images from simulated data using a ROI (region of interest) limited ART (algebraic reconstruction technique). Comparing the results to those obtained from length approximation indicates that more accurate reconstruction could be achieved from the weights calculated with the new method.