The tomographic reconstruction of the beating heart requires dedicated methods. One possibility is gated
reconstruction, where only data corresponding to a certain motion state are incorporated. Another one is motioncompensated
reconstruction with a pre-computed motion vector field, which requires a preceding estimation of
the motion. Here, results of a new approach are presented: simultaneous reconstruction of a three-dimensional
object and its motion over time, yielding a fully four-dimensional representation. The object motion is modeled
by a time-dependent elastic transformation. The reconstruction is carried out with an iterative gradient-descent
algorithm which simultaneously optimizes the three-dimensional image and the motion parameters. The method
was tested on a simulated rotational X-ray acquisition of a dynamic coronary artery phantom, acquired on a
C-arm system with a slowly rotating C-arm. Accurate reconstruction of both absorption coefficient and motion
could be achieved. First results from experiments on clinical rotational X-ray coronary angiography data are
shown. The resulting reconstructions enable the analysis of both static properties, such as vessel geometry and
cross-sectional areas, and dynamic properties, like magnitude, speed, and synchrony of motion during the cardiac
C-arm systems may be used as front ends for cone-beam CT. The resulting image quality is affected by several factors, including the source trajectory, the reconstruction algorithm, and the accuracy of the data. The standard source trajectory is a circular arc spanning a little more than 180 degrees. However, since a planar source trajectory satisfies Tuy's completeness condition only within a subset of the source plane, the resulting images are bound to exhibit "cone-beam artifacts" off the source plane. The cure consists in using a source trajectory that satisfies Tuy's completeness condition everywhere within the volume of interest. Such a source trajectory must be non-planar. To keep the scan time short, the source
trajectory should also consist of a single, smooth segment. A favorable source trajectory of this kind is a curve known as spherical spiral. We implemented a spherical spiral on a laboratory
C-arm system, along with a standard circular arc.
An anthropomorphic head phantom was scanned using both source trajectories and otherwise identical scan parameters.
Images were reconstructed using a short scan version of the FDK algorithm (circular arc) and the cone-beam Fourierfiltered
backprojection (CBFFBP) algorithm presented earlier. Images obtained with the circular arc showed cone-beam artifacts. Images obtained with the spherical spiral did not. The results also demonstrate the good performance of the CBFFBP algorithm.