Three-dimensional (3D) vessel data from CTA or MRA are not always available prior to or during endovascular
interventional procedures, whereas multiple 2D projection angiograms often are. Unfortunately, patient movement,
table movement, and gantry sag during angiographic procedures can lead to large errors in gantry-based imaging
geometries and thereby incorrect 3D. Therefore, we are developing methods for combining vessel data from
multiple 2D angiographic views obtained during interventional procedures to provide 3D vessel data during these
procedures. Multiple 2D projection views of carotid vessels are obtained, and the vessel centerlines are indicated.
For each pair of views, endpoints of the 3D centerlines are reconstructed using triangulation based on the provided
gantry geometry. Previous investigations indicated that translation errors were the primary source of error in the
reconstructed 3D. Therefore, the errors in the translations relating the imaging systems are corrected by minimizing
the L1 distance between the reconstructed endpoints, after which the 3D centerlines are reconstructed using epipolar
constraints for every pair of views. Evaluations were performed using simulations, phantom data, and clinical cases.
In simulation and phantom studies, the RMS error decreased from 6.0 mm obtained with biplane approaches to 0.5
mm with our technique. Centerlines in clinical cases are smoother and more consistent than those calculated from
individual biplane pairs. The 3D centerlines are calculated in about 2 seconds. These results indicate that reliable
3D vessel data can be generated for treatment planning or revision during interventional procedures.
Endovascular interventional procedures are being used more frequently in cardiovascular surgery.
Unfortunately, procedural failure, e.g., vessel dissection, may occur and is often related to improper guidewire and/or
device selection. To support the surgeon's decision process and because of the importance of the guidewire in
positioning devices, we propose a method to determine the guidewire path prior to insertion using a model of its elastic
potential energy coupled with a representative graph construction.
The 3D vessel centerline and sizes are determined for a specified vessel. Points in planes perpendicular to the
vessel centerline are generated. For each pair of consecutive planes, a vector set is generated which joins all points in
these planes. We construct a graph representing these vector sets as nodes. The nodes representing adjacent vector sets
are joined by edges with weights calculated as a function of the angle between the corresponding vectors (nodes). The
optimal path through this weighted directed graph is then determined using shortest path algorithms, such as topological
sort based shortest path algorithm or Dijkstra's algorithm. Volumetric data of an internal carotid artery phantom (Ø 3.5mm) were acquired. Several independent guidewire (Ø 0.4mm) placements were performed, and the 3D paths were
determined using rotational angiography.
The average RMS distance between the actual and the average simulated guidewire path was 0.7mm; the
computation time to determine the path was 3 seconds. The ability to predict the guidewire path inside vessels may
facilitate calculation of vessel-branch access and force estimation on devices and the vessel wall.
Multi-view imaging is the primary modality for high-spatial-resolution imaging of the vasculature. The 3D vascular structure can be reconstructed if the imaging geometries are determined using known corresponding point-pairs (or k-tuples) in two or more images. Because the accuracy improves with more input corresponding point-pairs, we propose a new technique to automatically determine corresponding point-pairs in multi-view (k-view) images, from 2D vessel image centerlines. We formulate the problem, first as a multi-partite graph-matching problem. Each 2D centerline point is a vertex; each individual graph contains all vessel-points (vertices) in an image. The weight ('cost') of the edges between vertices (in different graphs) is the shortest distance between the points' respective projection-lines. Using this construction, a universe of mappings (k-tuples) is created, each k-tuple having k vertices (one from each image). A k-tuple's weight is the sum of pair-wise 'costs' of its members. Ideally, a set of such mappings is desired that preserves the ordering of points along the vessel and minimizes an appropriate global cost function, such that all vertices (in all graphs) participate in at least one mapping. We formulate this problem as a special case of the well-studied Set-Cover problem with additional constraints. Then, the equivalent linear program is solved, and randomized-rounding techniques are used to yield a feasible set of mappings. Our algorithm is efficient and yields a theoretical quality guarantee. In simulations, the correct matching is achieved in ~98% cases, even with high input error. In clinical data, apparently correct matching is achieved in >90% cases. This method should provide the basis for improving the calculated 3D vasculature from multi-view data-sets.
Matching geometric objects is a fundamental problem in computational geometry with applications in many other areas, such as computer vision, biology,and archaelogy. In this paper, we study an important partial matching problem motivated from applications in several such areas. The input is in the form of sets of under-sampled slices of one (or more) unknown 3D objects, possibly generated by slicing planes of arbitrary orientations, the question we are interested in is whether it is 'possible' that two under-sampled sets have been taken from the same object. Alternatively, can we determine with 'certainty' that the given input samples cannot be from the same object. We present efficient algorithms for addressing these questions. Our algorithm is based on interesting geometric techniques and enables answering these queries either as plausible or a certain negative.
Biplane imaging is a primary method for visual and quantitative assessment of the vasculature. A key problem (called Imaging Geometry Determination problem or IGD for short) in this method is to determine the rotation-matrix (R) and the translation vector (t) which relate the two coordinate systems. In this paper, we propose a new approach, called IG-Sieving, to calculate R and t using corresponding points in the two images. Our technique first generates an initial estimate of R and t from the gantry angles of the imaging system, and then optimizes them by solving an optimal-cell-search problem in a 6-D parametric space (three variables defining R plus the three variables of t). To efficiently find the optimal imaging geometry (IG) in 6-D, our approach divides the high dimensional search domain into a set of lower-dimensional regions, (holding two variables constant at each optimization step), thereby reducing the optimal-cell-search problem to a set of optimization problems in 3D sub-spaces (one other variable is correlated). For each such sub-space, our approach first applies efficient computational geometry techniques to identify "possibly-feasible" IG’s, and then uses a criterion we call fall-in-number to sieve out good IGs. We show that in a bounded number of optimization steps, a (possibly infinite) set of near optimal IGs (which are equally good) can be determined. Simulation results indicate that our method can reconstruct 3D points with average 3D center-of-mass errors of about 0.8cm for input image-data errors as high as 0.1cm, which is comparable to existing techniques. More importantly, our algorithm provides a novel insight into the geometric structure of the solution space, which could be exploited to significantly improve the accuracy of other biplane algorithms.