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A Geometric Model for the Lumen of Blood Vessels in X-ray Angiography

C. R. Hardingham, D. J. Hawkes, A. C. F. Colchester

1989
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Procedings of the Alvey Vision Conference 1989
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We have developed a model for representing the image of segments of blood vessels in x-ray angiograms, and a software package for generating the model from digitized angiograms. The model is based on projections of linearly tapering cylinders and is suitable for the analysis of vessel lumen position, size and shape. This is of interest for research into the disease atherosclerosis. The system has been validated using a set of post mortem samples. The accuracy of representation of the lumen
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... s is between + 0% and +10% (95% confidence limits) and the accuracy of simple shape information is 81%. Atherosclerosis is a common arterial disease. It is obliterative and its principal effect is due to the encroachment of a lesion on the lumen, with consequent effect on blood flow through the artery. It is a focal process and many foci may be present (Davies, 1986 ). X-ray angiography is a method of imaging the lumen of an arterial system by introducing an iodine-containing contrast medium into the blood stream before taking an x-ray. Traditionally, the cross sectional area of the residual lumen is measured and compared with the normal area, to give an estimate of the severity of a lesion. In recent years there have been several publications indicating that the shape of the lesion is an important indicator of the severity and prognosis of disease (Ambrose et al, 1986 , Brown, 1981 , Levin et al, 1982 . Furthermore, there has been research into the 3-dimensional reconstruction of vascular trees from two or more projections (Hawkes et al, 1987) . There is therefore a need for a model to represent the position, size and shape of the image of an artery, describing the features required for further analysis. In the work preceding this project (Hawkes et al, 1988) , a technique of linear calibration and background subtraction was developed, which produces a grey level image proportional to the projection of contrast, if noise and blurring caused by the finite MTF of the system is ignored. This linear response of the image tc the projection of the object of interest permitted the development of the image analysis system described below. We have developed a model of the vessel image as a set of projections of generalized cylinders of elliptical cross section, and have implemented a package of computer programs, written in C and Prolog, to generate the model for digitized angiograms. The system has so far been used primarily in the analysis of lumen shape in atherosclerosis (Hawkes et al, 1989) , but is also of general applicability where projected images of cylindrical or near cylindrical objects are of interest. Although there is much research activity into quantitative angiography, there have been few publications regarding lumen shape reconstruction. Reiber et al. (1981) described research into a system for the three-dimensional reconstruction of lumen shape from two orthogonal views. There are two problems with this approach. First, two views are not always enough to reconstruct the lumen shape unambiguously. Secondly, it is not always possible to obtain two good orthogonal views of a vessel segment. The approach described here is to try and generate a useful representation of the lumen image, as seen from a single view. This can only provide limited information: as with angiographic assessment by eye, the appearance of the lesion is sensitive to the viewing angle. However, the aim is to provide information which is both useful on its own, and can be combined with the information from another view, if available. When the shape of a blood vessel's lumen is investigated, the usual assumption is that a normal vessel, in a segment between branch points, has a lumen which is close to being cylindrical. A certain amount of taper is expected, the artery narrowing distally, but this is small compared with the effect of significant arterial disease. Deviation in shape from that of a slowly tapering cylinder is usually taken as a sign of abnormality. The projection of a cylinder is semi elliptical in cross section. A semi ellipse is easily represented and manipulated computationally. The model chosen uses projections of tapering cylinders (PTC's), constrained to taper linearly. These can be used to identify two types of feature in the image. First, they can represent grey level profiles in the image which could be projections of parts of cylindrical objects. Second, they can represent parts of "ribbon like" objects, i.e. strips with near parallel edges and height consistently higher than the background. Both these features are of interest, the first in looking for possibly normal artery, and the second in identifying artery which may or may not be diseased. In order to interpret the PTC's, it is necessary to have information about the goodness of fit between the image and the PTC. The aims of this work were to find a method of representing the image of a non-branching, nearly straight segment of artery, using projections of tapering cylinders. The model must represent the artery image accurately and efficiently, identifying in particular the projections of parts of cylindrical objects. The Model The image may be thought of as a surface in three dimensions, the two dimensions of the digitized array and the grey level dimension. The convention used for describing this volume is to use x, y and z coordinates, where x and y are in 139 AVC 1989

doi:10.5244/c.3.24
dblp:conf/bmvc/HardinghamHC89
fatcat:cnrqeazpbvewnnpei4qdppuglu