Quantitative Volume Analysis Of Coronary Vessel Systems By 3-D Reconstruction From Biplane Angiograms

Quantitative evaluations on coronary vessel systems are of increasing importance in cardio-vascular diagnosis, therapy planning and surgical verification. Local evaluations, like stenosis analysis, are already available with sufficient accuracy. On the other hand, global evaluations on vessel segments or vessel subsystems are not yet common. Especially for the &agnosis of diffuse coronary artery diseases, we combined a 3-D reconstruction system operating on biplane angiogram with a length/volume calculation. The 3-D reconstruction results in a 3-D model of the coronary vessel system, consisting of the vessel skeleton and a discrete number of contours. To obtain a most accurate model, we focussed on exact geometry determination. Several algorithms for calculating missing geometric parameters and correcting remaining geometry errors were implemented and verified. The length/volume evaluation can be performed either on single vessel segments, on a set of segments, or on sub-trees. A volume model based on generalized elliptical conic sections is created for the selected segments. Volumes and lengths (measured along the vessel course) of those elements are summed up. In this way, the morphological parameters of a vessel subsystem can be set in relation to the parameters of the supplying segment proximal to it. These relations allow objective assessments of diffuse coronary artery diseases. sional measures defined on sets of sub-trees was selected and tested clinically. IT. 3-D RECONSTRUCTION A . Imaging Geometry and Point Reconstruction Standard biplane angiographic equipment consists of two x-ray systems having a common coordinate system [l]. In conventional methods, a fixed rotational origin of both systems is assumed where the projection axes intersect, the isocenter. For volume measurements, we need a very high reconstruction accuracy, because linear reconstruction errors raise to the third power. The classic isocenvic model could not satisfy this requirement: there is neither a stable isocenter, nor is there an adequate way to determine the required distances manually [21. In our geometric model, we use a variable iso-axis instead of a fixed isocenter. The distance of the projection axes creates a unique iso-axis orthogonal to both of them (fig. 2). The locations of x-ray sources and image intensifiers are determined in terms of distances to this iso-axis. The origin of the world coordinate system is defined as the weighted middle of the projection axes distance on the iso-axis. The angulation is obtained conventionally as a sequence of rotations, con-