Three-dimensional reconstruction of myocardial contrast perfusion from biplane cineangiograms by means of linear programming techniques.

The assessment of coronary flow reserve from the instantaneous distribution of the contrast agent within the coronary vessels and myocardial muscle at the control state and at maximal flow has been limited by the superimposition of myocardial regions of interest in the two-dimensional images. To overcome these limitations, we are in the process of developing a three-dimensional (3D) reconstruction technique to compute the contrast distribution in cross sections of the myocardial muscle from two orthogonal cineangiograms. To limit the number of feasible solutions in the 3D-reconstruction space, the 3D-geometry of the endo- and epicardial boundaries of the myocardium must be determined. For the geometric reconstruction of the epicardium, the centerlines of the left coronary arterial tree are manually or automatically traced in the biplane views. Next, the bifurcations are detected automatically and matched in these two views, allowing a 3D-representation of the coronary tree. Finally, the circumference of the left ventricular myocardium in a selected cross section can be computed from the intersection points of this cross section with the 3D coronary tree using B-splines. For the geometric reconstruction of the left ventricular cavity, we envision to apply the elliptical approximation technique using the LV boundaries defined in the two orthogonal views, or by applying more complex 3D-reconstruction techniques including densitometry. The actual 3D-reconstruction of the contrast distribution in the myocardium is based on a linear programming technique (Transportation model) using cost coefficient matrices. Such a cost coefficient matrix must contain a maximum amount of a priori information, provided by a computer generated model and updated with actual data from the angiographic views. We have only begun to solve this complex problem. However, based on our first experimental results we expect that the linear programming approach with advanced cost coefficient matrices and computed model will lead to acceptable solutions in the 3D-reconstruction of the myocardial contrast distribution from biplane cineangiograms.