Abstract

We present research in which both leftand right-ventricular deformation is estimated from tagged cardiac mgnetic resonance imaging using volumetric deformable models constructed from nonuniform rational B-splines (NURBS). The four model types considered and compared for the left ventricle include two Cartesian NURBS models — one with a cylindrical parameter assignment and one with a prolate spheroidal parameter assignment. The remaining two are non-Cartesian, i.e., prolate spheroidal and cylindrical, each with their respective prolate spheroidal and cylindrical parameter assignment regime. These choices were made based on the typical shape of the left ventricle. For each frame subsequent to end-diastole, an NURBS model is constructed by fitting two surfaces with the same parameterization to the corresponding set of epicardial and endocardial contours from which a volumetric model is created. Using normal displacements of the three sets of orthogonal tag planes as well as displacements of contour/tag line intersection points and tag plane intersection points, one can solve for the optimal homogeneous coordinates, in a weighted least-squares sense, of the control points of the deformed NURBS model at enddiastole using quadratic programming. This allows for subsequent nonrigid registration of the biventricular model at end-diastole to all later time frames. After registration of the model to all later time points, the registered NURBS models are temporally lofted in order to create a comprehensive four-dimensional NURBS model. From the lofted model, we can extract 3D myocardial deformation fields and corresponding Lagrangian and Eulerian

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