Lagrangian and Eulerian biventricular strains from anatomical NURBS models using tagged MRI

Abstract

We present current research in which both left and right ventricular deformation is estimated from tagged cardiac magnetic resonance imaging using volumetric deformable models constructed from nonuniform rational B-splines (NURBS). The four model types considered include Cartesian-based NURBS models with both a cylindrical and prolate-spheroidal parameterization, prolate spheroidal-based NURBS models with a prolate-spheroidal parameterization, and cylindrical-based NURBS models with a cylindrical parameterization. For each frame subsequent to end-diastole, a 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 end-diastole using quadratic programming. This allows for subsequent forward displacement fitting from end-diastole to all later time frames. After fitting to all time points of data, lofting the NURBS model at each time point creates a comprehensive 4-D NURBS model. From this model, we can extract 3-D myocardial deformation fields and corresponding strain maps which are local measures of non-rigid deformation. The results show that, in the case of simulated data, the quadratic Cartesian-based NURBS model outperformed its counterparts in predicting normal strain. This model was used to then calculate normal Lagrangian and Eulerian strains in canine data.