14 April 2005 Lagrangian and Eulerian biventricular strains from anatomical NURBS models using tagged MRI
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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.
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Nicholas J. Tustison, Amir A. Amini, "Lagrangian and Eulerian biventricular strains from anatomical NURBS models using tagged MRI", Proc. SPIE 5746, Medical Imaging 2005: Physiology, Function, and Structure from Medical Images, (14 April 2005); doi: 10.1117/12.597106; https://doi.org/10.1117/12.597106

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