Spline surface interpolation for calculating 3-D ventricular strains from MRI tissue tagging

Abstract

A method is developed and validated for approximating continuous smooth distributions of finite strains in the ventricles from the deformations of magnetic resonance imaging (MRI) tissue tagging "tag lines" or "tag surfaces." Tag lines and intersections of orthogonal tag lines are determined using a semiautomated algorithm. Three-dimensional (3-D) reconstruction of the displacement field on tag surfaces is performed using two orthogonal sets of MRI images and employing spline surface interpolation. The 3-D regional ventricular wall strains are computed from an initial reference image to a deformed image in diastole or systole by defining a mapping or transformation of space between the two states. The resultant mapping is termed the measurement analysis solution and is defined by determining a set of coefficients for the approximating functions that best fit the measured tag surface displacements. Validation of the method is performed by simulating tag line or surface deformations with a finite element (FE) elasticity solution of the heart and incorporating the measured root-mean-square (rms) errors of tag line detection into the simulations. The FE-computed strains are compared with strains calculated by the proposed procedure. The average difference between two-dimensional (2-D) FE-computed strains and strains calculated by the measurement analysis was 0.022 +/- 0.009 or 14.2 +/- 3.6% of the average FE elasticity strain solution. The 3-D displacement reconstruction errors averaged 0.087 +/- 0.002 mm or 2.4 +/- 0.1% of the average FE solution, and 3-D strain fitting errors averaged 0.024 +/- 0.011 or 15.9 +/- 2.8% of the average 3-D FE elasticity solution. When the rms errors in tag line detection were included in the 2-D simulations, the agreement between FE solution and fitted solution was 24.7% for the 2-D simulations and 19.2% for the 3-D simulations. We conclude that the 3-D displacements of MRI tag lines may be reconstructed accurately; however, the strain solution magnifies the small errors in locating tag lines and reconstructing 3-D displacements.

Three-dimensional motion reconstruction and analysis of the right ventricle using tagged MRI

“…The types of input data include tag intersections (2D tags) [35, 19, 331, 1D tags [23, 201 or a combination of 2D tags and segmented contour data [25,361. The 3D reconstruction approaches include: fitting a 3D displacement field composed of an analytic series to image data [23]; physics-based deformable modeling [18] applied to a parameterized superquadric 1241; curve and spline surface reconstruction of tag data to be used as input to linear optimization [20]; and nonlinear least-squares fitting of a finite element model [36]. Up to now the only MRI tagging study of the motion of the RV was an adaptation of the latter fitting method to a surface model of the RV free wall, using intersections of mid-wall contours with tags as input data.…”

Left ventricular motion reconstruction from planar tagged MR images: a comparison

“…Many methods have been proposed to reconstruct 3D motion of the LV from tagged MR images (Declerck 1997, Declerck et al 1998a, 1999, Denney and McVeigh 1997, Huang and Amini 1999, Moulton et al 1996, O'Dell et al 1995, O'Donnell et al 1996, Öztürk and McVeigh 1999a, Park et al 1996, Radeva et al 1997, Young 1998, Young and Axel 1992, and compute 3D strains at material points in the heart wall. All these methods except Huang and Amini (1999), Radeva et al (1997) and Young (1998) suppose that tag lines have been segmented in a preliminary step.…”

Automatic 3D tracking of cardiac material markers using slice-following and harmonic-phase MRI

“…In comparison to existing tag-based point tracking techniques [18,20,21,23,24,34], our method provides direct and fast measurements of 3-D motion with minimal (or no) user interaction. In phase-contrast tracking techniques [3,4], the integration of the velocity data introduces high timeresolution demands to achieve a good estimation of the 3-D motion trajectory.…”