Tracking and finite element analysis of stripe deformation in magnetic resonance tagging

Abstract

Magnetic resonance tissue tagging allows noninvasive in vivo measurement of soft tissue deformation. Planes of magnetic saturation are created, orthogonal to the imaging plane, which form dark lines (stripes) in the image. The authors describe a method for tracking stripe motion in the image plane, and show how this information can be incorporated into a finite element model of the underlying deformation. Human heart data were acquired from several imaging planes in different orientations and were combined using a deformable model of the left ventricle wall. Each tracked stripe point provided information on displacement orthogonal to the original tagging plane, i.e., a one-dimensional (1-D) constraint on the motion. Three-dimensional (3-D) motion and deformation was then reconstructed by fitting the model to the data constraints by linear least squares. The average root mean squared (rms) error between tracked stripe points and predicted model locations was 0.47 mm (n=3,100 points). In order to validate this method and quantify the errors involved, the authors applied it to images of a silicone gel phantom subjected to a known, well-controlled, 3-D deformation. The finite element strains obtained were compared to an analytic model of the deformation known to be accurate in the central axial plane of the phantom. The average rms errors were 6% in both the reconstructed shear strains and 16% in the reconstructed radial normal strain.

Model‐free reconstruction of three‐dimensional myocardial strain from planar tagged MR images

“…A three-dimensional strain map also can be reconstructed using finite-element analysis (7,15) or a prolate spheroidal basis function fit (8). These methods, however, require that a specific coordinate system be constructed before the strain map is computed, and in the case of the basis function fit, the accuracy of the fit is highly dependent on the coordinate system used.…”

“…This approach produces excellent results at the midwall, but careful preprocessing is required to get the heart in the correct coordinate system for reconstruction because the coordinate system foci and axes are critical to the reconstruction accuracy. Young et al (7,15) and Moulton et al (16) have developed three-dimensional strain reconstruction schemes based on a 16-element mesh and a piece-wise polynomial displacement…”

“…These methods, however, require that a specific coordinate system be constructed before the strain map is computed, and in the case of the basis function fit, the accuracy of the fit is highly dependent on the coordinate system used. In addition, the coordinate systems used in (7,8,15) are matched to the geometry of the particular heart being studied and, therefore, require that the entire heart be scanned. Relative to these approaches, the DMF algorithm presented in this paper has the following advantages.…”

Anisotropic filtering for model-based segmentation of 4D cylindrical echocardiographic images

“…Statistical information (mainly principal component analysis) has also been used to restrain the set of possible deformations of a left ventricle model (Jacob et al, 1999;Giachetti, 1998). Deformable surfaces have been recently used to reconstruct the heart motion from 3D echocardiographic images (Berger et al, 1999), but most of them rely on tagged MRI (Guttman et al, 1994;Reynard et al, 1995;Young et al, 1995;Park et al, 1996;Declerck et al, 1998).…”

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

“…But there are still significant challenges. For example, tracking of dense 3-D displacement inevitably requires long imaging times [3,7,18,19], manually intensive postprocessing [18,20,21] and/or interpolation techniques [22 -24].…”