Yudong Zhu

Estimation of deformation gradient and strain from cine-PC velocity data [cardiac magnetic resonance imaging]

Phase contrast magnetic resonance imaging (MRI) can provide in vivo myocardial velocity field measurements. These data allow densely spaced material points to be tracked throughout the whole heart cycle using, for example, the Fourier tracking algorithm. To process the tracking results for myocardial deformation and strain quantification, the authors developed a method that is based on fitting the tracking results to an appropriate local deformation model. They further analyzed the accuracy and precision of the method and provided performance predictions for several local models. In order to validate the method and the theoretical performance analysis, the authors conducted controlled computer simulations and a phantom study. The results agreed well with expectations. Human heart data were also acquired and analyzed, and provided encouraging results. At the signal-to-noise ratio (SNR) level and spatial resolution expected in clinical settings, the study predicts strain quantification accuracy and precision that may allow the technique to become a practical and powerful noninvasive approach for the study of cardiac function, although clinically acceptable data acquisition strategies for three-dimensional (3-D) data are still a challenge.

A spatiotemporal model of cyclic kinematics and its application to analyzing nonrigid motion with MR velocity images

The authors present a method (DMESH) for nonrigid cyclic motion analysis using a series of velocity images covering the cycle acquired, for example, from phase-contrast magnetic resonance imaging. The method is based on fitting a dynamic finite-element mesh model to velocity samples of an extended region, at all time frames. The model offers a flexible tradeoff between accuracy and reproducibility with controllable built-in spatiotemporal smoothing, which is determined by the fineness of the initially defined mesh and the richness of included Fourier harmonics. The method can further provide a prediction of the analysis reproducibility, along with the estimated motion and deformation quantities. Experiments have been conducted to validate the method and to verify the reproducibility prediction. Use of the method for motion analysis using displacement information (e.g., from magnetic resonance tagging) has also been explored.

In vitro verification of myocardial motion tracking from phase–contrast velocity data

The ability to track motion from cine phase-contrast (PC) magnetic resonance (MR) velocity measurements was investigated using an in vitro model. A computer-controlled deformable phantom was used for the characterization of the accuracy and precision of the forward-backward and the compensated Fourier integration techniques. Trajectory accuracy is limited by temporal resolution when the forward-backward technique is used. With this technique the extent of the calculated trajectories is underestimated by an amount related to the motion period and the sequence repetition time, because of the band-limiting caused in the cine interpolation step. When the compensated Fourier integration technique is used, trajectory accuracy is independent of temporal resolution and is better than 1 mm for excursions of less than 15 mm, which are comparable to those observed in the myocardium. Measurement precision is dominated by the artifact level in the phase-contrast images. If no artifacts are present precision is limited by the inherent signal-to-noise ratio of the images. In the presence of artifacts, similar in magnitude to those observed in vivo, the reproducibility of tracking a 2.2 x 2.2 mm2 region of interest is better than 0.5 mm. When the Fourier integration technique is used, the improved accuracy is accompanied by a reduction in precision. We verified that tracking three-dimensional (3D) motion from velocity measurements of a single slice can lead to underestimations of the trajectory if there is a through-plane component of the motion that is not truly represented by the measured velocities. This underestimation can be overcome if volumetric cine phase-contrast velocity data are acquired and full three-dimensional analysis is performed.

Three-dimensional motion tracking with volumetric phase contrast MR velocity imaging

Motion tracking based on single‐slice cine‐phase contrast magnetic resonance imaging data has limitations. In the presence of nontrivial three‐dimensional motion and deformation, volumetric data are necessary for accurate reconstruction of material point trajectories. A three‐dimensional Fourier tracking method that uses volumetric data for motion tracking is presented. The method reconstructs a material point trajectory by computing its various harmonics. For any given temporal sampling rate, a frequency domain perspective of the tracking problem indicates that the method is accurate in estimating all reconstructible harmonics of a trajectory. The algorithm incorporates an intra‐voxel linear spatial model into the integration to address potential tracking performance degradation due to possibly reduced spatial resolution, which may be most relevant in the slice direction (z) if the volumetric data are obtained as multiple two‐dimensional slices. The tracking method was evaluated on computer‐generated data sets that simulated various motion patterns. The method was also tested with two sets of in vitro data obtained using a phantom, one acquired as multiple two‐dimensional slices and the other using a three‐dimensional sequence capable of higher spatial resolution in the z direction. These studies demonstrated that the algorithm can achieve high sub‐voxel tracking accuracy. J. Magn. Reson. Imaging 1999;9:111–118

A spatiotemporal finite element mesh model of cyclical deforming motion and its application in myocardial motion analysis using phase contrast MR images

Presents a method for nonrigid cyclic motion analysis using a series of velocity images, acquired for example, from phase contrast magnetic resonance imaging. The method is based on fitting a global spatiotemporal finite element mesh model, which has controllable builtin spatial/temporal smoothing that is determined by the finesse of the initially defined mesh and richness of included Fourier harmonics, to velocity samples of an extended region at all time frames. If desired, the method can further provide a prediction of the analysis reproducibility along with the estimated motion and deformation quantities. Experiments have been conducted to validate the method and verify the reproducibility prediction.

Myocardial Spatiotemporal Tracking

The past two decades of magnetic resonance imaging (MRI) research witnessed the development of noninvasive technologies that are capable of both motion quantification and spatiotemporal resolution. Representative examples include the MR tagging [1–5] and the phase contrast MR velocity mapping techniques [6–10]. Among clinical applications that have been established, or are being developed, use of the technologies for evaluating cardiac motion may be one that is most rewarding, yet exceedingly challenging.