Reconstruction of dynamic contrast enhanced magnetic resonance imaging of the breast with temporal constraints

Abstract

A number of methods using temporal and spatial constraints have been proposed for reconstruction of undersampled dynamic magnetic resonance imaging (MRI) data. The complex data can be constrained or regularized in a number of different ways, for example, the time derivative of the magnitude and phase image voxels can be constrained separately or jointly. Intuitively, the performance of different regularizations will depend on both the data and the chosen temporal constraints. Here, a complex temporal total variation (TV) constraint was compared to the use of separate real and imaginary constraints, and to a magnitude constraint alone. Projection onto Convex Sets (POCS) with a gradient descent method was used to implement the diverse temporal constraints in reconstructions of DCE MRI data. For breast DCE data, serial POCS with separate real and imaginary TV constraints was found to give relatively poor results while serial/parallel POCS with a complex temporal TV constraint and serial POCS with a magnitude-only temporal TV constraint performed well with an acceleration factor as large as R=6. In the tumor area, the best method was found to be parallel POCS with complex temporal TV constraint. This method resulted in estimates for the pharmacokinetic parameters that were linearly correlated to those estimated from the fully-sampled data, with K(trans,R=6)=0.97 K(trans,R=1)+0.00 with correlation coefficient r=0.98, k(ep,R=6)=0.95 k(ep,R=1)+0.00 (r=0.85). These results suggest that it is possible to acquire highly undersampled breast DCE-MRI data with improved spatial and/or temporal resolution with minimal loss of image quality.

Fig. 1

Undersampling pattern for breast DCE data. The gray circles were not sampled, and the black circles were sampled. (A) The outer k-space sampling of eight adjacent time frames. (B) A typical k-space sampling pattern of one time frame.

Fig. 2

Comparison of reconstructions from full data and R=6 (using pattern shown in Fig. 1) data using different methods with all coils. (A) The 22nd time frame reconstructed from full k-space data using IFT. The corresponding time frame reconstructed from undersampled data using IFT method is shown in panel (B), the parallel+complex in (C), serial+complex in (D), serial+magnitude in (E), and the sliding window method in (F).

Fig. 3

RMSE plot for each time frame computed for different methods with one data set of all coils.

Fig. 4

Reconstructions results from all coils. a–e (left column): the 12th time frame of reconstructed images (from top to bottom, the left column is full sampled image, parallel+complex, serial+complex, serial+magnitude, sliding window). f–i (right column): the difference image between the corresponding left image and (A). Larger residual errors of the images reconstructed with the serial+magnitude and SW methods are evident in the bottom two rows of the right column. The left column images are scaled to [0,30]; and the right column images are scaled to [0,2].

Fig. 5

Comparison of dynamics of reconstructions from undersampled data (R=6) in two different breast lesion regions using different methods. (A) Images showing the one ROI in the breast lesion, indicated by the small black rectangle. (B) Comparison of mean signal intensity time curves for the lesion region shown in (A), and (C) is the magnified images of (B). The magnified image shows the signal intensity curve of SW methods have a larger deviation from that of the true images.

Fig. 6

The correlation plots between kinetic parameters (K^trans, k_ep) generated from images using parallel+complex and that using IFT of full-sampled k-space data, with K^trans plot shown in (A), k_ep plot shown in (B). The kinetic parameters data sets came from all four datasets’ lesion areas.

Fig. 7

The delta signal intensity values and model fits for images reconstructed from parallel+complex, sliding window and full-sampled data (denoted as “TCR,” “SW,” “True,” respectively). The delta signal intensity value is the intensity value with the mean value of the first ten time frames subtracted off. The plot demonstrates that in particular for the sliding window curve, the fit is much closer to the fully sampled data when the tissue curves increases sharply. This is because the sharp onset of the AIF used does not permit an exact fit to the curve.