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3D motion compensated reconstruction using pixel tracking for cardiac perfusion MRI: comparison with rigid shift correction1UCAIR, University of Utah, Salt Lake City, UT, United States, 2Physics, University of Utah, Salt Lake City, UT, United States
Synopsis
We developed a pixel tracking motion compensation reconstruction framework for 3D acquisitions. The method was compared to a rigid motion compensation reconstruction method and to reconstruction without motion compensation using a cardiac perfusion dataset acquired with a 3D stack-of-stars sequence. The pixel tracking motion compensation method improved reconstruction, while the rigid motion compensation led to blurring.
Introduction
Dynamic contrast enhanced MRI of the heart is used clinically to detect ischemia in the myocardium. 3D acquisitions (1) can provide whole heart coverage which is advantageous over 2D acquisitions. However, due to the large amount data required for fully sampling, typical 3D acquisitions are highly undersampled, thus the reconstructions rely heavily on compressed sensing methods. When a temporal prior such as temporal total variation (2,3) is used, breathing during the acquisition can cause inter-frame blurring or ghosting. 2D motion compensated (MC) reconstructions have been studied to improve the reconstruction, by using patch-based compensations (4), deformable registrations (5,6) or rigid shifts (7). However, less work has been done on 3D MC for cardiac perfusion MRI (8). Since the intrinsic property of motion is three dimensional, the 3D acquisitions may provide improved motion estimation and compensation since both in-plane and through-plan motion can be estimated and compensated. Here we extend a 2D pixel tracking spatiotemporal constrained reconstruction (PT-STCR) framework (9) and a rigid MC method (7) to 3D, and compared to reconstruction without MC.Methods
3D Pixel Tracking STCR
The 3D PT-STCR reconstruction includes two reconstruction stages. In the first stage, a reference image was reconstructed by using STCR with a low temporal constraint weight to better preserve inter-frame motion. The following cost function in equation (1) was minimized:
$$m=\mathrm{arg min}\left|\left|Am-d\right|\right|_2^2+\lambda_s\left|\left|\sqrt{(\nabla_xm)^2+(\nabla_ym)^2+\epsilon}\right|\right|_1+\lambda_{sl}\left|\left|\sqrt{(\nabla_zm)^2+\epsilon}\right|\right|+\lambda_t\left|\left|\sqrt{(\nabla_tm)^2+\epsilon}\right|\right|_1.(1)$$
Except for similar terms as in (9), $$$A$$$ includes a 3D stack-of-stars undersampling mask, $$$d$$$ is Cartesian k-space estimated from the acquired stack-of-stars data using slice-by-slice GROG interpolation (10) and a total variation along the slice direction was applied. Two sets of deformation maps were estimated from the reference images: forward maps that map each current time frame onto the next time frame and backwards maps, by using large deformation kinematics (11). In the reconstruction stage two, the temporal total variation term in equation (1) was replaced by the pixel tracking regularization: $$$\lambda_t\left|\left|\sqrt{(\nabla_tPm)^2+\epsilon}\right|\right|_1$$$, where $$$P$$$ is a reordering matrix obtained from the motion maps that aligns each pixel along the time direction. 30 and 70 conjugate gradient iterations were used for stage one and two separately, regularization parameters were $$$\lambda_t=0.04C, \lambda_s=0.003C, \lambda_{sl}=0.003C$$$ for stage one and $$$\lambda_t$$$ was increased to $$$0.2C$$$ for stage two, where $$$C$$$ is the average pixel intensity of $$$A^{-1}d$$$ (used as initial estimation of $$$m$$$ in stage one).
Rigid Motion Compensation
A rigid MC frame work was proposed in (7) that estimate rigid shifts between time frames from a SPIRiT (12) reference reconstruction, and apply linear phase shifts in acquired k-space. The modulated k-space is then used in compressed sensing reconstruction to obtain the rigid shift corrected images. To evaluate the rigid MC and the PT-STCR under the same circumstance, we modify the method as the following: 1. The reference reconstruction was done as for the PT-STCR. 2. After the 3D linear phase shifts were applied to the k-space data, another 70 iterations were performed for the final reconstruction using STCR with the same regularization parameters as for the PT-STCR. Figure 1 shows the flowcharts for both methods.
To evaluate both methods, one dataset that had considerable respiration motion acquired on a Siemens 3T (Prisma) scanner was reconstructed using PT-STCR, rigid MC and STCR with the same regularization parameters. The dataset was acquired at stress using an undersampled 3D stack-of-stars sequence (2,13) with parameters: resolution 1.8x1.8x5 mm3, 8 partitions, TR/TE = 1.54/0.77 ms, 80 ms saturation recovery time.
Results and Discussion
Figure 2 shows two time frames of all the 8 slices from the PT-STCR, rigid MC and STCR reconstructions. Figure 3 shows 2 other time frames with 4 center slices out of the 8. The rigid MC reconstruction is blurrier than the other two in the pre-contrast and LV enhancement frames, and has ghosting artifact in the RV enhancement frame. The PT-STCR outperforms the other two reconstructions in suppressing streaking artifact. Both the PT-STCR and rigid MC methods can improve the myocardium border sharpness. Figure 4 shows the line profiles of a middle slice. The rigid MC has the least motion since it corrects rigid shifts in k-space, however is blurrier than the other two methods. Dynamic images of the three reconstructions are shown in Figure 5.
The PT-STCR can preserve motion and improve the sharpness for 3D reconstructions. The rigid MC method results blurrier than the STCR, this may be caused by non-integral rigid shifts along the slice direction. Since the slice thickness (5mm) is typically larger than the in-plane voxel length (1.8mm), rigid shift correction in k-space is essentially an interpolation and may lead to blurring. The PT-STCR bypasses this issue since it does not relay on interpolation but only reordering of each pixel.
Acknowledgements
No acknowledgement found.References
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