Elastic AlignedSENSE for Dynamic MR Reconstruction: A Proof of Concept in Cardiac Cine
Abstract
:1. Introduction
2. Materials and Methods
2.1. Materials
2.2. Reconstruction Problem: Elastic AlignedSENSE
2.3. Methods Used for Performance Comparison
- Transformations are defined in opposite directions, as illustrated in Figure 2. In GWCS, the coordinate space is defined in the common reference image, and each frame (, N being the number of frames) is transformed so that it fits into such , i.e., we calculated with . Thus, in the optimization problem described in Equation (8), we aimed to find that , with . In the case of EAS, the coordinate space is defined in each frame —and coincides for all frames (, )—so that each frame is a deformed version of the pattern image , i.e., . In summary, the transformations have their origin in the space in which the coordinate system is defined, and the direction is the opposite of what “common sense” dictates. The reason for this is because the transformation defined in that way makes the underlying interpolation process more convenient.
- The common reference image in GWCS is the average of the registered images, following [26], while in EAS, the reference arises as a result of the optimization subproblem in Equation (4a), which is transformed to create the images of the final sequence and does not necessarily correspond to any pre-selected cardiac phase.
2.4. Combination of Elastic AlignedSENSE and Group-Wise Motion-Compensated Compressed Sensing
2.5. Performance Analysis and Hyperparameter Selection
- For each of the K datasets, the value of the parameter that maximizes the IQM is determined by sweeping in a range of candidate values; let , denote this value for the k-th dataset.
- The K datasets are split into P datasets for training and for testing. Let be the i-th training set and its corresponding test set, . Let denote the index within the set of the j-th element of , with . The purpose of this stage is to determine the optimum parameter for each . To this end, we accumulated the IQM for all datasets within , but dataset , using the parameter from the previous stage. The optimal value is the one that provides the maximum accumulated IQM out of the P accumulated quantities. Let denote that value.
- The final stage pursues finding which of the , is the optimum. This is accomplished by calculating the accumulated IQM in the datasets within , using ; the optimal parameter is the value that maximizes this quantity out of the accumulated IQM values.
3. Experiments
3.1. Experiment 1: Cartesian Acquisition
3.2. Experiment 2: Radial Acquisition
4. Results
4.1. Results of Experiment 1
4.2. Results of Experiment 2
5. Discussion
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Conflicts of Interest
References
- Menchón-Lara, R.M.; Simmross-Wattenberg, F.; Casaseca-de-la Higuera, P.; Martín-Fernández, M.; Alberola-López, C. Reconstruction techniques for cardiac cine MRI. Insights Imaging 2019, 10, 1–16. [Google Scholar] [CrossRef] [PubMed]
- Bluemke, D.A.; Boxerman, J.L.; Atalar, E.; McVeigh, E.R. Segmented K-space cine breath-hold cardiovascular MR imaging: Part 1. Principles and technique. Am. J. Roentgenol. 1997, 169. [Google Scholar] [CrossRef]
- Larson, A.C.; White, R.D.; Laub, G.; McVeigh, E.R.; Li, D.; Simonetti, O.P. Self-gated cardiac cine MRI. Magn. Reson. Med. 2004, 51, 93–102. [Google Scholar] [CrossRef][Green Version]
- Liu, J.; Spincemaille, P.; Codella, N.; Nguyen, T.; Prince, M.; Wang, Y. Respiratory and cardiac self-gated free-breathing cardiac CINE imaging with multiecho 3D hybrid radial SSFP acquisition. Magn. Reson. Med. 2010, 63, 1230–1237. [Google Scholar] [CrossRef] [PubMed][Green Version]
- Krämer, M.; Herrmann, K.H.; Biermann, J.; Reichenbach, J. Retrospective reconstruction of cardiac cine images from golden-ratio radial MRI using one-dimensional navigators. J. Magn. Reson. Imaging 2014, 40, 413–422. [Google Scholar] [CrossRef] [PubMed]
- Usman, M.; Ruijsink, B.; Nazir, M.; Cruz, G.; Prieto, C. Free breathing whole-heart 3D CINE MRI with self-gated Cartesian trajectory. Magn. Reson. Imaging 2017, 38, 129–137. [Google Scholar] [CrossRef] [PubMed][Green Version]
- Seo, H.; Kim, D.; Oh, C.; Park, H. Self-gated cardiac cine imaging using phase information. Magn. Reson. Med. 2017, 77, 1216–1222. [Google Scholar] [CrossRef] [PubMed]
- Tsao, J.; Boesiger, P.; Pruessmann, K.P. k-t BLAST and k-t SENSE: Dynamic MRI with high frame rate exploiting spatiotemporal correlations. Magn. Reson. Med. 2003, 50, 1031–1042. [Google Scholar] [CrossRef]
- Huang, F.; Akao, J.; Vijayakumar, S.; Duensing, G.R.; Limkeman, M. k-t GRAPPA: A k-space implementation for dynamic MRI with high reduction factor. Magn. Reson. Med. 2005, 54, 1172–1184. [Google Scholar] [CrossRef]
- Lustig, M.; Donoho, D.; Pauly, J.M. Sparse MRI: The application of compressed sensing for rapid MR imaging. Magn. Reson. Med. Off. J. Int. Soc. Magn. Reson. Med. 2007, 58, 1182–1195. [Google Scholar] [CrossRef]
- Jung, H.; Ye, J.C. Motion estimated and compensated compressed sensing dynamic magnetic resonance imaging: What we can learn from video compression techniques. Int. J. Imaging Syst. Technol. 2010, 20, 81–98. [Google Scholar] [CrossRef]
- Asif, M.S.; Hamilton, L.; Brummer, M.; Romberg, J. Motion-adaptive spatio-temporal regularization for accelerated dynamic MRI. Magn. Reson. Med. 2013, 70, 800–812. [Google Scholar] [CrossRef]
- Lingala, S.G.; DiBella, E.; Jacob, M. Deformation Corrected Compressed Sensing (DC-CS): A Novel Framework for Accelerated Dynamic MRI. IEEE Trans. Med. Imaging 2015, 34, 72–85. [Google Scholar] [CrossRef] [PubMed]
- Usman, M.; Atkinson, D.; Heathfield, E.; Greil, G.; Schaeffter, T.; Prieto, C. Whole left ventricular functional assessment from two minutes free breathing multi-slice CINE acquisition. Phys. Med. Biol. 2015, 60, N93–N107. [Google Scholar] [CrossRef]
- Royuela-del Val, J.; Cordero-Grande, L.; Simmross-Wattenberg, F.; Martín-Fernández, M.; Alberola-López, C. Nonrigid group-wise registration for motion estimation and compensation in compressed sensing reconstruction of breath-hold cardiac cine MRI. Magn. Reson. Med. 2016, 75, 1525–1536. [Google Scholar] [CrossRef] [PubMed][Green Version]
- Royuela-del Val, J.; Cordero-Grande, L.; Simmross-Wattenberg, F.; Martín-Fernández, M.; Alberola-López, C. Jacobian weighted temporal total variation for motion compensated compressed sensing reconstruction of dynamic MRI. Magn. Reson. Med. 2017, 77, 1208–1215. [Google Scholar] [CrossRef] [PubMed][Green Version]
- Batchelor, P.G.; Atkinson, D.; Irarrazaval, P.; Hill, D.L.G.; Hajnal, J.; Larkman, D. Matrix description of general motion correction applied to multishot images. Magn. Reson. Med. 2005, 54, 1273–1280. [Google Scholar] [CrossRef] [PubMed]
- Cordero-Grande, L.; Teixeira, R.P.A.; Hughes, E.J.; Hutter, J.; Price, A.N.; Hajnal, J.V. Sensitivity encoding for aligned multishot magnetic resonance reconstruction. IEEE Trans. Comput. Imaging 2016, 2, 266–280. [Google Scholar] [CrossRef][Green Version]
- Rueckert, D.; Sonoda, L.I.; Hayes, C.; Hill, D.L.G.; Leach, M.O.; Hawkes, D.J. Nonrigid registration using free-form deformations: Application to breast MR images. IEEE Trans. Med. Imaging 1999, 18, 712–721. [Google Scholar] [CrossRef]
- De Boor, C. A Practical Guide to Splines; Springer: New York, NY, USA, 1978. [Google Scholar]
- Sun, W.; Niessen, W.J.; Klein, S. Free-form deformation using lower-order B-spline for nonrigid image registration. In Medical Image Computing and Computer-Assisted Intervention–MICCAI 2014; Golland, P., Hata, N., Barillot, C., Hornegger, J., Howe, R., Eds.; Springer International Publishing: Cham, Switzerland, 2014; pp. 194–201. [Google Scholar]
- Menchón-Lara, R.M.; Royuela-del-Val, J.; Simmross-Wattenberg, F.; Casaseca-de-la-Higuera, P.; Martín-Fernández, M.; Alberola-López, C. Fast 4D elastic group-wise image registration. Convolutional interpolation revisited. Comput. Methods Programs Biomed. 2021, 200, 105812. [Google Scholar] [CrossRef] [PubMed]
- Nocedal, J.; Wright, S.J. Numerical Optimization; Springer: New York, NY, USA, 1999. [Google Scholar]
- Beatty, P.J.; Nishimura, D.G.; Pauly, J.M. Rapid gridding reconstruction with a minimal oversampling ratio. IEEE Trans. Med. Imaging 2005, 24, 799–808. [Google Scholar] [CrossRef]
- Knoll, F.; Schwarzl, A.; Diwoky, C.; Sodickson, D.K. gpuNUFFT-An Open Source GPU Library for 3D Regridding with Direct Matlab Interface. In Proceedings of the 22nd Annual Meeting of ISMRM, Milan, Italy, 10–16 May 2014; p. 4297. [Google Scholar]
- Polfliet, M.; Klein, S.; Huizinga, W.; Paulides, M.M.; Niessen, W.J.; Vandemeulebroucke, J. Intrasubject multimodal group-wise registration with the conditional template entropy. Med. Image Anal. 2018, 46, 15–25. [Google Scholar] [CrossRef]
- Becker, S.; Bobin, J.; Candès, E.J. NESTA: A fast and accurate first-order method for sparse recovery. SIAM J. Imaging Sci. 2011, 4, 1–39. [Google Scholar] [CrossRef][Green Version]
- Cruz, G.; Atkinson, D.; Buerger, C.; Schaeffter, T.; Prieto, C. Accelerated motion corrected three-dimensional abdominal MRI using total variation regularized SENSE reconstruction. Magn. Reson. Med. 2016, 75, 1484–1498. [Google Scholar] [CrossRef] [PubMed][Green Version]
- Wang, Z.; Bovik, A.C.; Sheikh, H.R.; Simoncelli, E.P. Image quality assessment: From error visibility to structural similarity. IEEE Trans. Image Process. 2004, 13, 600–612. [Google Scholar] [CrossRef] [PubMed][Green Version]
- Godino-Moya, A.; Royuela-del Val, J.; Usman, M.; Menchón-Lara, R.M.; Martín-Fernández, M.; Prieto, C.; Alberola-López, C. Space-time variant weighted regularization in compressed sensing cardiac cine MRI. Magn. Reson. Imaging 2019, 58, 44–55. [Google Scholar] [CrossRef]
- Feng, L.; Srichai, M.B.; Lim, R.P.; Harrison, A.; King, W.; Adluru, G.; Dibella, E.V.R.; Sodickson, D.K.; Otazo, R.; Kim, D. Highly accelerated real-time cardiac cine MRI using k-t SPARSE-SENSE. Magn. Reson. Med. 2013, 70, 64–74. [Google Scholar] [CrossRef][Green Version]
- Feng, L.; Grimm, R.; Block, K.T.; Chandarana, H.; Kim, S.; Xu, J.; Axel, L.; Sodickson, D.K.; Otazo, R. Golden-angle radial sparse parallel MRI: Combination of compressed sensing, parallel imaging, and golden-angle radial sampling for fast and flexible dynamic volumetric MRI. Magn. Reson. Med. 2014, 72, 707–717. [Google Scholar] [CrossRef][Green Version]
- Feng, L.; Axel, L.; Chandarana, H.; Block, K.T.; Sodickson, D.K.; Otazo, R. XD-GRASP: Golden-angle radial MRI with reconstruction of extra motion-state dimensions using compressed sensing. Magn. Reson. Med. 2016, 75, 775–788. [Google Scholar] [CrossRef] [PubMed][Green Version]
- Metz, C.; Klein, S.; Schaap, M.; van Walsum, T.; Niessen, W. Nonrigid registration of dynamic medical imaging data using nD+t B-splines and a group-wise optimization approach. Med. Image Anal. 2011, 15, 238–249. [Google Scholar] [CrossRef] [PubMed]
R = 8 | R = 10 | R = 14 | |
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Mean Running Time (min) | |
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1.9513 | |
6.4263 | |
2.2940 | |
3.7792 |
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Godino-Moya, A.; Menchón-Lara, R.-M.; Martín-Fernández, M.; Prieto, C.; Alberola-López, C. Elastic AlignedSENSE for Dynamic MR Reconstruction: A Proof of Concept in Cardiac Cine. Entropy 2021, 23, 555. https://doi.org/10.3390/e23050555
Godino-Moya A, Menchón-Lara R-M, Martín-Fernández M, Prieto C, Alberola-López C. Elastic AlignedSENSE for Dynamic MR Reconstruction: A Proof of Concept in Cardiac Cine. Entropy. 2021; 23(5):555. https://doi.org/10.3390/e23050555
Chicago/Turabian StyleGodino-Moya, Alejandro, Rosa-María Menchón-Lara, Marcos Martín-Fernández, Claudia Prieto, and Carlos Alberola-López. 2021. "Elastic AlignedSENSE for Dynamic MR Reconstruction: A Proof of Concept in Cardiac Cine" Entropy 23, no. 5: 555. https://doi.org/10.3390/e23050555