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Model-Based Iterative Reconstruction for Radial Fast Spin-Echo MRI
Kai Tobias Block, Martin Uecker, Jens Frahm
TL;DR
Radial FSE reconstruction ordinarily mixes spokes with different T2 weightings, producing averaged contrast and artifacts that hinder quantification. This work models the time-dependent multi-coil signal and jointly estimates spin-density and relaxivity maps through numerical optimization. Phantom and in vivo results show artifact-free maps relative to the reported TE-mixing and streaking problems, although the method is computationally intensive and depends on adequate temporal sampling.
Problem
Radial FSE data combine spokes with varying T2 weighting, while existing echo-time-sharing reconstructions introduce artifacts that limit T2-estimation accuracy.
Method
The method uses a time-dependent multi-coil signal model and numerical optimization to directly estimate spin-density and relaxivity maps from one radial data set.
Results
Phantom, simulated, and human-brain experiments produced maps without the reported TE-mixing and streaking artifacts, with iterative relaxivity estimates more accurate than gridding or KWIC in analyzed simulations.
Takeaways & Limitations
A single radial FSE acquisition can provide spin-density and relaxivity maps while exploiting all sampled data and avoiding intermediate echo-resolved reconstructions.
Takeaways & Limitations
The method has substantially higher computational requirements, and inaccurate estimates can occur when relaxation is too fast for the acquired echo train to capture.
Abstract
from arXiv · showhide
In radial fast spin-echo MRI, a set of overlapping spokes with an inconsistent T2 weighting is acquired, which results in an averaged image contrast when employing conventional image reconstruction techniques. This work demonstrates that the problem may be overcome with the use of a dedicated reconstruction method that further allows for T2 quantification by extracting the embedded relaxation information. Thus, the proposed reconstruction method directly yields a spin-density and relaxivity map from only a single radial data set. The method is based on an inverse formulation of the problem and involves a modeling of the received MRI signal. Because the solution is found by numerical optimization, the approach exploits all data acquired. Further, it handles multi-coil data and optionally allows for the incorporation of additional prior knowledge. Simulations and experimental results for a phantom and human brain in vivo demonstrate that the method yields spin-density and relaxivity maps that are neither affected by the typical artifacts from TE mixing, nor by streaking artifacts from the incomplete k-space coverage at individual echo times.
1 Introduction
Radial FSE sampling averages varying T2 weightings because every spoke passes through central k-space, creating reconstruction challenges but also embedding local signal-decay information. The proposed iterative method directly extracts spin density and relaxivity from the radial data while avoiding TE-mixing and incomplete-coverage artifacts.
- Radial FSE spokes share the center of k-space, so conventional reconstruction averages their differing T2 weightings.
- Because every echo time samples low spatial frequencies, a single radial data set contains local signal-decay information for T2 quantification.
- KWIC reconstructs echo-resolved images by mixing low-frequency data from the target echo with high-frequency data from other echo times, introducing TE-mixing artifacts.
- The proposed method directly estimates spin-density and relaxivity maps from acquired k-space data using numerical optimization and a time-dependent MRI signal model.
2 Theory
The reconstruction formulates multi-echo radial MRI as an inverse problem that jointly estimates spin density and relaxivity by matching modeled, coil-sensitive k-space signals to measured data. Numerical optimization, regularization, and time scaling make the large nonlinear problem tractable while preserving the embedded relaxation information.
- 2 Theory: The method jointly estimates spin-density and relaxivity maps so modeled snapshots at each echo time match the corresponding measured spokes.
- 2.1 Cost Function: An L2 cost function measures the mismatch between modeled and measured multi-coil k-space data, and nonlinear conjugate-gradient optimization minimizes it.
- 2.1 Cost Function: The forward model applies coil sensitivities, generates echo-time-dependent image snapshots, and evaluates their Fourier transforms at the acquired radial sampling positions.
- 2.2 Evaluation of Cost Function: FFT-based gridding accelerates cost-function and gradient evaluation, while gradients are computed for both spin-density and relaxivity components across coils and echo times.
- 2.3 Regularization: Finite-difference regularization of the maps’ Fourier transforms suppresses ill-conditioned intensity accumulations and artifacts, but requires choosing a weighting factor λ.
- 2.5 Scaling and Snapshot Calculation: Rescaling echo-time values balances sensitivity to spin density and relaxivity, reducing typical iteration counts from over 1000 to about 80.
- 2.5 Scaling and Snapshot Calculation: After estimation, snapshots can be generated at arbitrary echo times, providing a familiar image view without adding information.
3 Methods
The evaluation used simulated and experimental radial FSE data from a numerical phantom, a multi-coil water phantom, and human brain imaging. Reconstructions were compared across iterative, gridding, and KWIC approaches using the same radial acquisition framework.
- 3 Methods: Simulations used a numerical phantom with compartments having T2 relaxation times of 200 ms, 100 ms, 50 ms, and 1000 ms.
- 3 Methods: Experimental scans were performed at 2.9 T with a receive-only 12-channel head coil.
- 3 Methods: Phantom and simulated data used 160-pixel resolution, 120 mm FOV, and 568 Hz/pixel bandwidth, whereas human brain data used 224-pixel resolution and 208 mm FOV.
- 3 Methods: Each acquisition recorded 16 spin echoes separated by 10 ms after a slice-selective 90° excitation pulse.
- 3 Methods: The phantom comparison used the iterative method, KWIC with all 16 echoes, and KWIC with 8 neighboring echoes from 512 radial spokes.
4 Results
Across phantom, simulated, and in vivo experiments, the iterative reconstruction produced spin-density and relaxivity maps with fewer TE-mixing and streaking artifacts than KWIC and direct gridding. It remained effective under undersampling and noise, although extreme undersampling introduced minor streaking.
- Experimental Data: KWIC produced ring-like artifacts in rapidly relaxing phantom tubes, while the iterative maps avoided these artifacts.Sharing all echoes caused stronger artifacts; sharing eight echoes also produced streaking from incomplete outer-k-space coverage.
- Experimental Data: In vivo, the iterative brain maps avoided KWIC streaking, blurring, and sharp hyperintense structures, and agreed well with fully sampled Cartesian maps.The Cartesian comparison differed slightly in frontal-ventricle coverage because of slice thickness, not reconstruction technique.
- Experimental Data: The proposed method matched Cartesian snapshot contrast at the first, sixth, and last echoes without streaking artifacts.Direct gridding and Cartesian images served as references because their k-space data had equal echo times.
- Experimental Data: Even with 128 spokes from 8 repetitions, iterative reconstruction retained relatively good proton-density and relaxivity separation, whereas KWIC quality broke down under stronger undersampling.The in vivo comparison covered 512, 256, and 128 spokes acquired with 32, 16, and 8 repetitions, respectively.
- Simulated Data: ROI analysis found higher relaxivity accuracy for the iterative approach than for gridding or KWIC, including in the fully sampled simulation.KWIC and gridding deviations were attributed to ringing that smeared signal from the surrounding compartment into rapidly decaying compartments.
5 Discussion
The iterative reconstruction combines spokes acquired at different echo times through a signal model, avoiding the contrast–undersampling trade-off of existing radial FSE methods. Its accuracy is supported by simulated results, but computational cost and several practical factors constrain use.
- 5 Discussion: Signal modeling combines spokes from different echo times without restricting contrast changes to central k-space.This allows the method to exploit all sampled data while avoiding the usual trade-off between echo-time contrast accuracy and outer-k-space undersampling.
- 5.1 Computational Load: The method requires substantially more computation than conventional non-iterative methods, including 64 FFT and gridding steps for one cost-function evaluation.Gradient evaluation requires approximately twice as many operations, and one iteration may require several cost-function and gradient evaluations.
- 5.1 Computational Load: Parallel execution reduced the proof-of-principle runtime to about two minutes per slice for 200 iterations on the reported dual-processor system.
- 5 Discussion: The iterative approach estimates signal relaxivity with higher accuracy than the compared reconstructions in the reported ROI analysis.
- 5.1 Computational Load: Delayed reconstruction is likely to limit near-term use, although preliminary gridding reconstructions could provide immediate operator feedback.
- 5.2 Accuracy: Accuracy can be affected by coil-sensitivity bias, truncation artifacts, insufficient temporal sampling of fast relaxation, and deviations from mono-exponential decay.The latter two limitations are described as general problems for T2 estimation, while coil-profile characterization and finite sampling affect practical reconstruction accuracy.
- 5 Discussion: The approach can extend beyond FSE multi-echo data when an appropriate analytical signal model is available, with possible adaptations for other contrast mechanisms.
6 Conclusion
The work introduces an iterative reconstruction for radial multi-echo data that directly estimates spin-density and relaxivity from a signal model. It enables T2 quantification from one radial data set, but its computational intensity currently restricts applications requiring delayed reconstruction.
- 6 Conclusion: The proposed method models echo-time-dependent data and directly estimates spin-density and relaxivity maps through numerical optimization.
- 6 Conclusion: The method exploits all sampled data and enables efficient T2 quantification from a single radial data set.
- 6 Conclusion: Compared with Cartesian quantification techniques, radial data can be acquired in less time and with lower motion sensitivity.
- 6 Conclusion: The method is computationally intensive and currently limited to applications where delayed reconstruction is acceptable.
Appendix
The appendix defines the optimization objective and its derivatives used to estimate the reconstruction maps. The derivative expressions are obtained by applying the chain rule to the cost function.
- Appendix: The simplified cost function φ in Eq. (6) defines the optimization objective for the reconstruction.
- Appendix: The derivative of the cost function with respect to an estimate component u is obtained using the chain rule.
- Appendix: Substituting Eq. (7) yields the derivative with respect to a spin-density-map component ρv.
- Appendix: Derivatives with respect to relaxivity-map components are obtained analogously.