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MRI2Qmap: compressed-sampled multiparametric quantitative MRI reconstruction using learned spatial priors from multimodal MRI datasets
Mohammad Golbabaee1, Matteo Cencini2, Carolin M Pirkl3, Marion I Menzel3, Michela Tosetti4, and Bjoern H Menze5
1University of Bristol, Bristol, United Kingdom, 2INFN Pisa division, Pisa, Italy, 3GE Healthcare, Munich, Germany, 4IRCCS Stella Maris, Pisa, Italy, 5University of Zurich, Zurich, Switzerland

Synopsis

Keywords: MR Fingerprinting, Quantitative Imaging, MR Fingerprinting, Compressed sensing, Image reconstruction, AI/ML Image Reconstruction

Motivation: Deep learning excels at compressed-sensing image reconstruction given large training datasets. Applying this paradigm to accelerated quantitative MRI, including magnetic resonance fingerprinting (MRF), is challenging because quantitative imaging datasets for training are scarce.

Goal(s): Can we overcome this limitation using new sources of training data from routine, largely available weighted-MRI images?

Approach: We introduce MRI2Qmap, a plug-and-play quantitative image reconstruction algorithm based on deep image denoising models pretrained on large multimodal weighted-MRI datasets.

Results: We showed, for the first time, that spatial/structural priors learned from independently-acquired datasets of routine weighted-MRI images can be effectively used for quantitative MRI image reconstruction.

Impact: Thanks to the widespread use of MRIs, our approach could enable much larger datasets to be used for training potentially enhanced AI models for fast quantitative MRI/MRF image reconstruction.

Introduction

Magnetic Resonance Fingerprinting1 (MRF) and other highly-accelerated transient-state parameter mapping techniques4 excel in quantifying multiple tissue properties, but can suffer from aliasing artefacts due to compressed-sampled scans. Incorporating spatial image priors can mitigate these issues, with deep learning showing promise given large training datasets. However, applying this paradigm to MRF-type sequences is challenging due to the scarcity of quantitative imaging datasets for training. We introduce MRI2Qmap, a quantitative image reconstruction approach that can take advantage of learned spatial-domain image priors from independently-acquired, large datasets of routine weighted-MRI images. We validate our findings using simulated and in-vivo acquisitions.

Problem formulation

We propose an augmented Lagrangian formulation for quantitative MRI reconstruction from highly undersampled k-space data:$$min_{q,m,I}\frac{1}{2}\|y-\mathscr{E}m\|_2^2+\frac{\mu_1}{2}\|m-\mathscr{B}_{mrf}(q)+w\|_2^2+\frac{\mu_2}{2}\|I-\mathscr{B}_{mri}(q)+u\|_2^2+\sum_{j\in \mathscr{M}} \lambda_j \mathscr{R}_j(I_j)\;\;\;\;\;\;\;\;\;\;\;\;\text(eq1)$$ $$$q=\{\text{T1,T2,Proton density (PD)}\}$$$ are quantitative bioparameter maps (qmaps) to be estimated. $$$m$$$ is the timeseries of magnetisation images (TSMI). $$$\mathscr{B}_{mrf}$$$ is the Bloch response, encoding $$$q$$$ into identifiable time-signals (fingerprints) of TSMI voxel-wise $$$(m\approx\mathscr{B}_{mrf}(q) )$$$. $$$\mathscr{E}$$$ is the linear acquisition/forward operator linking TSMI to undersampled k-space measurements $$$y$$$. $$$\mathscr{E}$$$ includes coil sensitivities, nonuniform-FFT and temporal dimensionality-reduction2,3. As demonstrated in4-6 qmaps can synthesize multimodal weighted-MRI images $$$I=\{I_j\}_{j\in\mathscr{M}}$$$. MR signal equations $$$\mathscr{B}_{mri}$$$ (eq2) are used to approximate MRI images $$$I_j$$$ in contrast modalities $$$j\in\mathscr{M}=\{\text{T1w,T2w,PDw}\}$$$ from qmaps. $$$\mathscr{R}_j$$$ is regularisation for promoting spatial/structural image priors for synthesized MRI images $$$I_j$$$ in each modality, by which cleaning them and the linked qmaps from aliasing. $$$u,w$$$ are Lagrangian multipliers. First three terms of (eq1) enforce k-space consistent TSMI, TSMI-consistent qmaps (via $$$\mathscr{B}_{mrf}$$$), and regularised MRI-consistent qmaps (via $$$\mathscr{B}_{mri}$$$), respectively. Hyperparameters $$$\mu_1,\mu_2,\lambda_j>0$$$ govern weighting between terms and regularisations.

MRI2Qmap algorithm

MRI2Qmap adopts Plug-and-Play ADMM7,8 iterations to minimise (eq1). It comprises three main steps at each iteration (details in Fig1):
  • Solves least-squares to update kspace-consistent TSMI $$$m$$$ (step1).
  • Utilises three pretrained image denoising unets8 $$$\textbf{DRUNET}_j$$$ for spatial/structural restoration of synthesized MRI images $$$I$$$. Specifically, we use data-driven Plug-and-Play image priors8 where each regularisation’s shrinkage/proximal operator (step2) is carried out by a $$$\textbf{DRUNET}_j$$$ pretrained on a large modality-specific $$$j\in\{\text{T1w,T2w,PDw}\}$$$ MRI image dataset for AWGN denoising.
  • Implements a “fused MRF-MRI” dictionary matching (step4) to update qmaps $$$q$$$, ensuring joint consistency with TSMI $$$m$$$ and spatially-restored synthesised MRIs $$$I$$$. Two dictionaries of MRF fingerprints $$$D_{mrf}$$$ and (T1w,T2w,PDw)-MRI fingerprints $$$D_{mri}$$$ are simulated from $$$\mathscr{B}_{mrf},\mathscr{B}_{mri}$$$ response functions. Concatenated TSMI and synthesized-MRI images are then pixel-wise matched to the concatenated fingerprints of both dictionaries, to jointly guide quantitative mapping.

Methods

Methods were tested on simulated and healthy volunteer brain MRI data, using Quantitative Transient-state Imaging4 with ramp-up-and-down flip angle variations, TR/TE/TI = 12/0.46/18ms, 880 repetitions (timeframes), variable-density spiral readouts, 200x200 matrix size, 1mm in-plane resolution and 5mm slice-thickness. In-vivo data was acquired on an 8-coil 1.5T HDxT GE HealthCare MR scanner. Acquisition parameters were also used to simulate additional single-coil MRF data using "ground-truth" qmaps from MAGiC scans of another healthy brain (5 slices) with added Gaussian noise (SNR=35dB) to simulated k-space measurements.

Three $$$\textbf{DRUNET}_j(x,\sigma)$$$ with adjustable denoising parameters $$$\sigma$$$ were used8, each pretrained on >75k axial brain MRI images from IXI dataset11 in specific modalities $$$j\in\{\text{T1w,T2w,PDw}\}$$$. Notably, training MRI images are from different subjects than MRF data used for testing/evaluation. Training involved normalizing and random cropping 64x64 patches, adding gaussian noise STD $$$\sigma\sim\mathscr{U}[0.001,0.25]$$$, and minimizing MSE loss between denoised and original/clean patches using ADAM optimizer (1000 epochs, batch_size=32, LR_init=1e-4, LR_decay_rate 0.6 every 100 epochs).

Extended-Phase-Graph9 and SVDMRF10 techniques were employed to create MRF dictionary $$$D_{mrf}\in C^{d\times t}$$$ ($$$d\sim95k$$$ fingerprints of length $$$t=5$$$) covering a logarithmic grid $$$(T1,T2)\in[10,6000]\times [4,4000]ms$$$. MRI dictionary $$$D_{mri}\in C^{d\times 3}$$$ was generated using MR signal equations covering same T1-T2 grid:$$[D_{mri}]_{i,j}=\exp\left(-\frac{TE_j}{T2_i}\right). \sin(FA_j).\left(1-\exp\left(-\frac{TR_j}{T1_i}\right)\right)/\left(1-\cos(FA_j)\exp\left(-\frac{TR_j}{T1_i}\right)\right)\;\;\;\;\;\;\;\;\;\;\;\;\text(eq2)$$ with columns representing parameters $$$(TR(ms), TE(ms),FA^\circ)\in\{(9.7,4.6,8), (7000,100,90), (7000,8,90)\}$$$ close to IXI dataset for T1w, T2w and PDw scans.

Results and discussions

Figures 2,4,5 compare reconstructed qmaps (also synthesized MRIs in Fig2) for in-vivo and simulated data, using proposed MRI2Qmap and baselines SVDMRF10, LRTV3 (total variation spatial regularisation), and ADMM w/o reg2 (without spatial regularisation). Figure 3 reports reconstruction performance metrics on simulated data compared to available ground-truths. Algorithms’ parameters were searched to minimise T1-T2 errors (simulated data) or tuned by visual inspection (in-vivo data). MRI2Qmap outperforms other baselines in minimising aliasing artefacts, thanks to utilising efficient spatial image priors learned from multimodal MRI datasets.

Conclusion

We showed, for the first time, that spatial/structural priors learned from independently-acquired datasets of routine weighted-MRI images can be effectively used for quantitative MRI/MRF-type image reconstruction. Thanks to widespread use of MRIs, this could enable much larger datasets to be used for training potentially enhanced AI models for fast quantitative imaging. Future works include exploring MRI2Qmap’s potential for imaging pathologies using different MRI datasets/anatomies/acquisition protocols.

Acknowledgements

This research is primarily supported by the EPSRC grant EP/X001091/1 led by MG. CMP and MIM receive support from the European Union’s Horizon 2020 research and innovation programme, grant agreement No. 952172.

References

  1. D. Ma, et al. “Magnetic resonance fingerprinting,” Nature, vol. 495, no. 7440, pp. 187–192, 2013.
  2. J. Assländer, et al. “Low rank alternating direction method of multipliers reconstruction for MR fingerprinting.” Magnetic resonance in medicine, 79(1), 83-96, 2018.
  3. M. Golbabaee, et al. "Compressive MRI quantification using convex spatiotemporal priors and deep encoder-decoder networks." Medical image analysis 69 (2021): 101945.
  4. P. A. Gómez, et al. "Rapid three-dimensional multiparametric MRI with quantitative transient-state imaging." Scientific reports 10.1 (2020): 13769.
  5. P. Virtue, et al. "Direct contrast synthesis for magnetic resonance fingerprinting." Proc. Intl. Soc. Mag. Reson. Med. 2018.
  6. L. Peretti, et al. "Generating Synthetic Radiological Images with PySynthMRI: An Open-Source Cross-Platform Tool." Tomography 9.5 (2023): 1723-1733.
  7. S.V. Venkatakrishnan, et al. "Plug-and-play priors for model based reconstruction." Proc. IEEE GlobalSIP. 2013.
  8. K. Zhang, et al. "Plug-and-play image restoration with deep denoiser prior." IEEE Transactions on Pattern Analysis and Machine Intelligence 44.10 (2021): 6360-6376.
  9. M. Weigel “Extended phase graphs: dephasing, RF pulses, and echoes - pure and simple.” J. Magn. Reson. Imaging JMRI. 2015;41(2):266–295.
  10. DF. McGivney, et al. SVD compression for magnetic resonance fingerprinting in the time domain. IEEE TMI. 2014;33:2311–2322.
  11. “IXI Dataset,” http://brain-development. org/ixi-dataset/.

Figures

Fig1 MRI2Qmap algorithm. Key iterative steps: step1 updates kspace consistent TSMI mk using few lsqr iterations. Plug and Play step2 updates spatially restored synthesised MRI images Ik using pretrained multimodal MRI denoisers DRUNET. Step4 updates qmaps qk to be jointly consistent with TSMI and spatially-restored MRIs, using “fused MRF-MRI” dictionary matching. DictMatch inputs are $$$\gamma$$$-weighted concatenations of TSMI and MRI images (step3), and correspondingly MRF and MRI dictionaries Dcat= [Dmrf, $$$\gamma$$$Dmri]. Initialised q(0) uses MRF-only DictMatch.

Fig2 Reconstructed in-vivo quantitative maps by MRI2Qmap, LRTV, ADMM (w/o reg) and SVDMRF. Columns display skull stripped T1 T2 PD maps and synthesised T1w T2w PDw MRI images (eq2). Methods internal parameters were tuned by visual inspection. Method choice significantly impacts T2/PD maps and synthMRIs, with ADMM (without spatial regularisation) causing aliasing artifacts, and LRTV (with Total Variation regularisation) non-natural, over-smoothed boundaries. MRI2Qmap outperforms baselines by utilising efficient spatial image priors learned from multimodal MRI datasets.

Fig3 Measured T1, T2 and PD reconstruction performances on simulated MRF-type data using methods MRI2Qmap, LRTV, ADMM (w/o reg) and SVDMRF. Two left plots: Mean Absolute Percentage Errors (MAPE) of reconstructed (skull-tripped) T1 and T2 maps wrt. the ground-truths, averaged over tested brain slices. Right plot: average Proton Density (PD) reconstruction PSNRs. Internal parameters of all tested algorithms were tuned (Bayesian optimisation) to minimise their T1 and T2 MAPEs. MRI2Qmap outperforms baselines in terms of T1, T2 and PD reconstruction accuracies.

Fig4 Simulated MRF-type data (as in Fig 3): Rows display an axial slice of reconstructed T1, T2 and PD maps (skull-stripped, zoomed-in), along with their errors in comparison to the ground-truth (GT). The columns present reconstructions for the proposed MRI2Qmap algorithm compared to baselines LRTV, ADMM (w/o reg), and SVDMRF. Similar to findings in previous figures: MRI2Qmap surpasses the baselines by achieving the lowest T1, T2, and PD mapping errors, thanks to its utilisation of data-driven multimodal MRI image priors.

Fig5 Simulated MRF-type data: Rows display reconstructed T1 (left panel) T2 (right panel) maps of four remaining brain slices than Fig 4 ((skull-stripped, zoomed-in), along with their errors in comparison to the ground-truth (GT). The MRI2Qmap algorithm achieves the lowest T1, T2 mapping errors compared to the closest-competing baseline LRTV (results for PD maps and other baselines are not shown due to space limit, but same conclusions as in previous figures hold).

Proc. Intl. Soc. Mag. Reson. Med. 32 (2024)
0624
DOI: https://doi.org/10.58530/2024/0624