Magnetic Resonance Imaging Iterative reconstruction of radially-sampled 31P bSSFP data using prior information from 1H MRI  Kristian Rink, Nadia Benkhedah, Moritz C. Berger, Christine Gnahm, Nicolas G.R. Behl, Jonathan M. Lommen, Vanessa Stahl, Peter Bachert, Mark E. Ladd, Armin M. Nagel  Magnetic Resonance Imaging  Volume 37, Pages 147-158 (April 2017) DOI: 10.1016/j.mri.2016.11.013 Copyright © 2016 Elsevier Inc. Terms and Conditions

Fig. 1 Schemes of 3D density-adapted radially-sampled bSSFP sequences (not to scale). Frequency selectivity is achieved by Gaussian-shaped 31P excitation pulses. (A) Gradient scheme G1 features a straightforward layout with a single readout and a rewinder gradient [39]. (B) Gradient scheme G2 is composed of two point-reflected gradients to sample k-space from the center to the periphery and back acquiring two different contrasts [50]. (C) Gradient scheme G3 extends scheme G2 in order to obtain additional contrasts at the expense of a longer repetition time. Magnetic Resonance Imaging 2017 37, 147-158DOI: (10.1016/j.mri.2016.11.013) Copyright © 2016 Elsevier Inc. Terms and Conditions

Fig. 2 In vivo 31P MR spectrum of the human calf muscle obtained at B0=7T with a non-selective 1-pulse-acquire sequence. The shaded area indicates the FWHM of the Gaussian excitation pulse (3.5ppm). The peaks of the resolved metabolites are marked with vertical dashed lines and are assigned to phosphomonoester (PME), inorganic phosphate (Pi), phosphodiester (PDE), phosphocreatine (PCr), and adenosine 5′-triphosphate (ATP). Magnetic Resonance Imaging 2017 37, 147-158DOI: (10.1016/j.mri.2016.11.013) Copyright © 2016 Elsevier Inc. Terms and Conditions

Fig. 3 Conceptual workflow to obtain iteratively reconstructed 31P images. (A) Contrasts of 31P acquisitions obtained by 3D density-adapted radially-sampled bSSFP sequences. (B) Gridding-reconstructed and accumulated 31P image. (C) Gridding-reconstructed and oversampled 31P image. (D) 1H FLASH acquisition utilized as anatomical reference and registered on the oversampled 31P image (dashed arrow). (E) Binary mask utilized as prior knowledge. (F) Iteratively reconstructed 31P image with 1H MRI constraint. Note, that subfigures A and B are reconstructed by the gridding algorithm only for visualization in this illustration. Magnetic Resonance Imaging 2017 37, 147-158DOI: (10.1016/j.mri.2016.11.013) Copyright © 2016 Elsevier Inc. Terms and Conditions

Fig. 4 Central slices and corresponding profiles of the simulated cylindrical phantom. (A) Simulated phantom. (B) Simulated phantom with Gaussian noise. (C) Simulated binary mask, also representing the ground truth. (D,E) Gridding reconstructions of the radial acquisition representing subfigures A and B. (F,G) Iteratively reconstructed images from subfigures A and B with constraint C and a weighting factor of τBM=4 for the binary mask respectively τTV=0, terminated at 300 iterations. (H-K) Deviations of the reconstructed images from subfigures D-G to the ground truth C. Profiles of the central row are displayed below the slices of the simulations expressing the ideal (blue curves) and the noisy data (red curves). Magnetic Resonance Imaging 2017 37, 147-158DOI: (10.1016/j.mri.2016.11.013) Copyright © 2016 Elsevier Inc. Terms and Conditions

Fig. 5 Iterative reconstructions (greyscale) and deviation maps (colorscale) of the simulated noisy phantom investigating the number of iterations applied in the algorithm with τBM=4 and τTV=0. (A,B) Number of iterations #iter=100, (C,D) #iter=200, (E,F)#iter=300, (G,H) #iter=400, (I,J) #iter=500, (K,L)#iter=600. The deviations were determined to the ground truth (cf. Fig. 4C). The values for the mean deviation are indicated below the deviation maps. Furthermore, the centric profiles of the deviation maps are displayed in the diagram. Magnetic Resonance Imaging 2017 37, 147-158DOI: (10.1016/j.mri.2016.11.013) Copyright © 2016 Elsevier Inc. Terms and Conditions

Fig. 6 Iterative reconstructions (greyscale) and deviation maps (colorscale) of the simulated noisy phantom investigating the weighting factor for the constraint of the binary mask and τTV=0. (A,B) Weighting factor τBM=0.5, (C,D) τBM=1, (E,F)τBM=2, (G,H) τBM=4, (I,J) τBM=7, (K,L) τBM=15. While reconstructions with weighting factors of τ≤1 mainly exhibit deviations at the edges of the binary mask, reconstructions with τ>1 lead to deviations inside the mask. Magnetic Resonance Imaging 2017 37, 147-158DOI: (10.1016/j.mri.2016.11.013) Copyright © 2016 Elsevier Inc. Terms and Conditions

Fig. 7 Iterative reconstructions (greyscale) and deviation maps (colorscale) of the simulated noisy phantom investigating the weighting factor for the total variation constraint and τBM=0. (A,B) Weighting factor τTV=1·10−5, (C,D) τTV=1·10−4, (E,F)τTV=3·10−4, (G,H) τTV=5·10−4, (I,J) τTV=1·10−3, (K,L) τTV=5·10−3. Reconstructed images where a higher weighting factor was applied lead to higher deviations to the ground truth due to intensity adaption of neighboring voxels. Magnetic Resonance Imaging 2017 37, 147-158DOI: (10.1016/j.mri.2016.11.013) Copyright © 2016 Elsevier Inc. Terms and Conditions

Fig. 8 Deviations of the iteratively reconstructed analytical phantom to the ground truth. (A) Various numbers of iterations (cf. Fig. 5) for different weighting factors τBM, whereas τTV=0. (B) Different weighting factors for the binary mask τBM (cf. Fig. 6) applying 300 iterations and τTV=0. (C) Different weighting factors for the total variation regularization τTV (cf. Fig. 7) applying 300 iterations and τBM=0. Magnetic Resonance Imaging 2017 37, 147-158DOI: (10.1016/j.mri.2016.11.013) Copyright © 2016 Elsevier Inc. Terms and Conditions

Fig. 9 Transversal slice of phosphocreatine (PCr) contrasts in the human calf muscle in vivo with a nominal isotropic resolution of 10mm. The applied gradient schemes are shown in Fig. 1 and are processed by a gridding reconstruction. Contrasts of the same sequence are consolidated by boxes. The highest SNR was obtained with gradient scheme G2. Magnetic Resonance Imaging 2017 37, 147-158DOI: (10.1016/j.mri.2016.11.013) Copyright © 2016 Elsevier Inc. Terms and Conditions

Fig. 10 Superposition of the accumulated 31P-PCr (colorscale) and 1H (greyscale) acquisitions. The highest SNR is obtained with scheme G2. The images resulting from the gridding reconstruction imply that PCr is mainly detectable in muscle tissue excluding fat and bones. Taking this distribution into account, the acquisitions were reconstructed iteratively with an 1H MRI constraint yielding to enhanced signal values, suppressed background and sharper edges. Optimized parameters τBM=1 and τTV=0 were utilized for the iteratively reconstructed images applying 300 iterations. Iterative reconstructed images for two further volunteers are provided as additional material. Magnetic Resonance Imaging 2017 37, 147-158DOI: (10.1016/j.mri.2016.11.013) Copyright © 2016 Elsevier Inc. Terms and Conditions