a) Conventional gridding reconstruction vs. b) compressed sensing (CS) reconstruction with incorporated 1H image information for different undersampling factors (USFs). Even at high USFs (i.e. shorter acquisition time) the CS reconstruction shows a reduced background signal while fine structures are preserved.
(a) Sodium quantification in three regions of interest (ROI). Average error of DLCS with optimized parameters (optDLCS) maintains high accuracy and reduces the standard deviation in comparison to a conventional reconstruction with hamming filter (hNUFFT). b) In undersampled TSC maps (USF > 1) reconstructed with hNUFFT, undersampling artifacts are visible. c) The undersampling artifacts are reduced by optDLCS.
23Na MRI of the female breast
Due to a low in vivo sodium concentration, low MR sensitivity, and significantly shorter relaxation times, the image quality of sodium MRI is affected by noise and artifacts. However, a range of techniques is available to overcome these limitations. Advanced image acquisition pulse sequences, such as 3D density-adapted radial projection , enable efficient k-space sampling; multi-array coils and ultra-high magnetic field strengths  can be used to enhance the signal-to-noise ratio (SNR); for image reconstruction, sophisticated techniques, such as compressed sensing (CS) , enable reduced acquisition times and improved image quality.
The concept of CS is inspired by the compression of ordinary images using the JPEG 2000 format: images can be saved with a fractional amount of needed memory but virtually identical image quality. The idea behind CS is to perform already the MR measurement in a compressed manner. The k-space is not fully sampled, which reduces the acquisition time. Using a conventional linear reconstruction method such as gridding the final image would be corrupted by noise and undersampling artifacts. A non-linear iterative CS reconstruction technique, however, can reduce these artifacts and restore the original image. In principle, such a CS reconstruction works like a denoising technique. However, not only artifacts and noise are suppressed, but also fine structures. To overcome this problem, weighting factors – which represent known tissue boundaries – can be incorporated into the reconstruction . Since images of different nuclei are highly correlated, these weighting factors can be obtained from a high-resolution 1H MR image. In this way, the CS reconstruction works like an intelligent filter, which reduces unwanted artifacts, but simultaneously preserves fine structures.
We are currently working on combining CS with properly adjusted sequences for breast 23Na MRI making use of 1H image information. This allows shortening acquisition times and increases image quality (Fig. 1). This project is performed in close collaboration with the Medical University of Vienna (Prof. Siegfried Trattnig).
Dictionary-Learning Compressed Sensing for quantification of tissue sodium content
Tissue sodium content (TSC) is a potential biomarker for tissue integrity, for example in muscular diseases such as dystrophies and skeletal myopathies [5-7].
In this project, a CS reconstruction approach based on dictionary representations is applied  (DLCS) to accelerate TSC quantification in 23Na MRI. The reconstruction algorithm uses anisotropic 3D-filter kernels as dictionary entries to represent TSC maps (i.e. density weighted 23Na MR images). An iterative reconstruction scheme incorporates measured data and sparsified dictionary representation. Due to the lack of ground truth data for low SNR 23Na MRI, simulation approaches are employed to find best-applicable parameters for the reconstruction of in vivo TSC maps.
Volunteer studies of the TSC of skeletal muscles are conducted at 3 Tesla and 7 Tesla. The acquisition of TSC is based on 3D-radial density-adapted acquisition . An anisotropic field-of-view (FoV) is used to harness the longitudinal physiological structure of muscle tissue . Highly undersampled 23Na MRI is reconstructed by DLCS with optimized parameter to ensure accurate sodium quantification enabling low acquisition times (see Fig. 1) .
 Nagel AM, Laun FB, Weber MA, Matthies C, Semmler W, Schad LR.
Sodium MRI using a density‐adapted 3D radial acquisition technique.
Magn Reson Med. 2009 Dec;62(6):1565-73.
 Ladd ME, Bachert P, Meyerspeer M, Moser E, Nagel AM, Norris DG, Schmitter S, Speck O, Straub S, Zaiss M.
Pros and cons of ultra-high-field MRI/MRS for human application.
Prog Nucl Mag Res Sp 2018; 109: 1-50.
 Lustig M, Donoho D, Pauly JM.
Sparse MRI: The application of compressed sensing for rapid MR imaging.
Magn Reson Med. 2007 Dec;58(6):1182-95.
 Gnahm C, Nagel AM.
Anatomically weighted second-order total variation reconstruction of 23Na MRI using prior information from 1H MRI."
Neuroimage. 2015 Jan 15;105:452-61.
 Nagel AM, Weber MA, Borthakur A, Reddy R.
Skeletal Muscle MR Imaging Beyond Protons: With a Focus on Sodium MRI in Musculoskeletal Applications.
MRI Skl Musc. 2013;(77):115-133.
 Weber MA, Nagel AM, Marschar AM, Glemser P, Jurkat-Rott K, Wolf MB, Ladd ME, Schlemmer HP, Kauczor HU, Lehmann-Horn F.
7-T (35)Cl and (23)Na MR Imaging for Detection of Mutation-dependent Alterations in Muscular Edema and Fat Fraction with Sodium and Chloride Concentrations in Muscular Periodic Paralyses.
Radiology. 2016 Oct;281(1):326.
 Gerhalter T, Gast LV, Marty B, Martin J, Trollmann R, Schüssler S, Roemer F, Laun FB, Uder M, Schröder R, Carlier PG, Nagel AM.
23Na MRI Depicts Early Changes in Ion Homeostasis in Skeletal Muscle Tissue of Patients With Duchenne Muscular Dystrophy.
J Magn Reson Imaging. 2019 Feb 4. doi: 10.1002/jmri.26681.
 Behl NG, Gnahm C, Bachert P, Ladd ME, Magel AM.
Three-dimensional dictionary-learning reconstruction of (23)Na MRI data.
Magn Reson Med. 2016 Apr;75(4):1605-16.
 Nagel AM, Weber MA, Wolf M, Semmler W.
3D Density-Adapted Projection Reconstruction 23Na-MRI with Anisotropic Resolution and Field-of-View.
In: Proc. ISMRM. ISMRM; 2012:674.
 Lachner S, Zaric O, Utzschneider M, Minarikova L, Zbyn S, Hensel B, Trattnig S, Uder M and Nagel AM.
Compressed sensing reconstruction of 7 Tesla (23)Na multi-channel breast data using (1)H MRI constraint.
Magn Reson Imaging. 2019.