\({T_2}^{*}\) Accelerated quantification of tissue sodium concentration in skeletal muscle tissue: quantitative capability of dictionary learning compressed sensing

  • Matthias UtzschneiderEmail author
  • Nicolas G. R. Behl
  • Sebastian Lachner
  • Lena V. Gast
  • Andreas Maier
  • Michael Uder
  • Armin M. Nagel
Research Article
Part of the following topical collections:
  1. Basic Science - Reconstruction algorithms and artificial intelligence



To accelerate tissue sodium concentration (TSC) quantification of skeletal muscle using 23Na MRI and 3D dictionary-learning compressed sensing (3D-DLCS).

Materials and methods

Simulations and in vivo 23Na MRI examinations of calf muscle were performed with a nominal spatial resolution of \(\Delta x = \left( {3.0 \times 3.0 \times 15.0} \right){\text{ mm}}^{3}\). Fully sampled and three undersampled 23Na MRI data sets (undersampling factors (USF) = 3, 4.4, 6.7) were evaluated. Ten healthy subjects were examined on a 3 Tesla MRI system. Results of the simulation study and the in vivo measurements were compared to the ground truth (GT) and the fully sampled fast Fourier transform (NUFFT) reconstruction, respectively.


Reconstruction results of simulated data with optimized 3D-DLCS yielded a lower deviation (< 4%) from the GT than results of the NUFFT reconstruction (> 5%) and a lower standard deviation (SD). For in vivo measurements, a TSC of \(17 \pm 2.7 {\text{ mMol/l}}\) was observed. The mean deviation from the reference is lower for the undersampled 3D-DLCS reconstructions (3.4%) than for NUFFT reconstructions (4.6%). SD is reduced using 3D-DLCS. Compared to a fully sampled NUFFT reconstruction, acquisition time could be reduced by a factor of 4.4 while maintaining similar quantitative accuracy.


The optimized 3D-DLCS reconstruction enables accelerated TSC measurements with high quantification accuracy.


Magnet resonance imaging Muscle Skeletal Sodium Image reconstruction Compressed sensing 



We thank the Imaging Science Institute (Erlangen, Germany) for providing us with measurement time.

Author contributions

MU: responsible for study conception and design, acquisition of data, analysis and interpretation of data and drafting of manuscript. NGRB: involved in study conception and design and critical revision of the manuscript. SL: advised and contributed to/for study conception and design, analysis and interpretation of data and critical revision of the manuscript. LVG: advised and developed of methods for acquisition of data and contributed to analysis and interpretation of data, and critical revision of the manuscript. AM: contributions in analysis and interpretation of data and critical revision of the manuscript. MU: contributed to critical revision of the manuscript. AMN: responsible for study conception and design, analysis and interpretation of data, drafting of manuscript, and critical revision of the manuscript.

Compliance with ethical standards

Conflict of interest

The authors declare that they do not have any conflict of interest.

Ethical approval

All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional research committee (Ethics Committee of the Friedrich-Alexander Universität Erlangen Nürnberg, Reference number: 119_17 B).

Animal rights

This article does not contain any studies with animals performed by any of the authors.

Informed consent

Informed consent was obtained from all individual participants included in the study.

Supplementary material

10334_2019_819_MOESM1_ESM.pdf (2 mb)
Supplementary file1 (PDF 2078 kb)


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Copyright information

© European Society for Magnetic Resonance in Medicine and Biology (ESMRMB) 2020

Authors and Affiliations

  1. 1.Institute of RadiologyUniversity Hospital Erlangen, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU)ErlangenGermany
  2. 2.Pattern Recognition Lab, Department of Computer ScienceFriedrich-Alexander-Universität Erlangen-Nürnberg (FAU)ErlangenGermany
  3. 3.Division of Medical Physics in RadiologyGerman Cancer Research Center (DKFZ)HeidelbergGermany
  4. 4.Institute of Medical PhysicsFriedrich-Alexander-Universität Erlangen-Nürnberg (FAU)ErlangenGermany

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