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Fast quantitative 31P MRI using prior information from 1H MRI

Kristian Rink¹, Nicolas G.R. Behl¹, Christine Gnahm¹, Peter Bachert¹, and Armin M. Nagel^1,2

¹German Cancer Research Center (DKFZ), Heidelberg, Germany, ²University Hospital Erlangen, Erlangen, Germany

Synopsis

Phosphorus-containing biomolecules play a crucial role in the energy metabolism of the human body. Compared to hydrogen, the in vivo phosphorus MR signal is four orders of magnitude lower. In this study, a conventional gridding reconstruction applied on the phosphocreatine signal of the human calf was compared to a constraint iterative approach, which uses prior knowledge from hydrogen MRI data. For both reconstructions, different acquisition times were tested and phosphocreatine concentrations in the gastrocnemius and soleus muscles were estimated.

Purpose

Phosphorus (³¹P)-containing biomolecules play a crucial role in the energy metabolism of the human body. Compared to hydrogen (¹H), the in vivo ³¹P MR signal is four orders of magnitude lower ¹. In this study, a conventional gridding reconstruction applied on the phosphocreatine (PCr) signal of the human calf was compared to a constraint iterative approach, which uses prior knowledge from ¹H MRI data ². For both reconstructions, different acquisition times were tested and PCr concentrations in the gastrocnemius and soleus muscles were estimated.

Methods

Calf muscles of three healthy volunteers (2 male, 1 female, 24-29 y/o, BMI 19-25) were examined on a 7T whole body MR system (Magnetom 7T, Siemens Healthcare) using a double-resonant (³¹P/¹H) quadrature birdcage coil (Rapid Biomed) with an inner diameter of 26cm. A 3D radially-sampled and density-adapted ³ ³¹P balanced steady-state free-precession (bSSFP) sequence ⁴ (Fig. 1) was employed with the following parameters: TR=7.21ms, TE₁=2.34ms, TE₂=4.87ms, nominal α=30°, T_RO=1ms, 1000 projections, A₀=3.7mT/m, t₀=0.5ms, 1cm isotropic resolution and 2, 4 ,8, 16, 32, 64 averages leading to acquisition times of TA=14s, 29s, 58s, 2min, 4min, 8min. Due to the distinct chemical shift of ³¹P-containing molecules, frequency selective excitation was performed by a Gaussian RF pulse with a bandwidth of 3.5ppm (420Hz) full width at half maximum (FWHM) to differentiate PCr ⁵. Six reference tubes with a diameter of 2.8cm and 11.4cm length were filled with PCr concentrations of 10, 20, 30, 40, 50, 60mM in distilled water and placed next to the calf muscle in order to enable quantification of the ³¹P signal. The in vivo concentrations of gastrocnemius and soleus muscles were determined in both, gridding and iteratively reconstructed images, from a linear fit to the data.
The signal-to-noise ratio (SNR) was enhanced by accumulating the magnitudes of the acquisitions from each contrast (Fig. 2A-C). Additionally, the accumulated images were oversampled 8 times and a Hamming filter was used to reduce Gibbs ringing and to further increase the SNR for the gridding reconstructed images (Fig. 2D). To represent the anatomy of the calf, ¹H FLASH images (TR=8.1ms, TE=4.9ms, nominal α=10°, TA=6min, BW=500Hz/px, 1mm isotropic resolution) were acquired.
Furthermore, the ³¹P images were iteratively reconstructed (Fig. 2G) using prior knowledge in form of a binary mask (Fig. 2F) from ¹H data (Fig. 2E) ⁶. The binary mask M only comprises muscle tissue in which PCr is expected. Hence, non-zero pixel intensities of the ³¹P data outside the object, originating from noise or artifacts, are suppressed. Therefore, the reconstructed image is obtained by minimizing the objective function $$f(\pmb{x})=\frac{1}{2}\parallel\pmb{A}\cdot\pmb{x}-\pmb{y}\parallel_{2}^{2}+\tau\parallel\pmb{M}\cdot\pmb{x}\parallel_{2}^{2} ,$$ where A denotes the system matrix, describing the imaging process that maps the image vector x on the corresponding raw data vector y. The regularization is weighted with a constant factor τ to enable manual adjustment. While the first term ensures data consistency by including a squared L₂-norm, the second part of the objective function describes prior knowledge of the image in terms of the regularization. The iterative reconstruction was performed with 300 iterations and a weighting factor of τ=1 ⁷.

Results

Fig. 3 illustrates ³¹P images obtained with the gridding and iterative reconstructions. Images obtained by the gridding reconstruction require a minimum acquisition time of 2min to yield appropriate quality, whereas images reconstructed iteratively with the ¹H MRI constraint are applicable with an acquisition time of 29s.
Fig. 4 shows the signal-to-noise ratio (SNR) over the PCr concentration for different acquisition times. The mean concentrations obtained for the calf muscles are 20% lower for the iterative reconstruction and 35% for the gridding reconstruction compared to published data (homogeneous C_PCr=33±8mM ¹).
Fig. 5 illustrates the superposition of anatomical ¹H images with physiological ³¹P acquisitions. While for gridding reconstructed images tissue boundaries are blurred, the iterative reconstruction emphasizes sharp tissue boundaries. Furthermore, partial volume effects as well as Gibbs ringing artifacts are reduced with the constraint iterative approach.

Discussion

The PCr concentration estimated in the soleus compared to the gastrocnemius might be lower, since images were not corrected for B₁-inhomogeneity. This also might result in a bias of the measured absolute concentrations. Furthermore, the voxel size is rather large causing partial volume effects, which could be reduced at tissue transitions by the iterative reconstruction.

Conclusion

In this work, ³¹P/¹H images of the human calf were examined with signal-efficient acquisition techniques and innovative reconstruction algorithms. The use of an iterative reconstruction implementing prior knowledge from ¹H imaging allows for a reduction of the acquisition time by a factor of 4, while still yielding appropriate image quality, and thus enabling dynamic studies.

Acknowledgements

This work was funded by the Helmholtz Alliance ICEMED - Imaging and Curing Environmental Metabolic Diseases, through the Initiative and Networking Fund of the Helmholtz Association.

References

¹ Parasoglou P, Xia D, Chang G, Regatte RR. 3D-mapping of phosphocreatine concentration in the human calf muscle at 7T: Comparison to 3T: Imaging of Phosphocreatine in the Human Calf Muscle at 3T and 7T. Magn. Reson. Med. 2013;70:1619-1625. doi: 10.1002/mrm.24616.
² Ajraoui S, Parra-Robles J, Wild JM. Incorporation of prior knowledge in compressed sensing for faster acquisition of hyperpolarized gas images. Magn. Reson. Med. 2013;69:360-369. doi: 10.1002/mrm.24252.
³ Nagel AM, Laun FB, Weber M-A, Matthies C, Semmler W, Schad LR. Sodium MRI using a density-adapted 3D radial acquisition technique. Magn. Reson. Med. 2009;62:1565-1573. doi: 10.1002/mrm.22157.
⁴ Johnson KM, Fain SB, Schiebler ML, Nagle S. Optimized 3D ultrashort echo time pulmonary MRI. Magn. Reson. Med. 2013;70:1241-1250. doi: 10.1002/mrm.24570.
⁵ Rink K, Berger MC, Korzowski A, Breithaupt M, Biller A, Bachert P, Nagel AM. Nuclear-Overhauser-enhanced MR imaging of 31P-containing metabolites: multipoint-Dixon vs. frequency-selective excitation. Magn. Reson. Imaging 2015;33:1281-1289. doi: 10.1016/j.mri.2015.07.017.
⁶ Gnahm C, Bock M, Bachert P, Semmler W, Behl NGR, Nagel AM. Iterative 3D projection reconstruction of 23Na data with an 1H MRI constraint. Magn. Reson. Med. 2014;71:1720-1732. doi: 10.1002/mrm.24827.⁷ Rink K, Berger MC, Benkhedah N, Gnahm C, Bachert P, Nagel AM. 31P MR imaging applying a radial bSSFP data acquisition and 1H constraint iterative reconstruction. In Proc: ISMRM 2016, 3938.

Figures

Fig. 1: Diagram of the 3D radially-sampled and density-adapted bSSFP sequence composed of a spectrally selective ³¹P excitation pulse and two point-reflected gradients in order to acquire several contrasts. By adding up the contrasts the SNR per acquisition time could be increased.

Fig. 2: Conceptual workflow to obtain iteratively reconstructed ³¹P images:
(A) First contrast of the ³¹P acquisition (gridding reconstruction).
(B) Second contrast of the ³¹P acquisition (gridding reconstruction).
(C) Accumulated ³¹P image (gridding reconstruction) with a native resolution of 1cm³ (matrix size 32×32×32px³).
(D) Gridding-reconstructed and 8 times oversampled ³¹P image (matrix size 256×256×32px³) applying a Hamming filter.
(E) ¹H FLASH acquisition utilized as anatomical reference and registered on the oversampled ³¹P image.
(F) Binary mask employed as prior knowledge by serving as a ¹H MRI constraint.
(G) Iteratively reconstructed ³¹P image with ¹H MRI constraint.

Fig. 3: Transversal slice of the PCr images from the human calf muscle obtained with different reconstruction techniques. The averages and therefore the acquisition time was doubled after each measurement. Six reference phantoms with concentrations of 10, 20, 30 ,40, 50 and 60mM were placed next to the calf.

Fig. 4: Determination of the in vivo PCr concentrations in gastrocnemius (GM) and soleus (SM) muscles for different acquisition times, respectively number of averages. Therefore, linear fits based on the signals inside the reference phantoms were performed. The mean concentrations provided by the gridding reconstruction were C_grid,GM=23mM and C_grid,SM=20mM, and for the iterative reconstruction C_iter,GM=28mM and C_iter,SM=25mM.

Fig. 5: Superposition of the anatomical ¹H image (grayscale) and the physiological ³¹P image (colorscale). The gridding reconstructed image shown in this figure was obtained in an acquisition time of 2min (av=16) and the iteratively reconstructed image in 29s (av=4). The black marked areas indicate regions of interest (ROIs) used for the signal evaluations in the reference phantoms as well as the gastrocnemius and soleus muscles. The partial volume effect especially restricts the quantification of the gridding reconstructed image, which becomes obvious by comparing the ROIs positioned inside the reference phantoms.

Proc. Intl. Soc. Mag. Reson. Med. 25 (2017)

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