Phosphorus (³¹P)-containing biomolecules play a crucial role in the energy metabolism of all cells. In comparison to hydrogen (¹H), the in vivo MR signal of ³¹P is four orders of magnitude lower. Therefore, this study focuses on the development of a signal-effective ³¹P acquisition [1] combined with a constraint iterative reconstruction employing prior knowledge from recorded ¹H data [2].

Two healthy volunteers were examined on a 7 T whole body MR system (Magnetom 7 T, Siemens Healthcare, Germany) using a double-resonant (³¹P/¹H) quadrature birdcage coil (Rapid Biomed GmbH, Germany). Due to the distinct chemical shift of ³¹P-containing molecules, frequency selective excitation was performed by a Gaussian RF-pulse with a full width at half maximum (FWHM) of 3.5 ppm (420 Hz) to differentiate phosphocreatine (PCr) [3]. A 3D radially-sampled and density-adapted [4] balanced steady-state free-precession (bSSFP) sequence (cf. Fig. 1) was applied [5] with the following measurement parameters: TR=7.21 ms, TE₁=2.34 ms, TE₂=4.87 ms, nominal α=30°, TA=30 min, BW=1000 Hz/px, 1000 projections, A₀=3.7 mT/m, t₀=0.5 ms, 1.5 cm isotropic resolution, 84 averages. In order to enhance the signal-to-noise ratio (SNR), the absolute values of the acquisitions from each contrast (Fig. 2A) were summed up (Fig. 2B). A Hamming filter was used to reduce Gibbs ringing and to further increase the SNR for gridding-reconstructed images (Fig. 2C). To represent the anatomy of the head, ¹H Fast Low Angle Shot (FLASH) images (TR=8.1 ms, TE=4.9 ms, nominal α=10°, TA=6 min, BW=500 Hz/px, 1 mm isotropic resolution) were acquired. Furthermore, ³¹P images were iteratively reconstructed using prior knowledge from ¹H data (cf. Fig. 2). Therefore, the reconstructed image (Fig. 2F) is attained by minimizing the objective function $$ f(x) = \frac{1}{2} \parallel \!A x - y\parallel _{2}^{2} + \sum_{i} \tau_{i} R_{i} $$ 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 terms R_i are weighted with constant factors τ_i to enable a manually adjustable influence of the regularization. While the first term ensures data consistency by including a squared L₂-norm, the second part of the objective function describes the prior knowledge of the image in terms of the sum of regularizations. Information from registered ¹H images (Fig. 2D) was used to spatially confine the support region. This was done using a binary mask (Fig. 2E) comprising only brain tissue where PCr is expected. Hence, non-zero pixel intensities of the ³¹P data outside the object, which originate from noise or artifacts, were suppressed. This regularization is expressed by $$ R_{BM}(x) = \parallel \!BM \cdot x\,\parallel _{2}^{2} $$ where BM is a diagonal matrix of ones and zeros obtained from the binary mask [6]. The iterative reconstruction was performed with 300 iterations and a weighting factor of τ=4. Reconstructed images employing those parameters led to the lowest deviation to a ground truth image in analytical phantom studies.

Fig. 3 illustrates the superposition of anatomical ¹H images with physiological ³¹P acquisitions. While for gridding-reconstructed images combined with a Hamming filter tissue boundaries are blurred, the iterative reconstruction yields sharp tissue boundaries. Furthermore, partial volume effects as well as Gibbs ringing artifacts are reduced owing to the constraint iterative reconstruction. Consequently, those images represent the real PCr distribution better than conventionally reconstructed images. In order to achieve signal-effective ³¹P acquisitions, the contrasts of the point-reflected bSSFP sequence were summed up. Due to PCr relaxation times in the order of seconds, the contrasts of readouts RO₁ and RO₂ differ by less than 10% in terms of SNR. Another aspect of this study is that undersampling induces a noise-like behavior in the image domain. Hence, the iterative reconstruction is favored for a radial sampling scheme, which was applied in the measurements.In this work, ³¹P/¹H images of the human brain were examined applying a 3D radially-sampled and density-adapted bSSFP sequence in combination with different reconstruction algorithms. The iterative reconstruction is appropriate for mapping regions where sharp tissue boundaries occur and reduces partial volume effects as well as Gibbs ringing.