Phosphorus MR Spectroscopy provides quantitative information about energy metabolism^{[1, 2]}. At ultra-high magnetic fields (UHF), ³¹P-MR imaging of specific metabolites like phosphocreatine (PCr) is a possible alternative to lengthy MRSI approaches. In this study, we adapted an existing pipeline used for ¹H MRI^[3] to X-nuclei. At UHF we need to account for B₀ inhomogeneity, coil excitation field (B₁⁺) and sensitivity (B₁^-) and finally the intrinsic properties of studied nucleus (longitudinal T₁ and transversal T₂* relaxation rates). This work describes a novel method accounting for previously mentioned properties and leading to accurate absolute Phosphorus concentration calibration, manageable within acceptable time for Human investigations.

Our complete quantification pipeline is depicted in Figure 1.

Measurements were performed on a 7T Magnetom MR scanner (Siemens Healthcare, Erlangen, Germany) with a double-tuned (¹H/³¹P) mono-channel transmission coil, 8-channels phased array head coil (Resonance Research Inc. Billerica, USA)^[4].

Prior to all acquisitions B₀ shimming was performed using the proton channel.

The field for the ³¹P coil was computed using the XFL sequence^[5]. Multiple runs of Twisted Projection Imaging^[6] (TPI) sequences were acquired with 5 different TE ranging from 4.5 to 40ms. Estimation of a B₀ map is done with phase difference of the two first images with TE=4.5 and 10ms^[7]. T₂* was computed by fitting a mono-exponential decay based on all magnitude images.

Unless otherwise stated, TPI parameters were TR/TE = 100/0.5ms, FA=10°, isotropic FOV of 320mm and a 5mm isotropic resolution, linear portion p=0.75 and 7780 projections. TPI Images have been reconstructed by minimizing a wavelet-based least square criterion using FISTA algorithm^[8,9].T₁ was determined using the Variable Flip Angle Method^[10] with 2 TPI acquisitions of FA of 5° and 20°. Combining VFA acquisitions and previously determined parameters, we computed T₁ and M₀ by linear regression and obtained the spin density. The coil sensitivity profile has been derived from previously acquired TPI image with the lower FA (5°) by applying the low pass filter method^[11] to model its slow spatial variation. Our goal is to measure the concentration of a sphere filled with Phosphate Buffered Saline (PBS) solution at 40mmol/L. Tubes containing either pure water or diluted Phosphorus at known concentration surrounded the sphere. Their spatial arrangement is illustrated in Figure 2.

Intermediate and final results for our ³¹P Phosphorus quantification protocol are reported in Figure 3.

Panels (a) and (b) show a transversal slice of the 3D TPI images with flip angles of 5° and 20°, respectively. Panel (c) shows the map acquired with the XFL sequence and then interpolated. We can clearly notice that the targeted FA is not homogeneously reached everywhere which creates some inaccuracies. Panel (d) presents the B₁^- map computed from low order polynomial interpolation inside the spherical compartment of image (a) and assuming constant sensitivity elsewhere. Panel (e) illustrates the T₁ map with estimated mean value of 5.5s. T₂* was estimated at about 10ms in average. Panel (f) represents the magnetization map and panel (g) depicts the corrected spin density of our phantom.

Absolute concentration was obtained by means of a calibration step performed by measuring the spin density in each compartment (panel (g) presents the used ROI). Such setup allows estimating a 36.6mmol/L concentration in the sphere to be compared with a theoretical concentration of 40mmol/L. Figure (h) illustrates the estimated concentration distribution in our phantom based on calibration equation of Figure 4.

In this study we demonstrate the ability to perform accurate concentrations measurements of in vitro ³¹P by taking all properties of UHF acquisition in account.

Concentrations used in this study are in agreement with in vivo concentration of nuclei such as Sodium for instance. We achieved a satisfying isotropic resolution of 5mm with a total acquisition protocol lasting about 1.5 hour. More information about the reconstruction pipeline for TPI images is given in other submitted work^[9]. Moreover, using Multiple Echo Sequence might allow acquiring all echoes at the same time providing a 2-fold acceleration. In this study, perfect spoiling was assumed leading to a slightly overestimated T₁ value^[12]. Comparison with reference methods for both T₁^[13] and T₂*^[14] estimation will be performed. The computed B₀ map has not yet been taken into account as the result is not satisfying enough due to high TE values. Nevertheless, the initial B₀ shimming step ensures relatively good homogeneity. In the future, we plan to apply this pipeline for in vivo quantification of Phosphorylated metabolites and Sodium in the human brain.