Correlation-weighted ²³Na magnetic resonance fingerprinting in the brain

We developed a new sodium magnetic resonance fingerprinting (²³Na MRF) method for the simultaneous mapping of $T_1,T_{2,\text{long}}^{*},T_{2,\text{short}}^{*}$ and sodium density with built-in $\Delta B_1^{+}$ (radiofrequency transmission inhomogeneities) and $\Delta f_0$ corrections (frequency offsets). We based our ²³Na MRF implementation on a 3D FLORET sequence with 23 radiofrequency pulses. To capture the complex spin $\frac{3}{2}$ dynamics of the ²³Na nucleus, the fingerprint dictionary was simulated using the irreducible spherical tensor operators formalism. The dictionary contained 831,512 entries covering a wide range of $T_1,T_{2,\text{long}}^{*},T_{2,\text{short}}^{*},\Delta B_1^{+}$ factor and $\Delta f_0$ parameters. Fingerprint matching was performed using the Pearson correlation and the resulting relaxation maps were weighted with a subset of the highest correlation coefficients corresponding to signal matches for each voxel. Our ²³Na MRF method was compared against reference methods in a 7-compartment phantom, and applied in brain in five healthy volunteers at 7 T. In phantoms, ²³Na MRF produced values comparable to those obtained with reference methods. Average sodium relaxation time values in cerebrospinal fluid, gray matter and white matter across five healthy volunteers were in good agreement with values previously reported in the literature.