Fig. 1.

3D ECCENTRIC sampling and acquisition. (A) Circle center positions are parameterized in polar coordinates $\left(r_c,{\varphi }_c\right)$ that are chosen randomly in the ranges $r_c\in \left[0,\text{max}\left(k_{x,y}^{max}-r,r\right)\right]$ and ${\varphi }_c\in \left[0,2\pi \right]$. Two consecutive circles ($c$ and $c+1$ ) must respect the overlap rule described in (B): the distance between their respective centers, $\Delta$, must be greater or equal to the Nyquist distance, ${\Delta }_{Ny}$ . (C), to satisfy a systematic full sampling of the $k$-space center, a small subset ($<5\%$ ) of circles is positioned in rosette pattern in each ECCENTRIC encoding planes. (D), 3D $k$-space sampling is achieved by a stack of ECCENTRIC encoding planes with variable $k_{x,y}^{max}$ to realize an ellipsoid coverage. (E) Diagram of the 3D ECCENTRIC FID-MRSI sequence. First, a 4-pulse WET water suppression technique is used, followed by the Shinnar–Le Roux optimized excitation pulse. After the excitation, the Cartesian encoding is performed along the z-axis, simultaneously to the gradient ramp along the x- and y-axes to reach the desired $k$-space off-center position and velocity. Finally, a sinusoidal gradient wave-form is applied along the x- and y-axis during acquisition to produce the circular trajectory.