FIG. 1:

(A) circle center positions are parameterized in polar coordinates $\left(r_c,{\varphi }_c\right)$ that are chosen randomly in the ranges $r_c\in \left[0,\mathrm{m}\mathrm{a}\mathrm{x}\left(k_{xy}^{max}-r,r\right)\right]$ and ${\varphi }_c\in \left[\mathrm{0,2}\pi \right]$. Two consecutive circles ($c$ and $c+1$) are shown and must respect the overlap rule described in (B): the distance between their respective centers, $\mathrm{\Delta }$, must be greater or equal to the Nyquist distance, ${\mathrm{\Delta }}_{Ny}$. (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 $k_{x,y}^{\mathrm{m}\mathrm{a}\mathrm{x}}$ to realize an ellipsoid coverage. (E) Diagram of the FID-ECCENTRIC 3D sequence. First, a 4-pulse WET water suppression technique is used, preceding 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 waveform is applied along the x- and y-axis during acquisition to produce the circular trajectory.