A Small Surrogate for the Golden Angle in Time-Resolved Radial MRI Based on Generalized Fibonacci Sequences

In golden angle radial magnetic resonance imaging a constant azimuthal radial profile spacing of $111.246\ldots {}^{\circ }$ guarantees a nearly uniform azimuthal profile distribution in ${\rm k}$ -space for an arbitrary number of radial profiles. Even though this profile order is advantageous for various real-time imaging methods, in combination with balanced steady-state free precession (SSFP) sequences the large azimuthal angle increment may lead to strong image artifacts, due to the varying eddy currents introduced by the rapidly switching gradient scheme. Based on a generalized Fibonacci sequence, a new sequence of smaller irrational angles is introduced ( $49.750\ldots {}^{\circ }, 32.039\ldots {}^{\circ }, 27.198\ldots {}^{\circ }, 23.628\ldots{}^{\circ }, \ldots \!$ ). The subsequent profile orders guarantee the same sampling efficiency as the golden angle if at least a minimum number of radial profiles is used for reconstruction. The suggested angular increments are applied for dynamic imaging of the heart and the temporomandibular joint. It is shown that for balanced SSFP sequences, trajectories using the smaller golden angle surrogates strongly reduce the image artifacts, while the free retrospective choice of the reconstruction window width is maintained.