Fast and robust design of time-optimal k-space trajectories
Mathias Davids 1 , Michaela Ruttorf 1 , Frank G. Zoellner 1 , and Lothar R. Schad 1
Computer Assisted Clinical Medicine, Medical
Faculty Mannheim, Heidelberg University, Mannheim, BW,
Especially 3D parallel selective excitation pulses
require the synthesis of fast non-uniform k-space
trajectories. Since numerical approaches are usually
very time-consuming and impaired by numerical errors, a
novel analytic framework on rapidly designing
time-optimal trajectories was developed. The trajectory
is represented by analytic gradient basis functions that
are symbolically solved to traverse given k-space
control points. The trajectory is then globally
accelerated to fully utilize given hardware constraints
Gmax and Smax, yielding time-optimal analytic gradients.
Furthermore, this optimization uses an analytically
derived Jacobian which guarantees convergence within
seconds. Any arbitrarily shaped 2D/3D trajectory can be
modeled and optimized using the method.
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