Simple analytic spiral K-space algorithm

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Abstract
The exact, hardware‐constrained design of a spiral k‐space trajectory requires the solution of a differential equation, thereby making real‐time prescription difficult on scanners with limited computational power. This study describes a closed‐form approximate solution for interleaved Archimedian spiral trajectories that closely matches the exact design. Both slew rate‐limited and amplitude‐limited regimes are incorporated. Magn Reson Med 42:412–415, 1999.