Simple analytic variable density spiral design

Variable density spirals have been proposed in a variety of applications, including MR fluoroscopy, cardiac imaging, and MR spectroscopic imaging. In this work, a simple analytic solution for designing a flexible set of variable density spiral trajectory waveforms is presented. The method enables real-time waveform prescription on scanners with limited computational power. Both slew rate-limited and amplitude-limited regimes are incorporated in the design process.