### Abstract

Purpose Spiral-based trajectories for magnetic resonance imaging can be advantageous, but are often cumbersome to design or create. This work presents a flexible numerical algorithm for designing trajectories based on explicit definition of radial undersampling, and also gives several analytical expressions for charactering the base (critically sampled) class of these trajectories. Theory and Methods Expressions for the gradient waveform, based on slew and amplitude limits, are developed such that a desired pitch in the spiral k-space trajectory is followed. The source code for this algorithm, written in C, is publicly available. Analytical expressions approximating the spiral trajectory (ignoring the radial component) are given to characterize measurement time, gradient heating, maximum gradient amplitude, and off-resonance phase for slew-limited and gradient amplitude-limited cases. Several numerically calculated trajectories are illustrated, and base Archimedean spirals are compared with analytically obtained results. Results Several different waveforms illustrate that the desired slew and amplitude limits are reached, as are the desired undersampling patterns, using the numerical method. For base Archimedean spirals, the results of the numerical and analytical approaches are in good agreement. Conclusion A versatile numerical algorithm was developed, and was written in publicly available code. Approximate analytical formulas are given that help characterize spiral trajectories.

Original language | English (US) |
---|---|

Pages (from-to) | 278-285 |

Number of pages | 8 |

Journal | Magnetic Resonance in Medicine |

Volume | 71 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2014 |

Externally published | Yes |

### Fingerprint

### Keywords

- MRI
- spiral
- trajectory

### ASJC Scopus subject areas

- Radiology Nuclear Medicine and imaging

### Cite this

*Magnetic Resonance in Medicine*,

*71*(1), 278-285. https://doi.org/10.1002/mrm.24675

**Spiral trajectory design : A flexible numerical algorithm and base analytical equations.** / Pipe, James; Zwart, Nicholas R.

Research output: Contribution to journal › Article

*Magnetic Resonance in Medicine*, vol. 71, no. 1, pp. 278-285. https://doi.org/10.1002/mrm.24675

}

TY - JOUR

T1 - Spiral trajectory design

T2 - A flexible numerical algorithm and base analytical equations

AU - Pipe, James

AU - Zwart, Nicholas R.

PY - 2014/1/1

Y1 - 2014/1/1

N2 - Purpose Spiral-based trajectories for magnetic resonance imaging can be advantageous, but are often cumbersome to design or create. This work presents a flexible numerical algorithm for designing trajectories based on explicit definition of radial undersampling, and also gives several analytical expressions for charactering the base (critically sampled) class of these trajectories. Theory and Methods Expressions for the gradient waveform, based on slew and amplitude limits, are developed such that a desired pitch in the spiral k-space trajectory is followed. The source code for this algorithm, written in C, is publicly available. Analytical expressions approximating the spiral trajectory (ignoring the radial component) are given to characterize measurement time, gradient heating, maximum gradient amplitude, and off-resonance phase for slew-limited and gradient amplitude-limited cases. Several numerically calculated trajectories are illustrated, and base Archimedean spirals are compared with analytically obtained results. Results Several different waveforms illustrate that the desired slew and amplitude limits are reached, as are the desired undersampling patterns, using the numerical method. For base Archimedean spirals, the results of the numerical and analytical approaches are in good agreement. Conclusion A versatile numerical algorithm was developed, and was written in publicly available code. Approximate analytical formulas are given that help characterize spiral trajectories.

AB - Purpose Spiral-based trajectories for magnetic resonance imaging can be advantageous, but are often cumbersome to design or create. This work presents a flexible numerical algorithm for designing trajectories based on explicit definition of radial undersampling, and also gives several analytical expressions for charactering the base (critically sampled) class of these trajectories. Theory and Methods Expressions for the gradient waveform, based on slew and amplitude limits, are developed such that a desired pitch in the spiral k-space trajectory is followed. The source code for this algorithm, written in C, is publicly available. Analytical expressions approximating the spiral trajectory (ignoring the radial component) are given to characterize measurement time, gradient heating, maximum gradient amplitude, and off-resonance phase for slew-limited and gradient amplitude-limited cases. Several numerically calculated trajectories are illustrated, and base Archimedean spirals are compared with analytically obtained results. Results Several different waveforms illustrate that the desired slew and amplitude limits are reached, as are the desired undersampling patterns, using the numerical method. For base Archimedean spirals, the results of the numerical and analytical approaches are in good agreement. Conclusion A versatile numerical algorithm was developed, and was written in publicly available code. Approximate analytical formulas are given that help characterize spiral trajectories.

KW - MRI

KW - spiral

KW - trajectory

UR - http://www.scopus.com/inward/record.url?scp=84890791525&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84890791525&partnerID=8YFLogxK

U2 - 10.1002/mrm.24675

DO - 10.1002/mrm.24675

M3 - Article

VL - 71

SP - 278

EP - 285

JO - Magnetic Resonance in Medicine

JF - Magnetic Resonance in Medicine

SN - 0740-3194

IS - 1

ER -