## Abstract

A linear algebra based derivation is presented to demonstrate that linearly time scaling an entire gradient wave-form by a factor "R" exponentially increases its sensitivity to time derivatives of position by R^{(i + 1)}, where i refers to the i-th derivative of position (e.g., i = 1 is velocity). Thus, time scaling will preserve zero valued refocussing moments associated with artifact reduction techniques designed for motion occurring between excitation and detection. Typically, gradient waveforms for artifact reduction techniques are derived for use only at specific echo times. The time scaling described here allows for simple modification of refocussing gradient waveforms for use at variable echo times. Motion sensitivity associated with non-zero moment gradient waveforms can be easily predicted and modified using this technique, with consideration for field of view, resolution, and bandwidth. A clinical example is presented showing the predicted changes in sensitivity to nonrefocussed derivatives of position as the imaging gradients are time scaled. Further, trade-offs and alternatives in sensitivity to motion, slice thickness, image bandwidth, field of view and resolution will be discussed in conjunction with time scaling. This technique will have applicability in many situations involving MRI of moving tissue and a clinical example in cardiac imaging is presented.

Original language | English (US) |
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Pages (from-to) | 141-151 |

Number of pages | 11 |

Journal | Magnetic Resonance Imaging |

Volume | 8 |

Issue number | 2 |

DOIs | |

State | Published - 1990 |

Externally published | Yes |

## Keywords

- Gradient moments
- Magnetic resonance imaging
- Motion
- Time scaling

## ASJC Scopus subject areas

- Biophysics
- Biomedical Engineering
- Radiology Nuclear Medicine and imaging