### Abstract

q-space diffusion analysis is a method to obtain the probability density function of the translational displacement of diffusing water molecules. Several quantities can be extracted from the function that indicate a characteristic of the water diffusion in tissue, e.g., the mean displacement of the diffusion, probability for zero displacement, and kurtosis of the function. These quantities are expected to give information about the microstructure of tissues in addition to that obtained from the apparent diffusion coefficient (ADC); however, this method requires high q (i.e., high b) values, which are undesirable in practical applications of the method using clinical magnetic resonance (MR) imaging equipment. We propose a method to obtain certain quantities that indicate a characteristic of the diffusion and that uses low q-value measurements. The quantities we can obtain are the moments of translational displacement, R; the n-th order moment is defined as the average of R^{n} (n: integer). Kurtosis can also be calculated from the second and fourth moments. We tried to map the moments and kurtosis using clinical MR imaging equipment. We also estimated the inherent errors of the moments obtained. Our method requires precision in measuring spin echo signals and setting q values rather than using high q-value measurements. Although our results show that further error reductions are desired, our method is workable using ordinary clinical MR imaging equipment.

Original language | English |
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Pages (from-to) | 179-189 |

Number of pages | 11 |

Journal | Magnetic Resonance in Medical Sciences |

Volume | 5 |

Issue number | 4 |

DOIs | |

Publication status | Published - 01-12-2006 |

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### All Science Journal Classification (ASJC) codes

- Radiology Nuclear Medicine and imaging

### Cite this

*Magnetic Resonance in Medical Sciences*,

*5*(4), 179-189. https://doi.org/10.2463/mrms.5.179