### Abstract

Two-point measurement of tissue T_{1} from NMR intensity ratios consists of forming an a priori ratio function describing a T_{1} dependence of the ratio R(T_{1}) and computing T_{1} from an observed ratio Q by numerically solving R(T_{1}) - Q = 0 or an equivalent equation. Impact of R(T_{1}) designs on the numerical computation and dependence of relative speeds of three numerical methods on desired computational precisions q and on other factors are examined. All three methods begin with computing a table of R(T_{1}) entries in uniform T_{1} steps (ΔT_{1}). In two iterative methods, a step containing the T_{1} root is looked up, and the precise T_{1} location within the step is pinpointed to within a q value by either linear-interpolative (LI) or Newton-Raphson (NR) iteration. The third method simply consists of computing a large table of ΔT_{1} = q for a mere "look-up" with no iterative search. All three methods require a monotonous R(T_{1}) for uniformly effective computation over wide T_{1} ranges. Speeds of either iterative method for computing T_{1} images are expected to vary with ΔT_{1} and q with unsharp speed maxima at ΔT_{1} near 20, 6, and 2 ms for q = 10^{-1}, 10^{-2}, and 10^{-3}ms, respectively. Either iterative method is suitable for both low- and high-precision computations, the LI method being generally faster. The simple look-up is the fastest of the three for T_{1} image computation to low precisions of q {greater-than or approximate} 1 ms, is likely the slowest for that to q = 0.1 ms, and is impractical for that to q {less-than or approximate} 0.01 ms.

Original language | English (US) |
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Pages (from-to) | 311-319 |

Number of pages | 9 |

Journal | Magnetic Resonance Imaging |

Volume | 4 |

Issue number | 4 |

DOIs | |

State | Published - 1986 |

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### Keywords

- Magnetic resonance imaging
- Numerical method
- T computation

### ASJC Scopus subject areas

- Biophysics
- Biomedical Engineering
- Radiology Nuclear Medicine and imaging

### Cite this

_{1}computation from NMR intensity ratios.

*Magnetic Resonance Imaging*,

*4*(4), 311-319. https://doi.org/10.1016/0730-725X(86)91041-6