Numerical T1 computation from NMR intensity ratios

Max S. Lin, James W. Fletcher, Francis K. Herbig, Robert M. Donati

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

Two-point measurement of tissue T1 from NMR intensity ratios consists of forming an a priori ratio function describing a T1 dependence of the ratio R(T1) and computing T1 from an observed ratio Q by numerically solving R(T1) - Q = 0 or an equivalent equation. Impact of R(T1) 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(T1) entries in uniform T1 steps (ΔT1). In two iterative methods, a step containing the T1 root is looked up, and the precise T1 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 ΔT1 = q for a mere "look-up" with no iterative search. All three methods require a monotonous R(T1) for uniformly effective computation over wide T1 ranges. Speeds of either iterative method for computing T1 images are expected to vary with ΔT1 and q with unsharp speed maxima at ΔT1 near 20, 6, and 2 ms for q = 10-1, 10-2, and 10-3ms, 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 T1 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 languageEnglish (US)
Pages (from-to)311-319
Number of pages9
JournalMagnetic Resonance Imaging
Volume4
Issue number4
DOIs
StatePublished - 1986

    Fingerprint

Keywords

  • Magnetic resonance imaging
  • Numerical method
  • T computation

ASJC Scopus subject areas

  • Biophysics
  • Biomedical Engineering
  • Radiology Nuclear Medicine and imaging

Cite this