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Linear least‐squares method for unbiased estimation of T 1 from SPGR signals
Author(s) -
Chang LinChing,
Koay Cheng Guan,
Basser Peter J.,
Pierpaoli Carlo
Publication year - 2008
Publication title -
magnetic resonance in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.696
H-Index - 225
eISSN - 1522-2594
pISSN - 0740-3194
DOI - 10.1002/mrm.21669
Subject(s) - weighting , nonlinear system , flip angle , algorithm , monte carlo method , noise (video) , mathematics , linear model , linear regression , least squares function approximation , accuracy and precision , statistics , function (biology) , computer science , physics , artificial intelligence , magnetic resonance imaging , image (mathematics) , medicine , quantum mechanics , acoustics , radiology , evolutionary biology , biology , estimator
The longitudinal relaxation time, T 1 , can be estimated from two or more spoiled gradient recalled echo images (SPGR) acquired with different flip angles and/or repetition times (TRs). The function relating signal intensity to flip angle and TR is nonlinear; however, a linear form proposed 30 years ago is currently widely used. Here we show that this linear method provides T 1 estimates that have similar precision but lower accuracy than those obtained with a nonlinear method. We also show that T 1 estimated by the linear method is biased due to improper accounting for noise in the fitting. This bias can be significant for clinical SPGR images; for example, T 1 estimated in brain tissue (800 ms < T 1 < 1600 ms) can be overestimated by 10% to 20%. We propose a weighting scheme that correctly accounts for the noise contribution in the fitting procedure. Monte Carlo simulations of SPGR experiments are used to evaluate the accuracy of the estimated T 1 from the widely‐used linear, the proposed weighted‐uncertainty linear, and the nonlinear methods. We show that the linear method with weighted uncertainties reduces the bias of the linear method, providing T 1 estimates comparable in precision and accuracy to those of the nonlinear method while reducing computation time significantly. Magn Reson Med 60:496–501, 2008. © 2008 Wiley‐Liss, Inc.