A new linear least squares method for T1 estimation from SPGR signals with multiple TRs

Lin-Ching Chang; Cheng Guan Koay; Peter J. Basser; Carlo Pierpaoli M.D.

doi:10.1117/12.811618

13 March 2009 A new linear least squares method for T1 estimation from SPGR signals with multiple TRs

Lin-Ching Chang, Cheng Guan Koay, Peter J. Basser, Carlo Pierpaoli M.D.

Proceedings Volume 7258, Medical Imaging 2009: Physics of Medical Imaging; 72584O (2009) https://doi.org/10.1117/12.811618
Event: SPIE Medical Imaging, 2009, Lake Buena Vista (Orlando Area), Florida, United States

Abstract

The longitudinal relaxation time, T₁, can be estimated from two or more spoiled gradient recalled echo x (SPGR) images with two or more flip angles and one or more repetition times (TRs). The function relating signal intensity and the parameters are nonlinear; T₁ maps can be computed from SPGR signals using nonlinear least squares regression. A widely-used linear method transforms the nonlinear model by assuming a fixed TR in SPGR images. This constraint is not desirable since multiple TRs are a clinically practical way to reduce the total acquisition time, to satisfy the required resolution, and/or to combine SPGR data acquired at different times. A new linear least squares method is proposed using the first order Taylor expansion. Monte Carlo simulations of SPGR experiments are used to evaluate the accuracy and precision of the estimated T₁ from the proposed linear and the nonlinear methods. We show that the new linear least squares method provides T₁ estimates comparable in both precision and accuracy to those from the nonlinear method, allowing multiple TRs and reducing computation time significantly.

Citation Download Citation

Lin-Ching Chang, Cheng Guan Koay, Peter J. Basser, and Carlo Pierpaoli M.D. "A new linear least squares method for T1 estimation from SPGR signals with multiple TRs", Proc. SPIE 7258, Medical Imaging 2009: Physics of Medical Imaging, 72584O (13 March 2009); https://doi.org/10.1117/12.811618

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KEYWORDS

Signal to noise ratio

Monte Carlo methods

Data acquisition

Nonlinear optics

Brain

Error analysis

Magnetic resonance imaging

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