Optimization of Variable Flip Angles for T1ρ Mapping with MP-GRE Sequences

MATLAB scripts for data-driven optimization of magnetization-prepared gradient echo sequences used in T1ρ mapping.

We are sharing MATLAB scripts for data-driven optimization of variable flip angles in three types of MP-GRE sequences often used for T mapping. Optimized sequences have better accuracy, greater precision, and higher speed—advantages that can add up to T maps with significantly higher resolution

The types of sequences that can be optimized with our scripts are:

  • magnetization-prepared angle-modulated partitioned k-space spoiled GRE snapshots (MAPSS)
  • tailored variable flip angle MP-GRE with magnetization reset (MP-GRE-WR)
  • standard magnetization-prepared gradient echo (MP-GRE)
A diagram illustrating MP-GRE sequences.
The MATLAB scripts optimize three pulse sequences used for T mapping: MAPSS, shown in (a); MP-GRE-WR (b); and standard MP-GRE (c). The acquisition is Cartesian 3D, illustrated in (d). At each shot, several phase encoding positions given by view per shot (VPS) are acquired, according to the specified sampling patterns and ordering scheme. A balanced center-out ordering is used, as shown in (e).

The scripts offer three major improvements: 

  • better accuracy through adjustment of flip angles to minimize every modeled pulse sequence imperfection
  • greater precision through automatically increasing flip angles to improve the sequence’s signal-to-noise ratio while reducing undesirable effects, such as k-space filtering
  • higher speed through the use of sequence parameters to capture more data per unit of time (less idle time)
A diagram illustrating signal evolutions.
The proposed optimization searches for flip angles that give a more desirable MR signal evolution (in mk(α)). The optimization is driven by three essential terms: A(k, α) controls accuracy, F(k, α) controls filtering effects, and S(k, α) controls SNR. This example uses the MP-GRE-WR sequence with VPS = 128, TTSLs = 2, S = 1, and perfect magnetization reset. The mk(α) term is constructed with the signal evolution of the triplet [T1(k) = 3000 ms, T2(k) = 50 ms, T(k) = 58 ms].

In the related preprint cited below, we find that all three sequence types have higher singal-to-noise ratio (SNR) with the data-driven optimization than without, given equal aquisition time.

In some cases, the combined benefits of higher SNR and shorter scan time are so significant as to result in image resolution four times greater than that obtained with conventionally calculated flip angles.

A panel showing T1rho maps.
Left: T maps acquired with MAPPS. Right: T maps acquired with MP-GRE OVFA ZRT HR, an MP-GRE sequence optimized for speed and SNR. Top: maps of agarose gel (A.G.) at 3%, 4%, 5%, 6%, and 8% concentration, clockwise from bottom left. Bottom: maps of the human knee. The optimized sequence has fourfold higher resolution, almost the same SNR, and 1.6-times faster acquisition than MAPSS.

Zibetti MVW, De Moura HL, Keerthivasan MB, and Regatte RR.
Optimizing Variable Flip-Angles in Magnetization-Prepared Gradient Echo Sequences for Efficient 3D-T1rho Mapping
arXiv. Preprint posted online November 22, 2022. arXiv:2211.09214 []

Please cite this work if you are using MATLAB scripts for data-driven optimization of variable flip angles in MP-GRE sequences for T mapping.


Li X, Han ET, Busse RF, Majumdar S.
In vivo T(1rho) mapping in cartilage using 3D magnetization-prepared angle-modulated partitioned k-space spoiled gradient echo snapshots (3D MAPSS)
Magn Reson Med. 2008 Feb;59(2):298-307. doi: 10.1002/mrm.21414

Johnson CP, Thedens DR, Kruger SJ, Magnotta VA.
Three-Dimensional GRE T1ρ mapping of the brain using tailored variable flip-angle scheduling.
Magn Reson Med. 2020 Sep;84(3):1235-1249. doi: 10.1002/mrm.28198

Baboli R, Sharafi A, Chang G, Regatte RR.
Isotropic morphometry and multicomponent T1 ρ mapping of human knee articular cartilage in vivo at 3T.
J Magn Reson Imaging. 2018 Dec;48(6):1707-1716. doi: 10.1002/jmri.26173

Sharafi A, Xia D, Chang G, Regatte RR.
Biexponential T1ρ relaxation mapping of human knee cartilage in vivo at 3 T.
NMR Biomed. 2017 Oct;30(10):10.1002/nbm.3760. doi: 10.1002/nbm.3760

Zibetti MVW, Sharafi A, Keerthivasan MB, Regatte RR.
Prospective Accelerated Cartesian 3D-T1rho Mapping of Knee Joint using Data-Driven Optimized Sampling Patterns and Compressed Sensing.
Proc Intl Soc Magn Reson Med. 29 (2021). p. 3310.

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The software available on this page is provided free of charge and comes without any warranty. CAI²R and NYU Grossman School of Medicine do not take any liability for problems or damage of any kind resulting from the use of the files provided. Operation of the software is solely at the user’s own risk. The software developments provided are not medical products and must not be used for making diagnostic decisions.

The software is provided for non-commercial, academic use only. Usage or distribution of the software for commercial purpose is prohibited. All rights belong to the author (Marcelo Wust Zibetti) and NYU Grossman School of Medicine. If you use the software for academic work, please give credit to the author in publications and cite the related publications.

Please spell out your affiliation (e.g. “New York University” rather than “NYU”).


Questions about this resource may be directed to Marcelo Wust Zibetti, PhD.