Educational notebooks for learning about quantitative MRI, based on MRTwin_pulseq – a hands-on course on MRI sequence programming (see https://github.com/mzaiss/MRTwin_pulseq and https://www.youtube.com/watch?v=Gxso5ZCyZC8).
Pulseq (https://pulseq.github.io/) is an open-spource vendor-neutral sequence programming framework, defining MRI sequences based on a simple text file format that can be created via Python, Matlab, etc., and executed directly at a real MRI scanner.
MRzero-Core is a fast and accurate MRI simulator based on state-of-the-art PDG Bloch simulation (https://doi.org/10.1002/mrm.30055). It can parse and simulate sequences defined in Pulseq. Moreover, it is compatible with pytorch’s autograd, i.e., provides backward methods for automatic differentiation for numerical optimization.
- MRzero-Core (https://mrzero-core.readthedocs.io/en/latest/intro.html)
- pytorch
- matplotlib
- numpy
The following notebooks are provided, together with some suggestions for own investigations, experiments and exercises.
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demo_T1_IR.ipynb
- inversion recovery T1 mapping [1,2]: This is the “gold standard” T1 mapping method, extremely slow, but accurate and quite insensitive to many common problems like B1 inhomogeneity.
- Play around with different inversion times (TI) – how many are needed at minimum?
- Different TR, matrix size, fit models (2 parameters, magnitude data fitting versus 5 parameters complex fitting)?
- What could be problems with magnitude-only data? What if the noise level increases?
- Different initial and boundary conditions for the non-linear least squares fit?
- More advanced:
- Which inversion times should I pick for optimal T1 mapping performance (highest accuracy, least sensitivity to noise)? -> Read about optimal experimental designs, the Fisher information matrix and Cramer-Rao lower bounds, and try to implement it.
- How could we speed it up even more? Multiple k-space lines / imaging repetitions per inversion pulse? -> check the Look-Locker method [3], try to implement and fit it.
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demo_T1_VFA.ipynb
- The variable flip angle (VFA) method - a faster, widely used T1 mapping sequence based on the steady-state gradient echo signal (i.e., TR<<T1) [4-6].
- Acquire >=2 spoiled GRE images with different flip angles.
- Signal equation can be linearized to extract T1 by a simple linear least squares fit (slope & intercept).
- What happens if the flip angle is different across the brain (B1+ inhomogeneity)? How could it be corrected?
- What could be pro’s and con’s of the linearized fit compared to a non-linear least squares fit of the signal model (experiment with different noise levels)?
- Investigate the impact of gradient & RF spoiling. Different quadratic phase increments for RF spoiling?
- Which flip angles should be chosen for best T1 mapping results?
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demo_T2_SE.ipynb
- spin echo sequence with multiple echo times for T2 quantification - This is the T2 "gold standard" method and, similar to the inversion recovery in case of T1, extremely slow
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demo_DREAM_B0B1.ipynb
- a method based on stimulated echoes to map the transmit field (B1) and main field inhomogeneity (B0) [7]
- modified from https://mrzero-core.readthedocs.io/en/latest/playground_mr0/mr0_DREAM_STE_seq.html#dream-ste-seq
- Drain LE. A direct method of measuring nuclear spin-lattice relaxation times. Proc Phys Soc Sect A 1949;62(5):301–6.
- Hahn EL. An accurate nuclear magnetic resonance method for measuring spin-lattice relaxation times. Phys Rev 1949;76(1):145–6.
- Look DC, Locker DR. Time saving in measurement of NMR and EPR relaxation times. Rev Sci Instrum 1970;41(2):250–1.
- Fram EK, et al. Rapid calculation of T1 using variable flip angle gradient refocused imaging. Magn Reson Imaging 1987;5(3):201–8.
- Gupta RK. A new look at the method of variable nutation angle for the measurement of spin-lattice relaxation times using fourier transform NMR. J Magn Reson 1977;25(1):231–5.
- Deoni SCL, Rutt BK, Peters TM. Rapid combined T1 and T2 mapping using gradient recalled acquisition in the steady state. Magn Reson Med 2003;49(3):515–26.
- Nehrke K, Börnert P. DREAM—a novel approach for robust, ultrafast, multislice B1 mapping. Magnetic Resonance in Medicine. 2012;68(5):1517-1526. doi:10.1002/mrm.24158