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Typo for TC values in compute_T1_lookup_table() + definitions of TA/TB/TC based on Partial Fourier

Hello :)

First, nice and simple yet efficient repository! This repository is exactly what I was looking for: an user-friendly and simplistic pythonic implementation of the MP2RAGE T1 mapping technique. If someone would think small personal GitHub repositories like this one might be useless, now you have the proof that, even 4 years later, people are still using your work. :)

Regarding the issue, I believe that there is a typo at line ~235 of core.py in the function compute_T1_lookup_table() where TC is defined. It should be TC = TR_MP2RAGE - (TI_2 + (NR_RF * TR_GRE / 2)) but TC = TR_MP2RAGE - (TI_1 + (NR_RF * TR_GRE / 2)) is written.

Moreover, this might not be an issue per se depending if Partial Fourier was applied or not, but the variable NR_RF might have a different value than the one used in this script. Since the SlicePartialFourier parameter for MP2RAGE impacts the 'inner loop' (i.e., on the small flip angles and short TRs in each RAGE block, and not the 'outer loop' (i.e., long TRs)), this results in a different time when the center of k-space is reached than (n_gre * TR_gre)/2. Since you want to reach the center of k-space as early as possible, the PF factor is applied at the beginning of the RAGE block resulting in reaching the k-spoace center at t < (n_gre * TR_gre)/2. E.g., if PF=6/8 and NR_RF=200 --> NR_RFeff = 150 where the number of RF pulses before and after the k-space center go like this: NR_RF_bef = 50 and NR_RF_af = 100.

I am writing this in case it wasn't taken into account, but you have probably considered this in your own implementation and the latter comment can be ignored. :)

Thanks again for your work, greatly appreciated! :)

Marc

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