Examining mcDESPOT Mar 12, 2013 Jason Su

MRM 2012: Lankford and Does. On the Inherent Precision of mcDESPOT.

Results

Summary Good Bad Take-home message A well done analysis of the unconstrained situation Bad Very different constraint scenario from the one used in practice with Stochastic Region Contraction (SRC) Some doubts about step size and forward finite difference Take-home message Exchange rate and MWF could not both be estimated well Additional phase cycles may provide benefit

SRC vs. Unbiased Estimator Same tissue as in upper left of Lankford figure SRC produces a biased estimate but the coefficient of variation is well under Lankford’s 10% cut-off

pcMCDESPOT.c We have access to an old version of Sean’s source code Results produced with both the binary provided to us (though this itself is old) match those produced from this source, so it has likely the same core fitting However, there are some bugs in the code: DESPOT2-FM implements an incorrect signal equation, the off-resonance estimate from this is used in mcDESPOT fits The mcDESPOT SSFP signal equation models the magnetization before RF excitation, which is not measured what is in experiment

Problem: Model is Before RF Fit w/ Data Before RF Fit w/ Data After RF

Problem: “Gaussian” Sampling The code uses a Taylor approximation of the Gaussian CDF which is fairly inaccurate In addition, discrete uniform samples are drawn from a set of 999 bins Not well understood how the sampling affects SRC convergence but this is definitely not Gaussian

Problem: Cyclic Phase SRC needs to be properly adapted to handle cyclic parameters, i.e. off-resonance/phase Notably, this doesn’t lead to much change in the estimates of the other parameters.

Problem: Mean Normalization Mean normalization of SSFP data is used to reduce the fitting problem, but produces a fundamental ambiguity in the phase At cross-over points, phase0 = phase180: the most important information is the amplitude But this is thrown away with mean normalization

Mean Normalization -> Ambiguity With Mean Normalization No Mean Normalization DESPOT2-FM is demonstrated here for simplicity

Idea: 3 Phase Cycles We can still do mean normalization as long as the collected data provides a unique “signature” With 3 phase cycles, all signals will never be equal at the same time, so the combined set of data is not degenerate after normalization These results are based on a modification of Sean’s despot2.c

3-phase mcDESPOT Is 3 phase cycles the future? We can use some CRLB theory to examine how it would benefit an unbiased estimator There is a huge improvement in estimating the off-resonance There is some but little improvement elsewhere SNR is matched here for constant acquisition time Note that this is CRLB in relaxation time not rates like Lankford. I found calculating it for rates to be numerically unstable. 2NEX 1pc actually beats 2pc in some cases. In my previous slides, I thought I had SNR matched them but my code was using the labels to assign SNR and we switched from “DESPOT2” to “1pc” naming so it skipped that code block. This is quite different than Lankford, who notes that adding phases leads to a significant benefit.

Current & Future Work 3pc could be critical in scenarios with high banding Acquiring a phase90 SSFP may not be a common option on all scanners Re-implementing mcDESPOT fitting code in Python/Cython Fix implementation bugs Nearly eliminate the cost in processing addition phase cycles by taking advantage of redundancies in the signal equations A general, open source, parameter fitting framework What is the optimal way to sample the free parameter space? Flip angle, TR, phase cycle, etc.