1. Examining mcDESPOT
Mar 12, 2013
Jason Su

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

3. Results

4. 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

5. 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

6. 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

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

8. 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

9. 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.

10. 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

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

12. 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

13. 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.

14. 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.