Examining mcDESPOT

Mar 12, 2013Jason Su

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

mcDESPOT.

Results

Summary• Good

– 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

• 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

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

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

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

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.