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Single Component DESPOT Simulations. Jason Su Sep 23, 2012. Motivation. Developing and vetting simulation tools in the process of further analyzing the CRLB of mcDESPOT begun by Lankford and Does - PowerPoint PPT Presentation

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Single Component DESPOT Simulations

Single Component DESPOT SimulationsJason SuSep 23, 2012MotivationDeveloping and vetting simulation tools in the process of further analyzing the CRLB of mcDESPOT begun by Lankford and Does

Many of the concepts and indeed code that Sean wrote for his single component fitting algorithms were carried into the mcDESPOT fitting that is in current use at many sitesMethodsMethodsI implemented both formulations and verified that they are exactly equivalentThe simulations herein are performed with the matrix versionThis allowed the use of one function that can handle both single and multi-component models, so any verification done here gives me confidence in the mcDESPOT results

Data from a simulated tissue are fed into the DESPOT2(-FM) schemeT1 and M0 via DESPOT1, linearization of the SPGR data and fittingT2 via DESPOT2(-FM) fitting with known T1Linearization of phase-180 only SSFP data via DESPOT2Fitting of phase-0 and phase-180 data via SRC and DESPOT2-FM, also fits for off-resonance ()MethodsFlip anglesangles_spgr = [2 4 6 8 10 12 14]; % 16 18]; %degLankford uses the first 7/9 angles, not sure whyangles_ssfp = [6 14 22 30 38 46 54 62 70];

Simulated parameters are well within the bounds of the initial SRC range (T2 = 5-150ms, = 0-2)

T1 (ms)T2 (ms)M0900100100e30QuestionDESPOT2-FM and mcDESPOT both treat the SSFP theoretical signal before the RF pulseDoes the code implementation do this? We actually want to model the signal after the RF pulse.From the old source code available to us, it would appear that this is unfortunately the caseWill try to confirm this is the same as the executable we have from SeanI had to fix bugs in the code to get the source to compile properly, so it is definitely not the same source as the executable from Sean but the core fitting could still be the sameWhat problems does this cause in fitting data that is after RF?

Note that normal DESPOT2 considers signal after RFData Before RF: DESPOT2 Fit

Data Before RF: DESPOT2 Fit

Data After RF: DESPOT2 Fit

Data After RF: DESPOT2 Fit

DESPOT2DESPOT2Is deterministic so all the standard deviations are 0: i.e. after repeated runs on the same data, the same result is given

Off-resonance is not modeled, so ignore those plotsData Before RF: DESPOT2-FM

Data After RF: DESPOT2 Fit

DESPOT2-FMT2 is okay but off-resonance estimation is poor, sometimes very off in some trials

SRC fitting is used, which inherently gives results that change from trial to trial even though the data is identical, yielding a distribution of solutionsThis is different from the distribution due to noise in the input data that the CRLB characterizesThe distribution should hopefully be tight around the true answerT1 is still obtained from the deterministic DESPOT1 fitDESPOT2-FMThe results are again nearly identical regardless of whether the data is before or after RF. Why?There is no linearization, there should be no such immunity and we are fitting the before RF equationThe answer is an often undocumented part of the SRC fitting procedure, the phase-0 and phase-180 data are first normalized by their means along the flip angle dimensionSean has suggested this is a good way to remove the need to fit for M0, i.e. it simplifies the problem

DESPOT2-FM: The Nitty GrittyDESPOT2-FM: The Nitty GrittyDESPOT2-FM: The Nitty GrittyThe theoretical curve is also normalized to its mean, so it does take into account additional influence of T1 and T2 through the norm.This also conveniently removes the extra E2 bug.Could be that the idea for mean normalization came about originally as a patch for this unresolved bugIm sure there must be some influence on the stability or precision of the fitting by using such a complicated normalization factor as the mean, how to show this?

Actual Curves

Actual Curves

How DESPOT2-FM Sees Curves

These curves are generated with the mean values of T1, T2, and off resonance. Phase 0 looks off because the mean off-resonance is bad, thought the peak is correctly close to 0.22How DESPOT2-FM Sees Curves

QuestionOkay well this is all well and good but how do you know your source is actually what weve been using?Does the compiled source give the result as Seans executable?Compiled from Source

Provided Executable

AnswerSorry its the same core fitting as far as I can tell.

For sure the source we have isnt what was used to make the executable since there were bugs, but the guts seem to be the same.QuestionIs there a problem with the off-resonance fitting?SRC relies on being able to contain the solution within a lower and upper bound, however this breaks down in a cyclic spaceIndeed, with the initial range set as 0-2, the normal case of on-resonance is hard for SRC to fit forWe saw that this was previously the case with the strange bimodal distributionChangesOn my way to examining the off-resonance issue, I took small steps in modifying the source for DESPOT2-FMRemoved mean normalization and gave it the correct M0 (or we can pretend it read it from the DESPOT1 fit) call this noNormAlso fixed the signal equation, no additional E2 term call this fixedEqnAdditionally modified the SRC off-resonance range from -3, making the space centered around on-resonance call this offResNegative phases were avoided because there was some existing logic to throw away such values

Data Before RF: noNorm

Data After RF: noNorm

Effect of the NormalizationYup, its bad without normalization.

Were fitting the wrong equation and its before the RF, so things get even worse in the after RF caseData Before RF: noNorm Fit

This is how noNorm sees it33noNorm Curve Fit Mean Normalized

How it used to see it34Data After RF: noNorm Fit

How it used to see it35noNorm Curve Fit Mean Normalized

How it used to see it36Mean NormalizationNotice how after mean normalization, the fits look nearly identical despite having different T2 and off-resonances

This should translate to the CRLB showing this model has low precision in the presence of noiseData Before RF: fixedEqn

Data After RF: fixedEqn

Fixing the EquationHaving the fitting model match the simulation model is obviously good

Since the model is before RF, that fit is nearly spot on for T2, after RF is wrong of courseMuch of the error manifests as a bias in the off-resonance

Off-resonance fitting is still a problemData Before RF: offRes

Data Before RF: DESPOT2-FM

SRC and Off-ResonanceIt is a little curious that T2 is a bit more tightly distributed in the fixedEqn case but the bias is high, so still much worse overall

Rotating the off-resonance space is of course only a trial solution since it has only just shifted the problematic cases to phaseI think the correct way may be to set the range of values from 0-4 that way there is always buffer for any given phaseHowever, when SRC finds a good candidate at each contraction step, it should convert the phase to lie within a 2 range in some predictable manner so theres no instability about which way to go43What if we only changed the off-resonance code?

Seems about equivalent but maybe this has higher bias in T2, in the hundredths place instead of thousandths+. Not sure why the off-resonance in the previous case is more jagged.44Relevance to mcDESPOTmcDESPOT relies heavily on DESPOT2-FM for its initial off-resonance estimateFM is implemented identically as presented, with extra E2 and mean normalization

Subsequent for off-resonance is subject to the same issues of SRC and a cyclic dimension

Mean normalization is used, may worsen precision in noisy situations

Equations are still before RF