j ournal c lub : lankford and does. on the inherent precision of mcdespot. jul 23, 2012 jason su
TRANSCRIPT
JOURNAL CLUB:Lankford and Does. On the Inherent Precision
of mcDESPOT.
Jul 23, 2012Jason Su
Motivation• This paper is the first to perform a detailed analysis of the precision
and noise propagation through the mcDESPOT model– i.e. 2-pool exchange in SPGR and SSFP
• Examines if mcDESPOT is valid way to precisely estimate relaxation in 2-pool exchange– Given how similar the curve shapes are, this was an open question– There is a lot of focus on the precision of the MWF parameter, which is
justified given that most literature focuses on this map with mcDESPOT
• “The inclusion of intercompartmental water exchange rate as a model parameter makes mcDESPOT unique and especially compelling given the potential for the mean residence time of water in myelin to be a measure of myelin thickness”
Cramer-Rao Lower Bound
• Glossary:
– = the true parameters of the model (M0, T1s, T2s, MWF, exchange rate)
– = the fitted/estimated parameters– F = Fischer information matrix (FIM)– J = Jacobian of signal equation, – = signal equation
Cramer-Rao Lower Bound
• Interpretation:– Bounds the covariance matrix of the estimated
parameters (in a matrix sense)• Entries on the diagonal are the variances of each
parameter
– is the “gradient of the estimator bias”• For unbiased estimator, = I• Otherwise calculated numerically
Fisher Information Matrix
• Calculated numerically for a given tissue• Interpretation– Essentially the correlation matrix of the Jacobian
after accounting for noise– Shows the curvature of the parameter space– Want to be full rank, means the
inversion/parameter finding problem is well defined
Methods
• Almost all of the relevant matrices are calculated numerically for example tissues– From MSmcDESPOT data in WM (splenium):• T1,S = 916ms, T1,F = 434ms, T2,S= 60ms, T2,F= 10ms,
fF = 22%, kFS = 12.8 s-1
Methods• Used Monte Carlo simulations to
verify Cramer-Rao bound– Fitting via lsqnonlin() and X2 criterion– Each signal was fitted 100 times with
different initial, if 20/100 converged w/ less than 0.01%, considered global min
– If not achieved, repeat (but not aggregate all the fits)
• Much more noise used in constrained case– Seemed like some cyclic logic,
amount of noise based on CRLB but trying to verify just that
Results
Results
• Unconstrained fit has unacceptably high coefficient of var.– Large failure when T1/T2 ratio of fast and slow pools
same– Phase cycling improves precision in unconstrained case
(not shown)– Is coeff. of var. what we want, esp. for MWF?
• Constraining the fit by fixing T2s and exchange rate greatly improves the coefficient of var.
Results – Bad Constraints
Results
• Bias grows linearly increases with higher MWF
• Of note is that MWF is decently robust to the exchange rate assumption– As long as not assumed to be in fast exchange
regime
Discussion
• Low variance of in vivo data explanation– Constrained fit: this is true– Inadequate model leads to better precision?• High GM in Deoni spinal cord study (10%), not seen in
brain
• Why were the constrained parameters chosen to be fixed?
• Is there a dependence of CRLB on TR?
Discussion
• SRC is constrained but in a different manner:– T1,S = 550-1350ms
– T1,F = 250-600ms
– T2,S= 30-150ms
– T2,F= 1-40ms
– fF = 0.1-15%
– kFS = 4-13.3 s-1
• No combination allowed low variance estimates of both MWF and exchange rate– “Of course, the same is true for a conventional multiple spin echo
measurement of transverse relaxation.”
mcDESPOT Maps in NormalT1single T1fast
MWF
T2single T2slow
T1slow
T2fast Residence Time
0 – 0.234
0 – 137ms
0 – 555ms
0 – 9.26ms
0 – 1172ms
0 – 123ms
0 – 2345ms
0 – 328ms
Summary
• Good– A well done analysis of the unconstrained situation
• Bad– Very different constraint scenario
• Take-home message– Exchange rate and MWF cannot both be estimated well– Phase cycles may provide benefit