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