Journal Club: Lankford and Does. On the Inherent Precision of mcDESPOT .

1. Journal Club:Lankford and Does. On the Inherent Precision of mcDESPOT. Jul 23, 2012 Jason Su

2. 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”

3. 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

4. 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

5. 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

6. 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

7. 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

8. Results

9. 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.

10. Results – Bad Constraints

11. 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

12. 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?

13. 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.”

14. mcDESPOT Maps in Normal T1single T1slow MWF T1fast 0 – 0.234 0 – 1172ms 0 – 2345ms 0 – 555ms 0 – 137ms 0 – 9.26ms 0 – 123ms 0 – 328ms T2fast Residence Time T2single T2slow

15. 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