J OURNAL C LUB : Lankford and Does. On the Inherent Precision of mcDESPOT. Jul 23, 2012 Jason 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

Fisher Information Matrix

Methods Almost all of the relevant matrices are calculated numerically for example tissues – From MSmcDESPOT data in WM (splenium): T 1,S = 916ms, T 1,F = 434ms, T 2,S = 60ms, T 2,F = 10ms, f F = 22%, k FS = 12.8 s -1

Methods Used Monte Carlo simulations to verify Cramer-Rao bound – Fitting via lsqnonlin() and X 2 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

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: – T 1,S = ms – T 1,F = ms – T 2,S = ms – T 2,F = 1-40ms – f F = % – k FS = 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 Normal T1 single T1 fast MWF T2 single T2 slow T1 slow T2 fast Residence Time 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