Journal Club: mcDESPOT with B0
& B1 Inhomogeneity
Papers
• Deoni et al. Gleaning multicomponent T1 and
T2 information from steady-state imaging
data. Magn. Reson. Med. (2008) vol. 60 (6) pp.
1372-1387
• Deoni. Correction of main and transmit
magnetic field (B0 and B1) inhomogeneity
effects in multicomponent-driven equilibrium
single-pulse observation of T1 and T2. Magn.
Reson. Med. (2010)
mcDESPOT
• A whole-brain quantitative mapping technique
• Idea: collect SPGR and SSFP scans at several flip
angles
– These have a known theoretical steady-state signal
equation
– Fit the equation as it varies with flip angle to the
collected data at each voxel
– Gives us: T1, T2, and more
• Uses a two-compartment model for the signal
equation: a fast and slow relaxing species in
exchange
scDESPOT Theory
• DESPOT1: SPGR equation
– Find M0 and T1, minimize (SSPGR-ŜSPGR)2
Sˆ SPGR   
M 0 1  E 1  sin 
1  E 1 cos 
,
E1  e

TR
T1
• DESPOT2: SSFP equation

– Given T1, find M0 and T2, minimize (SSSFP-ŜSSFP)2
Sˆ SSFP   
M 0 1  E 1  sin 
1  E 1 E 2   E 1  E 2  cos 
,
E2  e

TR
T2
mcDESPOT Theory
• 2 component SPGR equation
– Find fF, fS, T1,F, T1,S, kFS=1/τF, kSF=1/τS
M SPGR
m SPGR
M SPGR 
1
xy ,F
TR  A S PGR
TR  A S PGR
sin   I  e
cos  
    SPGR  m SPGR I  e

M xy ,S 
f F 
   ,
 f S 
A SPGR
 1
 k FS

T
  1,F

k FS



k SF


1

 k SF 

T1,S

mcDESPOT Theory
• 2 component SSFP equation
– Find M0 and T1, minimize (SSPGR-ŜSPGR)2
M SSFP
M SSFP 
x ,F
 SSFP 
M x ,S 
M SSFP 
1
y ,F
TR  A SSFP
1
TR  A SSFP
 I A SSFP C  I  e
R  
    SSFP  e
M y ,S 
M zSSFP

,F
 SSFP 
M z ,S 

C   0

0
0
0
fF
T1,F
f S 

T1,S 
mcDESPOT Theory
A SSFP

1

 k FS

T2,F


k FS


  RF    F 
 

0


0



0


k SF

1
T2,S
 RF    F
0
0
0
0
 RF    S
0
0
k SF
0
0
0
0
 k SF
0

1
 k FS
T2,F
  RF    S 
k FS
0
0

1
T2,S
 k SF
0

1
T1,F
0
0
0
 k FS
k FS
k SF

1
T1,F















k FS


Simplifying Assumptions
• 2 component model
fS  1  fF
– Only need to find fF (the fast volume fraction)
• Chemical equilibrium

f F k FS  f S k SF
– Allows us to eliminate finding kSF=1/τS
• Both components are on the same resonance
 F   S

Fitting Method
• Genetic Algorithm
– Previous method, proved to be too slow
• Stochastic Region of Contraction
– Current method, processing time is still substantial
(about 24 hrs. for a 2mm isotropic brain)
– Supposedly good for avoiding local minima
– Not much literature on it (Berger and Silverman.
Microphone Array Optimization by Stochastic
Region Contraction.)
Stochastic Region of Contraction
• Has been offered as an alternative to
simulated annealing, which can be slow but is
very general
• SRC is good for objective functions with these
characteristics:
– Few large valleys, many small local minima is fine
– The neighborhood around the global minimum is
still lower than any other local minima
– Depends on <100 variables
Stochastic Region of Contraction
• Given an initial N-dimensional, rectangular,
search volume containing the global optimum
– Explore the objective function with random points
in the space
– Systematically contract the volume until it reaches
a satisfactorily small region that traps the global
optimum
Stochastic Region of Contraction
• Algorithm
– Define initial search space for: T1,F&S, T2,F&S, fF, τF,
Δωs
– Treat this rectangular box as a uniform distribution
and sample N times
– Compute the objective function for each sample
– Keep M of the best samples and define the new
box based on the ranges of the variables in these
samples
– Rinse and repeat until convergence
Stochastic Region of Contraction
When Things Go Wrong
• Simulation of artifacts
– B0 effects
– B1 and slab profile effects
• The key assumption of mcDESPOT is that the prescribed
flip angle is achieved everywhere in the volume
• Need to account for this if not the case
• In vivo at 1.5T (and some proof of concept 3T)
– 4 normal volunteers
B0 Solutions
• B0 mapping
• DESPOT2-FM with phase-cycled SSFP
– Requires collection of another set of 9 SSFP
images
– Modified signal equation and objective function as
presented earlier
When Things Go Wrong: B0 Artifacts
When Things Go Wrong: B0 Artifacts
B1 Solutions
• B1 mapping
– AFI, niDALL, Bloch-Siegert
• DESPOT1-HIFI with IR-SPGR (1 component)
– Requires addition of 1 IR-prepped scan
– Details of signal equation to derive B1 map not
covered here
– Gives κ(r):
 T  r    r    P  r 
When Things Go Wrong: B1 Artifacts
When Things Go Wrong: B1 Artifacts
When Things Go Wrong: B1 Artifacts
When Things Go Wrong: B1 Artifacts
In Vivo
In Vivo
In Vivo
• B0 and B1 effects are not enough to account
for the difference in MWF between mcDESPOT
and T2-MCRI (usu. in range of 8-9%)
Conclusions
• DESPOT1-HIFI does well even thought slab profile
changes with angle and assumes single component
– Alternatives should be considered though since anatomical
structures are visible on the maps: not the best B1 map
– Bloch-Siegert seems compelling but need a way to
incorporate slab profile as well
• DESPOT2-FM and phase-cycled SSFP has been a part of
the protocol at 1.5T and should also stay when we
move to 3T+
– Alternative B0 mapping methods should be considered if
they offer a significant benefit in acquisition time
Other Avenues to Explore
• 3 component model, is another pool skewing
the MWF?
• Are the 2 components actually on the same
resonance?