FAST AND RELIABLE WHOLE
BRAIN MYELIN IMAGING
Alireza Akhondi-Asl
Boston Children’s Hospital, and Harvard Medical School
300 Longwood Ave. Boston MA 02115 USA
Outline
• Quantitative myelin assessment
• Myelin Imaging
• T2-distribution models
• Our innovation
• CPMG and Stimulated echoes
• Fast Imaging
• Multi-slice 2D CPMG and Slice Profile
• Our innovation
• Our Imaging and Image Analysis Framework
• Results
• Simulation, Phantom, and brain image validation
• Conclusions
Myelin
• Myelin
is a layer of dielectric
material derived mainly from lipids
that form a sheath around neuronal
axons, cable-like projections that
transmit electro-chemical messages
along the length of cells.
• The myelin sheath around neuronal
axons is well known to be crucial to
support brain function.
• Myelin-related disorders affect an
estimated 3 million people around
the world.
• Multiple sclerosis (MS)
• schizophrenia
From mayorshealthline.wordpress.com
Quantitative Myelin Assessment
• Unfortunately, there are no known cures for myelin-related
diseases.
• In current practice, the diagnosis and management of
these diseases hinges on the assessment of symptoms
thought to arise from absence or loss of myelin.
• There is currently no effective mechanism for in vivo
quantitative assessment of the amount of myelin in the
CNS.
• Development of myelin imaging holds out the potential of
providing pathologically specific quantitative information
about myelin content.
Myelin Imaging
• The T2 spectrum of water in the brain
has multiple components
• myelin-bound water (the fastest
decaying)
• the intra/extra-cellular water of the
brain
• cerebrospinal fluid
• T2
relaxometry
is
the
most
advantageous and effective noninvasive MRI.
• Myelin
Water fraction (MWF) is
assessed from sequences that acquire
32 spin echoes spaced from 8ms to
256ms to cover the full spectrum of
T2=1/R2 decay.
• The very rapid decay of myelin-bound
water (MW) has made it challenging to
measure.
MWF=
From Wikipedia
Spin-echo sequence
From Wikipedia
• Echoes were first detected by Erwin Hahn in 1950.
• Total acquisition time:TRxNExNLxNS
• NS=30,NL=108,NE=32,TR=2s ~58hrs for whole brain!
• It is the most accurate T2 relaxomotery sequence.
T2 Spectrum Models (NNLS)
• non-negative
least
squares
(NNLS)
• fitting a discrete mixture of impulse
functions
• Each impulse function centered at
pre-specified T2 values across the
range of anticipated T2 values.
• Problems:
• Fails to exploit the continuity of the
•
•
•
•
true distribution of T2 in the tissue.
Large
number
of
unknown
parameters
Needs strong regularization
Very sensitive to the location of
impulse functions and utilized
threshold for MWF estimation.
The estimated T2 values are very
inaccurate.
T2 Spectrum Model
• We have developed an alternative representation
• Finite mixture of continuous distributions to describe the complete
T2 spectrum.
• The fraction of the myelin-bound water is the area under the fast
component curve divided by the total area of each component
curve.
• Advantages:
• The number of parameters that must be estimated is much smaller.
• More physically realistic model of the signal.
• Easy estimation of parameters
• More accurate MWF estimation
• Very accurate T2 estimation.
• Less sensitive to the threshold.
• Less noisy MWF estimates.
Generalized Inverse Gaussian (GIC)
Distribution
• Three-parameter family of
continuous distributions
• Wald (Inverse Gaussian)
• Gamma
• positive support
• closed form Laplace transform
• Not heavy tailed
• Extensively used in
geostatistics, statistical
linguistics, finance…
From Wikipedia
Wald Distribution
• A two-parameter family of
continuous distributions with
support on (0,∞).
• It has mean and shape
parameters.
• As shape parameter tends to
infinity, it becomes more like
a Gaussian distribution.
• The Wald distribution has
several properties analogous
to a Gaussian distribution.
Relation to Multi-exponential
• Multi-exponential fitting is
a special case of our
model
• Wald distribution has a
closed form Laplace
transform.
• When shape parameter
tends to infinity the Wald
distribution will be impulse
function.
Optimization
• We are interested to estimate
the parameters of the Wald
distributions and their mixture
weights using the observed
signals at different echo times.
However, in practice, we
observe yi, a noisy version of
the signal Si .
• We assume that zero mean,
additive white Gaussian noise
is added to the signal. Si.
• It has separable Non-linear
least squares (NLLS)
formulation.
• Variable Projection
• Fast
• Less sensitive to the initializations
• More accurate
Carr-Purcell-Meiboom-Gill (CPMG)
sequence
• It allows observation of multiple
echoes with a single excitation.
• It has been developed in 1980s.
• It uses hard pulse to excite the
whole brain!
• Total acquisition
time:TRxNLxNS
for whole brain!
• It is the base of almost all of T2
Amplitude
• NS=30,NL=108,TR=2s ~1.8 hrs
pubs.rsc.org
relaxomotery sequences.
• Problems:
• Sensitivity to B1 inhomogeneity which
leads to stimulated echoes.
• It is not fast enough.
Echo Number
Impact of B1 inhomogeneity on the observed
echoes.
B1 inhomogeneity compensation
• Optimized crushers
• SAR effect
• Perfect B1
• It is very expensive.
• The extended phase
graph (EPG)
• Gives an elegant
description of
magnetization response
in multiple refocusing
pulses with arbitrary flip
angles θ.
• It is an approximation
• It cannot be used when
slice selective RF pulses
are used.
Fast Myelin Imaging
• 3D Grase (3D CPMG)
• 7 slices in 16 mins (NL=108)
• ~1hr and 10 mins for whole brain with the desired resolution.
• Low SNR
• T2* effect
• GRE
• It is very fast but measures T2* not T2.
• MCDESPOT
• The measurements are not reliable.
• None of them are sufficiently fast or accurate.
Multi-Slice 2D CPMG
• We propose here to use multi-Slice 2D CPMG sequence for myelin
imaging.
• Nobody have used it for multi-component T2 relaxometry
• Both slice Profile and B1 inhomogeneity should be considered.
• It is fast and the results are reliable
• We can easily acquire 6 slices at the same time of single slice 2D CPMG
• Total acquisition time:TRxNLxNS/6
• The distribution of the flip angles can be used by sampling the slice
profile at limited number of points.
• Small tip angle (STA) approximation
• It is invalid and must be reconsidered to achieve accurate modeling of the
signal decay curve.
• NS=30,NL=108,TR=2s ~18 mins for whole brain!
• Using Partial Fourier and parallel imaging this time can be cut to half.
• Our preliminary results also show that we can get plausible results
with just 24 echoes (We do not need 32 echoes):
• High resolution whole brain myelin imaging in (1/2)*(24/32)*18 ~7 mins.
Multi-Slice 2D CPMG
Multi-Slice 2D CPMG sequence. 90o excitation and 180o refocusing RF pulses and Gradient of
the first three echoes of multi-slice 2D CPMG sequence are shown.
Considering Slice Profile in the Solution
• If we know the RF pulses and acquisition we can simulate
Bloch equation for different T2 and B1 values to generate
T2 curves.
• It is similar to EPG but it is very precise
• It is not parametric
• We need to compute these curves one time and we can use them
• So it is fast.
• We have the same equations
• We just replace EPG formulation with Bloch formulation.
The Bloch Equations
• The Bloch equations named after Felix Bloch relate the
time evolution of magnetization to the external magnetic
fields, the relaxation time, and other parameters:
Results: Simulation
(a) The slice profile of the first and second echoes for a spin with T2=75ms and B1=1.0 inhomogeneity scale
are shown. (b) The slice profile of the first echo for T2=75ms and B1=0.8 as well as the slice profile calculated
using the STA approximation. (c) and (d) Impact of non-ideal slice selective RF pulses on the signal decay curve
when T2=75ms and T2=20ms, respectively.
Results: Simulation
(a) CRLB of MWF estimation using MOIG distributions where the standard deviation is
normalized by the true MWF value. (b) Relative MAE for a range of SNRs and
inhomogeneity scales for MOIG and NNLS.
Results: Phantom Experiments
•
•
•
•
Two chamber phantom filled
with different levels of
gadolinium
doped
water
solutions.
T2 relaxation measurements
were performed on a 3T
Siemens TRIO scanner with a
single slice (4mm thick), T2
relaxometry sequence.
32 echoes were acquired with
a minimum echo time of 9ms.
21 cm FOV was used with a
matrix size of 192x192 (in
plane resolution of 1.1x1.1 mm
squared).
(a) The observed echo at 90ms and the regions used to construct the ROI’s utilized for the
experiment. Each ROI has three voxels inside one of the red rectangles with the longer and one voxel
inside the green rectangle with the short . (b) Comparison of the distribution of normalized error in
the estimation of the fraction of the first component using MOIG and NNLS based on 630 ROI’s. (c)
Box plot of the estimated fractions using MOIG and NNLS. (d) Scatter plot of the estimated fraction of
the shortest component using MOIG versus NNLS.
Results: Brain Data
(a)-(b) Estimated MWF map using MOIG distributions. (c)-(d) Estimated MWF map using NNLS. (e)-(f) Estimated
inhomogeneity scale maps using MOIG. (g)-(h) Estimated inhomogeneity scale maps using NNLS approach.
Results: Whole brain myelin imaging
MWF maps generated via
our analysis method for
twelve slices are shown. A
20 cm FOV was used with
the matrix size of 128x96
(phase resolution of 75%)
and total scan time of 17
minutes and 10 seconds for
the acquisition of 5x6=30
slices.
Results: Brain Data
(a) The scatter plot of test-retest analysis of NNLS algorithm. (b) The scatter plot of test-retest analysis of MOIG. Rsquared of fitted regression line of MOIG and NNLS was 0.79 and 0.70, respectively.
Summary of Current Myelin Imaging
Methods
• Limitations of Current state-of-the-art methods:
• The imaging process is very slow
• Currently, state-of-the-art methods can acquire 1 slice in 3.6 mins
• To cover whole brain with sufficient resolution we need at least 30 slices.
Therefore, ~1hr and 48mins required for whole brain imaging.
• Current T2 distribution models fail to exploit the continuity of the
true distribution of T2 in the tissue.
• Estimation of model parameters is sub-optimal
• In summary, current methods are slow, do not have
sufficient resolution and accuracy.
Proposed Myelin imaging Framework
• Imaging: Multi-slice 2D CPMG sequence.
• We can get 30 slices in ~ 17 mins.
• 6 times faster than current imaging methods.
• T2 distribution Model: Finite mixture of Wald distributions
• Number of parameters is much smaller.
• More physically realistic model of the signal
• Less noisy MWF estimates.
• Precise inhomogeneity modeling.
• Optimal parameter estimation: Robust and reliable estimation of the
parameters of a mixture of Wald distributions can be achieved with a
well-known technique called the variable projection method.
• This allows us to rapidly solve this nonlinear estimation problem with high accuracy.
Conclusions
• We have developed a framework for Myelin imaging
which is fast, has sufficient resolution and accuracy.
• Clinically feasible
• High resolution
• Accurate
• Sensitive to the small changes in the myelin.
THANK YOU!