Alireza AkhondiAsl Boston Childrens Hospital and Harvard Medical School 300 Longwood Ave Boston MA 02115 USA Outline Quantitative myelin assessment Myelin Imaging T2distribution models ID: 550639
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FAST And Reliable Whole Brain Myelin Imaging
Alireza Akhondi-AslBoston Children’s Hospital, and Harvard Medical School 300 Longwood Ave. Boston MA 02115 USASlide2
Outline
Quantitative myelin assessment Myelin ImagingT2-distribution modelsOur innovationCPMG and Stimulated echoesFast ImagingMulti-slice 2D CPMG and Slice ProfileOur innovationOur Imaging and Image Analysis FrameworkResultsSimulation, Phantom, and brain image validationConclusionsSlide3
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.comSlide4
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.Slide5
Myelin Imaging
The T2 spectrum of water in the brain has multiple componentsmyelin-bound water (the fastest decaying)the intra/extra-cellular water of the braincerebrospinal fluidT2 relaxometry is the most advantageous and effective non-invasive 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.
From Wikipedia
MWF=Slide6
Spin-echo
sequence
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.
From WikipediaSlide7
T2 Spectrum Models (NNLS)
non-negative least squares (NNLS)fitting a discrete mixture of impulse functionsEach 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 regularizationVery sensitive to the location of impulse functions and utilized threshold for MWF estimation.The estimated T2 values are very inaccurate.Slide8
T2 Spectrum Model
We have developed an alternative representationFinite 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 estimationVery accurate T2 estimation.Less sensitive to the threshold.Less noisy MWF estimates.Slide9
Generalized Inverse Gaussian (GIC) Distribution
Three-parameter family of continuous distributionsWald (Inverse Gaussian)Gammapositive supportclosed form Laplace transformNot heavy tailedExtensively used in geostatistics, statistical linguistics, finance…
From WikipediaSlide10
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.Slide11
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.Slide12
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 ProjectionFastLess sensitive to the initializationsMore accurateSlide13
Carr-Purcell-Meiboom
-Gill (CPMG) sequenceIt 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:TRxNLxNSNS=30,NL=108,TR=2s ~1.8 hrs for whole brain!It is the base of almost all of T2 relaxomotery sequences.
Problems:Sensitivity to B1 inhomogeneity which leads to stimulated echoes.It is not fast enough.
pubs.rsc.org
Impact of B1 inhomogeneity on the observed echoes.
Echo Number
AmplitudeSlide14
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.Slide15
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 SNRT2* effectGREIt is very fast but measures T2* not T2.MCDESPOTThe measurements are not reliable.
None of them are sufficiently fast or accurate. Slide16
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 relaxometryBoth slice Profile and B1 inhomogeneity should be considered.It is fast and the results are reliableWe can easily acquire 6 slices at the same time of single slice 2D CPMGTotal acquisition time:TRxNLxNS/6The distribution of the flip angles can be used by sampling the slice profile at limited number of points.
Small tip angle (STA) approximationIt 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
.Slide17
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. Slide18
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 preciseIt is not parametricWe need to compute these curves one time and we can use themSo it is fast.We have the same equations
We just replace EPG formulation with Bloch formulation.Slide19
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: Slide20
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. Slide21
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. Slide22
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. Slide23
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.Slide24
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.Slide25
Results: Brain Data
(a) The scatter plot of test-retest analysis of NNLS algorithm. (b) The scatter plot of test-retest analysis of MOIG. R-squared of fitted regression line of MOIG and NNLS was 0.79 and 0.70, respectively.Slide26
Summary of Current Myelin Imaging Methods
Limitations of Current state-of-the-art methods:The imaging process is very slowCurrently, state-of-the-art methods can acquire 1 slice in 3.6 minsTo 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-optimalIn summary, current methods are slow
, do not have sufficient resolution and accuracy.Slide27
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 distributionsNumber of parameters is much smaller. More physically realistic model of the signalLess 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.Slide28
Conclusions
We have developed a framework for Myelin imaging which is fast, has sufficient resolution and accuracy.Clinically feasibleHigh resolutionAccurateSensitive to the small changes in the myelin.Slide29
ThanK You!