benoit scherrer, isbi 2011, chicago toward an accurate multi-fiber assessment strategy for clinical...
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Benoit Scherrer, ISBI 2011, ChicagoBenoit Scherrer, ISBI 2011, Chicago
Toward an accurate multi-fiber assessment strategy for clinical practice.
Benoit Scherrer, Simon K. Warfield
Benoit Scherrer, ISBI 2011, ChicagoBenoit Scherrer, ISBI 2011, Chicago
Diffusion imaging Diffusion tensor imaging (DTI)
Describes the 3-D local diffusion with a 3-D tensor Requires relatively short acquisitions Reveals major fiber bundles = “highways” in the brain Assessment of underlying fiber bundles characteristics
(fractional anisotropy, radial diffusivity, …) Widely used
Good approximation for voxels containing a single
fiber bundle direction
But inappropriate for assessing multiple fiber
bundles orientations
Benoit Scherrer, ISBI 2011, ChicagoBenoit Scherrer, ISBI 2011, Chicago
Overcome the limitations of DTI Novel q-space sampling schemes
[Hagmann, P et al., 2006]
Cartesian q-space sampling
q-space : space of the diffusion-sensitizing gradients
Spherical q-space sampling
HARDI Single shell, multi-shell
[Hagmann, P et al., 2006] [Hagmann, P et al., 2006]
Benoit Scherrer, ISBI 2011, ChicagoBenoit Scherrer, ISBI 2011, Chicago
Overcome the limitations of DTI
Novel models for characterization of the DW-signal Non-parametric: DSI, QBI, E-QBI, … Parametric: SD, GDTI, DOT, …
do not characterize the proportions of each fiber bundle do not enable the assessment of the fiber bundle characteristics
Drawbacks: Describe the general shape of the diffusion profile Do not consider each fiber bundle independently
HARDICartesian
Benoit Scherrer, ISBI 2011, ChicagoBenoit Scherrer, ISBI 2011, Chicago
Consider in each voxel a mixture of independent fibersMulti-fiber modeling
Ball and stick model [Behrens 2003] [FSL]Estimate “sticks” to represent a fiber bundle
Multi-tensor representation of a MFM
Assessment of diffusion tensor parameters for each fiber bundle independently
Great interest for fiber integrity assessment
Individual fiber bundle well represented by a single tensor
multiple fiber bundles expected to be well represented by a set of tensors.
Were known to be numerically challenging and unstable.[Scherrer and Warfield, ISBI2010, ISMRM2010] : Theoretical demonstration that multiple b-values are required.Single non-zero b-value : collinearity in the parameters
Do not enable the fiber characteristics assessment
Benoit Scherrer, ISBI 2011, ChicagoBenoit Scherrer, ISBI 2011, Chicago
Contributions
A novel acquisition scheme for the assessment of multiple fibers.Combines CUbic and SPherical q-space sampling (CUSP)Acquisition of multiple b-values without increasing the TE
A novel procedure for the estimation of a multi-fiber model (MFM)Variational log-Euclidean frameworkEnsures valid and regularized tensor estimates
CUSP-MFMCUbe and SPhere Multi-Fiber Model
Benoit Scherrer, ISBI 2011, ChicagoBenoit Scherrer, ISBI 2011, Chicago
. CUbe and SPhere acquisition scheme .
Benoit Scherrer, ISBI 2011, ChicagoBenoit Scherrer, ISBI 2011, Chicago
CUSP acquisition scheme
Theoretical demonstrationISBI2010: Multiple b-values are necessary for the full MFM estimation
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How to satisfy this requirement?First remark: Pulsed-gradient spin echo (PGSE) sequence
b-value, echo time (TE) and gradient strength are linked
proton gyromagnetic ratioduration of the diffusion gradient pulsestime between diffusion gradient RF pulses
diffusion sensitizing gradient norm
Modify the nominal b-value different TE
[Perrin2005]
For a single-shell HARDI G=1 for all gradients
Benoit Scherrer, ISBI 2011, ChicagoBenoit Scherrer, ISBI 2011, Chicago
CUSP acquisition scheme
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How to satisfy the requirement of multiple b-values?
Multiple shell HARDI acquisition (G≤1) Nominal b-value = for the largest shellTE = TE for the highest b-value.Longer acquisition timeHigher geometric and intensity distortionLower SNR for all measurements
Separate single-shell HARDI acquisitions (G=1)Different nominal b-valuesSpatial misregistration caused by motions between scansDifferent TE => Different geometric distortions patterns
[Qin2009]
SNR at 3Tesla
We need multiple non-zero b-values.BUT do we really need a set of full shells ?
Benoit Scherrer, ISBI 2011, ChicagoBenoit Scherrer, ISBI 2011, Chicago
CUSP acquisition scheme
CUbe and SPhere q-space samplingCombine one HARDI shell and the gradients on the enclosing cube
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Never used for multiple fiber bundle assessment
Hexahedral gradients√2-norm : double the nominal b-value
Tetrahedral gradients √3-norm : nominal b-value x 3
Fix a nominal b-value (generally 1000s/mm2 for adult brains)
Inspired by [Conturo96], [Peled2009]
Gradients of the HARDI shell : unit-norm gradients
Provides multiple non-null b-values without modifying the TE Introduces high b-values, known to better characterize MFMs Does not increase the imaging time nor the distortion
Benoit Scherrer, ISBI 2011, ChicagoBenoit Scherrer, ISBI 2011, Chicago
. Novel MFM estimation procedure .
[ In conjunction with the CUSP acquisition… ]
Benoit Scherrer, ISBI 2011, ChicagoBenoit Scherrer, ISBI 2011, Chicago
Diffusion signal modeling Homogeneous Gaussian model (DTI)
Diffusion weighted signal Sk along a gradient gk (||gk ||=1) :
D: 3x3 diffusion tensor, S0: signal with no diffusion gradients, bk: b-value for the gradient direction k.
MFM DW signal modeling. For Nfibers=2: An isotropic compartment to model the diffusion of free water Nfibers anisotropic compartments related to the fibers
Diffusivity of free water Models the two fiber tracts
Fractions of occupancy
Benoit Scherrer, ISBI 2011, ChicagoBenoit Scherrer, ISBI 2011, Chicago
Log-Euclidean framework
log-Euclidean representation
Has been successfully applied to the one-tensor estimation [Fillard et al., 2007]
Tensor estimation Care must be taken to ensure non-degenerate tensors
We consider
Tensors with null or negative eigen-values are at an infinite distance
Benoit Scherrer, ISBI 2011, ChicagoBenoit Scherrer, ISBI 2011, Chicago
A Novel MFM fitting procedure
Variational frameworkSimultaneous estimation and regularization of f and L : minimizing the energy:
Least-square criteria: Spatial homogeneity :
Anisotropic regularization:
Gradient of the tensor field j
Benoit Scherrer, ISBI 2011, ChicagoBenoit Scherrer, ISBI 2011, Chicago
Evaluation
Numerical simulations 100 tensors crossing with a given angle in various configurations Simulation of the DW signal, corrupted by a Rician noise (SNR=30dB)
Ground truth HARDI35-MFM5B=0 + 1 shell 30directions
CUSP35-MFM5B=0 + 1 shell 16directions + 1xhexahedral+ 2xtetrahedral
CUSP-MFM achieves a better tensor estimation accuracy
Benoit Scherrer, ISBI 2011, ChicagoBenoit Scherrer, ISBI 2011, Chicago
Evaluation How to design a CUSP acquisition?
How many repetitions of the gradients with norm>1to counterbalance the lower SNR?
Evaluation of the relationship between three parameters: Number of total images acquisitions Optimal number of repetition of sqrt(2)-norm gradients Optimal number of repetition of sqrt(3)-norm gradients
Comparison of the estimation accuracy with the ground truthAverage log-Euclidean distance comparison of the full tensors
Simple linear model:
(blue is better)
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Benoit Scherrer, ISBI 2011, ChicagoBenoit Scherrer, ISBI 2011, Chicago
Evaluation
Quantitative evaluation
CUSP-MFM achieves in average the better angular resolution.
Simulation of various crossing angles Comparison with the ball-and-stick model (FSL)
Metric: Average minimum angle (Tuch2002)
Crossing Angle
AMA
Benoit Scherrer, ISBI 2011, ChicagoBenoit Scherrer, ISBI 2011, Chicago
Evaluation Quantitative evaluation
Average log-Euclidean distance between the tensors
Average absolute difference between the fractions
Comparison of three acquisition schemes
Introducing multiple b-values is better than employing a large number of directions
Crossing Angle
Whole tensors estimation accuracy Fractions estimation accuracy
Benoit Scherrer, ISBI 2011, ChicagoBenoit Scherrer, ISBI 2011, Chicago
Evaluation Tensors representing two uniform crossing fibers
Assessment of the fractional anisotropy along the tracts
Quantitative analysisHARDI35-MFM
CUSP35-MFM
The FA of two uniform crossing fibers is uniform with CUSP-MFM
Benoit Scherrer, ISBI 2011, ChicagoBenoit Scherrer, ISBI 2011, Chicago
Evaluation – real data
HARDI35-MFM CUSP35-MFM
HARDI35-FSL CUSP35-FSL
CUSP-MFM: Better tensor uniformity (regions 1, 2, 3) vs HARDI-MFM Better alignment of the two tensors when single fiber (4)
FSL: Not enough data to estimate correctly the ball-and-stick model?
Benoit Scherrer, ISBI 2011, ChicagoBenoit Scherrer, ISBI 2011, Chicago
Evaluation – real data Preliminary results
MFM tractography
HARDI45-1T CUSP45-MFM HARDI45-1T CUSP45-MFM
CUSP-MFM tracts better represent expected connectivity
Corticospinal tracts Arcuate fasciculus
Benoit Scherrer, ISBI 2011, ChicagoBenoit Scherrer, ISBI 2011, Chicago
Discussion
CUSP-MFM
CUSP-MFM enables to perform both tractography and individual fiber bundles’ characteristics assessment.
A novel acquisition scheme Satisfies the need of multiple b-values and introduces high b-values Does not increase the echo time: no impact on the distortion Provide the relation to design a CUSP acquisition
A novel multi-tensor fitting procedure log-Euclidean framework: ensures valid tensors Variational formulation: simultaneous estimation and regularization
Focus on very short duration acquisitions, compatible with routine clinical practice Evaluation
Benoit Scherrer, ISBI 2011, ChicagoBenoit Scherrer, ISBI 2011, Chicago
Discussion
Future works
Model selection Number of fibers at each voxel?
Investigation of the optimal CUSP Finer discretization of the cube edges? Optimal nominal b-value?
Full evaluation on real data: comparison with other approaches Q-Ball imaging, Spherical deconvolution, …