Toward an accurate multi-fiber assessment strategy for clinical practice.

Benoit Scherrer, ISBI 2011, ChicagoBenoit Scherrer, ISBI 2011, Chicago

Toward an accurate multi-fiber assessment strategy for clinical practice.

Benoit Scherrer, Simon K. Warfield


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


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]


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


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


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


. CUbe and SPhere acquisition scheme .


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



99

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 ?



CUbe and SPhere q-space samplingCombine one HARDI shell and the gradients on the enclosing cube

1010

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


. Novel MFM estimation procedure .

[ In conjunction with the CUSP acquisition… ]


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


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


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


. Evaluation .


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


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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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


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


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


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?


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


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


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, …


Thank you for your attention,

CUSP-MFM

Toward an accurate multi-fiber assessment strategy for clinical practice.

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Transcript of Toward an accurate multi-fiber assessment strategy for clinical practice.