Benoit Scherrer, ISBI 2011, Chicago Toward an accurate multi-fiber assessment strategy for clinical practice. Benoit Scherrer, Simon K. Warfield

Benoit 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, 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]

Benoit 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, Chicago Consider in each voxel a mixture of independent fibers Multi-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, 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 framework Ensures valid and regularized tensor estimates CUSP-MFM CUbe and SPhere Multi-Fiber Model

Benoit Scherrer, ISBI 2011, Chicago. CUbe and SPhere acquisition scheme.

Benoit Scherrer, ISBI 2011, Chicago CUSP acquisition scheme  Theoretical demonstration ISBI2010: Multiple b-values are necessary for the full MFM estimation 8  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 ratio duration of the diffusion gradient pulses time 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, Chicago CUSP acquisition scheme 9  How to satisfy the requirement of multiple b-values?  Multiple shell HARDI acquisition (G≤1)  Nominal b-value = for the largest shell  TE = TE for the highest b-value.  Longer acquisition time  Higher geometric and intensity distortion  Lower SNR for all measurements  Separate single-shell HARDI acquisitions (G=1) Different nominal b-values  Spatial misregistration caused by motions between scans  Different 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, Chicago CUSP acquisition scheme  CUbe and SPhere q-space sampling Combine one HARDI shell and the gradients on the enclosing cube 10 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, Chicago. Novel MFM estimation procedure. [ In conjunction with the CUSP acquisition… ]

Benoit Scherrer, ISBI 2011, Chicago Diffusion signal modeling  Homogeneous Gaussian model (DTI) Diffusion weighted signal S k along a gradient g k (||g k ||=1) : D: 3x3 diffusion tensor, S 0 : signal with no diffusion gradients, b k : b-value for the gradient direction k.  MFM DW signal modeling. For N fibers =2:  An isotropic compartment to model the diffusion of free water  N fibers anisotropic compartments related to the fibers Diffusivity of free waterModels the two fiber tracts Fractions of occupancy

Benoit 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, Chicago A Novel MFM fitting procedure  Variational framework Simultaneous 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, Chicago. Evaluation.

Benoit 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 truthHARDI35-MFM 5B=0 + 1 shell 30directions CUSP35-MFM 5B=0 + 1 shell 16directions + 1xhexahedral+ 2xtetrahedral CUSP-MFM achieves a better tensor estimation accuracy

Benoit Scherrer, ISBI 2011, Chicago Evaluation  How to design a CUSP acquisition? How many repetitions of the gradients with norm>1 to 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 truth Average log-Euclidean distance  comparison of the full tensors  Simple linear model: (blue is better) 35

Benoit 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, 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 accuracyFractions estimation accuracy

Benoit Scherrer, ISBI 2011, Chicago Evaluation  Tensors representing two uniform crossing fibers Assessment of the fractional anisotropy along the tracts Quantitative analysis HARDI35-MFM CUSP35-MFM The FA of two uniform crossing fibers is uniform with CUSP-MFM

Benoit Scherrer, ISBI 2011, Chicago Evaluation – real data HARDI35-MFMCUSP35-MFM HARDI35-FSLCUSP35-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, Chicago Evaluation – real data  Preliminary results MFM tractography HARDI45-1TCUSP45-MFM HARDI45-1TCUSP45-MFM CUSP-MFM tracts better represent expected connectivity Corticospinal tractsArcuate fasciculus

Benoit 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, 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, …

Benoit Scherrer, ISBI 2011, Chicago Thank you for your attention, CUSP-MFM