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

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

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

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

  2. 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 But inappropriate for assessing multiple fiber bundles orientations Good approximation for voxels containing a single fiber bundle direction

  3. Overcome the limitations of DTI • Novel q-space sampling schemes • q-space :space of the diffusion-sensitizing gradients [Hagmann, P et al., 2006] • Cartesian q-space sampling • Spherical q-space sampling [Hagmann, P et al., 2006] [Hagmann, P et al., 2006] • HARDI Single shell, multi-shell

  4. Overcome the limitations of DTI • Novel models for characterization of the DW-signal • Non-parametric: DSI, QBI, E-QBI, … • Parametric: SD, GDTI, DOT, … • Cartesian • HARDI • Drawbacks: • Describe the general shape of the diffusion profile • Do not consider each fiber bundle independently • do not characterize the proportions of each fiber bundle  do not enable the assessment of the fiber bundle characteristics

  5. Multi-fiber modeling Consider in each voxel a mixture of independent fibers • Ball and stick model [Behrens 2003] [FSL]  Do not enable the fiber characteristics assessment • Estimate “sticks” to represent a fiber bundle • Multi-tensor representation of a MFM • Individual fiber bundle well represented by a single tensor  multiple fiber bundles expected to be well represented by a set of tensors. • Assessment of diffusion tensor parameters for each fiber bundle independently Great interest for fiber integrity assessment • 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

  6. Contributions CUSP-MFMCUbe and SPhere Multi-Fiber Model • 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

  7. . CUbe and SPhere acquisition scheme .

  8. CUSP acquisition scheme • Theoretical demonstration ISBI2010: Multiple b-values are necessary for the full MFM estimation • How to satisfy this requirement? First remark:Pulsed-gradient spin echo (PGSE) sequence b-value, echo time (TE) and gradient strength are linked diffusion sensitizing gradient norm proton gyromagnetic ratio duration of the diffusion gradient pulses time between diffusion gradient RF pulses For a single-shell HARDI G=1 for all gradients [Perrin2005] Modify the nominal b-value  different TE

  9. CUSP acquisition scheme • How to satisfy the requirement of multiple b-values? • Separate single-shell HARDI acquisitions (G=1)Different nominal b-values • Spatial misregistration caused by motions between scans • Different TE => Different geometric distortions patterns • 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 SNR at 3Tesla We need multiple non-zero b-values.BUT do we really need a set of full shells ? [Qin2009]

  10. CUSP acquisition scheme • CUbe and SPhere q-space sampling Inspired by [Conturo96], [Peled2009] Combine one HARDI shell and the gradients on the enclosing cube Never used for multiple fiber bundle assessment • Fix a nominal b-value (generally 1000s/mm2 for adult brains) • Gradients of the HARDI shell : unit-norm gradients • Hexahedral gradients√2-norm : double the nominal b-value • Tetrahedral gradients √3-norm : nominal b-value x 3 • 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

  11. [ In conjunction with the CUSP acquisition… ] . Novel MFM estimation procedure .

  12. 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 Fractions of occupancy Diffusivity of free water Models the two fiber tracts

  13. Log-Euclidean framework • Tensor estimation • Care must be taken to ensure non-degenerate tensors •  log-Euclidean representation • Has been successfully applied to the one-tensor estimation [Fillard et al., 2007] • We consider • Tensors with null or negative eigen-values are at an infinite distance

  14. 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

  15. . Evaluation .

  16. 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-MFM 5B=0 + 1 shell 30directions CUSP35-MFM5B=0 + 1 shell 16directions + 1xhexahedral+ 2xtetrahedral CUSP-MFM achieves a better tensor estimation accuracy

  17. 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 truthAverage log-Euclidean distance  comparison of the full tensors 35 • Simple linear model: (blue is better)

  18. Evaluation • Quantitative evaluation • Simulation of various crossing angles • Comparison with the ball-and-stick model (FSL)Metric: Average minimum angle (Tuch2002) AMA CUSP-MFM achieves in average the better angular resolution. Crossing Angle

  19. Evaluation • Quantitative evaluation • Comparison of three acquisition schemes Whole tensors estimation accuracy Fractions estimation accuracy Crossing Angle Average log-Euclidean distance between the tensors Average absolute difference between the fractions Introducing multiple b-values is better than employing a large number of directions

  20. Evaluation • Tensors representing two uniform crossing fibers Assessment of the fractional anisotropy along the tracts HARDI35-MFM Quantitative analysis CUSP35-MFM The FA of two uniform crossing fibers is uniform with CUSP-MFM

  21. Evaluation – real data HARDI35-MFM CUSP35-MFM CUSP-MFM: Better tensor uniformity (regions 1, 2, 3) vs HARDI-MFM Better alignment of the two tensors when single fiber (4) HARDI35-FSL CUSP35-FSL FSL: Not enough data to estimate correctly the ball-and-stick model?

  22. Evaluation – real data • Preliminary results MFM tractography HARDI45-1T CUSP45-MFM HARDI45-1T CUSP45-MFM Corticospinal tracts Arcuate fasciculus CUSP-MFM tracts better represent expected connectivity

  23. Discussion CUSP-MFM • 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 Evaluation Focus on very short duration acquisitions, compatible with routine clinical practice CUSP-MFM enables to perform both tractography and individual fiber bundles’ characteristics assessment.

  24. Discussion Future works • Investigation of the optimal CUSP • Finer discretization of the cube edges? • Optimal nominal b-value? • Model selection • Number of fibers at each voxel? • Full evaluation on real data: comparison with other approaches • Q-Ball imaging, Spherical deconvolution, …

  25. Thank you for your attention, CUSP-MFM

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