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Diffusion model fitting and tractography: A primer

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Diffusion model fitting and tractography: A primer. Anastasia Yendiki HMS/MGH/MIT Athinoula A. Martinos Center for Biomedical Imaging. White-matter imaging. Axons measure ~ m in width They group together in bundles that traverse the white matter - PowerPoint PPT Presentation

Text of Diffusion model fitting and tractography: A primer

  • Diffusion model fitting and tractography: A primerAnastasia Yendiki

    HMS/MGH/MIT Athinoula A. Martinos Center for Biomedical Imaging

  • White-matter imagingAxons measure ~m in widthThey group together in bundles that traverse the white matter

    We cannot image individual axons but we can image bundles with diffusion MRIUseful in studying neurodegenerative diseases, stroke, aging, developmentFrom Gray's Anatomy: IX. NeurologyFrom the National Institute on Aging

  • Diffusion in brain tissueDifferentiate tissues based on the diffusion (random motion) of water molecules within them

    Gray matter: Diffusion is unrestricted isotropic

    White matter: Diffusion is restricted anisotropic

  • How to describe diffusionAt every voxel we want to know:Is this in white matter?If yes, what pathway(s) is it part of?What is the orientation of diffusion?What is the magnitude of diffusion?A grayscale image cannot capture all this!

  • Diffusion MRIMagnetic resonance imaging can provide diffusion encoding

    Magnetic field strength is varied by gradients in different directions

    Image intensity is attenuated depending on water diffusion in each direction

    Compare with baseline images to infer on diffusion processNo diffusion encodingDiffusion encoding in direction g1g2g3g4g5g6

  • Need to know: Gradient directionsTrue diffusion direction || Applied gradient direction Maximum attenuation

    True diffusion direction Applied gradient direction No attenuation

    To capture all diffusion directions well, gradient directions should cover 3D space uniformlyDiffusion-encoding gradient gDiffusion detectedDiffusion-encoding gradient gDiffusion not detectedDiffusion-encoding gradient gDiffusion partly detected

  • How many directions?Acquiring data with more gradient directions leads to:More reliable estimation of diffusion measuresIncreased imaging time Subject discomfort, more susceptible to artifacts due to motion, respiration, etc.

    DTI:Six directions is the minimumUsually a few 10s of directionsDiminishing returns after a certain number [Jones, 2004]HARDI/DSI:Usually a few 100s of directions

  • Need to know: b-valueThe b-value depends on acquisition parameters:b = 2 G2 2 ( - /3) the gyromagnetic ratioG the strength of the diffusion-encoding gradient the duration of each diffusion-encoding pulse the interval b/w diffusion-encoding pulses90180acquisitionG

  • How high b-value?Increasing the b-value leads to:Increased contrast b/w areas of higher and lower diffusivity in principleDecreased signal-to-noise ratio Less reliable estimation of diffusion measures in practice

    DTI: b ~ 1000 sec/mm2HARDI/DSI: b ~ 10,000 sec/mm2

    Data can be acquired at multiple b-values for trade-offRepeat acquisition and average to increase signal-to-noise ratio

  • Looking at the dataA diffusion data set consists of:A set of non-diffusion-weighted a.k.a baseline a.k.a. low-b images (b-value = 0)A set of diffusion-weighted (DW) images acquired with different gradient directions g1, g2, and b-value >0The diffusion-weighted images have lower intensity valuesBaselineimageDiffusion-weightedimagesb2, g2b3, g3b1, g1b=0b4, g4b5, g5b6, g6

  • Data analysis stepsPre-process imagesFSL: eddy_correct, rotate_bvecs

    Fit a diffusion model at every voxelDTK: DSI, Q-ball, or DTIFSL: Ball-and-stick (bedpost) or DTI (dtifit)

    Compute measures of anisotropy/diffusivity and compare them between populationsVoxel-based, ROI-based, or tract-based statistical analysis

    For tract-based: Reconstruct pathwaysDTK: Deterministic tractography using DSI, Q-ball, or DTI modelFSL: Probabilistic tractography (probtrack) using ball-and-stick modelDTK: www.trackvis.org, FSL: www.fmrib.ox.ac.uk/fsl

  • Models of diffusion

    ModelSoftwareDiffusion spectrum:Full distribution of orientation and magnitudeDTK (DSI option)Orientation distribution function (ODF):No magnitude infoDTK (Q-ball option)Ball-and-stick:Orientation and magnitude for up to N anisotropic compartments (default N=2)FSL (bedpost)Tensor:Single orientation and magnitudeDTK (DTI option)FSL (dtifit)

  • A bit more about the tensorA tensor can be thought of as an ellipsoid

    It can be defined fully by:3 eigenvectors e1, e2, e3 (orientations of ellipsoid axes)3 eigenvalues 1 , 2, 3 (lengths of ellipsoid axes)1 e12 e23 e3

  • Tensor: Physical interpretationEigenvectors express diffusion directionEigenvalues express diffusion magnitude1 e12 e23 e31 e12 e23 e3Isotropic diffusion:1 2 3Anisotropic diffusion:1 >> 2 3

  • Tensor: Summary measures Mean diffusivity (MD): Mean of the 3 eigenvalues Fractional anisotropy (FA): Variance of the 3 eigenvalues, normalized so that 0 (FA) 1FasterdiffusionSlowerdiffusionAnisotropicdiffusionIsotropicdiffusionMD(j) = [1(j)+2(j)+3(j)]/3[1(j)-MD(j)]2 + [2(j)-MD(j)]2 + [3(j)-MD(j)]2FA(j)2 =1(j)2 + 2(j)2 + 3(j)232

  • Tensor: More summary measuresAxial diffusivity: Greatest eigenvalue

    Radial diffusivity: Average of 2 lesser eigenvalues

    Inter-voxel coherence: Average angle b/w the major eigenvector at some voxel and the major eigenvector at the voxels around itAD(j) = 1(j)RD(j) = [2(j) + 3(j)]/2

  • Tensor: VisualizationDirection of eigenvector corresponding to greatest eigenvalueImage: An intensity value at each voxelTensor map: A tensor at each voxel

  • Tensor: VisualizationImage: An intensity value at each voxelTensor map: A tensor at each voxelDirection of eigenvector corresponding to greatest eigenvalueRed: L-R, Green: A-P, Blue: I-S

  • TractographyUse local diffusion orientation at each voxel to determine pathway between distant brain regions

    Local orientation comes from diffusion model fit (tensor, ball-and-stick, etc.)Deterministic vs. probabilistic tractography: Deterministic assumes a single orientation at each voxelProbabilistic assumes a distribution of orientations

    Local vs. global tractography: Local fits the pathway to the data one step at a timeGlobal fits the entire pathway at once

  • Deterministic vs. probabilisticDeterministic methods give you an estimate of model parametersProbabilistic methods give you the uncertainty (probability distribution) of the estimate

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  • Deterministic vs. probabilisticDeterministic tractography:One streamline per seed voxelSample 1Sample 2Probabilistic tractography:Multiple streamline samples per seed voxel (drawn from probability distribution)

  • Deterministic vs. probabilisticProbabilistic tractography:A probability distribution (sum of all streamline samples from all seed voxels)Deterministic tractography:One streamline per seed voxel

  • Local vs. globalGlobal tractography: Fits the entire pathway, using diffusion orientation at all voxels along pathway lengthLocal tractography: Fits pathway step-by-step, using local diffusion orientation at each step

  • Local tractography

    Results are not symmetric between seed and target regionsSensitive to areas of high local uncertainty in orientation (e.g., pathaway crossings), errors propagate from those areasBest suited for exploratory study of connections

    All connections from a seed region, not constrained to a specific target regionHow do we isolate a specific white-matter pathway? Thresholding?Intermediate masks?Non-dominant connections are hard to reconstruct

  • Global tractographyBest suited for reconstruction of known white-matter pathways

    Constrained to connection of two specific end regionsNot sensitive to areas of high local uncertainty in orientation, integrates over entire pathwaySymmetric between seed and target regionsNeed to search through a large solution space of all possible connections between two regions:Computationally expensiveSensitive to initialization

  • TRACULATRActs Constrained by UnderLying Anatomy

    Automatic reconstruction of probabilistic distributions of 18 major white-matter pathwaysNo manual labeling of ROIs needed Use prior information on pathway anatomy from training data:Manually labeled pathways in training subjectsFreeSurfer segmentations of same subjectsLearn neighboring anatomical labels along pathway

    Beta version available in FreeSurfer 5.1

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