Diffusion Tensor Imaging I. Jennifer Campbell

Diffusion Tensor Imaging I Jennifer Campbell

Diffusion Imaging Molecular diffusion The diffusion tensor Diffusion weighting in MRI Alternatives to the tensor Overview of applications

Diffusion MRI measures Brownian motion of water molecules Path of diffusing water molecule Water displacement distribution

Diffusion MRI measures Brownian motion of water molecules P(r r 0,! d) = 1 $ (r # r 0) T D #1 (r # r 0) ' exp 3 D(4"! d) % & 4! d ( ) ;< r 2 >= 6D! d

Diffusion MRI measures Brownian motion of water molecules Hindered diffusion: Apparent Diffusion Coefficient (ADC)

Diffusion MRI measures Brownian motion of water molecules P(r r 0,! d) = 1 % (r $ r 0) T (ADC) $1 (r $ r 0) ( exp 3 ADC"(4#! d) & ' 4! d ) *

Tissue structures determine which directions of motion are most probable White matter fibre bundle: oriented structure Water molecules prefer to travel parallel to fibre direction

Diffusion MRI Tractography

Tissue structures determine which directions of motion are most probable P(r r 0,! d) = 1 $ (r # r 0) T D #1 (r # r 0) ' exp 3 D (4"! d) % & 4! d ( )

Diffusion Imaging Molecular diffusion The diffusion tensor Diffusion weighting in MRI Alternatives to the tensor Overview of applications

The diffusion tensor! # # # " Dxx Dxy Dxz Dyx Dyy Dyz Dzx Dzy Dzz $ & & & % P(r r 0,! d) = 1 $ (r # r 0) T D #1 (r # r 0) ' exp 3 D (4"! d) % & 4! d ( )

The diffusion tensor "! 1 0 0 % $ $ $ 0! 2 0 0 0! 3 ' ' ' λ 1 λ 3 λ 2 e 1 # & P(r r 0,! d) = 1 $ (r # r 0) T D #1 (r # r 0) ' exp 3 D (4"! d) % & 4! d ( )

The diffusion tensor "! 1 0 0 % $ $ 0! 2 0 ' ' λ 1 λ 3 λ 2 e 1 $ 0 0! 3 ' # &

Measuring the diffusion tensor: diffusion weighted images (DWIs)

Computing the diffusion tensor b value describes the extent of diffusion weighting in the MRI sequence S(b) = Soe!bD b matrix used in 3D tensor calculation S(b) S(b) = Soexp(! " " b ij D ij ) 3 i=1 3 j=1 b

Computing the diffusion tensor b value describes the extent of diffusion weighting in the MRI sequence S(b) = Soe!bD b matrix used in 3D tensor calculation log(s(b)) S(b) = Soexp(! " " b ij D ij ) 3 i=1 3 j=1 b

Computing the diffusion tensor λ 1 λ 3 λ 2 e 1

Maps obtainable from diffusion tensor FA = 3 2 FA: anisotropy index (!1 "!) 2 + (! 2 "!) 2 + (! 3 "!) 2 (!1 2 +! 3 2 +! 3 2 ) trace of diffusion tensor MD =! = trace / 3 =!1 +! 2 +! 3 3 RGB plot: principal eigenvector (e 1 ) direction, scaled by FA

Diffusion tensor imaging (DTI) λ 1 λ 2 λ 3 cylindrical symmetry

Diffusion tensor imaging (DTI) λ, axial λ, radial T cylindrical symmetry

Diffusion tensor imaging (DTI) normal white matter

Diffusion tensor imaging (DTI) myelin degeneration: radial diffusivity increases FA decreases

Diffusion tensor imaging (DTI) normal white matter

Diffusion tensor imaging (DTI) axonal fragmentation: axial diffusivity decreases FA decreases

Diffusion tensor imaging (DTI) normal white matter

Diffusion tensor imaging (DTI) decreased axon density: radial diffusivity increases FA decreases

Diffusion tensor imaging (DTI) crossing fibres: FA lower than for single direction

Diffusion tensor imaging (DTI) degeneration of one fibre population in crossing case: FA increases

Diffusion tensor imaging (DTI) curvature: FA lower than for single direction

Diffusion tensor imaging (DTI) splay: FA lower than for single direction

Diffusion tensor imaging (DTI) normal tissue

Diffusion tensor imaging (DTI) cellular swelling: MD decreases

Diffusion Imaging Molecular diffusion The diffusion tensor Diffusion weighting in MRI Alternatives to the tensor Overview of applications

Diffusion weighted MR sequence TE S(b) = Soe!bD 90 180 echo b = t! k(t) 2 dt ; k(t) = " G(t ')dt ' 0 t! 0 G G b =! 2 G 2 " 2 (# $ " / 3) δ Δ Δ Stejskal-Tanner diffusion weighted sequence: pulsed-gradient spin-echo (PGSE)

Gradients, phase, and motion 180 echo G G B 0 + G B 0, B180 o 0 B 0 + G B 0

Gradients, phase, and motion 180 echo G G B 0 + G B 0, 180 o B 0 + G B 0 B 0

Acquisition parameters for diffusion weighted images (DWIs) series of DWIs: 3-6-30-60-100+ encoding directions full brain coverage: 15-20 minutes per 100 directions b value: 1000-3000 s/mm 2 ; b~1000 s/mm 2 best for tensor voxel size: roughly 2mm x 2mm x 2mm isotropic voxels typically used adjust for population being studied, e.g. infants, patients

Sequence modifications: isotropic diffusion weighting RF 90 180 Gx G G Gy G G Gz G G

Sequence design and artifacts diffusion MRI acquisitions generally use fast imaging techniques, e.g., single-shot EPI: reduce sensitivity to motion reduce acquisition time these sequences are prone to artifacts such as magnetic susceptibility induced distortion these artifacts confound registration with standard structural scans and make investigation of diffusion parameters difficult

Sequence design and artifacts to improve spatial resolution and reduce distortion, multi-shot imaging possible, but must use navigator echo to avoid phase errors can use other types of sequences, e.g., STEAM, SSFP,

Sequence design and artifacts Heidemann et al. 2010. single-shot EPI readout segmented EPI readout

Eddy-current induced distortion eddy currents are induced by the rapidly changing magnetic field gradients required for diffusion sensitization these eddy currents induce magnetic fields which distort the image. artifacts: shifting, sheering, stretching, compression, signal loss

Eddy-current induced distortion without correction/ compensation, can have image shifts up to, e.g., 5mm affine registration can correct for some, but not all, of this artifact problem largely alleviated with twice refocused balanced echo (TRBE) sequence

Eddy-current induced distortion TE TE 90 180 echo 90 180 180 echo G G G G G G δ Δ δ Δ Δ Twice refocused balanced echo (TRBE)

Signal to noise ratio (SNR); spatial resolution (b=1000 s/mm 2 ) (b=3000 s/mm 2 )

Signal to noise ratio (SNR); spatial resolution near noise floor, FA and trace are decreased. however, note that in regions of isotropic diffusion, noise increases FA tradeoff between SNR, spatial resolution, achievable b value Jones and Basser 2004.

Signal to noise ratio (SNR); spatial resolution Higher field strength (7T) Heidemann et al. 2010.

Diffusion Imaging Molecular diffusion The diffusion tensor Diffusion weighting in MRI Alternatives to the tensor Overview of applications

Diffusion weighted signal profile Diffusion weighted signal intensity: high value in directions perpendicular to fibres (lower diffusivity)

Probability of water displacement orientation distribution function (ODF) Diffusion tensor model

High Angular Resolution Diffusion Imaging (HARDI) q-ball imaging

High Angular Resolution Diffusion Imaging (HARDI) QBI DTI

Why use high angular resolution diffusion MRI? Reduce false positive and false negative tractography results due to crossings In voxels where fibres cross, single fibre approaches can yield: ambiguous fibre direction incorrect fibre direction only one fibre direction (that of fascicle with largest volume fraction) Examples of such regions: basis pontis, subcortical white matter, superior longitudinal fasciculus, acoustic radiations, projection from subgenual white matter to amygdala, optic chiasm, caudate nucleus, corpus callosum, cortical spinal tract, cingulate bundle.

Crossing fibre reconstruction approaches multi-tensor approaches (Alexander et al., Parker et al., others) Mixture models (Gaussian (Tuch et al.); Wishart (Jian et al.)) ball and multi-stick (Behrens et al.) Composite hindered and restricted model of diffusion (CHARMED) (Assaf et al.) diffusion spectrum imaging (DSI) (Wedeen et al.) q-ball imaging (QBI) (Tuch et al.) spherical deconvolution (Tournier et al., Anderson, others) other variants

Multi-tensor model Tuch et al. 2002 Hosey et al. 2008

Behrens ball and stick model Behrens et al. 2007

q-space analysis of diffusion MRI data the diffusion displacement distribution is the Fourier transform of the diffusion signal as a function of q, where q =! G"

Diffusion Spectrum Imaging (DSI) 3D diffusion pdf 2D diffusion Orientation Distribution Function (ODF) Wedeen et al. ; Canales-Rodrigue et al.

q-ball imaging direct calculation of the 2D diffusion ODF calculation uses Funk- Radon transform Tuch et al. MRM 2004

Crossing fibre detection: QBI vs. Deconvolution Diffusion ODF Deconvolved ODF

Composite hindered and restricted model of diffusion (CHARMED) hindered restricted

Composite hindered and restricted model of diffusion (CHARMED) restricted pool fraction F fractional anisotropy FA

Inferring higher angular resolution from limited datasets DTI QBI regularized DTI Curve Inference using neighbourhood information

Beyond crossing: other complex subvoxel geometries Curve Inference to distinguish fanning from bending fibres Savadjiev et al. NeuroImage 2008. subvoxel fanning of fibres Campbell et al. ISMRM 2011.

Effect of complex subvoxel geometry on simple scalar measures FA lower when there are multiple subvoxel orientations trace lower when there are multiple subvoxel orientations (Vos et al. ISMRM 2011) The way multiple populations share one voxel affects the signal profile, and hence, mean diffusivity and kurtosis Peled et al. ISMRM 2011.

Fibre directions and uncertainty

Fibre directions and uncertainty bootstrap analysis using tensors calculated from subsets of data cones of uncertainty subtending 95% confidence intervals Jones et al.

Fibre directions and uncertainty

Residual bootstrap deconvolution 1. fit diffusion weighted signal profile to spherical harmonic basis 2. perform N iterations of residual bootstrap 2 generation of synthetic signal profiles 3.calculate fibre orientation distribution function using spherical deconvolution for all iterations. 1 Savadjiev et al., 2008 2 Jones et al., 2003; Berman et al., 2008; Jeurisson et al., 2010; Haroon et al., 2007

Assignment of confidence that a fibre exists in a given direction 4. calculate mean orientation and uncertainty for the fibres single fibre double crossing triple crossing Campbell et al. ISMRM 2011

Fibre directions and uncertainty Behrens et al. 2007 Bayesian inference on marginal distribution of diffusion parameters performed in MCMC framework Hosey et al. 2008

Diffusion Imaging Molecular diffusion The diffusion tensor Diffusion weighting in MRI Alternatives to the tensor Overview of applications

Example: Stroke Moseley (1990): ADC decreases in ischemia. Causes: cell membrane permeability decreases lead to cellular swelling Early diagnosis: diffusion MRI can identify regions of ischemia within 30 minutes of arterial occlusion, while T 2 images show changes only after 2 hours Chronic stroke can also cause Wallerian degeneration, leading to reduced FA

Example: Multiple Sclerosis T 2 Image FA Image Reduced FA values suggest a possible breakdown in the structural integrity of axons passing through there

Example: Multiple Sclerosis FA decrease in NAWM: significant correlation with NA/Cr value (a measure of axonal integrity): r 2 =0.53, p=0.02 insignificant correlation with lateralization index in fmri finger tapping task (a measure of cerebro-functional compensation): r 2 =0.35, p=0.07 insignificant correlation with EDSS ( a measure of clinical disability): r 2 =0.38, p=0.06 Caramanos et al, ISMRM 2002

Tract-based spatial statistics (TBSS) project highest FA value in region ( centre of tract ) onto average FA skeleton reduces problems associated with, e.g., partial volume averaging, misalignment Interpretation may be difficult in the presence of pathology Smith et al., NIMG 2006

See Diffusion Tensor Imaging II for more applications