Diffusion-Weighted Imaging (DWI) is a variant of conventional Magnetic Resonance Imaging (MRI) based on the tissue water diffusion rate¹. Specifically, DWI refers to the acquired images, while Diffusion Tensor Imaging (DTI) refers to the tensor-based modeling of the DWI data.

To start, let’s quickly cover the imaging techniques. MRI is an non-invasive and versatile imaging techniques. The MRI scanner forms a strong oscillating magnetic field, at the specified resonance frequency. The receiving coil then collects the response signal from atoms excited by the pulses. Some commonly used scan modalities in brain imaging include:

• Structural MRI (T1w, T2w and PD): makes use of the fact that atoms in different tissues return to the equilibrium state with different speed after excitation, to provide anatomical contrasts
• Functional MRI (BOLD): measures changes in blood oxygen level, which reflect brain regional activations causing higher energy consumption
• Diffusion MRI (DWI and DTI): measures the rate of water diffusion which, through DTI modelling, can also be used to map white matter tracts

1. DWI

1.1. Basic Principles

In DWI, the strength of the MRI signal depends on the mean displacement of water molecules, where stronger signals indicate lower diffusion rates along the magnetic gradient field². The apparent diffusion coefficient (ADC) describes the diffusion rate of water within biological tissues.

Due to the random nature of Brownian motion, in the absence of structural restriction, water molecules diffuse in an isotropic manner (self-diffusion). This is also what happens inside most tissues, but with lower diffusion rates due to collision with large-scaled biological molecules (i.e. lower ADC). In contrast, in highly structured tissues like the white matter (WM), water movement is restricted by myelin sheaths of the axons, cell membranes and microfilament³. As a result, water diffusion is anisotropic, with higher diffusion rates along the axon (i.,e. higher ADC) but lower rates perpendicular to the axonal direction (i.e. lower ADC).

Isotropic diffusion and anisotropic diffusion⁴

1.2. Artifacts & Preprocessing

DWI tend to have low signal-to-noise ratio (SNR), low resolution, high susceptibility to motion artifacts, and high sensitivity to eddy current-induced distortions^1,2. As DWI is done through Echo Planar Imaging (EPI), it is also sensitive to EPI-related artifacts, e.g. field inhomogeneities. It was also reported that the vibration of the bed in the scanner could lead to small brain tissue movements (vibration artifact)¹.

For proper DTI analysis, the images should be acquired with sufficiently high b-values (strength of magnetic diffusion gradient, $1000-3000 s/mm^2$), spatial resolution ($1.5-2 mm$ isotropic for $3T$ images), field of view (FOV, $240 - 256mm$), acquisition matrix ($96\times96-128\times128)$, echo time (TE, $50-70ms$), and repetition time (TR, $8.5-12s$)^1,3. The number of diffusion directions can also affect the reliability of tensor calcuation, where a minimum of $30$ directions may be recommended for tractography². Finally, the signal-to-noise ratio (SNR) shoule ba at least $10:1$³.

With the appropriate raw data, preprocessing can then be done to reduce artifacts (and to exclude subjects/volumes/slices when the artifacts are uncorrectable). In general, the following steps should be considered^1,3:

1. Visual inspection of raw data for geometric distortions, signal dropouts, subtle system drifts, and missing slices. Automatic outlier detection methods may also be helpful.
2. File format conversion if necessary
3. Eddy current and motion correction, through affine and rigid body registration to the $b_0$ image 3.1. encoding vectors should be rotated in the same way as the image during registration to T1w 3.2. signal intensity should be modulated by the change in voxel volume
4. Skull stripping if necessary

Following these steps, tensors can be estimated. Visual inspection of tensor orientations and accounting for potential biases would be helpful.

1.2.1. HCP DWI preprocessing

The diffusion processing pipeline in HCP include the following steps:

1. Intensity normalization across runs
2. FSL topup for EPI distortion correction
3. FSL eddy for eddy current and motion correction
4. Gradient nonlinearity correction
5. Registration of mean $b_0$ image to T1w image (FSL flirt BBR + FreeSurfer bbregister)
6. Brain mask generated based on FreeSurfer segmentation

1.2.2. MRtrix3 DWI preprocessing

DWI preprocessing in MRtrix3 is done in two steps:

1. dwidenoise dwi.mif out.mif -noise noise.mif does noise level estimation and denoising
2. dwifslpreproc does eddy current and motion correction & susceptibility distortion correction using the FSL functions eddy, topup and applytopup

2. DTI Analysis

In the gray matter (GM) and cerebrospinal fluid (CSF), water movements are mostly isotropic (equally in all directions), while in the WM, water movements are anisotropic (differently in different directions), as water diffuses more rapidly along the axons than in other directions¹. Making use of this assumption, a 3x3 symmetric matrix (aka tensors) can be estimated at each voxel, usually through linear regression techniques, to model the diffusion process:

\[\bar{D} = \begin{bmatrix} D_{xx} & D_{xy} & D_{xz} \\ D_{xy} & D_{yy} & D_{yz} \\ D_{xz} & D_{yz} & D_{zz} \end{bmatrix} = E^T \begin{bmatrix}\lambda_1 & 0 & 0 \\ 0 & \lambda_2 & 0 \\ 0 & 0 & \lambda_3 \end{bmatrix}\]

Due to the symmetry, the tensor only really has a degree of freedome of 6. Minimally, a tensor can be determined with 6 encoding directions, while increasing the number of encoding directions can improve the accuracy of tensor estimation.

The tensors are difficult to visualise in their raw dimensionality. Hence, dimensionality reduction is generally necessary for visualisation purposes, resulting in 3-dimensional images of tractography. Alternatively, tensor glyphs may be employed for visualisation and quality control purposes, where tensors are represented in ellipsoides (or lines).

2.1. Diffusivity and Anisotrpy Features

Based on each tensor, eigenvalues ($\lambda_1$ or axial diffusivity, $\lambda_2$, $\lambda_3$) representing the magnitude of diffusion, and eigenvectors ($e_1$, $e_2$, $e_3$) representing the directions of maximal and minimal diffusion, can also be computed at each voxel. Several features of anisotropy or diffusivity can then be computed using the eigenvalues:

• Radial diffusivity $\lambda_\perp = \frac{\lambda_2 + \lambda_3}{2}$
• Mean diffusivity $MD = \frac{\lambda_1 + \lambda_2 + \lambda_3}{3} = \frac{tr(\Lambda)}{3}$
• Fractional anisotropy $FA = \sqrt\frac{3[(\lambda_1-\mathbb{E}[\lambda])^2 + (\lambda_2-\mathbb{E}[\lambda])^2 + (\lambda_3-\mathbb{E}[\lambda])^2]}{2(\lambda_1^2 + \lambda_2^2 + \lambda_3^2)}$

In particular, FA measures the relative degree of a anisotropy, ranging from 0 (isotropic) to 1 (anisotropic). FA values are scalar and hence do not reflect the directions of anisotropy, but colored FA maps can be plotted where color-coded direction information is provided by the eigenvectors. It should be noted that the directions derived from eigenvectors are still bidirectional, only indicating the axis of flow.

Scalar FA map and colored FA map⁴

The MD and FA values are commonly examined in relation to pathology. Typically, damaged tissues would have higher MD due to increased free diffusion and lower FA due to loss of coherence in the main preferred diffusion direction, but one should not assume that this is always the case¹. Lower FA can also be due to larger axon diameter, lower axon density, and/or thinner myelin sheaths². In studies of brain development, it has also been shown that MD decreases during childhood, adolescent, and into young adulthood, while FA increases⁵.

2.2. Voxel-based Analysis (VBA)

VBA compares diffusion maps in a voxel-wise manner across subjects in a standard space. While this allows direct correspondence to be drawn between voxel-wise features across subjects, the validity of the analysis relies on the accuracy of spatial normalisation (or registration) to the standard space. As DTI images are highly directional and topographical, it is preferrable to align the $b_0$ image to a T1 image and then to the standard template.

2.3. Tract-based Spatial Statistics (TBSS)

TBSS makes use of skeletonisation of group registered FA maps to detect group voxel-wise changes. The skeletonisation process aligns the local maxima of individual maps into a group map, thus allowing comparisons to be done with much fewer voxels. However, this assumes that the local maxima correspond to the same anatomical locations across subjects. Additional caution should be taken when investigating groups with more heterogeneous anatomy, such as children².

3. Tractography

WM tractography shows trajectories of fiber pathways (streamlines) in the 3-dimensional space, based on the eigenvectors of tensors. Essentially, tractography estimation assumes that the tangent to the fiber tract’s curve traced is always and everywhere parallel with the local peak in the orientation density function estimated from the data³.

Generation of tractography follows these steps:

1. Seeding: defintion of the seed regions of interest (ROIs), either manually or based on a-priori networks. Alternatively, seeding the whole-brain may be preferred for data-driven approaches.
2. Propagation: generation of fibers
   • Deterministic tractography: reconstructs one fiber per seed
   • Probabilistic tractography: generates probability maps showing the likelihood of each voxel being part of a fiber, as well as multiple fiber directions per seed
3. Termination of fiber tracking
   • conventional termination criteria¹:
     • minimum FA threshold ($0.1-0.3$ in adult, $0.1$ in infant)
     • turning angle threshold ($40-70\unicode{xB0}$)
   • additional biologically-relevant constraints⁶:
     • targeted tracking: selects streamlines using inclusion/exclusion regions based on prior anatomical knowledge (where such knowledge is available)
     • anatomically-constrained tractography (ACT):
       • fibers should reach at least the interface of GM and WM at both ends
       • fibers do not terminate either in the middle of WM or in CSF

The main difficulty in estimating tractography maps is the presence of multiple fibers along different directions in the same voxel, also referred to as crossing fibers^1,2. More sophisticated approaches involving, for instance, probability density functions instead of single tensors, may alleviate this issue.

3.1. Implementations

3.1.1. Anatomically-constrained tractography (ACT)

The following recommendations were given by the MRtrix3 team:

1. Distortion correction should be done with dwifslpreproc
2. T1w image may be registered to the diffusion image series with a rigid-body transform
3. A brain mask should be derived based on the anatomical image, and preferably dilated, for determining streamline termination criteria
4. Alternatively (and probably better), a tissue segmentation image can be obtained instead (e.g. using FSL FAST)
5. Run ACT with tckgen -act tissue_seg_image or tckgen -mask brain_mask

3.1.2. Tractography computation in FSL

First, probability density functions of diffusion parameters need to be estimated using the Bayesian Estimation of Diffusion Parameters Obtained using Sampling Techniques (BEDPOSTX). Essentially, bedpostx estimates the number of crossing fibers in each voxel. The output files from this tool can then be used for running probabilistic tractography.

Probabilistic tractography can then be done with probtrackx2, which iteratively attempts to build streamlines from seeds. A seed mask and a termination mask can be specified to define the starting and possible ending points for streamlines. A FA threshold can also be set as termination criteria.

3.2. White Matter Fiber Classification

WM fiber tracts can be divided into 3 types⁴:

1. Association fibers connects cortical areas within each hemisphere
   • e.g., cingulum, superior and inferior occipitofrontal fasiculi, uncinate fasiculus, superior and inferior longitudinal (arcuate and occipitotemporal) fasiculus
2. Projection fibers connects cortical areas with deep nuclei, brain stem, cerebellum, and spinal cord
   • e.g., corticospinal, corticobulbar, and corticopontine tracts, (internal capsule), and geniculocalcarine (optic radiations) tracts
3. Commissural fibers connects cortical areas across hemispheres
   • e.g., corpus callosum, anterior commissure

some WM fiber tracts ⁷

3.3. Structural Connectivity (SC)

Structural (or WM) connectivity aims at mapping long-range WM fiber connections between distinct GM areas⁶.

First, network nodes are typically defined based on a brain atlas. Here, issues may arise with inconsistencies between the brain atlas and the GM-WM interface (used for termination of fiber tracking) determined by segmentation on T1 images. The heuristic fix would be to assign streamline endpoints to the nearest voxel inside a parcel (if it is within a reasonable distance, e.g. $\approx 2mm$⁶). Alternatively, a surface-based approach may be preferable to ensure that streamline termination and brain parcellation are exactly compatible.

Then, connectivity between nodes can be estimated. There is no consensus on how connectivity should be measured. Some connectivity metrics include number of streamlines, probability of all streamlines, mean diffusivity along streamline paths. In addition, the streamline-to-node assignment has significant impact on the final connectome. A streamline could be assigned to only voxels at its endpoints, or all voxels it visited; the former may be considered more biologically meaninful if anatomically-constrained tractography has been used^6,8,9.

For FSL, SC matrix is estimated at the end of the probtrackx2 procedure. ROIs should be supplied as multiple mask files to generate a ROIxROI matrix. For MRtrix3, tck2connectome can be used to convert a tractogram into a SC matrix, based on a parcellation image. The labelconvert command can be used for converting parcellation images, where parcel indices do not actually increase monotonically from 1, into an image that MRtrix3 can use.

Many challenges are present in SC mapping. To list a few⁶:

1. The streamline count in a voxel does not represent the actual fiber density, and hence cannot serve as a valid biomarker of connectivity strength
2. Streamlines could be over-reconstructed in longer pathways, if seeding was done homogeneously throughout WM voxels
   • potentially avoided by seeding uniformly from the GM-WM interface
   • heuristically, it is also common to scale each streamline’s contribution to connectivity by its inverse length (but this will not help with point 3 below)
3. Streamlines could also be underestimated in longer pathways, due to the larger number of sampling points.

More recently, “tractogram filtering” and “microstructure-informed tractogram processing” techniques have been proposed, improving the biological relevance of the estimated tractograms. These methods potentially allow streamline counts to be a reasonable metric for connectivity.

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2. Koerte IK, Muehlmann M. 2014. Diffusion Tensor Imaing. In: Mulert C, Shenton M (eds), MRI in Psychiatry. https://doi.org/10.1007/978-3-642-54542-9_5 ↩ ↩² ↩³ ↩⁴ ↩⁵ ↩⁶

3. Jones DK, Knosche TR, Turner R. 2013. White matter integrity, fiber count, and other fallacies: The do’s and don’ts of diffusion MRI. NeuroImage. 73: 239-254. https://doi.org/10.1016/j.neuroimage.2012.06.081 ↩ ↩² ↩³ ↩⁴ ↩⁵

4. Jellison BJ, Field AS, Medow J, Lazar M, Salamat MS, Alexander AL. 2004. Diffusion tensor imaging of cerebral white matter: A pictorial review of physics, fiber tract anatomy, and tumor imaging patterns. American Journal of Neuroraiology. 25: 356-369. PMCID: PMC8158568 ↩ ↩² ↩³

5. Lebel C, Beaulieu C. 2011. Longitudinal development of human brain wiring continues from chidhood into adulthood. Journal of Neuroscience. 31: 10937-10947. https://doi.org/10.1523/JNEUROSCI.5302-10.2011 ↩

6. Yeh C-H, Jones, DK, Liang, X, Descoteaux M, Connely A. 2020. Mapping structural connectivity using diffusion MRI: Challenges and opportunities. Journal of Magnetic Resonance Imaging. 53: 1666-1682. https://doi.org/10.1002/jmri.27188 ↩ ↩² ↩³ ↩⁴ ↩⁵

7. Guevara Alvez PB. 2011. Inference of a human brain fiber bundle atlas from high angular resolution diffusion imaging. (Doctoral dissertation, Université Paris Sud-Paris XI) pdf on ResearchGate ↩

8. Yeh C-H, Smith RE, Dhollander T, Connelly A. 2017. Mesh-based anatomically-constrained tractography for effective tracking termination and structural connectome construction”. Proc. ISMRM. 58. pdf on ResearchGate ↩

9. St-Onge E, Daducci A, Girard G, Descoteaux M. 2018. Surface-enhanced tractography (SET). NeuroImage. 169: 524-539. https://doi.org/10.1016/j.neuroimage.2017.12.036 ↩