Diffusion Tensor Imaging (DTI)

The fundamental physical principle exploited by DTI. In white matter, water diffuses faster parallel to axon bundles than perpendicular to them because intact cell membranes and myelin sheaths restrict movement. This directional dependence is called anisotropy. In contrast, isotropic diffusion occurs in cerebrospinal fluid, where water moves freely in all directions. DTI measures this difference to infer tissue microstructure.

A mathematical 3x3 matrix that models water diffusion in three dimensions. For each voxel, the tensor is calculated from measurements in at least six non-collinear gradient directions. The tensor is then diagonalized to extract its three eigenvalues (λ1, λ2, λ3) and their corresponding eigenvectors (ε1, ε2, ε3). The primary eigenvector (ε1) points in the direction of maximum diffusion, which aligns with the local fiber tract orientation.

The most widely used scalar metric derived from the tensor. FA quantifies the degree of diffusion directionality on a scale from 0 to 1.

• FA ≈ 0: Isotropic diffusion (e.g., CSF, gray matter).
• FA ≈ 1: Highly anisotropic diffusion (e.g., tightly packed white matter tracts like the corpus callosum). FA is highly sensitive to microstructural changes but not specific; decreases can indicate demyelination, axonal loss, or edema.

The average magnitude of water diffusion within a voxel, calculated as the mean of the three eigenvalues: (λ1 + λ2 + λ3) / 3. MD is directionally invariant and measures overall water mobility. Elevated MD typically indicates increased extracellular space due to tissue damage, such as vasogenic edema or chronic infarction, while restricted MD can be seen in acute stroke or highly cellular tumors.

A computational method for reconstructing white matter pathways in 3D by following the principal diffusion direction (ε1) from voxel to voxel. Deterministic tractography generates a single streamline per seed point, while probabilistic tractography accounts for uncertainty, generating a distribution of possible paths. The resulting streamlines model the structural connectome, enabling surgical planning and network analysis.

Eigenvalue-derived metrics that offer greater pathological specificity than FA alone.

• Axial Diffusivity (AD): Equal to λ1, the diffusivity parallel to the axon. Decreased AD is associated with axonal injury in mouse models.
• Radial Diffusivity (RD): The average of λ2 and λ3, the diffusivity perpendicular to the axon. Increased RD is strongly correlated with demyelination. These metrics help distinguish the underlying pathology of white matter damage.

A scalar value between 0 and 1 that quantifies the degree of directionality of water diffusion within a voxel.

• FA = 0: Isotropic diffusion (unrestricted, equal in all directions), typical in cerebrospinal fluid or gray matter.
• FA ≈ 1: Highly anisotropic diffusion (directionally constrained), typical in tightly packed white matter tracts like the corpus callosum.

FA maps are the most common summary metric derived from the diffusion tensor, serving as a sensitive but non-specific biomarker for white matter microstructural integrity. Decreased FA often indicates demyelination, axonal injury, or inflammation.

The rotationally invariant average of the three tensor eigenvalues (λ1, λ2, λ3), representing the overall magnitude of water diffusion within a voxel, independent of direction.

• Elevated MD: Indicates increased extracellular water, commonly observed in vasogenic edema, tissue necrosis, or atrophy.
• Reduced MD: Indicates cytotoxic edema, the hallmark of acute ischemic stroke where cellular swelling restricts diffusion.

MD is mathematically distinct from the Apparent Diffusion Coefficient (ADC), though the terms are often used interchangeably in clinical contexts when derived from a full tensor model.

The foundational MRI pulse sequence that sensitizes the signal to the random thermal motion of water molecules by applying strong magnetic field gradients.

• b-value: A key acquisition parameter (measured in s/mm²) that determines the strength and duration of diffusion weighting. Higher b-values (e.g., b=1000) increase sensitivity to slow-moving water but reduce the signal-to-noise ratio (SNR).
• b0 Image: An image acquired with b=0, providing a T2-weighted reference without diffusion weighting.

DTI requires DWI data acquired along at least 6 non-collinear gradient directions to mathematically fit the 3D diffusion tensor.

A mathematical 3x3 symmetric matrix that characterizes the magnitude and directionality of water diffusion in each voxel.

• Eigenvalues (λ1, λ2, λ3): Represent the magnitude of diffusion along the three orthogonal principal axes.
• Primary Eigenvector (ε1): The direction of maximum diffusion, assumed to align with the local fiber orientation.
• Tensor Shape Metrics: Linear anisotropy (Cl), planar anisotropy (Cp), and spherical anisotropy (Cs) describe whether diffusion is cigar-shaped, pancake-shaped, or spherical.

The tensor model is a Gaussian approximation and fails in voxels containing crossing, kissing, or fanning fibers, motivating higher-order models like High Angular Resolution Diffusion Imaging (HARDI).

An advanced acquisition and modeling framework that overcomes the crossing fiber limitation of DTI by sampling diffusion along dozens to hundreds of gradient directions at high b-values.

• Q-Ball Imaging: A model-free HARDI technique that computes the Orientation Distribution Function (ODF) using the Funk-Radon transform.
• Constrained Spherical Deconvolution (CSD): Estimates the fiber Orientation Distribution Function by deconvolving a measured signal with a response function for a single fiber population.

HARDI resolves complex fiber architectures like the crossing of the superior longitudinal fasciculus and corticospinal tract, providing more accurate tractography than DTI.