DiffusionsTensorModell

The DiffusionsTensorModell, known in English as the diffusion tensor model, is a mathematical framework used in diffusion magnetic resonance imaging (dMRI) to describe the diffusion of water molecules in tissue. The diffusion process is modeled by a symmetric positive definite 3×3 tensor D, so that the diffusion-weighted signal for a gradient direction g with b-value b is S(b,g) = S0 exp(-b g^T D g). The tensor has six independent components, which are estimated from measurements acquired with multiple diffusion-encoding directions.

From the diffusion tensor, scalar indices such as fractional anisotropy (FA) and mean diffusivity (MD) quantify diffusion properties, while axial diffusivity and radial diffusivity describe diffusion along the principal fiber direction and perpendicular to it. These metrics are used to infer white matter architecture, detect microstructural changes, and assist in tractography to map white matter tracts in the brain.

Acquisition and limitations: Diffusion tensor imaging (DTI) typically uses diffusion-weighted MRI with several gradient directions and at least one or more diffusion weightings. Data are preprocessed to correct for motion and eddy currents. The model assumes Gaussian diffusion and a single dominant fiber orientation per voxel, which limits accuracy in regions with crossing fibers or complex microstructure. Noise, partial volume effects, and low angular resolution can bias estimates. Extensions beyond the simple diffusion tensor model, such as diffusion kurtosis imaging and high-angular-resolution diffusion methods (e.g., q-ball imaging, diffusion spectrum imaging), address these limitations.

History: The diffusion tensor model emerged in the 1990s through work by P. J. Basser and colleagues and has since become a standard tool in neuroscience and clinical research.