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Week 06: Diffusion Tensor Imaging (DTI)

While functional MRI maps the brain's cortical processors, Diffusion Tensor Imaging maps the structural wiring connecting them. This week covers Brownian motion, Stejskal-Tanner diffusion weighting gradients, the diffusion tensor ellipsoid, Fractional Anisotropy (FA), Mean Diffusivity (MD), and tractography.

Interactive Demos & Activities

• DTI Tensor & Tractography Explorer

  Primary Week Simulator · Tensor Fitting, Streamlines & the Crossing-Fiber Problem

  Shape the diffusion tensor by its eigenvalues and watch the six Stejskal-Tanner gradient measurements it would produce, then seed deterministic streamlines into a synthetic corpus-callosum / corticospinal crossing. Tune the FA stopping threshold, turning-angle limit, step size, and Euler vs. Runge-Kutta integration to see tracts terminate at the intersection, and to see them jump bundles and fabricate a connection when the angle limit is relaxed.

• Interactive Fractional Anisotropy (FA) Simulator

  Real-Time Tensor Simulation · Brownian Motion

  Adjust the FA slider from 0.0 to 0.95+ to observe how water diffusion transitions from an isotropic sphere (free fluid in CSF) to a highly constrained ellipsoid parallel to densely packed, myelinated axonal fiber bundles.

• 129Xe Microstructural Diffusion Primer

  Restricted Diffusion Physics · ADC Mapping

  Explore how restricted Brownian motion is quantified using Apparent Diffusion Coefficient (ADC) mapping to probe microscopic anatomical barriers.

Topics Covered

• Brownian Motion & Restricted Diffusion: Einstein's diffusion equation, isotropic diffusion in CSF, and anisotropic restriction by axonal membranes and myelin sheaths.
• The Diffusion Tensor Matrix: Applying diffusion gradients across $\ge 6$ non-collinear directions to calculate the $3 \times 3$ symmetric diffusion tensor and its principal eigenvalues ($\lambda_1, \lambda_2, \lambda_3$).
• Tractography & Structural Connectomics: Deterministic streamline algorithms (Euler/Runge-Kutta), probabilistic tractography, fiber crossing limitations, and whole-brain structural connectivity graphs.