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Diffusion

Status: ✅ released. The core effect — water molecules diffusing, and the gradient waveform G(t) encoding their displacement into signal attenuation.

Forward (dmipy-sim)

Spins random-walk through the geometry and accumulate phase φ = γ∫G·r dt; the ensemble signal is S/S₀ = ⟨cos φ⟩, from first principles. Restriction, hindrance and free diffusion all emerge from the same walk — the walls the walker meets are the only difference.

  • Free / hindered / restricted in FreeDiffusion, Box1D, Sphere, Cylinder, Ellipsoid, packed ensembles, myelinated cylinders, and arbitrary meshes.
  • Arbitrary encoding — PGSE, OGSE, b-tensor (LTE/PTE/STE) and free G(t); see Acquisition sequences.

See the forward-engine overview.

Inverse (dmipy-fit)

Each compartment contributes an analytical attenuation E_diff(b) (or the b-tensor generalisation), combined in a MultiCompartmentModel and fit on the GPU. Orientation dispersion (Watson / Bingham), diameter distributions, CSD and the named literature models (NODDI, SMT, NEXI, VERDICT, SANDI, …) are all built on this — see the inverse overview and the Model catalog.

Validated against

Free/box/sphere/cylinder/ellipsoid diffusion vs analytical and MISST reference signals, and the extra-axonal tortuosity scale sweep — see the sim repo's examples/validation/ and the canonical-WM parity example.