Permeability & exchange

Status: ✅ released. Membranes are not perfect walls — water crosses them, and that exchange between compartments leaves a measurable, time-dependent signature.

Forward (dmipy-sim)

permeability=κ (m/s) on any closed geometry adds a Powles (2004) bidirectional crossing: at each wall collision the walker transmits with probability p = min(1, 2κ·d⊥/D), otherwise reflects. It is baked into the walk (one walk per κ) and works on spheres, cylinders, packed ensembles, myelin (dual-wall) and meshes. The generalized Kärger derivation connects the microscopic crossing rule to the macroscopic exchange time.

Inverse (dmipy-fit)

Exchange is fit with a generalized Kärger model (X0GeneralizedKarger, wrapping any two compartments); NEXI is the stick + zeppelin + tortuosity special case (reference_models.nexi()), analytical and on the GPU — see the Model catalog.

Why it's entangled with relaxation

Permeability and surface relaxivity are two readouts of the same wall. A model that fits exchange while ignoring the surface-relaxivity weighting between compartments can misread the exchange clock — the surface-relaxivity study and the preprint quantify this coupling on the intra-axonal fraction and the myelin water fraction.

Validated against

First-principles 1D→2D→3D permeability ladders against exact eigenvalues (the sim repo's slow-marked tests/validation/).