Physics effects

One MRI signal carries many physical effects at once — diffusion, relaxation, exchange, susceptibility. dmipy's mission is to put them on the same footing: every effect read out of the same substrate, each simulated forward in dmipy-sim and inverted analytically in dmipy-fit. This page is the map of that programme — what's released, and what's next.

Effect	Status	Forward (sim)	Inverse (fit)
Diffusion	✅ Released	restricted / hindered / free random walk	E_diff(b) per compartment
Permeability & exchange	✅ Released	Powles membrane crossing	Kärger / NEXI
Surface relaxivity & relaxation	✅ Released	Brownstein–Tarr wall loss + T2	occupancy-gated T2 / ρ factors
Susceptibility	✅ Released	off-resonance field on the walk — iron spheres / myelin hollow-cylinder / voxel grid	\(R_2'\) transverse term
Magnetization transfer	✅ Released	emergent wall sticking + short-\(T_2\) bound pool	Z-spectrum (two-pool)

Every released effect ships with a first-principles validation ladder and a matched analytical inverse, so a number that comes out of a fit can be traced to the wall collisions that produced it. The surface-relaxivity study is the worked example of why this matters — two effects (diffusion and relaxation) reading the same wall, and the bias that follows when a model accounts for only one.

The orthogonal axis: coherence gating

The effects above are what the signal loses. Coherence gating is a meta-effect that sets when each acts. The transverse wall/field channels collapse into one apparent rate \(1/T_2^{\mathrm{app}} = 1/T_2 + \rho_2\,S/V + R_2' + k_f\), their longitudinal siblings into another \(1/T_1^{\mathrm{app}} = 1/T_1 + \rho_1\,S/V + k_{\mathrm{MT}}^{\parallel}\), and the coherence state \(\chi_\perp\) selects between them — the transverse bundle acts only while transverse, the longitudinal bundle only while stored, and diffusion and permeability/exchange act in both. A stimulated echo (PGSTE) parks the magnetization along \(z\) for a mixing time to pause the whole \(T_2^{\mathrm{app}}\) bundle while exchange keeps running — the lever dmipy uses to separate effects a spin echo sees only in combination, most directly surface relaxivity from permeability.