Skip to content

Biophysical constants

Every physical constant in the substrate is defined once, with a cited source. The catalogue lives in dmipy_sim.substrate.biophysical_constants (the forward-truth engine owns the ground truth) and dmipy-fit re-exports it verbatim as dmipy_fit.audit.biophysical_constants, so there is exactly one value — and one reference — for each. Read them through the accessor, never hard-code:

from dmipy_sim.substrate import biophysical_constants as bc
bc.get_value('D_intra_axonal')      # 1.7e-9  (m^2/s)
bc.get_constant('D_intra_axonal')   # full record: value, unit, citation, note

Every value below links to its source paper.

Diffusivities

Constant Default Description Reference
D_csf 3e-09 m^2/s CSF diffusivity at body temperature Pierpaoli 1996
D_extra_axonal 1.2e-09 m^2/s Extra-axonal hindered diffusivity (typical WM) Fieremans 2011
D_extra_axonal_intrinsic 1.7e-09 m^2/s Intrinsic (pre-tortuosity) extra-axonal diffusivity used by the Monte Carlo substrate, where the apparent perpendicular reduction emerges from the explicit packed geometry. Beaulieu 2002
D_intra_axonal 1.7e-09 m^2/s In vivo intra-axonal parallel diffusivity Beaulieu 2002
D_water_25C 2.299e-09 m^2/s Free water self-diffusion coefficient at 25 deg C (lab temperature) Mills 1973
D_water_37C 3.05e-09 m^2/s Free water self-diffusion coefficient at 37 deg C (in vivo body temperature) Mills 1973

Relaxation times

Constant Default Description Reference
T2_csf 2 s T2 relaxation time of CSF Piechnik 2009
T2_extra_axonal 0.08 s T2 relaxation time of extra-axonal water MacKay 1994
T2_intra_axonal 0.07 s T2 relaxation time of intra-axonal water MacKay 1994
T2_myelin 0.015 s T2 relaxation time of myelin water MacKay 1994

Microstructure & geometry

Constant Default Description Reference
axon_radius_mean 3.05e-07 m Mean axon radius in human corpus callosum Aboitiz 1992
axon_radius_std 2.15e-07 m Standard deviation of axon radius in corpus callosum Aboitiz 1992
g_ratio_corpus_callosum 0.7 dimensionless (inner/outer radius) Mean g-ratio (inner axon radius / outer myelin radius) in human corpus callosum. Relatively conserved across WM tracts in healthy adults (range ~0.65–0.75). Used as canonical value in the hollow-cylinder susceptibility model: Δχ_a·(1−g²) determines the dipolar field amplitude. Stikov 2015
g_ratio_typical 0.7 Typical g-ratio (inner/outer myelin radius) in WM Stikov 2015
gamma_scale_diameter 3.04e-07 m (Gamma scale over diameter) Gamma scale parameter (diameter) of the canonical axon-diameter distribution. Aboitiz 1992
gamma_shape_diameter 2 dimensionless (Gamma shape α over diameter) Gamma shape parameter of the axon-diameter distribution used in the canonical packed-cylinder white-matter substrate. Aboitiz 1992
myelin_water_fraction 0.15 Typical myelin water fraction in normal-appearing WM. CAUTION: values differ by method (~10% STAIR, ~10-15% MESE/GRASE at 3T) and by region (CST ~0.21 vs CC genu ~0.09-0.15). mcDESPOT yields ~2x higher values than MESE (known positive bias). MacKay 1994

Membrane & surface

Constant Default Description Reference
kappa_membrane 1e-05 m/s Axonal membrane permeability Nilsson 2013
rho2_axon_membrane 1.16e-06 m/s T2 surface relaxivity of the axon membrane (axolemma). Use paired with corrected T2_bulk_intra, not T2_apparent. Barakovic 2023

Physical constants

Constant Default Description Reference
gamma_proton 2.675e+08 rad/s/T Proton gyromagnetic ratio CODATA 2021