Datasets:

SubstrateCommons
/

winther-g6-axons

Twenty-nine real myelinated axons, segmented from synchrotron X-ray nano-holotomography of monkey corpus callosum, each walked once by a Monte-Carlo diffusion simulator and frozen so that any acquisition can be computed afterwards without re-simulating.

The morphology is not ours. It is the G6 configuration set of Winther et al. (2024), distributed by them under CC-BY-4.0. This dataset contributes the computation and a documented, self-certifying container. Meshes are used as published — full length, no cropping, smoothing or re-meshing.

Cross-sections of axon06 along its length, plus a 3-D view. Axon (inner) and myelin (outer) surfaces as published — the calibre and tortuosity vary along the fibre, which is the morphology under study. Generated by report_assets.fig_substrate.

What you can replay

A replay pack stores the walk, not a table of pre-computed signals, so the forward model is evaluated at read time:

you supply	exact?
any gradient waveform (PGSE, PGSTE, OGSE, CPMG, free-form)	yes, within the stored temporal band
B₀ magnitude and direction	yes — the susceptibility basis is geometry-only
isotropic and anisotropic myelin susceptibility	yes
surface relaxivity ρ	yes — boundary local time is stored (C2)
bulk T₂ / T₁ per compartment	yes (C1)

packs/axonNN.rpk         29 replay packs   (~71 MB each)
field/axonNN.field.rpk   29 susceptibility field companions, masked (14–36 MB each)
manifest.json            per-substrate metadata + SHA-256
figures/                 the figures on this page, and the scripts that make them

Total 2.54 GiB. The field companions are stored masked — an axon meanders, so a bounding box around it is ~92% empty, and only the voxels a walker can reach are kept (10.1× smaller, values identical at the stored voxels). The mask is derived from the companion itself, so no mesh is needed to use one.

Provenance and fidelity


diffusivity D₀	0.6 × 10⁻⁹ m²/s (ex vivo, source study)
echo time	36 ms
myelin χ_iso	+1.06 × 10⁻⁶ (source study); Δχ_a = 0 as the reference value
field grid	0.131 µm, partial-volume myelin mask, no k-space apodisation
walkers seeded	52,000 per axon at uniform density (intra + frozen myelin)
codec error	6.96e-04 – 1.09e-03 (median 8.76e-04)
Monte-Carlo floor	4.88e-03 – 1.98e-02 (median 9.33e-03)
self-certifying	29 / 29 (codec error below the pack's own floor)

Each pack measures and stores its own replay fidelity against its Monte-Carlo floor, so the error you would incur is a property you can read, not one you have to trust.

Quote the per-axon floor rather than a dataset-wide number: it spans 4× across the set because it tracks each substrate's own internal-gradient variance, not the compression.

Is the physics right?

Against an exact answer, not against another simulation. For an infinite coaxial hollow cylinder the answer is known in closed form, with no fitting freedom to hide an error in:

the field inside the lumen is exactly zero at every orientation;
inside the sheath at θ = 90°, ΔB/B₀ = χ[−1/6 − ½(R_i²/r²)cos 2φ];
inside a solid cylinder the interior is uniform at χ/6·(3cos²θ − 1).

	measured	exact
lumen field	0.131% of χ·B₀	0
sheath amplitude	0.9996× analytic	1
sheath structure, signed	corr +0.9995, slope +0.999	+1
solid-cylinder interior (θ=90°)	−0.1649 χ·B₀	−1/6

All are permanent gates in the generator's test suite (test_susceptibility_field_oracle.py), not one-off checks, and the sheath comparison is signed — an inverted field fails it. The lumen null is the sharp one: a hard binary myelin source rings into the lumen at ~2.6% of χ·B₀ through the non-decaying dipole kernel, which would silently inflate intra-axonal dephasing; partial-volume occupancy suppresses it to ~0.1%.

Susceptibility dephasing vs B₀ orientation

Intra-axonal spin-echo signal at b = 0 as B₀ rotates from parallel to the fibre (0°) to perpendicular (90°) — no diffusion weighting, so this isolates the susceptibility dephasing. Every one of the 29 axons is shown.

The angular dependence matches the source study in shape (both minimise at 90°). The magnitude differs: contrast 0.037 here against 0.015 published, i.e. ~2.4× more attenuation at 90°. That comparison, and the field-solver question it raises, is analysed separately rather than resolved on this page — note only that the two are validated against different references, and the closed-form check above is the one with an exact answer.

Reproduce the curve yourself

The figure above is not stored — it is computed from one pack at read time. This is the whole point of the format, so here it is in full:

import numpy as np
from huggingface_hub import hf_hub_download
from dmipy_sim import bank
from dmipy_sim.bank import read_rpk

path = hf_hub_download("SubstrateCommons/winther-g6-axons", "packs/axon06.rpk",
                       repo_type="dataset")
pk = read_rpk(path)
TE = (pk.n_t - 1) * pk.dt

class B0Only:                       # b = 0: isolate the susceptibility dephasing
    G = np.zeros((1, pk.n_t, 3))
    dt = pk.dt

signal = []
for deg in (0, 15, 30, 45, 60, 75, 90):
    t = np.deg2rad(deg)
    s = bank.replay_susc(pk, B0Only, b0_dir=[np.sin(t), 0.0, np.cos(t)],
                         B0=7.0, chi_iso=1.06e-6, refocus_time=TE / 2,
                         relaxation=False, complex_signal=True, compartment=1)
    signal.append(float(np.real(s[0])))

print([round(x, 4) for x in signal])
# [0.9243, 0.9337, 0.9457, 0.9462, 0.9322, 0.9159, 0.9121]

Nothing in that loop was decided when the pack was built. B0=7.0 could be 3, chi_iso could be anything including an anisotropic component, compartment=1 could be the myelin pool, B0Only.G could be any gradient waveform you like, and refocus_time places the spin echo wherever you want it. Each is a parameter of the replay, not of the simulation — which is why one 71 MB file answers a question nobody asked when it was written. Requires pip install dmipy-sim.

Seeding and confinement

The intra-axonal pool is seeded by an exact ray-parity containment test, and confinement is verified against independent ray parity rather than against the seeding test itself: of 509 genuinely interior seeds, 1.4% lie outside the surface at TE, and those end 0.07 µm beyond the wall — within the one-triangle accuracy of the test that measures them.

Citation

The substrate morphology is the source study's; please cite it:

Winther et al., Susceptibility-induced internal gradients reveal axon morphology and cause anisotropic effects in the diffusion-weighted MRI signal, Sci. Rep. 14:29636 (2024). doi:10.1038/s41598-024-79043-5 — morphology dataset resources.drcmr.dk, CC-BY-4.0

Packs generated with dmipy-sim.

Downloads last month: 32

Number of rows:

Total file size:

2.73 GB

Winther G6 Axons — Monte-Carlo Replay Packs