| --- |
| license: cc-by-4.0 |
| task_categories: [other] |
| tags: [mri, diffusion-mri, monte-carlo, microstructure, replay-pack, rpk, myelin, susceptibility, axon] |
| pretty_name: Winther G6 Axons — Monte-Carlo Replay Packs with Susceptibility |
| --- |
| |
| # Winther G6 Axons — Monte-Carlo Replay Packs |
|
|
| 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) | |
|
|
| ## Contents |
|
|
| ``` |
| 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: |
|
|
| ```python |
| 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`](https://github.com/dmrai-lab/dmipy-sim). |
|
|
