Results

χ-separation (2026)

Susceptibility source separation splits the net susceptibility χ into a paramagnetic part χ⁺ (iron) and a diamagnetic part χ⁻ (myelin, calcium). On this dataset each method is fed the ground-truth local field, R2′ and χ_total, and its recovered χ⁺ and χ⁻ maps are scored separately. It extends the in-silico Challenge 2.0 phantom, so the susceptibility ground truth is the same one behind the In silico dataset.

The phantom

The χ-separation phantom is generated with qsm-forward, which ports and extends the neuropoly Susceptibility-Separation-Phantom (Ridani et al., 2026), itself an extension of the Challenge 2.0 head phantom. It adds three things the plain QSM phantom lacks: the χ⁺/χ⁻ source maps (the scoring targets), an R2′ map, and a source-separation-aware signal model. The χ⁺/χ⁻ split and relaxation model follow the reference phantom; qsm-forward additionally offers a matched spin-echo acquisition and a multi-compartment signal model.

The forward model

Relaxation: R2, R2*, and R2′

The gradient-echo magnitude decays at R2* = R2 + R2′. R2 is the irreversible rate; R2′ is the reversible rate from static field inhomogeneity around susceptibility sources, and it is the channel source separation draws on. The phantom simulates R2 independently from per-tissue literature T2 values and adds it to R2′ to reach R2*, with no fixed ratio between them (the common κ shortcut, R2* ≈ 1.9·R2′ from Dimov et al., 2022, is avoided because it makes recovering R2′ = R2* − R2 degenerate). The R2′ map is shipped directly as a provided input; qsm-forward can instead simulate a matched spin echo (--save-se) that lets a method derive R2′ from paired GRE/SE data (Stoll, 2025), a capability this dataset does not currently ship.

The relaxivity D_r

Relaxivity converts a susceptibility source into the reversible relaxation it produces. χ-separation uses a single kernel shared by both source types:

R2′ = D_r · ( |χ⁺| + |χ⁻| ),   D_r = 137 Hz/ppm

One kernel for both, because in the static-dephasing regime (Yablonskiy & Haacke, 1994) reversible relaxation depends on the magnitude of the field perturbation, not its sign. D_r = 137 Hz/ppm is the value Shin et al. (2021) measured. A split (D_r⁺ ≠ D_r⁻) is left off by default, since the two relaxivities are not recoverable from one QSM and one R2′ map; it stays available as an opt-in (--dr-neg) for sensitivity studies.

The multi-compartment magnitude

Field-domain methods need only R2′ and the field. Signal-domain separators (e.g. DECOMPOSE) fit the multi-echo complex signal per voxel, where a plain mono-exponential decay carries nothing to separate. With --chisep-multicompartment the voxel magnitude becomes the modulus of a sum of compartments:

S(TE) = | C₊·e^(−(R2 + D_r|χ⁺| + i·ω·χ⁺)·TE)
        + C₋·e^(−(R2 + D_r|χ⁻| + i·ω·χ⁻)·TE)
        +  C₀·e^(−R2·TE) |,     ω = (2/3)·γ·B₀

Each compartment is a static-dephasing exponential with its own decay and off-resonance, so the pools beat against each other and give the non-mono-exponential magnitude those methods rely on. The rates reuse the same D_r kernel as R2′, so the effective R2* is unchanged and field-domain methods see identical inputs; only the shape of the decay is enriched. It defaults to off.

Reproduce the phantom

From the same Challenge 2.0 maps, add the source-separation outputs:

qsm-forward head ./qsm-challenge-2.0 bids_chisep \
  --save-field --save-chi-pos --save-chi-neg --save-r2prime \
  --chisep-signal --chisep-multicompartment

--save-chi-pos/--save-chi-neg write the scoring targets, --save-r2prime the provided R2′ input, and the --chisep-* flags select the source-separation signal model. qsm-forward writes a standard BIDS tree; point qsm-ci run straight at the NIfTIs.

Citations

• Separation phantom: Ridani S., De Leener B., Alonso-Ortiz E. “A realistic in-silico brain phantom for quantifying susceptibility anisotropy-induced error in susceptibility separation.” bioRxiv 2026. doi:10.64898/2026.04.07.716972.
• χ-separation model & D_r: Shin H.G., Lee J., Yun Y.H., et al. “χ-separation: Magnetic susceptibility source separation toward iron and myelin mapping in the brain.” NeuroImage 2021;240:118371. doi:10.1016/j.neuroimage.2021.118371.
• Static-dephasing regime: Yablonskiy D.A., Haacke E.M. “Theory of NMR signal behavior in magnetically inhomogeneous tissues: the static dephasing regime.” Magn Reson Med 1994;32(6):749–763. doi:10.1002/mrm.1910320610.
• DECOMPOSE: Chen J., et al. “Decompose QSM to sub-voxel diamagnetic and paramagnetic components based on gradient-echo MRI data.” NeuroImage 2021. doi:10.1016/j.neuroimage.2021.118735.
• SUSEP-Net: Li, Gao, Sun, et al. “SUSEP-Net: simulation-supervised contrastive learning for susceptibility source separation via a sub-voxel QSM network.” arXiv:2506.13293, 2025. doi:10.48550/arXiv.2506.13293.
• WaveSep: Fang Z., Shin H.G., van Zijl P., Li X., Sulam J. “WaveSep: A Flexible Wavelet-Based Approach for Source Separation in Susceptibility Imaging.” MLCN, MICCAI 2023. doi:10.1007/978-3-031-44858-4_6.
• κ approximation: Dimov A.V., et al. “Magnetic susceptibility source separation solely from gradient echo data: histological validation.” Tomography 2022;8(3):1544–1551. doi:10.3390/tomography8030127.
• χ-sep spin-echo model: Stoll P. “Development of a Deep Learning Framework for Iron and Myelin Mapping from Quantitative Susceptibility Maps.” MSc thesis, ETH Zurich, 2025.

In vivo · 2016 Reconstruction Challenge

This dataset is real acquired brain data from the 2016 QSM Reconstruction Challenge: a single-orientation 3 T scan of one volunteer. Each method inverts the ground-truth local tissue field to a susceptibility map, scored against two reference reconstructions rather than a true susceptibility (none exists in vivo). Only the dipole-inversion stage is scored, so the ranking reads as agreement with a reference, not accuracy against ground truth.

The challenge and its references

The 2016 Reconstruction Challenge (Langkammer et al., 2018) took the χ₃₃ component of a susceptibility-tensor (STI) reconstruction as its reference, hoping to sidestep the orientation bias of COSMOS. Twenty-seven submissions were scored on RMSE, HFEN, SSIM and regional error. The lesson was as much about metrics as algorithms: tuned to minimise those errors, the winning maps were over-smoothed and lost fine structure, and near-identical scores hid visibly different maps. A follow-up (Milovic et al., 2020) then showed the χ₃₃ reference itself did not match the measured phase once anisotropy, microstructure and noise were accounted for.

QSM-CI scores each method against both available references: the multi-orientation COSMOS reconstruction and the STI χ₃₃ map. Source: the 2016 challenge (qsm.neuroimaging.at); the local tissue field and both reference χ maps are in ppm.

Citations

• 2016 Challenge report: Langkammer C., Schweser F., Shmueli K., et al. “Quantitative susceptibility mapping: Report from the 2016 reconstruction challenge.” Magn Reson Med 2018;79(3):1661–1673. doi:10.1002/mrm.26830.
• 2016 Challenge lessons: Milovic C., Tejos C., Acosta-Cabronero J., et al. “The 2016 QSM Challenge: Lessons learned and considerations for a future challenge design.” Magn Reson Med 2020;84(3):1624–1637. doi:10.1002/mrm.28185.
• COSMOS reference: Liu T., Spincemaille P., de Rochefort L., Kressler B., Wang Y. “Calculation of susceptibility through multiple orientation sampling (COSMOS).” Magn Reson Med 2009;61(1):196–204. doi:10.1002/mrm.21828.