Module r2star_qsm 

R2*-QSM: susceptibility source separation from gradient-echo data alone.

Dimov et al. separate paramagnetic (χ+, iron) and diamagnetic (χ−, myelin) susceptibility from GRE data alone — R2* from the multi-echo magnitude plus a conventional QSM (χ_total) from the phase — with no separate R2/R2’ measurement. Per voxel the model is

  R2*      = 𝓇·(|χ+| + |χ−|)      (a single relaxometric constant for both sources)
  χ_total  = χ+ + χ−               (χ+ ≥ 0, χ− ≤ 0)

which inverts in closed form to

  χ+   = (χ_total + R2*/𝓇) / 2
  |χ−| = (R2*/𝓇 − χ_total) / 2

with the physical constraints χ+ ≥ 0, |χ−| ≥ 0 enforced by clipping.

Relaxometric constant. Dimov calibrated 𝓇 = 274 Hz/ppm at 3 T (a single value for both sources). R2* susceptibility-induced decay scales linearly with B0 while χ does not, so at the acquisition field 𝓇 = 274·(B0/3) Hz/ppm.

This is the paper’s voxel-level solve; the full method adds a field data-consistency term (auto-satisfied when χ_total is supplied) and an edge-masked L1 regularisation, both omitted here.

Reference: Dimov, A.V., et al. (2022). “Magnetic susceptibility source separation solely from gradient echo data: histological validation.” Tomography, 8(3):1544-1551 (and J. Neuroimaging 2022, https://doi.org/10.1111/jon.13014). R2* susceptibility model: Yablonskiy & Haacke, Magn. Reson. Med. 1994.

Structs

R2starQsmParams

Parameters for r2star_qsm / r2star_qsm_from_magnitude.

Functions

fit_r2star_weighted_loglinear 🔒

R2* (Hz) by magnitude-weighted log-linear least squares over echoes.

r2star_qsm

Closed-form R2*-QSM separation from a QSM and an R2* map.

r2star_qsm_from_magnitude

R2*-QSM separation fitting R2* from multi-echo magnitude, then separating.