Function r2prime 

pub fn r2prime(
    r2star: &[f64],
    r2: &[f64],
    mask: &[u8],
    r2_coverage: Option<&[u8]>,
) -> Result<R2PrimeMap, InputError>

Compute R2’ = R2* − R2, clamped at zero, over the region where R2 was measured.

R2* (from a gradient-echo acquisition) captures reversible + irreversible dephasing; R2 (from a spin-echo acquisition) captures only the irreversible part. Their difference R2’ is the reversible dephasing that chi-separation uses to constrain the paramagnetic/diamagnetic split. Noise can make R2* < R2 in some voxels, so negative values are clamped to zero, as r2primenet does: every R2′ QSM.rs makes is non-negative, and the χ-separation methods are given that map.

R2’ is only defined where R2 exists. R2 comes from a multi-echo spin-echo acquisition, and a MESE is routinely a slab — a band of slices rather than the whole head — because whole-brain MESE is expensive. Subtracting over the whole brain mask would then compute R2' = R2* − 0 = R2* outside the slab, overstating R2’ by roughly the tissue R2 (~10-20 Hz in brain at 3 T) with nothing in the output to show it: the map looks plausible, and every R2’-consuming method inherits the error. So this returns the coverage alongside the map, and leaves R2’ at zero outside it; what to do with the remainder — restrict the downstream outputs to it, or fill it with r2primenet — is a policy decision for the caller, not this function.

Coverage is the intersection of three things:

• mask — where an R2’ is wanted at all (the brain mask);
• r2_coverage, when given — where the R2 acquisition reached. Only the caller knows this; it is a geometric fact about the acquisition, not something the R2 map reveals;
• r2 > 0 — a finite, positive R2. R2 = 0 means T2 = ∞, which no tissue has, so a zero is an absent measurement rather than a measured zero. This is exact for an R2 map from r2_epg, which returns exactly zero outside its own fit mask; for an R2 map resampled from another grid, interpolation can leave small non-zero values just outside the acquired FOV, and only an explicit r2_coverage excludes those.

Passing r2_coverage = None therefore falls back to the r2 > 0 heuristic — conservative, and right for an EPG-derived R2, but weaker than telling the function where the acquisition was.

Arguments

• r2star - R2* map in Hz [nx*ny*nz]
• r2 - R2 map in Hz [nx*ny*nz] (co-registered to r2star)
• mask - Binary brain mask [nx*ny*nz]
• r2_coverage - Optional binary mask of where the R2 acquisition reached [nx*ny*nz]

Returns

R2PrimeMap: the R2’ map in Hz and the coverage it is valid over.

Errors

If r2, mask or r2_coverage is not the same length as r2star: R2 from a separate spin-echo acquisition has to be resampled onto the R2* grid first.