estatics¶

Fits a mono-exponential decay to multi-echo gradient-echo data and returns an R2* map together with the echo series extrapolated to TE = 0. When you acquired several contrasts (proton-density, T1 and MT weighted, say), the decay is shared across all of them, which makes the R2* estimate more robust to motion between acquisitions.

nitorch estatics [OPTIONS] -c [NAME] [CONTRAST-OPTIONS] -e FILE...
                 [-c [NAME] [CONTRAST-OPTIONS] -e FILE...]...

Description¶

estatics implements the ESTATICS model of Weiskopf et al. (2014) with the nonlinear, total-variation-regularised fitting scheme of Balbastre et al. (2020). Let \(S_{c,e}(\mathbf{x})\) be the magnitude signal of echo \(e\) of contrast \(c\) at voxel \(\mathbf{x}\), acquired at echo time \(\mathrm{TE}_{c,e}\). The model is

where each contrast \(c\) has its own log-intercept \(\beta_c\) (its signal at TE = 0) but all contrasts share the decay rate \(R_2^*\). The original ESTATICS fit is a least-squares fit of the logarithm of the data. This command instead fits the model directly in the magnitude domain, with a Gaussian or non-central chi noise model, and regularises the maps with a (joint) total-variation penalty. It estimates the noise level of every contrast itself.

The reconstruction (output) space defaults to the mean space of all contrasts, so images need not share the same field of view or resolution. With --register, the contrasts are first aligned rigidly.

With --meetup, the command additionally estimates one distortion field per contrast along the readout direction, which corrects the geometric distortions of bipolar multi-echo readouts without a field map or reversed-polarity acquisition. See MEETUP distortion correction.

Command-line layout¶

Each contrast is introduced by -c and followed by the options that describe it. The echoes of a contrast are listed after -e. A command with two contrasts looks like this:

nitorch estatics -c pdw -te 2.3 4.6 6.9 ms -e pdw_e1.nii.gz pdw_e2.nii.gz pdw_e3.nii.gz \
                 -c t1w -te 2.3 4.6 6.9 ms -e t1w_e1.nii.gz t1w_e2.nii.gz t1w_e3.nii.gz

The optional NAME right after -c labels the contrast. It is only used to select the reconstruction space with --recon-space. A contrast can be as small as a single echo series, and a single contrast is allowed.

Echoes and echo times¶

Each file after -e is one echo (a 3D volume) or a series of echoes stacked along the fourth dimension. All files of a contrast are concatenated in the order you give them, and that order must match the order of the echo times.

The echo times are obtained as follows.

1. With -te, you give them explicitly. The values may be followed by a unit, ms or s (or sec). Without a unit, they are interpreted as seconds. The list must have as many values as the contrast has echoes.
2. With -te and -sp, you give the first echo time and the echo spacing. The \(n\)-th echo then has time \(\mathrm{TE}_0 + n\,\Delta\), where the number of echoes is the total number of volumes in the -e files. Here the unit of the spacing is mandatory (ms or s). Remember to give a unit for the first echo time as well.
3. Without -te, the echo time is read from the header of each file. NITorch does not read BIDS JSON sidecars. It reads the TE= field from the description string of NIfTI headers (for example TR=24ms/TE=2.3ms/FA=6deg), and the echo time stored in the header of FreeSurfer .mgh/.mgz files. A value in that string without a unit is read as seconds. A single header holds a single echo time, so for 4D files you must use -te or -sp.

All units are converted to seconds internally, and R2* is therefore returned in s^-1.

Arguments¶

estatics takes no positional arguments. Input files are given with -e inside a contrast.

Options¶

Contrast¶

These options describe one contrast and apply to the -c they follow.

Reconstruction¶

Optimisation¶

General¶

Regularisation¶

The log-intercepts and the R2* map are smoothed jointly during the fit, so that noise in one echo series does not leak into the others, yet edges are preserved. --regularization jtv, the default, penalises the joint total variation of all maps: the penalty shares one edge-weight map across them, so an edge that is visible in one contrast protects the same edge in the others. tv weights each map separately, tkh applies a plain membrane (Tikhonov) penalty that blurs edges, and no fits each voxel independently.

The weights --lam-intercept and --lam-decay act on the log-intercepts and on R2* respectively. If the maps look too noisy, increase them. If fine structure is lost, decrease them. If both are zero, no penalty is applied whatever --regularization says.

MEETUP distortion correction¶

Bipolar multi-echo readouts alternate the readout direction from one echo to the next, so that B0 inhomogeneity displaces voxels along the readout direction in opposite senses in odd and even echoes. With --meetup, estatics fits, jointly with the decay model, one displacement field per contrast along the readout direction, under the assumption that consecutive echoes alternate in polarity. The fields are regularised by their bending energy (--lam-meetup). The readout direction is that given by -rd, or by default the voxel axis with the most voxels.

When the distortion model is on, the command also writes the estimated fields and a corrected version of every echo, see Output files. Please cite Balbastre et al. (ISMRM 2022) if you use this option.

Output files¶

All outputs are written as 32-bit floating-point images, in the format of the corresponding input file. Without -o, they are written next to the input files. Because the names below do not depend on the command line, a second run in the same directory overwrites the results of the first.

The maps are in the reconstruction space (--recon-space), whereas _unwrapped echoes keep the space of their input.

Examples¶

Fit R2* to a single series of five echoes whose echo times are stored in the file headers:

nitorch estatics -c -e echo-1.nii.gz echo-2.nii.gz echo-3.nii.gz echo-4.nii.gz echo-5.nii.gz

Give the echo times explicitly, as a first echo time and a constant spacing, for a 4D file that holds all echoes:

nitorch estatics -c -te 2.3 ms -sp 2.3 ms -e multiecho.nii.gz

Fit the multi-contrast model to proton-density, T1 and MT weighted series. The decay is shared, and each series gets a TE = 0 image:

nitorch estatics \
    -c pdw -e pdw_e1.nii.gz pdw_e2.nii.gz pdw_e3.nii.gz pdw_e4.nii.gz \
    -c t1w -e t1w_e1.nii.gz t1w_e2.nii.gz t1w_e3.nii.gz t1w_e4.nii.gz \
    -c mtw -e mtw_e1.nii.gz mtw_e2.nii.gz mtw_e3.nii.gz mtw_e4.nii.gz

Align the contrasts first, use the space of the T1-weighted series, and write to a separate directory. The global options come before the contrasts:

nitorch estatics --register --recon-space t1w --likelihood chi -o derivatives/ \
    -c pdw -e pdw_e1.nii.gz pdw_e2.nii.gz pdw_e3.nii.gz \
    -c t1w -e t1w_e1.nii.gz t1w_e2.nii.gz t1w_e3.nii.gz

Correct readout distortions of a bipolar acquisition, with the readout along the antero-posterior axis, and weaken the penalty on the R2* map:

nitorch estatics --meetup --lam-decay 0.01 \
    -c pdw -rd ap -e pdw_e1.nii.gz pdw_e2.nii.gz pdw_e3.nii.gz pdw_e4.nii.gz

References¶

• Weiskopf N, Callaghan MF, Josephs O, Lutti A, Mohammadi S. Estimating the apparent transverse relaxation time (R2*) from images with different contrasts (ESTATICS) reduces motion artifacts. Frontiers in Neuroscience (2014). doi:10.3389/fnins.2014.00278
• Balbastre Y, Brudfors M, Azzarito M, Lambert C, Callaghan MF, Ashburner J. Joint total variation ESTATICS for robust multi-parameter mapping. MICCAI (2020). arXiv:2005.14247
• Balbastre Y, et al. Model-based multi-parameter mapping. Medical Image Analysis (2021). arXiv:2102.01604 (optimisation scheme used by this implementation)
• Balbastre Y, et al. Distortion correction in multi-echo MRI without field mapping or reverse encoding. Proc. ISMRM (2022). (--meetup)

See also¶

• greeq: fit PD, R1, R2* and MTsat directly from multi-echo, multi-flip-angle data.
• epic: denoise and correct bipolar multi-echo data with a pre-computed field map.
• topup: estimate a field map from reverse-polarity images.
• File formats: the image formats NITorch reads and writes.