# Susceptibility Distortion Correction (SDC)¶

Please note that all routines for susceptibility-derived distortion correction
have been excised off of *fMRIPrep* for utilization on other projects
(e.g., dMRIPrep).
For more detailed documentation on
SDC
routines, check on www.nipreps.org/sdcflows.

## Introduction¶

SDC methods usually try to make a good estimate of the field inhomogeneity map. The inhomogeneity map is directly related to the displacement of a given pixel \((x, y, z)\) along the PE direction (\(d_\text{PE}(x, y, z)\)) is proportional to the slice readout time (\(T_\text{ro}\)) and the field inhomogeneity (\(\Delta B_0(x, y, z)\)) as follows ([Jezzard1995], [Hutton2002]):

\[d_\text{PE}(x, y, z) = \gamma \Delta B_0(x, y, z) T_\text{ro} \qquad (1)\]

where \(\gamma\) is the gyromagnetic ratio. Therefore, the displacements map \(d_\text{PE}(x, y, z)\) can be estimated either via estimating the inhomogeneity map \(\Delta B_0(x, y, z)\) or via image registration (see below).

## Correction methods¶

The are five broad families of methodologies for mapping the field:

Phase Encoding POLARity(PEPOLAR; also calledblip-up/blip-down;`init_pepolar_unwarp_wf()`

): acquire at least two images with varying PE directions. Hence, the realization of distortion is different between the different acquisitions. The displacements map \(d_\text{PE}(x, y, z)\) is estimated with an image registration process between the different PE acquisitions, regularized by the readout time \(T_\text{ro}\). Corresponds to 8.9.4 of BIDS.

Direct B0 mapping sequences(`init_fmap_wf()`

): some sequences (such as SE) are able to measure the fieldmap \(\Delta B_0(x, y, z)\) directly. Corresponds to section 8.9.3 of BIDS.

Phase-difference B0 mapping(`init_phdiff_wf()`

): to estimate the fieldmap \(\Delta B_0(x, y, z)\), these methods measure the phase evolution in time between two close GRE acquisitions. Corresponds to the sections 8.9.1 and 8.9.2 of the BIDS specification.

“Fieldmap-less” estimation(experimental;`init_syn_sdc_wf()`

):fMRIPrepnow experimentally supports displacement field estimation in the absence of fieldmaps via nonlinear registration.

Point-spread function acquisition: Not supported by BIDS, and hencefMRIPrep.

In order to select the appropriate estimation workflow, the input BIDS dataset is
first queried to find the available field-mapping techniques
(see `init_sdc_estimate_wf()`

).
Once the field-map (or the corresponding displacement field) is estimated, the
distortion can be accounted for
(see `init_sdc_unwarp_wf()`

).

### Calculating the effective echo-spacing and total-readout time¶

To solve (1), all methods (with the exception of the
fieldmap-less approach) will require information about the in-plane
speed of the EPI scheme used in
acquisition by reading either the \(T_\text{ro}\)
(total-readout time) or \(t_\text{ees}\) (effective echo-spacing).
See corresponding implementations under *SDCFlows*:

`get_ees()`

`get_trt()`

### From the phase-difference map to a field map¶

To solve (1) using a phase-difference map,
the field map \(\Delta B_0(x, y, z)\) can be derived from the phase-difference
map (`phdiff2fmap()`

)

### References¶

- Jezzard1995
P. Jezzard, R.S. Balaban Correction for geometric distortion in echo planar images from B0 field variations Magn. Reson. Med., 34 (1) (1995), pp. 65-73, doi:10.1002/mrm.1910340111.

- Hutton2002
Hutton et al., Image Distortion Correction in fMRI: A Quantitative Evaluation, NeuroImage 16(1):217-240, 2002. doi:10.1006/nimg.2001.1054.