# 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:

1. Phase Encoding POLARity (PEPOLAR; also called blip-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.

2. 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.

3. 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.

4. “Fieldmap-less” estimation (experimental; init_syn_sdc_wf()): fMRIPrep now experimentally supports displacement field estimation in the absence of fieldmaps via nonlinear registration.

5. Point-spread function acquisition: Not supported by BIDS, and hence fMRIPrep.

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:

### 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.