# Susceptibility Distortion Correction (SDC)¶

## 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 \(\Delta B_0(x, y, z)\) (sdc_phasediff and sdc_direct_b0) or via image registration (sdc_pepolar, sdc_fieldmapless).

## Correction methods¶

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

- sdc_pepolar (also called
blip-up/blip-down): 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.- sdc_direct_b0: 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.
- sdc_phasediff: 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.
- sdc_fieldmapless: FMRIPREP now experimentally supports displacement field estimation in the absence of fieldmaps via nonlinear registration.
Point-spread function acquisition: Not supported by FMRIPREP.

In order to select the appropriate estimation workflow, the input BIDS dataset is first queried to find the available field-mapping techniques (see sdc_base). Once the field-map (or the corresponding displacement field) is estimated, the distortion can be accounted for (see sdc_unwarp).

### 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):

### 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:

### 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. |

[Huntenburg2014] | Huntenburg, J. M. (2014) Evaluating Nonlinear Coregistration of BOLD EPI and T1w Images. Berlin: Master Thesis, Freie Universität. PDF. |

[Treiber2016] | Treiber, J. M. et al. (2016) Characterization and Correction of Geometric Distortions in 814 Diffusion Weighted Images, PLoS ONE 11(3): e0152472. doi:10.1371/journal.pone.0152472. |

[Wang2017] | Wang S, et al. (2017) Evaluation of Field Map and Nonlinear Registration Methods for Correction of Susceptibility Artifacts in Diffusion MRI. Front. Neuroinform. 11:17. doi:10.3389/fninf.2017.00017. |