# 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:

1. 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.
2. 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.
3. 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.
4. sdc_fieldmapless: FMRIPREP now experimentally supports displacement field estimation in the absence of fieldmaps via nonlinear registration.
5. 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.