# 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: