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Susceptibility Distortion Correction (SDC)

Introduction

:abbr:`SDC (susceptibility-derived distortion correction)` 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 :abbr:`PE (phase-encoding)` 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) (:ref:`sdc_phasediff` and :ref:`sdc_direct_b0`) or via image registration (:ref:`sdc_pepolar`, :ref:`sdc_fieldmapless`).

Correction methods

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

  1. :ref:`sdc_pepolar` (also called blip-up/blip-down): acquire at least two images with varying :abbr:`PE (phase-encoding)` 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 :abbr:`PE (phase-encoding)` acquisitions, regularized by the readout time T_\text{ro}. Corresponds to 8.9.4 of BIDS.
  2. :ref:`sdc_direct_b0`: some sequences (such as :abbr:`SE (spiral echo)`) are able to measure the fieldmap \Delta B_0(x, y, z) directly. Corresponds to section 8.9.3 of BIDS.
  3. :ref:`sdc_phasediff`: to estimate the fieldmap \Delta B_0(x, y, z), these methods measure the phase evolution in time between two close :abbr:`GRE (Gradient Recall Echo)` acquisitions. Corresponds to the sections 8.9.1 and 8.9.2 of the BIDS specification.
  4. :ref:`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 :ref:`sdc_base`). Once the field-map (or the corresponding displacement field) is estimated, the distortion can be accounted for (see :ref:`sdc_unwarp`).

Calculating the effective echo-spacing and total-readout time

To solve :ref:`(1) <eq_fieldmap>`, all methods (with the exception of the fieldmap-less approach) will require information about the in-plane speed of the :abbr:`EPI (echo-planar imaging)` scheme used in acquisition by reading either the T_\text{ro} (total-readout time) or t_\text{ees} (effective echo-spacing):

.. autofunction:: fmriprep.interfaces.fmap.get_ees
.. autofunction:: fmriprep.interfaces.fmap.get_trt


From the phase-difference map to a field map

To solve :ref:`(1) <eq_fieldmap>` using a :ref:`phase-difference map <sdc_phasediff>`, the field map \Delta B_0(x, y, z) can be derived from the phase-difference map:

.. autofunction:: fmriprep.interfaces.fmap.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.
[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.