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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.