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Susceptibility Distortion Correction (SDC)

Introduction

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 PE (phase-encoding) direction (dPE(x, y, z)) is proportional to the slice readout time (Tro) and the field inhomogeneity (ΔB0(x, y, z)) as follows ([Jezzard1995], [Hutton2002]):


dPE(x, y, z) = γΔB0(x, y, z)Tro  (1)

where γ is the gyromagnetic ratio. Therefore, the displacements map dPE(x, y, z) can be estimated either via estimating the inhomogeneity map ΔB0(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 (phase-encoding) directions. Hence, the realization of distortion is different between the different acquisitions. The displacements map dPE(x, y, z) is estimated with an image registration process between the different PE (phase-encoding) acquisitions, regularized by the readout time Tro. Corresponds to 8.9.4 of BIDS.
  2. sdc_direct_b0: some sequences (such as SE (spiral echo)) are able to measure the fieldmap ΔB0(x, y, z) directly. Corresponds to section 8.9.3 of BIDS.
  3. sdc_phasediff: to estimate the fieldmap ΔB0(x, y, z), these methods measure the phase evolution in time between two close GRE (Gradient Recall Echo) 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) <eq_fieldmap>, all methods (with the exception of the fieldmap-less approach) will require information about the in-plane speed of the EPI (echo-planar imaging) scheme used in acquisition by reading either the Tro (total-readout time) or tees (effective echo-spacing):

fmriprep.interfaces.fmap.get_ees

fmriprep.interfaces.fmap.get_trt

From the phase-difference map to a field map

To solve (1) <eq_fieldmap> using a phase-difference map <sdc_phasediff>, the field map ΔB0(x, y, z) can be derived from the phase-difference map:

fmriprep.interfaces.fmap.phdiff2fmap

References

Huntenburg2014

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

Hutton2002

Hutton et al., Image Distortion Correction in fMRI: A Quantitative Evaluation, NeuroImage 16(1):217-240, 2002. doi:`10.1006/nimg.2001.1054 <https://doi.org/10.1006/nimg.2001.1054>`_.

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 <https://doi.org/10.1002/mrm.1910340111>`_.

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 <https://doi.org/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 <https://doi.org/10.3389/fninf.2017.00017>`_.