Susceptibility Distortion Correction (SDC)

Please note that all routines for susceptibility-derived distortion correction have been excised off of fMRIPrep for utilization on other projects (e.g., dMRIPrep). For more detailed documentation on SDC routines, check on www.nipreps.org/sdcflows.

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 \(\Delta B_0(x, y, z)\) or via image registration (see below).

Correction methods

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

  1. Phase Encoding POLARity (PEPOLAR; also called blip-up/blip-down; init_pepolar_unwarp_wf()): 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. Direct B0 mapping sequences (init_fmap_wf()): 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. Phase-difference B0 mapping (init_phdiff_wf()): 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. “Fieldmap-less” estimation (experimental; init_syn_sdc_wf()): fMRIPrep now experimentally supports displacement field estimation in the absence of fieldmaps via nonlinear registration.

  5. Point-spread function acquisition: Not supported by BIDS, and hence fMRIPrep.

In order to select the appropriate estimation workflow, the input BIDS dataset is first queried to find the available field-mapping techniques (see init_sdc_estimate_wf()). Once the field-map (or the corresponding displacement field) is estimated, the distortion can be accounted for (see init_sdc_unwarp_wf()).

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). See corresponding implementations under SDCFlows:

  • get_ees()

  • get_trt()

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 (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.