Merge pull request #248 from nipreps/docs/refactor-content-organization

DOC: Bring implementation details to the foreground of documentation

Author: oesteban

docs/_static/sdcflows-OHBM21-fig1.png

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 # The master toctree document.
 master_doc = "index"
 
+numfig = True
+
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docs/conf.py

@@ -7,5 +7,6 @@ Contents
     :maxdepth: 3
 
     installation
+    methods
     api
     changes

docs/index.rst

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+Methods and implementation
+==========================
+*SDCFlows* defines a clear :abbr:`API (application programming interface)` that divides
+the problem of susceptibility distortions (SD) into two stages:
+
+#. **Estimation**:
+   the MRI acquisitions in the protocol for :abbr:`SD (susceptibility distortions)` are
+   discovered and preprocessed to estimate a map of B\ :sub:`0` non-uniformity in Hz (:math:`\Delta B_0`).
+   The theory behind these distortions is well described in the literature ([Jezzard1995]_, [Hutton2002]_),
+   and further discussed below (see a summary in :numref:`fig-1`).
+   *SDCFlows* builds on freely-available software to implement three major strategies for estimating
+   :math:`\Delta B_0` (Eq. :math:`\eqref{eq:fieldmap-1}`).
+   These strategies are described below, and implemented within :py:mod:`sdcflows.workflows.fit`\ .
+
+#. **Application**:
+   the B-Spline basis coefficients used to represent the estimated :math:`\Delta B_0` map mapped into the
+   target :abbr:`EPI (echo-planar imaging)` scan to be corrected, and a displacement field in NIfTI
+   format that is compatible with ANTs is interpolated from the B-Spline basis.
+   The voxel location error along the :abbr:`PE (phase-encoding)` will be proportional to :math:`\Delta B_0 \cdot T_\text{ro}`,
+   where :math:`T_\text{ro}` is the *total readout time* of the target :abbr:`EPI (echo-planar imaging)` (:numref:`fig-1`).
+   The implementation of these workflows is found in the submodule :py:mod:`sdcflows.workflows.apply`\ .
+
+.. _fig-1:
+
+.. figure:: _static/sdcflows-OHBM21-fig1.png
+   :width: 100%
+   :align: center
+
+   Susceptibility distortions in a nutshell
+
+.. admonition:: BIDS Specification
+
+    See the section `Echo-planar imaging and *B0* mapping
+    <https://bids-specification.readthedocs.io/en/latest/04-modality-specific-files/01-magnetic-resonance-imaging-data.html#echo-planar-imaging-and-b0-mapping>`__.
+
+Fieldmap estimation: theory and methods
+---------------------------------------
+The displacement suffered by every voxel along the :abbr:`PE (phase-encoding)` direction
+can be derived from Eq. (2) of [Hutton2002]_:
+
+.. math::
+
+    \Delta_\text{PE} (i, j, k) = \gamma \cdot \Delta B_0 (i, j, k) \cdot T_\text{ro},
+    \label{eq:fieldmap-1}\tag{1}
+
+where
+:math:`\Delta_\text{PE} (i, j, k)` is the *voxel-shift map* (VSM) along the :abbr:`PE (phase-encoding)` direction,
+:math:`\gamma` is the gyromagnetic ratio of the H proton in Hz/T
+(:math:`\gamma = 42.576 \cdot 10^6 \, \text{Hz} \cdot \text{T}^\text{-1}`),
+:math:`\Delta B_0 (i, j, k)` is the *fieldmap variation* in T (Tesla), and
+:math:`T_\text{ro}` is the readout time of one slice of the :abbr:`EPI (echo-planar imaging)` dataset
+we want to correct for distortions.
+
+Let :math:`V` represent the *fieldmap* in Hz (or equivalently,
+*voxel-shift-velocity map*, as Hz are equivalent to voxels/s), with
+:math:`V(i,j,k) = \gamma \cdot \Delta B_0 (i, j, k)`, then, introducing
+the voxel zoom along the phase-encoding direction, :math:`s_\text{PE}`,
+we obtain the nonzero component of the associated displacements field
+:math:`\Delta D_\text{PE} (i, j, k)` that unwarps the target :abbr:`EPI (echo-planar imaging)` dataset:
+
+.. math::
+
+    \Delta D_\text{PE} (i, j, k) = V(i, j, k) \cdot T_\text{ro} \cdot s_\text{PE}.
+    \label{eq:fieldmap-2}\tag{2}
+
+.. _sdc_direct_b0 :
+
+Direct B0 mapping sequences
+~~~~~~~~~~~~~~~~~~~~~~~~~~~
+.. admonition:: BIDS Specification
+
+    See the section `Types of fieldmaps - Case 3: Direct field mapping
+    <https://bids-specification.readthedocs.io/en/latest/04-modality-specific-files/01-magnetic-resonance-imaging-data.html#case-3-direct-field-mapping>`__
+    in the BIDS specification.
+
+Some MR schemes such as :abbr:`SEI (spiral-echo imaging)` can directly
+reconstruct an estimate of *the fieldmap in Hz*, :math:`V(i,j,k)`.
+These *fieldmaps* are described with more detail `here
+<https://cni.stanford.edu/wiki/GE_Processing#Fieldmaps>`__.
+
+.. _sdc_phasediff :
+
+Phase-difference B0 estimation
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+.. admonition:: BIDS Specification
+
+    See the section `Types of fieldmaps - Case 2: Two phase maps and two magnitude images
+    <https://bids-specification.readthedocs.io/en/latest/04-modality-specific-files/01-magnetic-resonance-imaging-data.html#case-2-two-phase-maps-and-two-magnitude-images>`__
+    in the BIDS specification.
+
+    Some scanners produce one ``phasediff`` map, where the drift between the two echos has
+    already been calculated, see the section
+    `Types of fieldmaps - Case 1: Phase-difference map and at least one magnitude image
+    <https://bids-specification.readthedocs.io/en/latest/04-modality-specific-files/01-magnetic-resonance-imaging-data.html#case-1-phase-difference-map-and-at-least-one-magnitude-image>`__.
+
+The fieldmap variation in T, :math:`\Delta B_0 (i, j, k)`, that is necessary to obtain
+:math:`\Delta_\text{PE} (i, j, k)` in Eq. :math:`\eqref{eq:fieldmap-1}` can be
+calculated from two subsequent :abbr:`GRE (Gradient-Recalled Echo)` echoes,
+via Eq. (1) of [Hutton2002]_:
+
+.. math::
+
+    \Delta B_0 (i, j, k) = \frac{\Delta \Theta (i, j, k)}{2\pi \cdot \gamma \, \Delta\text{TE}},
+    \label{eq:fieldmap-3}\tag{3}
+
+where
+:math:`\Delta \Theta (i, j, k)` is the phase-difference map in radians,
+and :math:`\Delta\text{TE}` is the elapsed time between the two GRE echoes.
+
+For simplicity, the «*voxel-shift-velocity map*» :math:`V(i,j,k)`, which we
+can introduce in Eq. :math:`\eqref{eq:fieldmap-2}` to directly obtain
+the displacements field, can be obtained as:
+
+.. math::
+
+    V(i, j, k) = \frac{\Delta \Theta (i, j, k)}{2\pi \cdot \Delta\text{TE}}.
+    \label{eq:fieldmap-4}\tag{4}
+
+This calculation is further complicated by the fact that :math:`\Theta_i`
+(and therefore, :math:`\Delta \Theta`) are clipped (or *wrapped*) within
+the range :math:`[0 \dotsb 2\pi )`.
+It is necessary to find the integer number of offsets that make a region
+continuously smooth with its neighbors (*phase-unwrapping*, [Jenkinson2003]_).
+
+.. _sdc_pepolar :
+
+:abbr:`PEPOLAR (Phase Encoding POLARity)` techniques
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+.. admonition:: BIDS Specification
+
+    See the section `Types of fieldmaps - Case 4: Multiple phase encoded directions ("pepolar")
+    <https://bids-specification.readthedocs.io/en/latest/04-modality-specific-files/01-magnetic-resonance-imaging-data.html#case-4-multiple-phase-encoded-directions-pepolar>`__.
+
+Alternatively, it is possible to estimate the field by exploiting the symmetry of the
+distortion when the :abbr:`PE (phase-encoding)` polarity is reversed.
+*SDCFlows* integrates two implementations based on FSL ``topup`` [Andersson2003]_,
+and AFNI ``3dQwarp`` [Cox1997]_.
+By default, FSL ``topup`` will be used.
+
+.. _sdc_fieldmapless :
+
+Fieldmap-less approaches
+~~~~~~~~~~~~~~~~~~~~~~~~
+Many studies acquired (especially with legacy MRI protocols) do not have any
+information to estimate susceptibility-derived distortions.
+In the absence of data with the specific purpose of estimating the :math:`B_0`
+inhomogeneity map, researchers resort to nonlinear registration to an
+«*anatomically correct*» map of the same individual (normally acquired with
+:abbr:`T1w (T1-weighted)`, or :abbr:`T2w (T2-weighted)` sequences).
+One of the most prominent proposals of this approach is found in [Studholme2000]_.
+
+*SDCFlows* includes an (experimental) procedure, based on nonlinear image registration
+with ANTs' symmetric normalization (SyN) technique.
+This workflow takes a skull-stripped :abbr:`T1w (T1-weighted)` image and
+a reference :abbr:`EPI (Echo-Planar Imaging)` image, and estimates a field of nonlinear
+displacements that accounts for susceptibility-derived distortions.
+To more accurately estimate the warping on typically distorted regions, this
+implementation uses an average :math:`B_0` mapping described in [Treiber2016]_.
+The implementation is a variation on those developed in [Huntenburg2014]_ and
+[Wang2017]_.
+
+The process is divided in two steps.
+First, the two images to be aligned (anatomical and one or more :abbr:`EPI (echo-planar imaging)` sources) are prepared for
+registration, including a linear pre-alignment of both, calculation of a 3D :abbr:`EPI (echo-planar imaging)` *reference* map,
+intensity/histogram enhancement, and *deobliquing* (meaning, for images where the physical
+coordinates axes and the data array axes are not aligned, the physical coordinates are
+rotated to align with the data array).
+Such a preprocessing is implemented in
+:py:func:`~sdcflows.workflows.fit.syn.init_syn_preprocessing_wf`.
+Second, the outputs of the preprocessing workflow are fed into
+:py:func:`~sdcflows.workflows.fit.syn.init_syn_sdc_wf`,
+which executes the nonlinear, SyN registration.
+To aid the *Mattes* mutual information cost function, the registration scheme is set up
+in *multi-channel* mode, and laplacian-filtered derivatives of both anatomical and :abbr:`EPI (echo-planar imaging)`
+reference are introduced as a second registration channel.
+The optimization gradients of the registration process are weighted, so that deformations
+effectively possible only along the :abbr:`PE (phase-encoding)` axis.
+Given that ANTs' registration framework performs on physical coordinates, it is necessary
+that input images are not *oblique*.
+The anatomical image is used as *fixed image*, and therefore, the registration process
+estimates the transformation function from *unwarped* (anatomically *correct*) coordinates
+to *distorted* coordinates.
+If fed into ``antsApplyTransforms``, the resulting transform will effectively *unwarp* a distorted
+:abbr:`EPI (echo-planar imaging)` given as input into its *unwarped* mapping.
+The estimated transform is then converted into a :math:`B_0` fieldmap in Hz, which can be
+stored within the derivatives folder.
+
+.. danger ::
+
+    This procedure is experimental, and the outcomes should be scrutinized one-by-one
+    and used with caution.
+    Feedback will be enthusiastically received.
+
+Other (unsupported) approaches
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+There exist some alternative options to estimate the fieldmap, such as mapping the
+point-spread-function [Zaitsev2004]_, or by means of nonlinear registration of brain
+surfaces onto the distorted :abbr:`EPI (echo-planar imaging)` data [Esteban2016]_.
+
+Estimation tooling
+~~~~~~~~~~~~~~~~~~
+The workflows provided by :py:mod:`sdcflows.workflows.fit` make use of several utilities.
+The cornerstone of these tools is the fieldmap representation with B-Splines
+(:py:mod:`sdcflows.interfaces.bspline`).
+B-Splines are well-suited to plausibly smooth the fieldmap and provide a compact
+representation of the field with fewer parameters.
+This representation is also more accurate in the case the images that were used for estimation
+are not aligned with the target images to be corrected because the fieldmap is not directly
+interpolated in the projection, but rather, the position of the coefficients in space is
+updated and then the fieldmap reconstructed.
+
+Unwarping the distorted data
+----------------------------
+:py:mod:`sdcflows.workflows.apply` contains workflows to project fieldmaps represented by B-Spline
+basis into the space of the target :abbr:`EPI (echo-planar imaging)` data.
+
+Discovering fieldmaps in a BIDS dataset
+---------------------------------------
+To ease the implementation of higher-level pipelines integrating :abbr:`SDC (susceptibility distortion correction)`,
+*SDCFlows* provides :py:func:`sdcflows.utils.wrangler.find_estimators`.
+
+Explicit specification with ``B0FieldIdentifier``
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+.. admonition:: BIDS Specification
+
+    See the section `Expressing the MR protocol intent for fieldmaps - Using *B0FieldIdentifier* metadata
+    <https://bids-specification.readthedocs.io/en/latest/04-modality-specific-files/01-magnetic-resonance-imaging-data.html#using-b0fieldidentifier-metadata>`__.
+
+If one or more ``B0FieldIdentifier``\ (s) are set within the input metadata (following BIDS' specifications),
+then corresponding estimators will be built from the available input data.
+
+Implicit specification with ``IntendedFor``
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+.. admonition:: BIDS Specification
+
+    See the section `Expressing the MR protocol intent for fieldmaps - Using *IntendedFor* metadata
+    <https://bids-specification.readthedocs.io/en/latest/04-modality-specific-files/01-magnetic-resonance-imaging-data.html#using-intendedfor-metadata>`__.
+
+In the case no ``B0FieldIdentifier``\ (s) are defined, then *SDCFlows* will try to identify as many fieldmap
+estimators as possible within the dataset following a set of heuristics.
+Then, those estimators may be linked to target :abbr:`EPI (echo-planar imaging)` data by interpreting the
+``IntendedFor`` field if available.
+
+Fieldmap-less by registration to a T1-weighted image
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+If none of the two previous options yielded any workable estimation strategy, and provided that
+the argument ``fmapless`` is set to ``True``, then :py:func:`~sdcflows.utils.wrangler.find_estimators`
+will attempt to find :abbr:`BOLD (blood-oxygen level-dependent)` or :abbr:`DWI (diffusion-weighted imaging)`
+instances within single sessions that are consistent in :abbr:`PE (phase-encoding)` direction and
+*total readout time*, assuming they have been acquired with the same shimming settings.
+
+If one or more anatomical images are found, and if the search for candidate
+:abbr:`BOLD (blood-oxygen level-dependent)` or :abbr:`DWI (diffusion-weighted imaging)` data
+yields results, then corresponding fieldmap-less estimators are set up.
+
+It is possible to force the fieldmap-less estimation by passing ``force_fmapless=True`` to the
+:py:func:`~sdcflows.utils.wrangler.find_estimators` utility.
+
+References
+----------
+.. [Jezzard1995] Jezzard, P. & Balaban, R. S. (1995) Correction for geometric distortion in
+    echo planar images from B0 field variations. Magn. Reson. Med. 34:65–73.
+    doi:`10.1002/mrm.1910340111 <https://doi.org/10.1002/mrm.1910340111>`__.
+.. [Hutton2002] Hutton et al., (2002) Image Distortion Correction in fMRI: A Quantitative
+    Evaluation, NeuroImage 16(1):217-240. doi:`10.1006/nimg.2001.1054
+    <https://doi.org/10.1006/nimg.2001.1054>`__.
+.. [Jenkinson2003] Jenkinson, M. (2003) Fast, automated, N-dimensional phase-unwrapping
+    algorithm. MRM 49(1):193-197. doi:`10.1002/mrm.10354
+    <https://doi.org/10.1002/mrm.10354>`__.
+.. [Andersson2003] Andersson, J. (2003) How to correct susceptibility distortions in spin-echo
+    echo-planar images: application to diffusion tensor imaging. NeuroImage 20:870–888.
+    doi:`10.1016/s1053-8119(03)00336-7 <https://doi.org/10.1016/s1053-8119(03)00336-7>`__.
+.. [Cox1997] Cox, R. (1997) Software tools for analysis and visualization of fMRI data. NMR Biomed.
+    10:171–178, doi:`10.1002/(sici)1099-1492(199706/08)10:4/5%3C171::aid-nbm453%3E3.0.co;2-l
+    <https://doi.org/10.1002/(sici)1099-1492(199706/08)10:4/5%3C171::aid-nbm453%3E3.0.co;2-l>`__.
+.. [Studholme2000] Studholme et al. (2000) Accurate alignment of functional EPI data to
+    anatomical MRI using a physics-based distortion model,
+    IEEE Trans Med Imag 19(11):1115-1127, 2000, doi: `10.1109/42.896788
+    <https://doi.org/10.1109/42.896788>`__.
+.. [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>`_.
+.. [Huntenburg2014] Huntenburg, J. M. (2014) `Evaluating Nonlinear
+    Coregistration of BOLD EPI and T1w Images
+    <http://pubman.mpdl.mpg.de/pubman/item/escidoc:2327525:5/component/escidoc:2327523/master_thesis_huntenburg_4686947.pdf>`__,
+    Berlin: Master Thesis, Freie Universität.
+.. [Zaitsev2004] Zaitsev, M. (2004) Point spread function mapping with parallel imaging techniques and
+    high acceleration factors: Fast, robust, and flexible method for echo-planar imaging distortion correction,
+    MRM 52(5):1156-1166. doi:`10.1002/mrm.20261 <https://doi.org/10.1002/mrm.20261>`__.
+.. [Esteban2016] Esteban, O. (2016) Surface-driven registration method for the structure-informed segmentation
+    of diffusion MR images. NeuroImage 139:450-461.
+    doi:`10.1016/j.neuroimage.2016.05.011 <https://doi.org/10.1016/j.neuroimage.2016.05.011>`__.