Mitigating the effects of brain cropping

In some datasets, the DWI images do not provide coverage of the entire brain cerebrum and cerebellum, due to poor placement of the imaging field of view and/or subject movement leading to that area of the brain shifting outside the FoV for at least one DWI volume. In such cases, it would be erroneous to infer a change in any fixel-wise metric in that area if subjects for which no valid image data are available were to contribute to the assessment. It is therefore necessary to properly track where each subject possesses valid image data and where they do not, and to modify the processing of and inference from such data accordingly.

The way to achieve this at the point of statistical inference is for the fixel data to contain the value NaN (Not A Number) in any location where a valid quantitative metric could not be obtained for that particular subject. Such data are removed from the GLM on a fixel-by-fixel basis. This technique is explained in greater detail and demonstrated in [Smith2019a].

The following instructions describe a way to modify to a typical Fixel-Based Analysis pipeline, in order to ensure that any location in the template image where image data for a particular subject may have been affected by such cropping will contain the value NaN. It is however recommended that you manually inspect the results of these processing steps in order to ensure that the manipulations of the data are operating as intended.

  1. Replace zero-filled values in the DWI with NaN

    When the FSL command eddy (invoked by MRtrix3’s dwifslpreproc) cannot reconstruct valid image data for all DWI volumes in a particular voxel, it fills that voxel with zero values. The following sequence of commands identifies such voxels, and replaces the values stored within those voxels with NaN:

    mrmath dwi.mif norm - -axis 3 | mrthreshold - - -abs 0.0 -comparison gt -nan | mrcalc dwi.mif - -mult dwi_nan.mif

    Note that this command must be run after dwifslpreproc, but before any upsampling of the DWI data: the latter introduces an interpolation step, such that some voxels in the upsampled image will be decreased in intensity due to this effect, but will not be precisely zero.

    If data upsampling is performed subsequent to this step, regions of the image containing these NaN values will become larger. This occurs because any voxels for which performing 3D interpolation will attempt to sample from an input voxel containing the value NaN will itself obtain a value of NaN.

  2. Ignore other instructions elsewhere regarding brain masks

    Filling voxels outside of the brain with values of NaN achieves a comparable effect to providing a brain mask: voxels containing such values will not contribute to various calculations just as though they were to lie outside of a provided brain mask. As such, explicitly providing a brain mask that does not exclude any voxels not already excluded by step 1 would not have any consequence.

  3. Use NaN fill value in mrtransform

    When transforming subject FOD data to template space, instruct the mrtransform command to fill voxels in template space outside of the input image FoV with the value NaN, rather than zeroes (using the -nan option); this will ensure that any voxel in template space for which valid subject data are not available will contain the value NaN, regardless of which step in the pipeline led to that fact.

  4. Substitute template mask with number of valid subjects

    Upon generation of the study-specific population template, the intersection of all subject brain masks in template space will not be utilised. Indeed it is not entirely appropriate to transform individual subjects’ brain masks to template space, as the results of such would not reflect the propagation of NaN values described at the end of point 1.

    It may however instead be useful to know, for each voxel in template space, how many subjects possess valid image data in that location:

    for_each * : mrconvert IN/fod_in_template_space_NOT_REORIENTED.mif -coord 3 0 -axes 0,1,2 - "|" mrcalc - -finite IN/valid_data_template_space_mask.mif -datatype bit
    mrmath */valid_data_template_space_mask.mif sum ../template/valid_data_num_subjects.mif

    It may then be useful to apply a threshold to this image (mrthreshold) in order to inform the derivation of a voxel mask for statistical inference; e.g. one may wish to exclude altogether from analysis those voxels with less than some number of subjects; this choice is left open to the researcher.

  5. Propagate NaN values to fixel quantitative metrics

    For voxels in template space for which no valid data are available for a particular subject, we want fixel data to contain the value NaN rather than 0.0. This is done by projecting the voxel mask representing those voxels for which valid subject data are available into the template fixel mask, and then modifying the fixel values accordingly:

    mkdir ../template/valid_data_masks/
    for_each * : voxel2fixel IN/valid_data_template_space_mask.mif ../template/fd/ ../template/valid_data_masks/ PRE.mif
    mkdir ../template/fd_nan/
    cp ../template/fd/index.mif ../template/fd/directions.mif ../template/fd_nan/
    for_each * : mrcalc ../template/fd/PRE.mif ../template/valid_data_masks/PRE.mif -div ../template/fd_nan/PRE.mif

    This is performed after the fixelcorrespondence step, and must be performed independently for each fixel metric of interest.

  6. When runing fixelcfestats, the presence of NaN values in the input data will be detected automatically, and this fact will be reported to the user.

    This command should be expected to take approximately 4 to 5 times longer to complete than typical usage where all input data are finite.