Diffusion gradient scheme handling

An essential piece of information for DWI processing is the diffusion-weighted (DW) gradient scheme, also known as the “DW gradient table”, the “DW encoding”, the “b-vectors”, the “bvecs”, and other variations on the theme. This table provides information about the diffusion sensitisation gradients applied during acquisition of each imaging volume in a DWI dataset, usually in the form of the b-value and the (unit) vector for the DW gradient direction. In this page we will describe the details of how this information is typically stored / represented, and how MRtrix3 handles / manipulates this data.

Gradient table storage

MRtrix3 allows the DW gradient table to be read directly from, or written to, the image headers for specific image formats; notably DICOM (folder or .dcm) (read-only) and the MRtrix image formats (.mih / .mif) (read/write). MRtrix3 applications will automatically make use of this information when it is available for the input dataset through storage of the table within the image header, without requiring explicit intervention from the user. In addition, MRtrix3 commands can also import or export this information from/to two different external file formats: typically referred to as the MRtrix format and the FSL format. These differ in a number of respects, as outlined below.

MRtrix format

This format consists of a single ASCII text file, with no restrictions on the filename. It consists of one row per entry (i.e. per DWI volume), with each row consisting of 4 space-separated floating-point values; these correspond to [ x y z b ], where [ x y z ] are the components of the gradient vector, and b is the b-value in units of s/mm². A typical MRtrix format DW gradient table file might look like this:

         0           0           0           0
         0           0           0           0
-0.0509541   0.0617551    -0.99679        3000
  0.011907    0.955047    0.296216        3000
 -0.525115    0.839985    0.136671        3000
 -0.785445     -0.6111  -0.0981447        3000
  0.060862   -0.456701    0.887536        3000
  0.398325    0.667699      0.6289        3000
 -0.680604    0.689645   -0.247324        3000
  0.237399    0.969995   0.0524565        3000
  0.697302    0.541873   -0.469195        3000
 -0.868811    0.407442     0.28135        3000


It is important to note that in this format, the direction vectors are assumed to be provided with respect to real or scanner coordinates. This is the same convention as is used in the DICOM format. Also note that the file does not need to have the file type extension .b (or any other particular suffix); this is simply a historical convention.

Image header

When using the MRtrix image formats (.mih / .mif), MRtrix3 has the capability of embedding the diffusion gradient table within the header of the image file. This provides significant advantages when performing image processing:

  • The table accompanies the image data at all times, which means that the user is not responsible for tracking which diffusion gradient table corresponds to which image file, or whether or not a particular gradient table file reflects some manipulation that has been applied to an image.
  • In MRtrix3 commands that require a diffusion gradient table, and/or make modifications to the image data that require corresponding modifications to the diffusion gradient table, these data will be utilised (and/or modified) automatically, without requiring explicit intervention from the user.

For these reasons, the general recommendation of the MRtrix3 team is to make use of the MRtrix image formats (.mih / .mif) whenever possible.

This embedding is achieved by writing an entry into the Image Header key-value pairs, using the key dw_scheme. The value of this entry is the complete diffusion gradient table, stored in the MRtrix format. However, this entry should generally not be accessed or manipulated directly by users; instead, users should rely on the internal handling of these data as performed by MRtrix3 commands, or where relevant, use the command-line options provided as part of specific MRtrix3 commands, as detailed later.

FSL format

This format consists of a pair of ASCII text files, typically named bvecs & bvals (or variations thereof). The bvals file consists of a single row of space-separated floating-point values, all in one row, with one value per volume in the DWI dataset. The bvecs file consists of 3 rows of space-separated floating-point values, with the first row corresponding to the x-component of the DW gradient vectors, one value per volume in the dataset; the second row corresponding to the y-component, and the third row to the z-component. A typical pair of FSL format DW gradient files might look like:

0 0 -4.30812931665e-05 -0.00028279245503 -0.528846962834659 -0.781281266220383 0.014299684287952  0.36785999072309 -0.66507232482745  0.237350171404029  0.721877079467007 -0.880754419294581 0 -0.870185851757858 ...
0 0 -0.002606397951389 -0.97091525561761 -0.846605326714759  0.615840299891175 0.403330065122241 -0.70377676751476 -0.67378508548543 -0.971399047063277 -0.513131073140676 -0.423391107245363 0 -0.416501756655988 ...
0 0 -0.999996760803023  0.23942421337746  0.059831733802001 -0.101684552642539 0.914942902775223  0.60776414747636 -0.32201498900359  0.007004078617919 -0.464317089148873  0.212157919445896 0 -0.263255013300656 ...
0 0 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 ...

It is important to note that in this format, the gradient vectors are provided with respect to the image axes, not in real or scanner coordinates (actually, it’s a little bit more complicated than that, refer to the FSL wiki for details). This is a rich source of confusion, since seemingly innocuous changes to the image can introduce inconsistencies in the b-vectors. For example, simply reformatting the image from sagittal to axial will effectively rotate the b-vectors, since this operation changes the image axes. It is also important to remember that a particular bvals/bvecs pair is only valid for the particular image that it corresponds to.

Using the DW gradient table in MRtrix3 applications

Querying the DW gradient table

As mentioned above, MRtrix3 will use the DW gradient table from the image headers when it is available. Currently, only the DICOM (folder or .dcm) and MRtrix image formats (.mih / .mif) support this. The DW gradient table can be queried for any particular image using the mrinfo command in combination with the -dwgrad option. For example:

$ mrinfo DICOM/ -dwgrad
mrinfo: [done] scanning DICOM folder "DICOM/"
mrinfo: [100%] reading DICOM series "BRI 64 directions ep2d_diff_3scan_trace_p2"
          0           0           0           0
  -0.999994  0.00167109  0.00300897        3000
         -0    0.999996  0.00299996        3000
  0.0261389     0.65148   -0.758215        3000
  -0.590138   -0.767763   -0.249553        3000
   0.236087   -0.527069   -0.816371        3000
   0.893005   -0.261931    -0.36597        3000
  -0.797405    0.126351   -0.590068        3000
  -0.233751    0.930868   -0.280794        3000
  -0.936406    0.141569   -0.321095        3000
  -0.505355   -0.845584     0.17206        3000
  -0.346203   -0.848909     0.39937        3000
  -0.457204   -0.633042    0.624678        3000
    0.48716   -0.391994   -0.780395        3000
   0.617871    0.674589   -0.403938        3000
   0.577709   -0.102522    0.809779        3000
   0.825818   -0.523076   -0.210752        3000


Exporting the DW gradient table

This information can also be exported from the image headers using the -export_grad_mrtrix option (for the MRtrix format) or -export_grad_fsl option (for the FSL format) in commands that support it. For example:

$ mrinfo dwi.mif -export_grad_mrtrix grad.b

results in a grad.b file in MRtrix format, while:

$ mrconvert DICOM/ dwi.nii.gz -export_grad_fsl bvecs bvals
mrconvert: [done] scanning DICOM folder "DICOM/"
mrconvert: [100%] reading DICOM series "BRI 64 directions ep2d_diff_3scan_trace_p2"
mrconvert: [100%] reformatting DICOM mosaic images
mrconvert: [100%] copying from "DICOM data...ns ep2d_diff_3scan_trace_p2" to "dwi.nii.gz"
mrconvert: [100%] compressing image "dwi.nii.gz"

converts the DWI data in the DICOM/ folder to Compressed NIfTI (.nii.gz), and exports the DW gradient table to FSL format if found in the DICOM headers, resulting in a pair of bvecs & bvals files.

Importing the DW gradient table

If the image header already contain the DW information, then no further action is required - the MRtrix3 application will be able to find it and use it directly. If this is not the case (e.g. the image format does not support including it in the header), or the information contained is not correct, MRtrix3 applications also allow the DW gradient table to be imported using the -grad option (for the MRtrix format) or the -fslgrad option (for the FSL format). Note that this will override the information found in the image headers if it was there. This can be used during conversion using mrconvert, or at the point of use. For example:

$ mrconvert dwi.nii -fslgrad dwi_bvecs dwi_bvals dwi.mif

will convert the dwi.nii from NIfTI & NIfTI-2 (.nii) to MRtrix image formats (.mih / .mif), embedding the DW gradient table information found in the dwi_bvecs & dwi_bvals files (in FSL format) directly into the output image header. As another example:

$ dwi2tensor DICOM/ -grad encoding.b tensor.nii

will process the DWI dataset found in the DICOM/ folder (in DICOM (folder or .dcm) format), but override any DW gradient information in the DICOM data with the table stored in the MRtrix format file encoding.b.

Operations performed by MRtrix3 when handling DW gradient tables

MRtrix3 applications will perform a number of sanity checks and modifications to the information in the DW gradient table, depending on the nature of the operation, and its original format.

When using the FSL format

In this format, the gradient vectors are provided relative to the image axes (as detailed in the FSL wiki). To convert them to the internal representation used in MRtrix3 (and in the MRtrix format gradient table), these vectors need to be transformed into the real / scanner coordinate system. To do this requires knowledge of the DWI dataset these vectors correspond to, in particular the image transform. In essence, this consists of rotating the gradient vectors according to the rotation part of the transform (i.e. the top-left 3×3 part of the matrix). This will introduce differences between the components of the gradient vectors when stored in MRtrix format compared to the FSL format, particularly for images not acquired in a pure axial orientation (i.e. images where the rotation part of the image transform is identity). Indeed, as mentioned earlier, there is an additional confound related to the handed-ness of the coordinate system; see the FSL wiki for details.


Never perform a manual conversion between MRtrix and FSL gradient table formats using a text editor or basic shell script. This poses a risk of introducing an unwanted rotation / reflection of the gradient directions, with concomitant errors in later processing.

Note that in this operation, what matters is the transform as stored in the NIfTI headers (i.e. the sform / qform); the transform as reported by mrinfo can differ substantially from this (while still being consistent with the data), as the MRtrix3 image loading backend will try to provide the image transform in a near-axial orientation (by inverting / exchanging columns of the transform, and adjusting the Strides to match - see The image transfom for details). To find out the actual transform that was stored in the NIfTI header, use mrinfo with the -norealign option.

When copying or converting

Applications like mrconvert that don’t actually need to interpret the DW gradient table will simply pass the information through to the output unmodified. If the DW gradient table was found in the input image header, it will be written to the output image header if the image format supports it (i.e. if the output is in MRtrix image formats (.mih / .mif) - DICOM is not supported for writing). If the DW gradient table is imported via the -grad or -fslgrad option, it will also be passed through as-is (although including the modifications mentioned above in the When using the FSL format section). If the output image format does not allow storing the DW gradient table in the image header, the -export_grad_mrtrix or -export_grad_fsl options can be used to write it out to separate files, ready for use with third-party applications, or directly within MRtrix3 if users prefer to keep their data organised in this way.

When using the information for processing

Applications that actually need to make use of the DW gradient information (e.g. dwi2tensor, dwi2fod, dwiextract, ...) will perform additional sanity checks and modifications of these data, beyond those described above. These include:

  • verifying that the number of volumes in the DWI dataset matches the number of entries in the DW gradient table;
  • where relevant, verifying that the DW gradient tables contains the data in a shell structure, by clustering similar b-values together (see mrinfo‘s -shell and -shellcount options);
  • normalising the gradient vectors to unit amplitude;
  • scaling the b-values by the square of the gradient vector amplitude - see b-value scaling for details.


mrinfo will also perform most of these checks. While there is no technical reason for it to interpret the DW gradient information, in practice it is generally helpful to view the information as it would be interpreted by other MRtrix3 applications. If this is not desired, you can add the -raw_dwgrad option to mrinfo to disable these modifications when querying the DW gradient table.

b-value scaling

On MRI scanners that do not explicitly allow for multi-shell datasets, a common workaround is to set the scanning protocol according to the largest desired b-value, but use gradient vector directions that have less than unit norm. This results in diffusion sensitisation gradients with reduced strength, and hence images with lower b-values.

For example, if this was the desired gradient table:

0    0    0    0
1    0    0  700
1    0    0 2800

This could be achieved on some systems by supplying this custom diffusion vectors file, now nominally containing only b = 0 and b = 2800 s/mm²:

0    0    0    0
0.5  0    0 2800
1    0    0 2800

By default, MRtrix3 applications will automatically scale the b-values by the squared amplitude of the gradient vectors (so that the stored gradient table is equivalent to the first example), in order to more sensibly reflect the nature of the image data.

While this scaling allows such datasets to be processed seamlessly, it will introduce minor variations in the b-values for other datasets, due to minor rounding errors in the components of the direction vectors. These are benign, and have no consequence on the correct operation of MRtrix3 applications, since the deviations are typically very small, and the strategy used to group b-values into shells is robust to such variations. If however this becomes a problem (e.g. for third-party applications), this feature can be disabled using the -bvalue_scaling option for those applications that support it.