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.

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.

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:

bvecs:
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 ...

bvals:
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¶

Most MRtrix3 applications that don’t actually need to interpret the DW gradient table will typically simply pass the information through to the output unmodified. Any information found in the input image header – including the DW gradient table – is simply 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 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.

However, any MRtrix3 application that manipulates the DW gradient table in any way (for example, using the -grad or -fslgrad option) 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. This includes applications such as mrconvert, mrinfo, mrcat, and other most obvious DW-specific applications such as dwi2tensor and dwi2fod.

The specific steps performed by MRtrix3 include:

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

Note

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 you need to display the raw DW gradient table before any modification, use mrinfo with the -property dw_scheme option.

### b-value shells¶

For a number of MRtrix3 processing steps, it is necessary for DWI data to be arranged in “shells”: that is, sets of volumes within which the strength of diffusion sensitisation is identical, and only the direction of diffusion sensitisation varies, and hence when visualised in q-space such a set of volumes construct a “shell” of points at a fixed distance from the origin. Data acquired in such a fashion is, for instance, necessary for application of the spherical deconvolution model.

However sometimes even if data were acquired with the intent of being utilised in this fashion, the reported b-values of such volumes may not be precisely equivalent; e.g.:

5 5 1489.96 2994.94 1489.99 3009.96 1499.95 2989.96


Intuitively, these data look like there are three unique b-values: 0, 1500 and 3000; but the actual reported values are slightly different. This can be due to e.g.:

• The scanner vendor reporting a b-value that is calculated based on the comprehensive set of all gradients applied during acquisition (this regularly deviates by 5-20 s/mm² from the nominal intended b-value);
• Imprecise gradient vector directions leading to minor modulation of the b-value once those vector directions are normalised to unit length (see b-value scaling below).

In order to robustly handle such data, some MRtrix3 commands will internally run a clustering algorithm that groups DWI volumes according to b-value similarity. So for instance, if one were to run the dwiextract command on the data above, specifying the option -shell 3000, those volumes with reported b-values 2994.94, 3009.96 and 2989.96 would be extracted, despite the b-value not being precisely 3000 in each case.

The behaviour of this algorithm can be interrogated directly using the mrinfo command, using the following command-line options:

• -shell_bvalues: The mean b-value of those volumes attributed to each discrete shell;
• -shell_sizes: The number of volumes attributed to each discrete shell;
• -shell_indices: The indices of the specific volumes attributed to each shell; note that the first volume of the 4D series has index 0; volumes within each shell are separated by commas, while shells are separated by spaces.

It is possible that in some instances, this automatic grouping of volumes with near-equivalent b-values into shells within MRtrix3 may not yield the results wanted by the user. Rather than modifying the gradient table data directly, it is possible in some instances that modifying the underlying parameters within the b-value clustering algorithm may be sufficient to alter this behaviour. The following two variables can be set within the MRtrix Configuration file:

• BValueEpsilon: If the minimal difference in b-value between two groups of volumes is at least this amount (in s/mm²), then those two groups will be classified as two separate shells, rather than agglomerated into a single shell.
• BZeroThreshold: Any volume for which the b-value is this value or lesser will be classified as a “b = 0” volume, and therefore assigned to the group of all volumes that are classified as “b = 0”.

Note

There can be some ambiguity around the relationship between the common definition of “shell” in the diffusion MRI field, and the interpretation of b = 0 volumes in MRtrix3. A DWI acquisition that involves acquisition of some number of b = 0 volumes, and some number of volumes at some fixed non-zero b-value, e.g. b = 3000, would conventionally be referred to as a “single-shell” acquisition. However, internally within MRtrix3, such data would be interpreted as consisting of two “shells”: one at b = 0, and one at b = 3000. The nominally b = 0 volumes can still be utilised as a “shell” in various applications given that, when treated as a discrete set, they possess effectively an equivalent b-value, and the condition of “different sensitisation directions” is essentially irrelevant in this specific case.

## 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 detect this and automatically scale the b-values by the squared amplitude of the gradient vectors if required (so that the stored gradient table is equivalent to the first example), in order to more sensibly reflect the nature of the image data. Note that this is only applied if the DW gradient table looks like it corresponds to a multi-shell scheme, which is detected heuristically based on whether the gradient vector norms deviate from unity by more than 1%.

While this scaling allows such datasets to be processed seamlessly, it may introduce unexpected variations in the b-values for other datasets. Alternatively, if the provided diffusion gradient table is malformed, and contains the correct b-values but non-unity-norm directions, this scaling will result in a reported diffusion gradient table that contains b-values other than those expected.

If this scaling becomes a problem (e.g. for third-party applications), this feature can be explicitly enabled or disabled using the -bvalue_scaling option in mrconvert when initially importing or converting the raw data.

### 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.

Warning

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 -config RealignTransform false option.