To whom it may concern,
As this was a side project, it took longer than anticipated.
Summary:
A phantom was measured with a Bruker Biospec 11.7T small-animal scanner using Paravision 360 v3.6 and the DtiStandard (Spin Echo) sequence.
Fiber tracts were estimated for all flips and swaps of the b-vectors. The streamline (fiber) length distribution was used as a quantitative metric.
The following was tested only on the subject type “Other”:
Subject file: SUBJECT_type=Other
The FOV orientation was set to transverse and acquired in the following orientations:
Method file:
PVM_SPackArrSliceOrient = sagittal / axial / coronal
The readout axis remained at its default setting.
Result for the new order:
Within DSI 2024 OCT 31 (newer versions were not used, as scans are forced into templates):
Axial scan: new order (R, P, −S) / (X, Y, −Z)
Coronal / sagittal scan: new order (P, R, −S) / (Y, X, −Z)
All signs may be flipped simultaneously, which yields an equivalent result. For example,
(R, P, −S) / (X, Y, −Z) is equivalent to (−R, −P, S) / (−X, −Y, Z).
Exemplary result for default and correct orientation between image and gradients, as well as the statistics are attached.

When the measurement was exported to NIfTI format via Paravision, the correct relation was preserved by the diffusion matrix in image space:
PVM_DwBMatImag, where the largest eigenvalue corresponded to the b-value and the associated eigenvector to the b-vector. Which also corresponds to the manual.
Final note:
Please verify how different processing pipelines may misalign the image–gradient relationship. For example, DSI introduced a flip in the second component of the b-vectors when exporting or loading them from external files. This required correction, depending on whether a given pipeline already applied that flip internally.
The data and pipeline will be provided as soon as I find time to wrap this up.--
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That is understandable. I was wondering whether we could start collecting these results openly on a single page until the logic behind the correct orientation relation is identified.
My idea was to include it in the Bruker section of https://dsi-studio.labsolver.org/doc/gui_t1.html or create a general Google Groups post linked from there.
In that post, people could provide their setup, if the relationship between image and gradients differs from the ones already collected.
As a side note, for our setup we found that “VisuAcqGradEncoding” specifies the correct order in DSI Studio, although the signs are not correct.
Andreas