Diffusion tensor MRI datasets

This page will attempt to document, collect and/or reference various diffusion tensor datasets, to facilitate research in diffusion tensor analysis and visualization.

General Information

The datasets here are in NRRD format, which is a human-readable ASCII header and a raw data file. The advantages of NRRD over comparable formats include its use in SCIRun and the BioTensor programs, as well as two powerful command-line tools: unu and tend, which access functionality in the nrrd and ten libraries of teem, respectively. Unu does operations on N-dimensional arrays without any application-specific knowledge of what is in the array; tend does operations on tensor volumes conforming to the layout described below. As demonstrated below, piping invocations of these programs together allows a number of non-trivial operations to be done quickly, and in a way which facilitates data inspection and batch pre-processing. Both programs can be invoked with no other command-line options to get a listing of the available sub-commands and what they do. Note: unless otherwise noted, the unu and tend commands demonstrated below should work with teem version 1.6.0 or later; pre-compiled binaries are the easiest way to get started.

The values in the dataset are 32-bit floats (C type "float"), written in raw, big-endian, which opposite of Intel and AMD PCs (little-endian), but the same as everyone else (Macs, SGI, Sun, etc). There are seven values per voxel:

  1. "confidence": this is a mask image, which is 1.0 in regions where the tensors are meaningful and useful, and 0.0 where the tensors are noise (such as air). This is not always a sharp threshold: some fuzziness of intermediate values allows this volume to be isosurfaced usefully (at value 0.5).
  2. Dxx
  3. Dxy
  4. Dxz
  5. Dyy
  6. Dyz
  7. Dzz
The Dxx, Dxy, ... values are the six unique entries in the (symmetric) diffusion tensor, as measured in the scanner's coordinate system. If exact units are known for the tensor coefficients are known, they are indicated per-dataset.

Communicating sampled tensor fields is complicated by issues of raster order and coordinate transforms, and these need to be described in order for the data to be interpreted meaningfully. There are actually three coordinate systems relevant for describing a sampled tensor field:

  1. The measurement frame: the coordinate frame in which the tensor is represented as a matrix (the Dxx, Dxy, ..., values listed above).
  2. The sampling frame: The regular grid on which the tensor samples lie in space. It has three perpendicular axes which span the spatial domain of the tensor volume.
  3. The raster frame: Not really a frame on its own, just an ordering of the axes of the sampling frame, and an ordering of the samples along the axes of the sampling frame, as imposed by the ordering of the sample values in memory or on disk.
Starting with the assumption of a right-handed ordered basis {X,Y,Z} for the measurement space in which the tensors are expressed, we impose the convention that the sampling frame's axes are also aligned with the X, Y, and Z directions. This in turn imposes an ordering and a direction on each of the axes of the sampling space.

Working from the other direction, that of the underlying ordering of values in memory or on disk, the three coordinates by which the samples are indexed can be ordered from fast to slow. As one linearly traverses contiguous values in memory, one of the coordinates will change fastest, one coordinates changes "medium" fast, and the remaining coordinate changes slowest. (For example, in normal interleaved storage of RGB images, the raster axis ordering from fast to slow is RGB, horizontal, and then vertical.) The fast-to-slow ordering of the raster coordinates induces a fast-to-slow ordering of the axes of the sampling frame.

We adopt the convention that the fast-to-slow ordering of sampling frame axes, and the ordering defined by the {X,Y,Z} ordered basis of the measurement frame, be the same. Thus the relationship between the measurement and raster frames is:

Furthermore, samples with a higher memory location should be spatically located at a higher coordinates in sampling space.

Synthetic twisting helix

The dataset consists of these two files:
This dataset is a good test or demonstration of the relationships between the raster, sampling, and world coordinate frames. From fast to slow, the volume grid dimensions are 38, 39, and 40; errors in this ordering will result in fragmented structures, looking nothing like the helical coils shown above in a cuboid glyph rendering. Note that the coil is right-handed, which determines the correct spatial ordering of the slices along the Z axis. Finally, notice that the tensors on the coil surface also twist. If your tensors do not twist smoothly along the surface of the coil, than the sampling and measurement frames are in disagreement. Like the helical coils themselves, this twisting is also right-handed. On the other hand, if you cut through the diameter of the coils (along the minor eigenvector of the tensor), and look at how the individual tensors are twisting (moving vertically in the middle of the second image, aboved), this is left-handed.

This dataset was created with a tend command from teem version 1.7.0:

tend helix -s 38 39 40 -r 0.5 -R 1.2 -S 2 -o dt-helix.nhdr
The renderings above were also generated with teem (as EPS files):
echo "1   1 1 1   -1 -1 -3" \
 | emap -i - $CAM -o emap.nrrd
tend glyph -i dt-helix.nhdr -emap emap.nrrd -bg 0.7 0.7 0.7 -sat 0.8 \
   $CAM -ur -0.92 0.92 -vr -1.0 1.2 \
   -psc 345 -gsc 0.03 -atr 0.6 -o whole.eps
tend slice -i dt-helix.nhdr -a 2 -p 0 \
 | tend glyph -emap emap.nrrd -bg 0.7 0.7 0.7 -sat 0.8 \
   $CAM -ur -0.3 0.3 -vr 0.2 0.8 \
   -wd 1.6 0.8 0 -psc 900 -gsc 0.03 -atr 0.6 -o slice.eps
rm -f emap.nrrd
Acknowledgment: Something along these lines would be appreciated, but is not required:
Synthetic tensor dataset produced with the tend program in the Teem toolkit; <http://teem.sourceforge.net>

Human brain, Feb 2000

The dataset consists of these two files:
This is a 148 x 190 x 160 scan of Gordon Kindlmann's brain. The voxel size is 1mm x 1mm x 1mm. MRI Scanning parameters for this data are not currently available.

Beware that not all samples have positive eigenvalues: probably due to noise, and the fact that only 6 diffusion-weighted images were used, so that there was no redundancy in the tensor estimation. Hence, you may want to run the data through "tend evalclamp"

The first image above was generated by:

tend slice -i gk2-rcc-mask.nhdr -a 1 -p 90 \
 | tend evecrgb -c 0 -a fa \
 | unu axdelete -a -1 \
 | unu resample -s = x2 x2 -k box \
 | unu quantize -b 8 -o gk2-y90.png
The second image, a glyph-based visualization of the same slice, was created by these steps; the ray-tracing took a few minutes.

Acknowledgement: If you use this data in publication, you must provide the following acknowlegement:

Brain dataset courtesy of Gordon Kindlmann at the Scientific Computing and Imaging Institute, University of Utah, and Andrew Alexander, W. M. Keck Laboratory for Functional Brain Imaging and Behavior, University of Wisconsin-Madison.