Diffusional Kurtosis Imaging

Diffusion kurtosis imaging (DKI) extends conventional diffusion tensor imaging (DTI) by estimating the kurtosis of the water diffusion probability distribution function^{1 to 4}. The kurtosis is a general, dimensionless statistic for quantifying the non-Gaussianity of any distribution⁵. A positive kurtosis means the distribution is more strongly peaked and has heavier tails than a Gaussian distribution with the same variance. Water diffusion in biological tissues is non-Gaussian due to the effects of cellular microstructure (e.g., cell membranes and organelles). This is particularly evident in brain where water diffusion is strongly restricted by myelinated axons. Qualitatively, a large diffusional kurtosis suggests a high degree of diffusional heterogeneity and microstructural complexity.

Because diffusion in brain is anisotropic, DKI requires the introduction of a diffusional kurtosis tensors (which are calculated together from a single diffusion-weighted image data set), several rotationally invariant metrics can be computed. These include standard DTI-metrics, such as the mean diffusivity and fractional anisotropy, as well as metrics reflecting the diffusional kurtosis, such as the mean, axial, and radial kurtoses. The diffusional kurtosis metrics are strongly linked to cellular microstructure, as this is the main source of diffusional non-Gaussianity in tissues. The extra information provided by DKI can also resolve intra-voxel fiber crossings and thus be used to improve fiber tractography of white matter^{6 to 7}.

An advantage of DKI is that it is relatively simple to implement for human imaging on conventional MRI clinical scanners. DKI protocols differ from DTI-protocols in requiring at least 3 b-values (as compared to 2 b-values for DTI) and at least 30 independent diffusion gradient directions (as compared to 6 for DTI). Typical protocols for brain have b-values of 0, 1000, 2000 s/mm² with diffusion directions. Image post-processing requires the use of specialized alogorithms^{4 to 8}.

DKI has been most commonly used for the study of the human brain^{9 to 52}, although applications to other body parts such as lung⁵³, prostate cancer^{55 to 58}, breast cancer⁵⁹, calf muscle⁶⁰ and the liver⁶¹ have been investigated. There are also several technical studies involving DKI^{62 to 71}. Animal models have been studied as well using diffusional kurtosis imaging^{10,11,22,33,43,72,73}.

The Center for Biomedical Imaging would like to acknoledge Ali Tabesh, Ph.D. and Emilie McKinnon for their hard work to help create the DKE software. 

Get Started With DKI Imaging

• Gather your DKI data. More information about DKI Protocols.
• Process your DKI data. More information about DKI Data Processing
• Analyze your results.

Changes to DKE

DKE 2.6 (February 25, 2015)

• The addition of two new parametric maps: KFA and MKT.
• The diffusion and kurtosis tensors are now written as outputs.
• Bruker format support.
• Small change in median filtering.
• Minor bug fixes.
• Linux version.

DKE 2.5.1 (December 27, 2012)

• The length of user-defined gradient sets was not recognized properly.

DKE 2.5.0.1 (September 24, 2012)

• Vista read-only issue fixed.
• DCMDICTPATH not set properly in x86 package.

DKE 2.5.0 (September 17, 2012)

• Initial release.
• Only MATLAB Compiler Runtime required.
• GUI added.

DKE Modules

The DKE Fiber Tractography (FT) Module performs white matter FT using the DKI approximation of the diffusion orientation distribution function (dODF). This module uses the diffusion and kurtosis tensors from DKE and should be run with DKE version 2.6 or later. DKE requires the installation of the MATLAB Compiler Runtime 2012a (MCR)

DKE Help

• Download DKE Manual (PDF)
• Download FT Manual (PDF)
• Download MCR

Gradient Vectors: Use Siemens 30-direction
B-values: [0 1000 2000]

Diffusional kurtosis imaging (DKI) extends conventional diffusion tensor imaging (DTI) to the calculation of the diffusional kurtosis and related kurtosis metrics^{1 to 4}. For a certain diffusion direction vector n and diffusion weighting b, the DKI approximation to diffusion signal intensity S (n,b) is given by:

with,

Where S₀ is the signal intensity for b=0, D_ij and W_ijkl are the elements of the second order diffusion tensor D and fourth order kurtosis tensor W. Both tensors are fully symmetric⁸. Consequently D has 6 and W has 15 independent parameters. In order to solve the equation at least two nonzero b-values and 15 distinct gradient directions are required⁸.

Protocols

Recommended DKI protocols for Siemens scanners:

• Prisma (PDF)
• Tim Trio (short) (PDF)
• Tim Trio (long) (PDF)
• Verio (PDF)

Example protocols from other vendors:

• Phillips* (PDF) 
• GE** (PDF)
• Bruker: Rats^*** and Mice^****

Note: It is important to keep TE the same for all signal acquisitions.

We thank Masaaki Hori, M.D* (Department of Radiology, Juntendo University School of Medicine) and Dr. Muftuler Tugan** (Medical College of Wisconsin) who provided us with their DKI protocols.
***For protocol details for rats we refer to Weber RA, Hui ES, Jensen JH, Nie X, Falangola MF, Helpern JA, Adkins DL. Diffusional kurtosis and diffusion tensor imaging reveal different time-sensitive stroke-induced microstructual changes. Stroke. 2015 Feb; 46(2): 545 to 50.
****For protocol detail for mice we refer to Nie X, Hamlett ED, Granholm AC, Hui ES, Helpern JA, Jensen JH, Boger HA, Collins HR, Falangola MF. Evidence of altered age-related brain cytoarchitecturein mouse models of down syndrome: a diffusional kurtosis imaging study. Magn Reson Imaging 2014 Dec 16.

Frequently asked questions

PyDesigner

NEW: Please check out the latest in DKI data processing using PyDesigner.

Register and Download DKE Software

You can register and download the current version of DKE software for your operating system at the following link. Download DKE Software

Changes to DKE:

DKE 2.6 (February 25, 2015)

• The addition of two new parametric maps: KFA and MKT
• The diffusion and kurtosis tensors are now written as outputs.
• Bruker format support.
• Small change in median filtering.
• Minor bug fixes.
• Linux version.

DKE 2.5.1 (December 27, 2012)

• The length of user-defined gradiant sets was not recognized properly.

DKE 2.5.0.1 (September 24, 2012)

• Vista read-only issue fixed.
• DCMDICTPATH not set properly in x86 package.

DKE 2.5.0 (September 17, 2012)

• Initial release.
• Only MATLAB Compiler Runtime required.
• GUI added.

DKE Modules

The DKE Fiber Tractography (FT) Module performs white matter FT using the DKI approximation of the diffusion orientation distribution function (dODF). This module uses the diffusion and kurtosis tensors from DKE and should be run with DKE version 2.6 or later.

• Download DKE Fibertracking

DKE requires the installation of the MATLAB Compiler Runtime 2012a (MCR)

• Download MCR

DKE Help

• Download DKE Manual (PDF)
• Download FT Manual (PDF)

Example Dataset

If you don't have a DKI dataset, you can download the example dataset from our DKE project on NITRC. The DKI files are in DICOM and NIfTI format. You can also download parametric maps and tensors output from DKE.

Download Example Dataset on NITRC

Gradient Vectors: Use Siemens 30-direction

B-values: [0 1000 2000]

DKE generates a set of kurtosis (axial, mean, radial) parametric maps. DKE also generates diffusivity (axial, mean, radial) and fractional anisotropy maps using either DKI or diffusion tensor imaging signal models.* In the latest version of DKE, we added the creation of two new parametric maps; KFA and MKT.

Kmean (MK) - Mean kurtosis, the diffusional kurtosis averaged over all gradient directions⁸.

Kax (K_II) - Axial kurtosis, the diffusional kurtosis in the direction of highest diffusion⁸.

Krad (K_I) - Radial kurtosis, the mean direction kurtosis perpendicular to the direction of highest diffusion⁷.

MKT - Mean kurtosis tensor⁷³.

K2 (K₂) - Kurtosis along the direction of the eigenvector corresponding to the second diffusion tensor eigenvalue.

K3 (K₃) - Kurtosis along the direction of minimum diffusivity.

Dmean (MD) - Mean diffusivity, the diffusivity averaged over all gradient directions.

Dax (D_II) - Axial diffusivity, the diffusivity in the direction of the highest diffusion.

Drad (D_l) - Radial diffusivity, the mean directional diffusivity perpendicular to the direction of highest diffusion.

D2 (D₂) - Diffusivity along the direction of the eigenvector corresponding to the second diffusion tensor eigenvalue.

D3 (D₃) - Diffusion along the direction of minimum diffusivity.

FA - Fractional anisotropy, degree of anisotropy of the diffusion tensor⁷⁴.

KFA - Kurtosis fractional anisotropy, degree of anisotropy of the kurtosis tensor⁷⁵.

DT - Diffusion tensor

KT - Kurtosis tensor

* Output maps with the extension_dti are the results from DTI processing.

How do I view the results?

DKE outputs images in a NIfTI format. There are several programs readily available online that are compatible with NIfTI: MRICron and ImageJ are two recommended software programs.

How do I analyze the results?

A typical output will contain the following set of parametric maps: Dmean (Mean diffusion), Dax (Axial diffusivity), Drad (Radial diffusivity), Kmean (Mean kurtosis), Kax (Axial kurtosis), Krad (Radial Kurtosis) and fa (Fractional Anisotropy). From here there are several things that can be done. One option is to execute a voxelwise analysis using software like FSL SPM. Another option is to perform an ROI (Region of Interest) analysis. If a structural image is available, use software like freesurfer to segment the structural image into clinically important areas like the corpus callosum and the hippocampus. These regions can be overlaid on the parametric maps of DKE and be used as a mask. From here, these regional specific results can be imported into any computational software like Matlab, where a statistical analysis can be performed. If structural images are not available, use a standard labels atlas like the John Hopkins White Matter Labels Atlas (supplied with FSL and MRICron), which contains a set of clinically important brain labels. Once all images (DKE parametric maps and Atlas) are brought into the same space, use these labels as a mask for a statistical analyses. There are many different ways the DKE output can be used and the former are, of course, mere suggestions.

Which B values should be used?

When performing a DKI analysis you need at least 3 b-values, from which one is a b0 (i.e., b=0). Care needs to be taken when choosing your b-values. If the b-value is too low, there will be little change in your signal intensity and you results will be sensitive to noise. If it is too high the parameters are not estimated accurately (do to the neglecting of the higher order term O(b³)).⁴ Typically when performing a DKI analysis your b-values will be higher than for DTI (this is wanted because of the addition of the second order term in the equations). We found that using a maximum b-value of 2000 s/mm² results in an accuracy of about 20percent or better for the diffusional kurtosis and a accuracy of roughly 7percent or better for the diffusion coefficient^.4 (under the assumption that signal decay in the brain is biexponential). In practice the optimal choice is a compromise between precision and accuracy and for DKI using a maximum between 2000 s/mm² and 3000 s/mm² seems appropriate.⁴ If only a set of 2 b-values (a b=0 and a b non-zero) is available, DKE can be run with the option DTI only and then 2 b-values are sufficient.

What kind of gradient table does DKE expect?

When using the GUI, the current release DKE assumes that the gradient directions are the same for all nonzero B-values. For a protocol with 30 gradient direction, import a text file with a matrix of the size [30x3]. Each row corresponds to a gradient vector. A common tool to find the gradient table is dcm2nii. Before using the .bvec file as a user defined input, transpose the matrix (so every row corresponds to a G_x, G_y, G_z,) and remove the row that corresponds to the b=0 image (0,0,0). When using a 4D nifti as input, it is very important that the order of the images corresponds to the order of the gradient table. If a DICOM set is used DKE will order the images according to the information stored in the DICOM tag (0018, 0024) SequenceName.

If a different gradient set was used for each b-value, you can use the command prompt and run .dat file by specifying a X-(nbval-1) cell array of file names in the fn_gradients options, with each cell specifying the gradient file name for the corresponding nonzero b-value. More info on how to run DKE with the command prompt can be found in the manual under DKE help.

I am using a Phillips Scanner and my results appear to be wrong?

We have found that when using DKE protocol on a Phillips scanner it creates a trace image after each B-value (averaging of all three dimensional images). Make sure that these images are removed out of your folder when running DKE, as they have the same series in the description in the header DKE cannot recognize them. Again, dcm2nii has a special option for doing this. Make sure before running DKE that your images and gradient table are ordered in the same way (when using NifTI). If a DICOM set is used DKE will order the images according to the information stored in the DICOM tag (0018, 0024) SequenceName. Unfortunately some Phillips Scanners do not produce SequenceName tag and DKE will have to be run using a 4D NifTI.

All the parametric maps look correct, besides the FA map.

The functional anisotropy is very sensitive to inputting the correct gradient directions. When the FA map contains lower values than expected, there is most likely a mistake in the order of your gradient table.

The results have some areas that are very grainy/appears to have information missing?

Try processing the data with the weak filtering option or even no filtering. An outlier removal median filter with a 3x3x3 voxel window is applied to voxels that violate the minimum directional kurtosis constraints. Strong filtering will correct voxels where any constraint violation was detected. When one of the maps has an area with a lot of violating voxels, erroneous results can arise. We created a softer version of this approach called weak filtering. During weak filtering only voxels with less than 15 unviolated constraints will be filtered. When it is suspected that your data is of lower quality, it is recommended to set the filtering option to weak filtering.

I am using a 4D nifti when running DKE and my results appear to be wrong?

Several things might have happened. Please check the images in the 4D nifti are ordered in the right way. DKE expects the 4D nifiti to be build up like this: 1 b=0 image, all b(1) images, all b(2) images... When using multiple b=0 zero images or multiple averages, it is recommended to use the raw dicoms. If this is not possible, create your own averages (creating just one B0 image and only one set of B (1) images, etc.) first before running DKE (i.e with matlab).

Some of the diffusion-weighted images are not usable do to motion or table vibration artifacts.

When running DKE in the command window, in the .dat file you can specify which indices of gradient directions are to be used for the DKI map estimations. This can be specified in the parameter idx_gradients. For example, when using 20 gradient directions and the images created with the second gradient direction were unusable. Idx_gradients should be specified as: [1 3 4 5 6 7 8 10 11 12 13 14 15 16 17 18 19 20]. There must be as many cells as there are nonzero b-values. So when using 2 nonzero b-values; specify a Idx_gradient {1} and a Idx_gradient{2}.

How do I launch DKE in the command prompt and what are the advantages?

When running DKE in the command window several extra parameters can be fine-tuned. You will need to alter the DKE processing parameters file. This is created every time you run DKE using the GUI and is located in the same folder as your images. Open DKEParameters.dat using a text editor. Here you will be able to adjust the settings.

In the terminal window run dke by specifying both the path for DKE and your DKEParameters.dat file.

>"C:\Program Files\DKE\dke.exe" "C:\Users\Documents\Project1\DKEParameters.dat"

You can find details about how to use the parameter file in the manual under DKE help.

How do I use DKE with Bruker Data?

Bruker data right now is not supported in the GUI, so you will have to run DKE in the command window. Open DKEParameters.dat and change the preprocessing_options.format from dicom to bruker. You will also need to specify the coreg_flag and the navg. Make sure your method file is located in the same folder as your images.

How do I run DKE on Linux?

Open a terminal cd to the folder that contains the executable. Run dke with ./run_dke.sh

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