Diffusion Tensor Analysis


Introduction

The tensor analysis tool will take a previously computed diffusion tensor image (generated from the [ Tensor Utility ]), and create a series of diffusion-derived maps. It will also calculate region of interest (ROI) statistics of these maps, when an ROI mask is provided. Finally, the tensor analysis program also provides a set of visualization tools to depict tensors and vector fields. In order to invoke tensor analysis, choose the "Diffusion" menu, and select the "Tensor analysis" item.

1. Loading the diffusion tensor

Once you have computed the diffusion tensor using the tensor utlility tool, invoke the tensor analysis program from the Diffusion menu in the main viewer. To load the tensor, click on Load in the Tensor pane, and select the tensor image. When loading is complete, the tensor image will be displayed in the main viewer. Note that because the tensor is symmetric, you will only see 6 components out of a total of 9 elements.

Normally, you will not need to change the ordering of the tensor components in the Components drop-down box. However, if the tensor image was created with third-party software, it may be possible that the ordering is different. Hence, in addition to the xx-xy-xz-yy-yz-zz ordering, xx-yy-zz-xy-xz-yz is also provided.



If you have saved an anatomical mask in the tensor utility tool, or have an ROI mask for analysis (see [ Segmentation ]), you can load it in the Region of Interest mask. Simply disable the option Estimate from tensor, then click on Load. The program also allows you to have multiple regions of interest in the same mask. They have to be labeled consecutively from 1,2,...,n. After loading the multiple ROI mask, you should see the correct number of regions displayed in the option Number of regions in mask.

It is often the case that in the presence of noise and artifacts, a few tensors may yield negative (likely very small magnitude) eigenvalues. Since this is not physically possible, you may choose to exclude these regions from the diffusion maps and statistics. You can enable that option by checking Mask out regions with negative eigenvalues. The default behavior is to include these regions, but to make their eigenvalues positive.

Once the tensor image is loaded and, optionally, also the mask, click on Compute! to calculate the diffusion maps and generate statistics.

2. Results

Once the diffusion maps are computed, you will be taken to the Results pane, where a list of the results will be displayed. By default, the Fractional Anisotropy (FA) map is displayed in the main viewer. You may select different results and display them using the Display button.

Some of the result items are grayed out, which means they are not computed by default. To enable their calculation, double-click on them, or select the item and press "On/Off". Then, go back to the Tensor pane, and click Compute! once more.


Please note that diffusion maps are only shown at the regions of interest. At this moment, you may choose to save any of the computed results.

3. Statistics

Basic diffusion map statistics are calculated for each one of the regions in the ROI mask. The statistics are displayed in a report format, and can be saved as a text file. You can then import this file into statistical analysis programs or text editors.



4. Visualization

The tensor analysis tool provides a series of visualization options, ranging from vector to tensor plots and the ability of managing their colormaps. See below for a summary of the display options.

To view vector fields and tensors, make sure the viewer is in 3D display mode.



4.1 Plotting the principal eigenvector field (Fast Eigenvector)

In the Display pane, select the View menu, and enable the option "Fast eigenvector". By default, the eigenvectors are displayed on the three orthogonal planes, however this can be changed in the Location menu. Make sure this matches what you are currently displaying. Important: as you move through the slices in the main viewer, you will need to click Refresh to replot the vector field on the newly selected slices.

 
(a) Principal eigenvector displayed as lines.                                (b) Principal eigenvector displayed as tubes.

In the Eigenvectors tab, you can fine-tune the display of the eigenvector plot. You may select a diffusion map to filter the results and control the lower and upper bounds. Vectors will only be displayed if they are within the selected range of values. Eigenvectors can be viewed as Lines, Tubes, or Arrows, and can be custom-scaled (see Glyph scale factor option). Tensor analysis does not allow scaling vectors by their magnitude.

4.2 Plotting the tensor field

Alternatively, you can also display the tensor ellipsoids by checking the option "Tensor" in the View menu. The same type of filtering options are available for managing the tensor visualization, which is accessible by the Tensors tab. Tensors can be viewed as Ellipsoids, Cuboids or Sheets.


Tensors displayed as sheets (axis with smallest magnitude is discarded).

4.3 Display the directionality map

The directionality map, also called the color tensor or directionally-encoded colormap, represents the principal eigenvector by means of a color representation. The most common scheme is to represent the x component as red, the y component as green and the z component as blue. Normally, the brightness is modulated by a second measure, such as fractional anisotropy.

     
                                            Transaxial cut of a direcionality map.

To compute the directionality map, click on the "Directionality" tab, select the intensity modulation method, the color scheme (absolute value is the default), and the number of colors for quantization. Then click the Apply! button. The resulting map will be shown in the main viewer.

4.4 Coloring the results

 The colormap editor is a straightforward way to color your diffusion images. You can define the number of colors to be used and the scalar range that it will represent. The resulting colormap will be a linear gradient between two colors, color 1: and 2:, both specified in HSVA (hue, saturation, value, alpha) coordinates. The alpha parameter corresponds to opacity.

You can apply a colormap to any of the diffusion maps that were calculated by the tensor analysis tool. First select the diffusion map to be displayed from the Results tab. Click on Display. Now in the Display tab, select Results and customize the colormap accordingly. Once you ready, click on Apply!. Now the diffusion map should be displayed in the colormap you have selected. Below is an example of coloring the FA map with a hot color scheme.
 
   

5. Transformations

A subset of tensor transformations can be found in the Tensor Analysis tool. This is to allow convenient transformation in situations where the transformation is not known prior to the tensor analysis. Using the visualization tools described above, one can determine by looking at the orientation of the vector or tensor fields when a transformation is required.

To apply a transformation, choose the Transform tab and select the type of transformation. For flips, the result is instantaneous and will update any visualization glyphs present in the main viewer. 



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