Structural brain network construction using ε-neighbor method

(c) Moo K. Chung, Nagesh Aldur
Department of Biostastics and Medical Infomatics
Waisman Laboratory for Brain Imaging and Behavior
University of Wisconsin-Madison

April 24, 2010

Based on the ε-neighbor algorithm [1] [2], the brain connectivity of DTI fibers can be obtained as an adjacency matrix. The algorithm was first introduced in OHBM [1] then refiend in [2]. [3] performs the ε-neighbor network consruction on a template so the resulting networks have identical node positions in the template. [4] modfied the ε-neighbor method to be applicable to arbitrary connectivty matrix. Here we present the ε-neighbor algorithm and visualization and analysis tools. The codes have been tested under Matlab versions 7.5 on a Mac computer (intel processor) with 4GB memory and MATLAB 7.5. If you are using the Matlab codes/sample data given here for your publication, please reference [2].

Fiber bundle visualization
July 7, 2010

Let's load the FA map of the template used in [1] [2]. We have to swap x- and y-coordinates since the MATLAB convention is slightly different from the usual NII-format. You need to unzip file from the link below.

surf = isosurface(d);
figure_patch(surf,[0.74 0.71 0.61],0.2); hold on;

We will superimpose white matter fiber bundles on top of the FA-map. SL.mat contains information about 10000 tracts stored as cell data structure. To extract coordinates of the i-th tract, call SL{i}.

load SL.mat
for i=1:30:10000 % subsampling 1 for every 30 tracts
    if size(tract,2)> 10
        hold on

To obtain the two end points of tracts and color them as read, we run

hold on; plot3(endp(:,1,1),endp(:,1,2), endp(:,1,3),'.r')
hold on; plot3(endp(:,2,1),endp(:,2,2), endp(:,2,3),'.r')

The resulting image is shown in Figure 1.

Figure 1. White matter fiber bundles obtained from a streamline-based algorithm. The tracts are sparsely subsampled for better visualization. The end points are colored as red. The surface is the isosurface of the template FA map so some tracts are expected to be outside of the surface. The
ε-neighbor method will use the proximity of the ends points in constructing the network graph.

ε-neighbor algorithm
July 7, 2010

The ε-neighbor algorithm is run directly on the list of fiber bundles SL.mat. adj is the adjacency matrix, prob is the fiber concentration density, which is computed by counting the number of tracts that is connecting to the given node within ε-neighbor. vertices is the coordinates of the constructed nodes. Figure 2 shows the resulting graphs superimposed on top of the FA template and the corresponding adjacency matrices.

[adj, prob, vertices]=tract2graph(SL,10);
figure; imagesc(-adj); colormap('bone');

Figure 2. Scalable 3D connectivity graphs constructed from the proposed algorithm and the corresponding adjacency matrices. The nodes are indexed by numbers. From the left to right, graphs are at 20, 10 and 6mm resolution.

3D graph display
April 28, 2010

Download a sample data dtigraph.mat that contains the adjacency matrix adj consisting of zeros and ones, and vertices that contain the coordiantes of nodes.

load dtigraph.mat;

To compute the degree of nodes, we sum the adjaceny matrix either along the row or the column direction. The node degree can be displayed in 3D:


The number 0.001 is added to avoid an error associted with using the default MATLAB command scatter3 that can't drow a ball of 0 radius.

Figure 3. 3D structural brain network showing the node degree.

April 22, 2010

  1. Chung, M.K. Adluru, N. Dalton, K. M., Alexander, A.L., Davidson, R.J. 2010. Characterization of structural connectivity in autism using graph networks with DTI. 16th Annual Meeting of the Organization for Human Brain Mapping. 938.
  2. Chung, M.K. Adluru, N. Dalton, K. M., Alexander, A.L., Davidson, R.J. 2011. Scalable brain network construction on white matter fibers", Proc. SPIE 7962, 79624G; doi:10.1117/12.874245
  3. Adluru, N., Chung, M.K., Dalton, K.M., Alexander, A.L., Davidson, R.J. 2010. Characterizing brain connectivity using ε-radial nodes: application for classifying autism. MICCAI workshop on Computational Diffusion MRI.
  4. Kim, S.-G., Chung, M.K., Hanson, J.L., Avants, B.B., Gee, J.C., Davidson, R.J., Pollak, S.D. 2011. Structural connectivity via the tensor-based morphometry. IEEE International Symposium on Biomedical Imaging (ISBI).