Modular dissociation

Welcome to the data and code sharing tutorial for the article “The functional brain favours segregated modular connectivity at old age unless targeted by neurodegeneration” which is currently under review.

This paper is now in preprint format and can be downloaded from BioRxiv here: Peraza et al. (under review)

Needed Toolboxes

Below is a list of toolboxes/libraries used in my research report. All of these are open source and can be downloaded from their original sources.

The database for this tutorial is published in Figshare. This database contains a PDF file describing the variables as well as a Matlab file with all participant matrices from the NKI cohort. Download the matlab data file NKImatrices_Peraza.mat and you will be ready for this tutorial!

We start adding the toolboxes we need to the Matlab path. My custom functions for modular variability/dissociation (MV/MD), and local/global network thresholding are stored in the MDToolbox folder,

addpath MDToolbox

Also, add the toolbox for the minimum spanning tree (MST, needed for local thresholding). The function that estimates the MST belongs to the MTNA Toolbox and can be downloaded from the link provided,

addpath matlab_networks_routines\code

Finally, we add the Brain Connectivity Toolbox, BCT to the Matlab path,

addpath BCT\2017_01_15_BCT

Load the NKI database matrices

load('NKImatrices_Peraza.mat')

After loading the mat file to the Matlab workspace you will see several variables. These comprise basic demographics for age and sex, and the connectivity matrices. These connectivity matrices were estimated using Pearson correlations and the functional atlases from an independent older adult group in Peraza et al. 2017. These atlases are available on the Figshare repository.

Now, download the MNI coordinate system used in my study from the Figshare database and load the ROI coordinates (in MNI). For the example in this tutorial, we will use the 100 ROI atlas and matrices, but the same principles apply to the other atlases.

load('MNIcoordinateSystem\MNI100roi_atlas.mat')
coords=MNI100coords(:,1:3);     %Ignore the fourth columns
clear MNI100coords              %delete the variable and keep coords

Select one participant from the NKI database, and this participant can be random for the purposes of this tutorial. It this case I choose the 100th participant from the younger adult connectivity matrices, and we specify as well as the average node degre we wish to threshold the connectivity matrix:

pat = 100;
pat_matrix = abs(Connectome100_YA_NKI(:,:,pat)); %The absolute value
deg = 4;                                         % Average node degree (whole network)

Remember that in this investigation I took the absolute value of the connectivity matrix. Hence, the variable pat_matrix stores the absolute value of the Pearson correlations.

Now we perfom local thresolding of this connectivity matrix. Local thresholding is implemented in function localThresholding.mat within the MDToolbox, and takes the weighted connectivity matrix and the average node degree as parameters.

newmatLT=localThresholding(pat_matrix,deg);
newmatLT=newmatLT(:,:,2);

With the thresholded matrix, estimate network commnunities with the Louvain’s algorithm (from the BCT). For this example I will run Louvain’s 50 times. Current publications recommend > 500 iterations of the algorithm, although this number depends on the network size. For the code below, I am comparing and saving (at each iteration of the for loop) the new estimated community stored in CiLT variable that shows a higher modularity index Q.

modularityLT=0;
for iter=1:50 
    [auxCiLT,aux_Q] = community_louvain(newmatLT .* pat_matrix);
    if aux_Q > modularityLT
        modularityLT=aux_Q;
        CiLT=auxCiLT;
    end
end

Now let’s do the same for the global thresholding of the connectivity matrix, and save the estimated community definition in the CiGT vector.

newmatGT=globalThresholding(pat_matrix,4,'binary');
modularityGT=0;
for iter=1:50 
    [auxCiGT,aux_Q] = community_louvain(newmatGT .* pat_matrix);
    if aux_Q > modularityGT
        modularityGT=aux_Q;
        CiGT=auxCiGT;
    end
end

Now, inspect the estimated community defnitions with the following code and by borrowing some functions from the BCT toolbox. Plot the community matrices for the local and global threshold approaches.

figure
[X,Y,INDSORT] = grid_communities(CiLT);   % call function
imagesc(newmatLT(INDSORT,INDSORT));       % plot ordered adjacency matrix
hold on;                                  % hold on to overlay community visualization
plot(X,Y,'r','linewidth',2);
title('Locally thresholded matrix - communities')
hold off;

Local Threshold

figure
[X,Y,INDSORT] = grid_communities(CiGT); % call function
imagesc(newmatGT(INDSORT,INDSORT));           % plot ordered adjacency matrix
hold on;                                 % hold on to overlay community visualization
plot(X,Y,'r','linewidth',2);
title('Globally thresholded matrix - communities')
hold off;

Global Threshold

Notice how local and global thresholding methods led to different community definitions. When the connectivity matrix is thresholded locally communities are less sparse and larger, while in global threshold few communities concentrate the mayority of the strongest links. This is because local thresholding is based on the k nearest neighbour graph (k-NNG) which favours creation and segregation of communities. Remember as well that modularity Q is larger when matrices are localy thresholded.

With these two definitions, we can compute the modular dissociation/variability statistic, which is defined by

MD definition

where the numerators represent the number of nodes in common between communities X(i) and X(j), and the denominators represent the number of nodes within the community. Here node s belongs to the network i and similar for network j.

This definition of Modular Dissociation (MD) is implemented in the MDToolbox function ModularVariance.mat and it is executed as follows:

MD_LTGT=ModularVariance(CiLT,CiGT);

We can now see the nodal MD values with a scatter3 plot in Matlab, and using the MNI coordinate definition for the 100-ROI atlas,

figure
scatter3(coords(:,1),coords(:,2),coords(:,3),100.^MD_LTGT,'o','fill','MarkerFaceColor','b')
title('Modular Dissociation - Example')

MD example

Notice the brain shape of the nodal arrangement, and how the motor-sensory, occipital and temporal cortices show, for this participant, low values of MD while high values are present in the frontal cortex.

I hope you liked this tutorial and don’t forget to visit our lab webpage www.lewybodylab.org, which has further information about Lewy body dementia research.

Best.

Modular dissociation

Needed Toolboxes

Data sharing tutorial