Explicitly Nonlinear Connectivity-Matrix Independent Component Analysis in Resting fMRI Data
Poster No:
1788
Submission Type:
Abstract Submission
Authors:
Sara Motlaghian1, Vince Calhoun2
Institutions:
1Georgia State University, Atlanta, GA, 2GSU/GATech/Emory, Decatur, GA
First Author:
Co-Author:
Introduction:
Connectivity-matrix independent component analysis (cmICA) is a data-driven method to calculate brain voxel maps of functional connectivity. It is a powerful approach, but one limitation is that it can only capture linear relationships. In this work, we focus on measuring the explicitly nonlinear relationships between the voxel connectivity to identify brain spatial maps which demonstrate explicitly nonlinear dependencies and are typically ignored. We expand cmICA using normalized mutual information (NMI) after removing the linear relationships and find highly structured resting networks which would be completely missed by existing functional connectivity approaches. Results revealed resting fMRI networks that show linear-only, nonlinear-only, and both linear+nonlinear relationships with unique spatial patterns.
Methods:
In this work we combined two methods in order to identify maps that show explicitly nonlinear activation. In [https://doi.org/10.1101/2022.06.22.497262], we introduced a method to measure the explicitly nonlinear similarity between two time courses. We want to elaborate that method to find explicitly nonlinear (EN) brain map components. To do so, one of the barriers to implementing ICA is the absence of time variable which cancels during measuring nonlinearity. So we propose to utilize the connectivity matrix (cmICA) method instead, which first was introduced in [https://doi.org/10.1016/j.neuroimage.2018.06.024] to identify spatial map components.
We did the following steps:
First we canceld the linear correlation between each pair of voxels. Removing the linear information can be done for a given vector x and y, by fitting a linear model y' = αx + β. Here y' is the best linear estimation of y when x is given, the slope is denoted by α, and β is the y-intercept. We can cancel the linear effect by calculating z = y – y'. The explicitly nonlinear dependency of x and z is the same as x and y. Next, we use NMI(x,z) to evaluate the EN dependency of x and y. To assure symmetricity, we took the average of the results when switching x and y.
The symmetric matrices from the previous step, next are passed to cmICA. The maps identified by cmICA are divided in matched with linear maps and EN only maps.
We did the following steps:
First we canceld the linear correlation between each pair of voxels. Removing the linear information can be done for a given vector x and y, by fitting a linear model y' = αx + β. Here y' is the best linear estimation of y when x is given, the slope is denoted by α, and β is the y-intercept. We can cancel the linear effect by calculating z = y – y'. The explicitly nonlinear dependency of x and z is the same as x and y. Next, we use NMI(x,z) to evaluate the EN dependency of x and y. To assure symmetricity, we took the average of the results when switching x and y.
The symmetric matrices from the previous step, next are passed to cmICA. The maps identified by cmICA are divided in matched with linear maps and EN only maps.
Results:
We implemented EN-cmICA brain connectivity for 311 rsfMRI datasets resulting in 33 EN spatial maps. These maps reveals a set of maximally independent regions where, in each region, the voxels show a high level of explicitly nonlinear similarity. Each region is considered as one spatial map.
We divided EN maps in to two groups of components:
Group A) EN components that are not similar to any linear components (i.e., brain networks showing uniquely nonlinear information)
Group B) EN components that are highly (spatially) similar to linear maps (i.e., brain networks showing both linear and nonlinear information).
We divided EN maps in to two groups of components:
Group A) EN components that are not similar to any linear components (i.e., brain networks showing uniquely nonlinear information)
Group B) EN components that are highly (spatially) similar to linear maps (i.e., brain networks showing both linear and nonlinear information).
Conclusions:
The EN-cmICA process identifies EN maps that are uniqe and are not found from the conventional ICA approach. This findings help to uncover more about brain activities.
Modeling and Analysis Methods:
fMRI Connectivity and Network Modeling 1
Segmentation and Parcellation 2
Keywords:
Data analysis
Other - cmICA, mutual information
1|2Indicates the priority used for review
Provide references using author date format
S. M. Motlaghian, A. Belger, J. R. Bustillo, A. Faghiri, J. M. Ford, A. Iraji, K. Lim, D. H. Mathalon, R. Miller, B. A. Mueller, D. O’Leary, G. Pearlson, S. G. Potkin, A. Preda, T.G. van Erp, V. D. Calhoun
bioRxiv 2022.06.22.497262; doi: https://doi.org/10.1101/2022.06.22.497262
Wu, L., Caprihan, A., Bustillo, J., Mayer, A., & Calhoun, V. (2018). An approach to directly link ICA and seed-based functional connectivity: Application to schizophrenia. NeuroImage, 179, 448-470. https://doi.org/10.1016/j.neuroimage.2018.06.024