# Project

## Longitudinal brain connectivity analysis via coupled harmonic bases

**There is a great deal of interest in using large scale brain imaging studies to understand how brain connectivity evolves over time for an individual and how it varies over different levels/quantiles of cognitive function. To do so, one typically performs so-called tractography procedures on diffusion MR brain images and derives measures of brain connectivity expressed as graphs. The nodes correspond to distinct brain regions and the edges encode the strength of the connection. The scientific interest is in characterizing the evolution of these graphs over time or from healthy individuals to diseased. We pose this important question in terms of the Laplacian of the connectivity graphs derived from various longitudinal or disease time points - quantifying its progression is then expressed in terms of coupling the harmonic bases of a full set of Laplacians. We derive a coupled system of generalized eigenvalue problems (and corresponding numerical optimization schemes) whose solution helps characterize the full life cycle of brain connectivity evolution in a given dataset. Finally, we show a set of results on a diffusion MR imaging dataset of middle aged people at risk for Alzheimer's disease (AD), who are cognitively healthy. In such asymptomatic adults, we find that a framework for characterizing brain connectivity evolution provides the ability to predict cognitive scores for individual subjects, and for estimating the progression of participant's brain connectivity into the future.**

*Abstract.***Figure**: The evolution of top 50 most changing fiber tracts of the real data derived from the coupled harmonic bases. The tract colors represent their strong (blue) and weak (red) connectivity strengths. Cross-sectional coupling (red arrows) via l-norm in each row. Longitudinal coupling (blue arrows) via rotation constraints in each column.

**Figure**: Brain connectivity evolves as the cognitive stage changes from healthy to diseased.

**Figure**: From brain image to adjacency matrix: (a) Diffusion tensor ellipsoids from dMRI. (b) Gray matter regions as meaningful graph nodes. (c) Fiber tracts (axonal pathways between brain regions) estimated via tractography as graph edges between gray matter nodes. (d) Symmetric adjacency matrix representation of the graph.

**References:**

**Seong Jae Hwang**, Nagesh Adluru, Maxwell D. Collins, Sathya N. Ravi, Barbara B. Bendlin, Sterling C. Johnson, Vikas Singh, "Coupled Harmonic Bases for Longitudinal Characterization of Brain Networks",

*Computer Vision and Pattern Recognition (CVPR)*, 2016.

[pdf]

[supplementary]

[poster]

[code will be available here]

[MATLAB toolbox for high quality fiber tract 3D visualization]

**Acknowledgment:**