Network models for changing degree distributions of functional brain networks

Abstract

The purpose of this study was to investigate degree distributions of functional brain networks. Particular functional brain networks were constructed from the fMRI measurements of three groups of participants namely, young healthy participants, elderly healthy participants and elderly participants with Alzheimer disease. Functional brain networks were constructed for three different correlation thresholds of voxel activity correlated over time. We have noticed that the character of degree distribution changes when the value of correlation threshold decreases. In order to explain the degree distribution changes with the changes of value of correlation threshold, we created two different, yet related network models. The crucial factor both models contain is an increasing noise as the voxel activity correlation threshold is lowered, which in our models corresponds to an increase of the number of random correlations between the voxels – nodes of the functional network. The models account for how initially scale-free character of the degree distribution changes as the correlation threshold is lowered based on the processes of network growth and edge addition. The two models differ in the manner of preferential and random edge addition while the second model is a refinement of the first one. On average, the second model leads to a better quantitative match with the data. To our knowledge, such functional brain network models, which take into account the correlation threshold as an independent variable have not been introduced before.