Dynamic Model of Functional Brain Networks

Functional brain networks are networks created with a help of fMRI measurements of the in vivo brain activity [3], [4]. I elaborated a dataset, which contains functional brain networks of young participants, healthy elderly participants and elderly participants with diagnosed Alzheimer disease. All networks were measured at the three different correlation thresholds. In this paper I present a data driven mathematical model of functional brain networks. It is based on the threshold related shape of the degree distribution. The model is numerically simulated and results of the simulation are compared to the real dataset. 1 Functional brain networks Functional Magnetic Resonance Imaging (fMRI) is a technique for gaining high resolution images of neural activity in the brain [3], [4]). FMRI images are captured in a series of two dimensional slices, with each slice representing a cross section of the brain less than 10 mm thick. A single slice is comprised of a rectangular grid of discrete 3D regions (3×3×10 mm) known as voxels (volumetric pixels). A full 3D image of the brain is achieved by combining these slices together. fMRI is an ideal technique for deriving functional connectivity. One can ask to which extend spatially distinct regions of the brain exhibit similar behavior over time. By modeling this functional connectivity as a network, we can explore the ways in which regions of the brain interact, and use techniques from the graph theory to evaluate the topological characteristics of these functional networks of interaction. In this paper I used the brain fMRI data collected by Buckner [1], (data set no. 2-2000-118W from the fMRI Data Center: http://www.fmridc.org). The participants were divided into three groups: healthy young (HY) participants, healthy elderly (HE) participants and elderly participants with diagnosed Alzheimer disease (AD) (AE group). Structural and functional MRI data were acquired from 41 subjects in total. The HY group had 14 subjects (9 females/5 males) with the mean age 21.1 years (SD 2.0). The HE had 15 subjects (9 females/6 males) of the mean age 75.1 years (SD 6.9). The AE group had 12 subjects (7 females/5 males) of the mean age 77.1 years (SD 5.3). There was no statistically significant difference in the mean age of the latter two groups. The standardized data were then used in [3], [4] to create functional brain networks for each participant in all three groups. These data were further elaborated by me. Functional brain networks, contrary to the structural neuronal brain networks, are temporal networks. Certain type of the functional brain network exists only during that time, when the brain is involved in the cognitive task and reflects the functional cooperation of different brain areas. Since the smallest unit of the measured fMRI signal is an integrated signal of the neurons contained in one voxel, voxels are thus natural candidates for the nodes of the functional brain network. If the two voxels functionally cooperate (based on the underlying physical connectivity), the measured signal is highly correlated over time. To measure the amount of the signal correlation, the Pearson correlation coefficient is calculated for all the voxel pairs: