The goal of this work is to identify functional connectivity (FC) changes and invariant properties in healthy people across the life span, using a novel graph model that accounts for anatomical distance between nodes.

Our research bases on a recently proposed graph model for representing FC in healthy people¹. The weights of the links are computed according to the following mathematical formula

$$ W_{ij}(t)=k(i)k(j)e^{-(\eta D_{ij}-F_{i,j}^{s}(t))}$$

being W(t)=[W_ij(t)] the matrix of weights at the age t (in years), k(i),k(j) the degrees of nodes i,j, η a parameter which penalizes the formation of long connections², D=[D_ij] the structural connectivity matrix, and F^s(t)=[F_ij^s(t)] the FC matrix at time t, suitably thresholded, as described in the Methods.

The resulting weights keep into account not only the statistical dependency between pairs of nodes, but also their anatomical distance and their degrees, so that centrality of nodes is emphasized.

Resting-state fMRI (rfMRI) images (TR/TE=2500/30 ms; resolution=3.1x3.1x2.5mm³; 39 axial slices; 160 volumes) were acquired from 133 healthy right-handed volunteers (age range: 6-79 yrs; M/F: 51/82). High-resolution T1-weighted scans were also collected for anatomical reference. After standard preprocessing with FSL³, data were coregistered to MNI space using the Advanced Normalization Tools (ANTs)⁴.

For each subject, the average rfMRI time-series from 94 regions of interest (ROIs) defined by the Harvard-Oxford anatomical atlas were extracted. Subject-specific FC matrices were estimated by correlating each pair’s time-series.

The Euclidean distance between all the centroids of these regions was estimated and used as common structural connectivity index for all the subjects.

In order to compute the FC threshold, we firstly computed, by means of a histogram, the distribution of the functional values for the whole population. Then we selected the center values of the most populated bins, and set the threshold as the average of these center values. As no estimate is available for parameter η in the human brain, we assumed the value provided for macaques² for any age t. The structural connectivity matrix D has been considered independent from time.

The extraction of a meaningful age-dependent representative graph required a second thresholding procedure on the weights of the corresponding population, in order to point out both the strongest functional values and the importance of the node degrees. Therefore, we grouped together all subjects having the same age. After collecting the distribution of values of the related matrices W, we thresholded each matrix with the center of the bin enclosing the highest values. Then, the resulting graphs of each subject have been joined together to get a Group Graph G(t), where links are weighted with the average values of each member, representing the resting state description of the whole t-aged group. As a final step the common active links can be extracted from the Group Graphs G(t1),…,G(tn) of differently t1,…,tn aged groups, so forming a Matching Graph M(t₁,…,t_n). Preliminary analyses were performed on two groups of 25 year-old (N=4) and 62 year-old subjects (N=3).

The two groups showed both common (M(25,62)) and age-specific connections (G(25) and G(62), see figure 1). From the preliminary data, several interesting results can be already discussed in view of a deeper analysis. First of all, the most important resting state network areas, including the default mode and frontal-executive networks, are included in M(25,62), consistent with the literature⁵. Second, the comparison of G(25) and G(62) might suggest that the density of active links increases with age. Further, several pathways detected in G(25) and G(62) are preserved in M(25,62), which could be interpreted as the age-related brain reserve capacity, i.e. the brain’s ability to effectively manage the increasing changes in normal aging and to cope with pathological damage. A main role seems to be played by the precuneus and the cingulate gyrus, which are characterized by high functional strength and degree, consistent with their role as hubs in cognition, as previously described in the literature⁶. These findings seem to agree with the results in⁷, where a general correspondence between functional and structural connectivity has been demonstrated across the cortex, pointing out that the structural core contains many connecting hubs, and centrality appears highest in the posterior cingulate cortex and in the Cuneus/Precuneus.By exploiting a recent mathematical model for assigning weights to the functional connectivity, we have investigated changes and invariant properties of the functional connectivity in two different age groups of healthy people at rest. Results of this pilot study highlighted a number of interesting properties, whose investigation deserves to be deepened and extended to other age groups across the life span.