Development of modularity in the neural activity of children's brains

Abstract

We study how modularity of the human brain changes as children develop into adults. Theory suggests that modularity can enhance the response function of a networked system subject to changing external stimuli. Thus, greater cognitive performance might be achieved for more modular neural activity, and modularity might likely increase as children develop. The value of modularity calculated from functional magnetic resonance imaging (fMRI) data is observed to increase during childhood development and peak in young adulthood. Head motion is deconvolved from the fMRI data, and it is shown that the dependence of modularity on age is independent of the magnitude of head motion. A model is presented to illustrate how modularity can provide greater cognitive performance at short times, i.e. task switching. A fitness function is extracted from the model. Quasispecies theory is used to predict how the average modularity evolves with age, illustrating the increase of modularity during development from children to adults that arises from selection for rapid cognitive function in young adults. Experiments exploring the effect of modularity on cognitive performance are suggested. Modularity may be a potential biomarker for injury, rehabilitation, or disease.

Figures

Figure 1

Brain neural activity is clustered into modules. a) fMRI neural activity data are projected onto Brodmann areas, shown as colored regions. b) Neural activity between different Brodmann areas is correlated for subjects watching 20 minutes of Sesame Street, shown here for one adult subject. Only the elements of the correlation matrix above a cutoff are retained (white). c) Modules are defined as the clusters that maximize Newman’s modularity. The four modules identified from the 84 Brodmann areas for this subject are shown, of size 16 (green), 20 (red), 27 (yellow), and 21 (orange). The modularity is 0.6441, with contributions of 0.1585, 0.1310, 0.1592, and 0.1954 from each module respectively. d) The four modules of neural activity for this subject.

Figure 2

a) Average modularity of the neural activity in the brain for the child and adult cohorts. Modularity is greater for adults than for children. Modularity is computed from the correlation matrix of neural activity between Brodmann areas. The number of entries in the correlation matrix above the cutoff, denoted by edges, is chosen so that the matrix is fully connected yet still sparse. Modularity computed using different values of the cutoff persistently shows a higher value for adults than for children. The error bars are one standard error. b) top) The three Brodmann areas whose domains grow the most in size from children to adults, and bottom) the three Brodmann areas whose domains shrink the most, for 400 edges.

Figure 3

Calculation of modularity when the full matrix of correlations is used. Calculations were performed using Brodmann areas as nodes and a 84×84 matrix of correlations. Calculations were also performed without masking the data to Brodmann areas, and using the original data at a resolution of 12 mm and a 2160×2160 correlation matrix or a resolution of 8 mm and a 6426×6426 correlation matrix. The p-values for the significance of the difference between the modularity of adults and children are 7 × 10−5, 9 × 10−5, and 4 × 10−5, respectively. These results confirm the generality of the results in Fig. 2. Modularity develops during childhood.

Figure 4

The correlation of modularity with age, IQ score, and Euclidean norm (EN) from AFNI for children. Also shown is the correlation of EN with age.

Figure 5

The correlation of modularity with Euclidean norm from AFNI (EN) for adults. The correlation is small and not significant, p-value = 0.32.

Figure 6

The distribution of the values of 〈Si〉adult − 〈Si〉child They are ordered from smallest to largest; j(i) denotes this ordering.

Figure 7

Pictorial representation of the hierarchical matrix. The levels are 4 (black), 3 (red), 2 (orange), 1 (yellow), and 0 (white). matrix.

Figure 8

More modular neural architectures give better performance at short times (a or d, short time) and less modular memory architectures can give better performance at long times (a or d, long time). The greater modularity in adults than children, Fig. 2, is consistent with either cognitive performance at short times is more important in adults than children (top arrow) or that memories are less clustered in adults than children (bottom arrow). Overlap is a measure of the probability that the neural state correctly recalls a memory. The modularity of the connection matrix is M. The timescale is of order seconds. The clustering of the stored patterns is denoted by p.

Figure 9

a) The clustering of memories versus age, after the bottom arrow in Fig. 8. b) The average modularity versus age predicted by quasispecies theory (solid). Here, the fitness is 10× the overlap in Fig. 8, and the rate of mutation is μ = 0.1 [46]. Also shown is the adiabatic approximation to the modularity, M∞ (dashed) as well as the modularity that maximizes the fitness, M* (dotted).

Figure 10

Hierarchical Hopfield model results. Here p = 0.8.

Figure 11

Hierarchical Hopfield model results. Here p = 0.6.