Brain signaling becomes less integrated and more segregated with age

Abstract

The integration-segregation framework is a popular first step to understand brain dynamics because it simplifies brain dynamics into two states based on global vs. local signaling patterns. However, there is no consensus for how to best define what the two states look like. Here, we map integration and segregation to order and disorder states from the Ising model in physics to calculate state probabilities, $P_{\text{int}}$ and $P_{\text{seg}}$, from functional MRI data. We find that integration/segregation decreases/increases with age across three databases, and changes are consistent with weakened connection strength among regions rather than topological connectivity based on structural and diffusion MRI data.

Keywords: Aging; Statistical Physics; dMRI; fMRI.

Figure 1.. Calculating the probability that the brain exhibits integrated or segregated dynamics (PintorPseg).

The schematic demonstrates the procedure for one individual’s fictitious functional MRI scan with 4 brain regions and only two time points shown. First, we binarize data based on nearest neighbor scans in time. If the functional MRI (fMRI) signal increases, a value of 1 is assigned; decreases, −1. Then, we calculate the average spin state of the brain, called synchrony. Finally, we collect synchrony values across the entire time series to create a synchrony distribution. We appropriately set the synchrony threshold based on Ising model theory to delineate between integrated and segregated microstates. Additional details can be found in the Methods. Figure created with Biorender.com.

Figure 2.. Adjusting the number of brain regions (Neff) helps capture experiment.

The modified Ising model with $N_{\text{eff}}=40$ (yellow line) better captures the synchrony distribution (blue histogram) of an arbitrarily chosen individual in the Cambridge Centre for Ageing and Neuroscience data set (subject id: CC110045). The orange line corresponds to the Ising model with $N$ equal to the number of regions in the Seitzman atlas (Seitzman et al., 2020).

Figure 3.. Pseg rises in aging brains across three data sets.

Data points correspond to medians, while error bars correspond to standard errors for bins of 5 years. The variable $\rho$ corresponds to the Spearman correlation coefficient between age and $P_{\text{seg}}$ calculated over all N individuals, with the p-value in parenthesis.

Figure 4.. Simulating the random removal of edges results in Pseg increases.

Five edges are randomly removed from a starting diffusion MRI structure (arbitrarily chosen UK Biobank individual, subject ID: 6025360 , 51 years old), under the Harvard-Oxford atlas (64 regions). An Ising system is simulated with $N_{\text{eff}}=N=64$ for the corresponding diffusion MRI structure. Spin states, denoted by dark blue and red node colors in the schematic, are recorded across 2500 time steps to calculate $P_{\mathrm{s}\mathrm{e}\mathrm{g}}$. Then, the entire procedure is repeated for the updated structure after edge removal, for a total of 83 times (Methods). Orange data points on the right plot correspond to individual Ising systems, where N reflects the total number. The variable $\rho$ corresponds to the Spearman correlation coefficient calculated over all orange data points between average degree and $P_{\mathrm{s}\mathrm{e}\mathrm{g}}$, with the p-value in parenthesis. Magenta data points correspond to medians, while error bars correspond to upper and lower quartiles for bin sizes of one degree. The schematic on the left is created with Biorender.com.

Figure 5.. Adjusting the effective number of brain regions (Neff) helps capture synchrony distributions’ variances across individuals in the Cambridge Centre for Ageing data set.

Each data point corresponds to an individual.

Figure 6.. The effective number of regions Neff is identified by minimizing the root mean square error (RMSE) of the fourth moment of synchrony between theory and experiment across all individuals.

Each data point corresponds to the sum over all individuals’ RMSEs in the respective data set. Note that the y-axis should be scaled by 10⁻³.