Introduction
A system organized to criticality is able to switch phases from small inputs[1]. Prior research indicates that neural systems are organized to near-criticality across multiple scales[2]. One modality for which criticality analysis is novel is fMRI. fMRI allows for the analysis of resting state brain networks (RSNs), groups of units that coactivate with one another and reflect specific cognitive processes[3,4].
As a step towards characterizing the critical dynamics of brain networks, it is necessary to first assess the reliability with which critical metrics can be estimated. To identify network-specific factors from individual-specific ones, we compared metrics obtained for each RSN across scanners and across participants.
Methods
The metrics of criticality examined are derived using a new method, phenomenological renormalization group (pRG) [5]. In this approach, units are paired based on correlation. These pairs are summed together and normalized. A correlation matrix is calculated between the new clusters. This process is repeated such that, at each iteration n of coarse-graining, the number of units, k represented by each cluster is 2n.
Following coarse-graining, several metrics are calculated: μ, the power law exponent describing the covariance eigenspectra decay for a cluster of size K (λ ~ (r/K)-μ) and α, the scaling exponent for cluster variance (σ2(K) ~ Kα). These analyses are performed for each network within each participant at each scan strength (3T, 7T).
Results
pRG analysis in fMRI data yielded power-law relationships showing scaling of variance with cluster size and eigenvalues with rank. Within individuals, we compared exponents obtained from 7T and 3T scans for each network. While values of exponents varied across networks, we found a high degree of correlation between exponents in 3T and 7T data: 0.791 (μ) and 0.523 (α) for participant 1. For participant 2, correlation coefficients were 0.818 (μ) and 0.934 (α).
We examined whether exponents were similar between participants. When comparing exponents of distinct networks between participants 1 and 2, we found correlation coefficients of 0.368 (μ) and 0.5493 (α) for 3T and coefficients of 0.747 (μ) and 0.795 (α) for 7T.
Discussion
Our results indicate that RSNs possess critical dynamics that correlate with themselves across scanner strengths and individuals, indicating that RSNs have intrinsic dynamics likely reflecting different cognitive processes.
Interestingly, there is a large difference in α correlation coefficients (3T vs 7T) between participants 1 and 2. This may indicate that the stability of critical dynamics between scanner strengths varies across individuals. Also, the stronger correlations between participants at 7T compared with 3T are likely because of the stronger signal-to-noise ratio at 7T.
Future directions are to assess reliability of criticality metrics in future participants and to characterize specific metrics of criticality within RSNs.
References
1. Fontenele, A. J., et al. (2019). Criticality between cortical states. Physical Review Letters, 122(20), 208101.
2. Hengen, K. B., & Shew, W. L. (2024). Is criticality a unified set-point of brain function? (p. 2024.09.02.610815). bioRxiv. https://doi.org/10.1101/2024.09.02.610815
3. Meshulam, L., et al. (2019). Coarse Graining, Fixed Points, and Scaling in a Large Population of Neurons. Physical Review Letters, 123(17), 178103. https://doi.org/10.1103/PhysRevLett.123.178103
4. O’Byrne, J., & Jerbi, K. (2022). How critical is brain criticality? Trends in Neurosciences, 45(11), 820–837. https://doi.org/10.1016/j.tins.2022.08.007
5. Rosazza, C., & Minati, L. (2011). Resting-state brain networks: Literature review and clinical applications. Neurological Sciences, 32(5), 773–785.
Acknowledgement
VM was supported through a PhD candidate research assistantship at the University of Minnesota. fMRI data was able to collected through use of Center for Magnetic Resonance Research resources at the University of Minnesota. Analysis was conducted using Minnesota Supercomputing Institute resources at the University of Minnesota.
