Rationale:
The brain stem is the primary center of involuntary control of breathing, while several cortical regions contribute to its voluntary modulation.
1 In order to evaluate the role of different structures in volitional respiration, a functional network can be constructed and analyzed to detect the backbone of this network.
Methods:
We used EEG data recorded in epilepsy patients with implanted intracranial electrodes who performed a set of breathing tasks, constructed a functional network of their brain activity and analyzed the resulting dynamics. Specifically, we computed the Forman’s curvature for each network -- a discrete analogue of the standard notion of curvature,2,3 adopted for discrete structures, such as datasets, networks and graphs4-6.The effective geometry of the network can be defined through “weights” that empirically characterize the contribution of nodes and edges.7 The vertexes that acquire high absolute curvature are the “hubs” of information represented by the selected weights, while the most Forman-curved links dominate the information flow. We used different measures for weighing the individual signals (e.g., entropy, PSD) and the couplings between signals (correlation, mutual information, power-time correlation), to obtain complementary descriptions of the network dynamics.
Results:
First, we found that different measures consistently highlight breath-controlling brain areas. Second, the precise dynamics of Forman curvature evaluated for individual patients appears to capture the specifics of breathing dynamics at several timescales.
Conclusions:
These results suggest a new venue for better understanding the neurophysiology of breathing modulation, may enable targeted methodology for brain stimulation and help SUDEP prevention.
1 Herrero, J. L., Khuvis, S., Yeagle, E., Cerf, M., & Mehta, A. D. (2018). Breathing above the brain stem: volitional control and attentional modulation in humans. Journal of Neurophysiology, 119(1), 145–159.doi:10.1152/jn.00551.2017
2 Forman. Bochner's Method for Cell Complexes and Combinatorial Ricci Curvature. Discrete & Computational Geometry. 2003;29(3):323-74. doi: 10.1007/s00454-002-0743-x.
3 Lewiner T, Lopes H, Tavares G, editors. Visualizing Forman’s Discrete Vector Field2003; Berlin, Heidelberg: Springer Berlin Heidelberg.
4 Weber M, Jost J, Saucan E. Forman-Ricci Flow for Change Detection in Large Dynamic Data Sets. Axioms. 2016;5(4):26. PubMed PMID: doi:10.3390/axioms5040026.
5 Weber M, Saucan E, Jost J. Characterizing complex networks with Forman-Ricci curvature and associated geometric flows. Journal of Complex Networks. 2017;5(4):527-50. doi: 10.1093/comnet/cnw030.
6 Sreejith RP, Jost J, Saucan E, Samal A. Systematic evaluation of a new combinatorial curvature for complex networks. Chaos, Solitons & Fractals. 2017;101:50-67. doi: https://doi.org/10.1016/j.chaos.2017.05.021.
7 Weber M, Stelzer J, Saucan E, Naitsat A, Lohmann G, Jost J. Curvature-based methods for brain network analysis. arXiv preprint arXiv:170700180. 2017. Herrero, J. L., Khuvis, S., Yeagle, E., Cerf, M., & Mehta, A. D. (2018).
Funding: CURE research grant