Abstract
Metastability refers to the fact that the state of a dynamical system spends a large amount of time in a restricted region of its available phase space before a transition takes place, bringing the system into another state from where it might recur into the previous one. beim Graben and Hutt (2013) suggested to use the recurrence plot (RP) technique introduced by Eckmann et al. (1987) for the segmentation of system's trajectories into metastable states using recurrence grammars. Here, we apply this recurrence structure analysis (RSA) for the first time to resting-state brain dynamics obtained from functional magnetic resonance imaging (fMRI). Brain regions are defined according to the brain hierarchical atlas (BHA) developed by Diez et al. (2015), and as a consequence, regions present high-connectivity in both structure (obtained from diffusion tensor imaging) and function (from the blood-level dependent-oxygenation—BOLD—signal). Remarkably, regions observed by Diez et al. were completely time-invariant. Here, in order to compare this static picture with the metastable systems dynamics obtained from the RSA segmentation, we determine the number of metastable states as a measure of complexity for all subjects and for region numbers varying from 3 to 100. We find RSA convergence toward an optimal segmentation of 40 metastable states for normalized BOLD signals, averaged over BHA modules. Next, we build a bistable dynamics at population level by pooling 30 subjects after Hausdorff clustering. In link with this finding, we reflect on the different modeling frameworks that can allow for such scenarios: heteroclinic dynamics, dynamics with riddled basins of attraction, multiple-timescale dynamics. Finally, we characterize the metastable states both functionally and structurally, using templates for resting state networks (RSNs) and the automated anatomical labeling (AAL) atlas, respectively.
Highlights
Mapping the brain’s functional-structural relationship remains one of the most complex challenges in modern neuroscience (Park and Friston, 2013), in part due to the highly dynamic multi-scale nature of the brain’s processes and structures as observed by different measurement modalities, which leads to technical and mathematical difficulties for establishing dynamically invariantFrontiers in Computational Neuroscience | www.frontiersin.org beim Graben et al.relations across scales
We compute the optimal number of metastable states n − 1 determined by the recurrence structure analysis (RSA) as a measure of complexity for all subjects and for module numbers ranging from 3 to 100 from normalized rsfMRI BOLD signals
We introduced a novel framework to track the spatiotemporal dynamics of resting state functional magnetic resonance imaging (fMRI) BOLD signals
Summary
Mapping the brain’s functional-structural relationship remains one of the most complex challenges in modern neuroscience (Park and Friston, 2013), in part due to the highly dynamic multi-scale nature of the brain’s processes and structures as observed by different measurement modalities, which leads to technical and mathematical difficulties for establishing dynamically invariantFrontiers in Computational Neuroscience | www.frontiersin.org beim Graben et al.relations across scales. As a result, which precise function emerges at the macro-scale (as measured by BOLD signals) from the underlying static neuronal architecture is not yet fully understood This rests on a many-to-one functionstructure relationship, which is hard to resolve and novel methodologies are demanded. For structural connectivity, functional connectivity, and effective connectivity the entries of the network’s connectivity matrix indicate the anatomical links (white-matter tracts connecting different gray matter regions), the correlation strength and the causal strength between pairs of imaging regions of interest, respectively (Alonso Montes et al, 2015) Features of this matrix can be exploited by using for example standard tools from linear algebra that rely upon spectral analysis (e.g., invariants such as eigenvalues) and other related/complementary methods, such as independent component analysis (ICA) (Bell and Sejnowski, 1997), partial least squares (PLS) (Krishnan et al, 2011), and many more. Mapping between these different matrices and accounting for temporal dynamics is of paramount interest and an active research area in brain mapping
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
