Ordinal methods for a characterization of evolving functional brain networks

Abstract

Ordinal time series analysis is based on the idea to map time series to ordinal patterns, i.e., order relations between the values of a time series and not the values themselves, as introduced in 2002 by C. Bandt and B. Pompe. Despite a resulting loss of information, this approach captures meaningful information about the temporal structure of the underlying system dynamics as well as about properties of interactions between coupled systems. This—together with its conceptual simplicity and robustness against measurement noise—makes ordinal time series analysis well suited to improve characterization of the still poorly understood spatiotemporal dynamics of the human brain. This minireview briefly summarizes the state-of-the-art of uni- and bivariate ordinal time-series-analysis techniques together with applications in the neurosciences. It will highlight current limitations to stimulate further developments, which would be necessary to advance characterization of evolving functional brain networks.

Astrocytes are active: An information theoretic approach reveals differences in Ca2+ signaling patterns among distinct astrocyte subtypes

“…This approach has been well documented experimentally (e.g. with neuronal MRI data) and theoretically [35][36][37][38][39][40][41][42][43] . A limitation of correlations is that the global characteristics of a network are studied by assessing each cell's connections to others in the network.…”

The time-evolving epileptic brain network: concepts, definitions, accomplishments, perspectives

“…Recent developments in characterizing two-dimensional stochastic processes (Rydin Gorjão et al, 2019;Aslim et al, 2021) based on the Kramers-Moyal expansion might provide novel insights into stochastic interactions in the future. Likewise, a further improved characterization of the temporal structure of the brain's dynamics could be achieved with bivariate ordinal time-series-analysis techniques (Lehnertz, 2023) that allow one to assess both strength and direction of an interaction. Moreover, while there is an increasing interest in so-called higher-order Frontiers in Network Physiology frontiersin.org interactions (Battiston et al, 2021;Bianconi, 2021;Boccaletti et al, 2023) (interactions between more than pairs of brain regions), it remains unclear how to estimate the relevant higher-order interactions from time-series data and what advantages such hyper networks will provide aside from theoretical arguments.…”

“…Considering the recent promising developments of centrality concepts and metrics to characterize properties of edges as well as the edges' time-varying role in the larger network (Bröhl and Lehnertz, 2019;Bröhl and Lehnertz, 2022;Contisciani et al, 2022;Altafini et al, 2023), adopting an edge-centric perspective (cf. Faskowitz et al, 2022;Novelli and Razi, 2022) could lead to a further improved understanding of the time-evolving epileptic brain network and its control (Sinha et al, 2022;Lehnertz et al, 2023;Frauscher et al, 2023).…”

“…Despite the well-known observation that vulnerability to seizure activity in any one part of the network is influenced by activity everywhere else in the network, and that the network as a whole is responsible for the clinical and electrographic phenomena that we associate with human seizures (Spencer, 2002), we still lack a sufficient quantitative assessment of the time-evolving epileptic brain network's metrics (from the local to the global network scale) that would help to improve understanding of how the network generates seizures (Kuhlmann et al, 2018;Lehnertz, 2021;Lehnertz et al, 2023) as well as other pathophysiological phenomena (Weiss et al, 2022).…”

“…Choosing treatment: Currently, clinical decisions regarding treatment options are primarily guided by the epilepsy syndrome and its burden. Despite several options [e.g., pharmacological treatment (Kwan and Brodie, 2000;Wandschneider and Koepp, 2016;Höller et al, 2018;Höller and Nardone, 2021), surgical treatment (Téllez-Zenteno et al, 2007), nutritional treatment (Pizzo et al, 2022), neurostimulation (Schulze-Bonhage, 2019;Piper et al, 2022); see Lehnertz et al (2023) for an overview of network-based treatment concepts], the treatment is successful in only about half of the cases. Moreover, from a clinical point of view, the goal of epilepsy treatment is seizure freedom and if this is not possible reduction of seizure frequency and burden of the disease.…”