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Topological analysis of LFP data

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Fedorov,  L
Department Human Perception, Cognition and Action, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Murayama,  Y
Department Physiology of Cognitive Processes, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Logothetis,  NK
Max Planck Institute for Biological Cybernetics, Max Planck Society;
Department Physiology of Cognitive Processes, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Citation

Fedorov, L., Dijkstra, T., Murayama, Y., Bohle, C., & Logothetis, N. (2019). Topological analysis of LFP data. Poster presented at 28th Annual Computational Neuroscience Meeting (CNS*2019), Barcelona, Spain. doi:10.1186/s12868-019-0538-0.


Cite as: http://hdl.handle.net/21.11116/0000-0004-3F37-9
Abstract
The Local Field Potential (LFP) summarizes synaptic and somatodendritic currents in a bounded ball around the electrode and is dependent on the spatial distribution of neurons. Both fine-grained properties and the temporal distribution of typical waveforms in spontaneous LFP have been used to identify global brain states (see e.g. [1] for P-waves in stages of sleep). While some LFP signatures have been studied in detail (in addition to Pons, see e.g. sleep spindles in the Thalamus and areas of the cortex [2], sharp-wave-ripples [3] in the Hippocampus and k-complexes [4]), it stands to understand the relationship between simultaneous signaling in cortical and subcortical areas. To characterize the mesoscale spontaneous activity, we quantify data-driven properties of LFP and use them to describe different brain states. Inspired by [5], we treat frequency-localized temporary increases in LFP power simultaneously recorded from Cortex, Hippocampus, Pons and LGN as Neural Events that carry information about the brain state. Here, we give a fine-grained characterization of events in the 0-60Hz frequency range that differentiates the onset and offset intervals from the ongoing short-term oscillation within the event’s duration. For example, a fixed-amplitude oscillatory interval can be conceptually thought of as a temporally resolved sample from a circle, whereas the onset and offset can be regarded as samples from spirals. Thus, the change within an event corresponds to a topological change of the trajectory in phase space. We use topological data analysis to detect this change in topology. In detail, we look at barcodes computed using persistence homology [6] of the delay embedding [7, 8] of consecutive windows within a neural event. A persistence barcode can be seen as a topological signature [9] of the reconstructed trajectory. We rely on the difference between a circle and a spiral in homology when this qualitative change is inferred from looking at consecutive barcodes. This feature (Fig. 1) describes the onset-duration- offset intervals for each oscillation, yet is agnostic to event type, recording site or brain state.